SOU\R HEATING AND COOLING 
 
 OF RESIDENTIAL BUILDINGS 
 
 DESIGN OF SYSTEMS 
 
 1980 EDITION 
 
 4i 
 
 ENERGY 
 EFFICIENCY 
 
 U.S. DEPARTMENT OF COMMERCE 
 Economic Development Administration 
 
 * i ♦ ♦ 
 
♦ * 
 
 SOLAR HEATING AND COOLING 
 
 OF RESIDENTIAL BUILDINGS 
 
 DESIGN OF SYSTEMS 
 
 1980 EDITION 
 
 Prepared by 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 
 COLORADO STATE UNIVERSITY 
 
 i<2X 
 
 •?. 
 
 / 
 
 U.S. Department of Commerce 
 Philip M. Klutznick, Secretary 
 
 Luther H. Hodges, Jr., Deputy Secretary 
 
 Robert T. Hall , Assistant Secretary 
 for Economic Development 
 
 SEPTEMBER 1980 
 
NOTICE 
 
 This manual was prepared as an account of work sponsored 
 by an agency of the United States Government. Neither the 
 United States nor any agency thereof, nor their employees, 
 makes any warranty, expressed or implied, or assumes any 
 legal liability or responsibility for any third party's use 
 or the results of such use of any information, apparatus, 
 product or process disclosed in this manual, or represents 
 that its use by such third party would not infringe privately 
 owned rights. 
 
 For sale by the Superintendent of Documents, U.S. Government Printing Office 
 Washington, D.C. 20402 
 
FOREWORD 
 
 "Solar Heating and Cooling of Residential Buildings," a two-volume 
 manual, was developed with technical assistance funding from the 
 Economic Development Administration, U.S. Department of Commerce. The 
 Solar Energy Applications Laboratory of Colorado State University 
 prepared the materials. 
 
 Since its publication in 1977, the first edition has provided practical 
 information for architects, mechanical engineers, contractors and tech- 
 nicians concerned with the steady rise of energy costs. Wide acceptance 
 of the manual marks a contribution by EDA toward nationwide efforts to 
 help conserve America's hard pressed energy resources. 
 
 The present edition of both volumes — "Design of Systems" and "Sizing, 
 Installation and Operation of Systems" — updates the first edition. 
 New material reflects recent research and practical experience in the 
 fast-growing field of solar energy — a form of energy that can contrib- 
 ute substantially to the reduction of fuel imports, lead to increased 
 production of housing, and create opportunities for expanded employment. 
 
 (JU» 
 
 3 tA+JUL. 
 
 Robert T. Hall 
 
 Assistant Secretary 
 
 for Economic Development 
 
Digitized by the Internet Archive 
 
 in 2012 with funding from 
 
 LYRASIS Members and Sloan Foundation 
 
 http://www.archive.org/details/solarheatingcooOOunit 
 
PREFACE 
 
 This manual was prepared primarily for use in conducting a 
 practical training course on the design of solar heating and cooling 
 systems for residential and small office buildings, but may also be 
 useful as a general reference text. The content level is appropriate 
 for persons with different and varied backgrounds, although it is as- 
 sumed that readers possess a basic understanding of heating, ventilat- 
 ing, and air-conditioning systems of conventional (non-solar) types. 
 
 This edition is a revision of the manual with the same title, first 
 printed and distributed by the U. S. Government Printing Office in 
 October 1977. The manual has been reorganized, new material has been 
 added, and outdated information has been deleted. 
 
 If this manual is used for a practical level training course, there 
 should be need for a minimum of supplementary material to conduct the 
 course. The content level has been carefully evaluated and tested to be 
 appropriate for practitioners in the building industry, such as con- 
 tractors, engineers, and architects. 
 
 Only active solar systems are described in this manual. Other 
 text-books and workshop manuals are available for passive designs. 
 Liquid and air-heating solar systems for combined space and service 
 water heating or service water heating only are included in this manual. 
 Furthermore, only systems with proven experience are discussed to any 
 extent. 
 
 The training course curriculum and this manual for Design of 
 Systems for space and water heating were developed by the staff of the 
 Solar Energy Applications Laboratory and vocational education 
 
specialists at Colorado State University in cooperation with the NAHB 
 Research Foundation. A national advisory committee selected from vari- 
 ous sectors of the home-building industry, university sources, private 
 practice, and government, was established to provide advice and general 
 guidance to the CSU project staff. 
 
 ACKNOWLEDGMENTS 
 
 The original manual was prepared by the following staff members of 
 the Solar Energy Applications Laboratory at Colorado State University: 
 C. Byron Winn, Susumu Karaki , George 0. G. Lof, Gearold Johnson, Dan S. 
 Ward, William S. Duff, and Sanford B. Thayer. Ivan E. Valentine and 
 Milton E. Larson are the vocational education specialists at Colorado 
 State University who participated in the program, and Ralph J. Johnson 
 and H. W. Anderson of the NAHB Research Foundation provided expert 
 advice regarding home building practices. The present edition was 
 revised and rewritten by Susumu Karaki and George Lof. 
 
 Development of the training course and preparation of the original 
 manual were made possible by a matching grant from the Economic Develop- 
 ment Administration, U.S. Department of Commerce, with Colorado State 
 University providing the matching funds. Financial assistance was also 
 received from the U.S. Department of Housing and Urban Development for 
 video-taping lectures during early trial presentations. 
 
 Financial assistance for preparing this revised manual was received 
 from the Solar Heating and Cooling Research and Development Branch, 
 Office of Conservation and Solar Applications, U. S. Department of 
 Energy. Vincent Rice was the project monitor. 
 
Special appreciation is expressed to Diana Rose and Wendy Asa for 
 their diligence and perseverance in typing and preparing the manuscript. 
 Their patience and service are truly appreciated. 
 
CONTENTS OF MANUAL 
 
 MODULE 1 COURSE OUTLINE 
 
 MODULE 2 INTRODUCTION TO SOLAR HEATING AND COOLING SYSTEMS 
 
 MODULE 3 SOLAR RADIATION 
 
 MODULE 4 SOLAR COLLECTORS 
 
 MODULE 5 HEATING AND COOLING LOAD ANALYSES 
 
 MODULE 6 SYSTEM SIZING AND APPROXIMATE METHODS FOR ESTIMATING 
 SYSTEM PERFORMANCE 
 
 MODULE 7 COMPONENTS OF LIQUID SYSTEMS 
 
 MODULE 8 COMPONENTS OF AIR SYSTEMS 
 
 MODULE 9 DOMESTIC HOT WATER SYSTEMS 
 
 MODULE 10 SOLAR SYSTEMS FOR SPACE HEATING 
 
 MODULE 11 DESIGN PROCEDURES 
 
 MODULE 12 ECONOMIC CONSIDERATIONS 
 
 MODULE 13 OTHER ECONOMIC CONSIDERATIONS 
 
 MODULE 14 INSTALLATION OF SOLAR SYSTEMS 
 
 MODULE 15 OPERATIONAL CHECK-OUT 
 
 MODULE 16 FUNDAMENTALS OF SOLAR COOLING 
 
 MODULE 17 FUTURE PROSPECTS FOR SOLAR HEATING AND COOLING SYSTEMS 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 1 
 
 COURSE OUTLINE 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
1-i 
 TABLE OF CONTENTS 
 
 OBJECTIVES 1-1 
 
 INTRODUCTION 1-1 
 
 COURSE SCHEDULE 1-2 
 
 COURSE CONTENT 1-4 
 
1-1 
 
 OBJECTIVES 
 
 The training course is designed to develop the capability of each 
 trainee to design solar heating and cooling systems for small buildings 
 used as residences and offices. Specific objectives of the course are 
 to develop capabilities of trainees to: 
 
 1. Identify different types of solar systems and their 
 components. 
 
 2. Differentiate between experimental and proven systems. 
 
 3. Design solar systems for heating space and service water. 
 
 4. Calculate expected system performance of a specified solar 
 heating system. 
 
 5. Recognize installation procedures and problems. 
 
 6. Measure and evaluate system performance. 
 
 7. Recognize maintenance requirements. 
 
 8. Explain system operation to system owners. 
 
 INTRODUCTION 
 
 The Solar Energy Applications Laboratory at Colorado State 
 University prepared this manual to be used in conjunction with a train - 
 ing course on the practical aspects of designing solar systems for space 
 and service water heating. In determining curriculum content, a rigor- 
 ous procedure was followed to (1) develop course standards, (2) estab- 
 lish needs of contractors, engineers and architects to design and in- 
 stall solar systems, (3) delineate objectives for the course and (4) 
 develop the curricular materials. The manual is modularized for 
 
1-2 
 
 flexibility in conducting the course and it is not essential (although 
 preferable) to follow the modules in numerical order. 
 
 So that the order of the modules can be rearranged, and so that the 
 material may be conveniently used as a reference manual, there is some 
 repetition and duplication. For example, components of liquid and air 
 systems are covered not only in Modules 7 and 8 but also in the sections 
 on heating systems (Modules 2 and 10). When the manual is used as a 
 course textbook, these duplications may be employed as review material 
 or they may be passed over. 
 
 At Colorado State University the training course is conducted in 
 five consecutive days, but the period of presentation may be varied to 
 suit the needs at a particular location. Evening hours may be utilized 
 during which one or more modules can be presented and discussed, or a 
 shorter period than five days may be chosen and some material may be 
 deleted. Each module has stated objectives, and examinations may be 
 given to determine achievement levels of the trainees. 
 
 COURSE SCHEDULE 
 
 A course arrangement suitable for a five-day period is suggested on 
 the following page. The modules are arranged, first to introduce 
 trainees to fundamental concepts of solar systems and components, and 
 then provide an approximate method of sizing systems. This is followed 
 by a more detailed discussion of components and a detailed method of 
 system design. After methods to estimate performance are discussed, 
 economic issues are addressed. Installation concerns and system per- 
 formance measurement procedures conclude the course. 
 
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 COURSE EVALUATION 
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1-4 
 
 COURSE CONTENT 
 
 TOUR OF SOLAR HOUSES 
 
 A pre-course tour of solar houses is provided to give trainees an 
 opportunity to see different types of systems and different styles of 
 solar homes. The duration of the tour is about three hours. 
 
 MODULE 1 - COURSE OUTLINE 
 
 The objectives of the course are discussed, and course schedule is 
 presented. The purpose is to outline clearly to participants what is 
 expected in the course. 
 
 MODULE 2 - INTRODUCTION TO SOLAR HEATING AND COOLING SYSTEMS 
 
 This module presents the types of solar systems covered in this 
 manual and training course. Because of the varied backgrounds expected 
 of trainees, this introductory module is used to establish a common 
 foundation for all trainees in the course. 
 
 MODULE 3 - SOLAR RADIATION 
 
 A procedure to calculate solar radiation on tilted collectors is 
 the principal content of the module. It is also important to understand 
 the variability of the energy source. 
 
 MODULE 4 - SOLAR COLLECTORS 
 
 The basic principles of flat-plate solar collectors are discussed 
 in this module. Parameters which characterize collector performance are 
 explained and factors which affect efficiency are discussed. Differ- 
 ences between air and liquid-type collectors are explained. 
 
1-5 
 
 MODULE 5 - HEATING AND COOLING LOAD ANALYSES 
 
 For sizing furnaces, boilers, and air-conditioners for building 
 space conditioning systems it is advisable to make heating and cooling 
 load calculations. To design economical solar systems, such calcula- 
 tions are essential. Simple procedures for heating and cooling load 
 analyses are described in the module. 
 
 MO DULE 6 - SYSTEM SIZING AND APPROXIMATE METHODS FOR ESTIMATING SYSTEM 
 PERFORMANCE 
 
 Collector areas are selected arbitrarily or based upon economic 
 
 criteria. Component sizes are based on collector area and simple rules. 
 
 These design rules are presented and approximate methods to estimate 
 
 system performance are described. 
 
 MODULE 7 - COMPONENTS OF LIQUID SYSTEMS 
 
 Components for air and liquid systems are basically different 
 although their functions are similar. Storage heat exchangers, controls 
 and pumps for liquid systems are discussed in this module. 
 
 MODULE 8 - COMPONENTS OF AIR SYSTEMS 
 
 Thermal energy storage, controls and blowers for air systems are 
 described in this module. 
 
 MODULE 9 - DOMESTIC HOT WATER SYSTEMS 
 
 Different types of service water heating systems are described, 
 operating characteristics are explained and a simple sizing procedure is 
 presented. 
 
1-6 
 
 MODULE 10 - SOLAR SYSTEMS FOR SPACE HEATING 
 
 Detailed operating characteristics of solar heating systems are 
 described in this module. 
 
 MODULE 11 - DESIGN PROCEDURES 
 
 The f-chart method for estimating system performance is the 
 detailed design method that is generally used. The procedure is flex- 
 ible in that components of different sizes may be included in the sys- 
 tem, but application is limited to specified types of solar systems. 
 
 MODULE 12 - ECONOMIC CONSIDERATIONS 
 
 Procedures for calculating life-cycle costs of solar and 
 conventional heating systems are presented. Various factors pertinent 
 to the analysis are also explained. 
 
 MODULE 13 - OTHER ECONOMIC CONSIDERATIONS 
 
 Since life-cycle costing involves many assumptions, more simple 
 approaches in determining economic viability of solar systems are ex- 
 plained in this module. 
 
 MODULE 14 - INSTALLATION OF SOLAR SYSTEMS 
 
 Designers of solar systems should be generally aware of preferred 
 installation procedures and problems which may arise during installa- 
 tion. Through understanding of installation problems, designs can be 
 made to minimize installation costs. 
 
1-7 
 
 M ODULE 15 - OPERATIONAL CHECK-OUT 
 
 All systems must be checked after installation to determine that 
 the system operates properly. Items of concern and procedures for 
 orderly inspection and testing are described. 
 
 MODULE 16 - FUNDAMENTALS OF SOLAR COOLING 
 
 Various solar cooling alternatives are described in this module. 
 Absorption cooling systems, Rankine-cycle systems and desiccant cooling 
 are described. 
 
 MODULE 17 - FUTURE PROSPECTS FOR SOLAR HEATING AND COOLING SYSTEMS 
 Components of systems that are under development with prospects for 
 future use are discussed. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 2 
 
 INTRODUCTION TO SOLAR HEATING AND COOLING SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
2-1 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 Page 
 2-iii 
 
 OBJECTIVES .... 
 INTRODUCTION .... 
 SOLAR HEATING AND COOLING SYSTEMS 
 LIQUID-HEATING SOLAR SYSTEMS . 
 
 A BASIC SYSTEM . 
 
 DRAIN-BACK SYSTEM . 
 
 DUAL-LIQUID SYSTEM . 
 
 NEED FOR AUXILIARY HEATING 
 
 METHODS OF HEAT DELIVERY . 
 
 SERVICE WATER HEATING 
 
 LIQUID SYSTEM COMPONENTS . 
 
 Solar Collectors for Liquid Heating 
 Thermal Storage Units 
 AIR-HEATING SOLAR SYSTEMS 
 
 A BASIC SYSTEM . 
 
 SYSTEM OPERATION 
 
 SERVICE WATER HEATING 
 
 SYSTEM COMPONENTS . 
 
 Solar Collectors for Air Heating 
 Heat Storage in Air Systems 
 AUXILIARY HEATERS 
 
 2-1 
 
 2-1 
 
 2-1 
 
 2-2 
 
 2-2 
 
 2-3 
 
 2-3 
 
 2-5 
 
 2-6 
 
 2-6 
 
 2-7 
 
 2-7 
 
 2-11 
 
 2-12 
 
 2-12 
 
 2-13 
 
 2-15 
 
 2-16 
 
 2-16 
 
 2-16 
 
 2-19 
 
2-ii 
 
 HYDRONIC SYSTEMS .... 
 
 2-19 
 
 AIR FURNACES 
 
 2-20 
 
 HEAT DISTRIBUTION 
 
 2-21 
 
 AUTOMATIC CONTROLS 
 
 2-21 
 
 SOLAR COOLING 
 
 2-23 
 
2- \ i i 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 2-1 Schematic Diagram of a Simplified Liquid Type Solar 
 
 Heating System ........ 2-2 
 
 2-2 Drain-Down System for Solar Collection and Storage. 2-4 
 
 2-3 Solar Collection in Non-Freezing Liquid and Heat 
 
 Exchange with Water Storage ..... 2-4 
 
 2-4 Schematic Arrangement of a Solar Domestic Hot Water 
 
 (DHW) Subsystem 2-6 
 
 2-5 Typical Liquid-Heating Collector with Tubular Liquid 
 
 Passages ......... 2-8 
 
 2-6 Liquid-Heating Collector with Flow Between Metal 
 
 Plates 2-8 
 
 2-7 Corning Glass Company Evacuated Tube Collector . 2-10 
 
 2-8 Schematic of the Owens-Illinois Evacuated Tube Solar 
 
 Collector 2-10 
 
 2-9 Schematic Diagram of an Air-Heating Solar System 
 
 (Simplified) 2-13 
 
 2-10 Air-Heating Solar System 2-14 
 
 2-11 Air Collector with Ducts Beneath Absorber and 
 
 Internal Manifolds ....... 2-17 
 
 2-12 Air Collector with Perforated Absorber Plate . . 2-17 
 
 2-13 Pebble Bed Heat Storage Unit 2-18 
 
 2-14 Typical Use of Auxiliary in Liquid (Hydronic) 
 
 Distribution System ....... 2-19 
 
 2-15 Solar Heat from Liquid System to Warm Air 
 
 Distribution System ....... 2-20 
 
 2-16 Typical Controls for a Liquid-Heating Solar System. 2-22 
 
 2-17 Solar Heating and Cooling System .... 2-24 
 
2-1 
 
 OBJECTIVES 
 
 At the end of this module, the trainee should be able to: 
 
 1. Identify the principal characteristics of solar heating and 
 cooling systems. 
 
 2. Describe the basic functions of key components of solar 
 heating and cooling systems. 
 
 3. Recognize the advantages and limitations of different designs 
 of components and systems. 
 
 INTRODUCTION 
 
 The purpose of this module is to provide a brief introduction to 
 the types of solar heating and cooling systems that are available and in 
 current use, and to explain the basic functions of the systems and their 
 key components. Methods of solar heat collection, storage, and control 
 are outlined, and the use of these components in complete systems with 
 auxiliary heat supply is described. 
 
 SOLAR HEATING AND COOLING SYSTEMS 
 
 A solar heating and/or cooling system can be defined as any system 
 which utilizes solar energy to heat and/or cool a building, although a 
 distinction is usually made between "active" and "passive" types. In 
 contrast with architectural features which permit direct solar entry 
 into the building, active systems require special equipment for collect- 
 ing solar energy in liquid or air, storing heat, and distributing heat 
 
2-2 
 
 to the rooms. They can be integrated directly into conventional HVAC 
 systems in buildings with provisions for controlled collection and 
 distribution of solar and auxiliary heat. Heat may be collected in a 
 liquid, usually water, or in a gas, always air, for transport to storage 
 or use. Both types are important and extensively used. 
 
 LIQUID-HEATING SOLAR SYSTEMS 
 
 A BASIC SYSTEM 
 
 Figure 2-1 is a simplified schematic drawing of a liquid-heating 
 solar system, representative of those widely available today. The key 
 components are a solar collector, a tank for heat storage in hot water, 
 an auxiliary furnace, and a system for delivering heat to the building. 
 Many solar heating systems also include a heat exchanger for transfer- 
 ring heat from a non-freezing collector fluid to water storage. 
 
 <5 
 
 SOLAR 
 
 THERMAL 
 
 STORAGE 
 
 UNIT 
 
 (WATER TANK) 
 
 AUXILIARY 
 HEATER 
 
 (FURNACE 
 
 OR 
 
 BOILER) 
 
 HEAT 
 
 DISTRIBUTION 
 
 SYSTEM 
 
 <& 
 
 <D 
 
 PUMP 
 
 AUTOMATIC PUMP/ BLOWER 
 
 VALVE /DAMPER 
 
 Figure 2-1. 
 
 Schematic Diagram of a Simplified Liquid Type Solar Heating 
 System 
 
2-3 
 
 Facilities for providing solar heat to the domestic hot water supply are 
 also commonly used. 
 
 Solar radiation is absorbed in the collector, the temperature of a 
 liquid, usually water, being pumped through the collector increases, and 
 the heated water is transferred to a storage tank (or, in some cases, 
 directly to the heat distribution system). The thermal storage unit is 
 usually essential because heat is ordinarily required at night and 
 during cloudy periods. The solar collector and thermal storage unit can 
 operate independently of heating demands, so solar energy can be col- 
 lected and stored whenever there is sufficient incident solar radiation. 
 
 DRAIN-BACK SYSTEM 
 
 If water is used in the solar collectors in a cold climate, some 
 freeze protection method must be provided. A common arrangement shown 
 in Figure 2-2 permits the collector to drain into the storage tank 
 whenever operation of the circulating pump stops. When the solar in 
 tensity is sufficient for heat collection, a pump circulates water 
 through the collectors and the storage tank. When the pump shuts off, 
 water in the collector drains into the storage tank while air enters the 
 collector tubes through an atmospheric vent. An alternate design pro- 
 vides a down-flow pipe large enough for air from the top of the vented 
 storage tank to rise through the pipe as water drains down when the pump 
 operation ceases. In some systems, automatic valves operate to drain 
 the collector only when freezing temperatures are approached. 
 
 DUAL-LIQUID SYSTEM 
 
 Figure 2-3 shows another method for freeze protection, by which 
 solar heat is collected in a non-freezing liquid, usually a water-glycol 
 
2-4 
 
 AIR 
 VENT 
 
 INLET 
 MANIFOLD 
 
 *\} 
 
 OUTLET MANIFOLD 
 
 (INTERNAL OR EXTERNAL 
 TO COLLECTOR ARRAY) 
 
 FLOW 
 
 SOLAR 
 THERMAL 
 STORAGE 
 
 Figure 2-2. Drain-Down System for Solar Collection and Storage 
 
 VENT OR RELIEF VALVE 
 
 J EXPANSION 
 TANK 
 
 FLOW 
 
 HEAT 
 EXCHANGER 
 
 ^ 
 
 COLLECTOR 
 PUMP 
 
 ^3- 
 
 VENT 
 
 I 
 
 SOLAR 
 
 THERMAL 
 
 STORAGE 
 
 Figure 2-3, 
 
 HEAT EXCHANGER 
 PUMP 
 
 Solar Collection in Non-Freezing Liquid and Heat Exchange 
 with Water Storage 
 
2-5 
 
 solution. To avoid the cost of several hundred gallons of glycol 
 anti-freeze in the storage liquid, water is used for heat storage and a 
 heat exchanger is provided for transfer of heat from the collector fluid 
 to storage. A second pump is required unless the heat exchanger is 
 located inside the storage tank. 
 
 The advantages of this design are the minimal risk of freezing (and 
 damage) from incomplete collector drainage or venting, and the absence 
 of corrosion caused by alternate exposure of the collector tubes to 
 water and air in the drain-back system. The possibility of corrosion 
 and freezing in the drain-back system (in Figure 2-2) can thus be com- 
 pared with the cost penalty of the heat exchanger, additional pump and 
 piping, and temperature loss in the exchanger for the design in Figure 
 2-3. 
 
 NEED FOR AUXILIARY HEATING 
 
 An auxiliary furnace is required as a back-up to the heating system 
 for use when the solar collector/thermal storage subsystem is unable to 
 meet heating demands. Although the collector and storage could be sized 
 large enough to meet the full heating requirements throughout the year, 
 the cost would be prohibitive in most climates. An economical design 
 involves a smaller solar system and an auxiliary furnace or boiler 
 capable of meeting the full heating demand (at design conditions) when 
 solar collection is not possible and when stored heat is inadequate. 
 This combination results in more effective use of the solar equipment 
 throughout the heating season and a lower annual total cost. 
 
2-6 
 
 METHODS OF HEAT DELIVERY 
 
 Heat can be delivered to the building in several ways. With 
 a warm-air distribution system, heat is usually supplied to air from 
 stored hot water by use of a liquid-to-air heat exchanger ("fan-coil") 
 with pump and blower for circulating the two fluids. Space heating 
 may also be provided by circulating the hot water to all parts of the 
 building where individual fan-coil units or "radiator" surfaces such as 
 baseboard strip heaters (finned tubing) are used. 
 
 SERVICE WATER HEATING 
 
 Service hot water may be solar heated either in a system for that 
 purpose only, or in combination with a space heating system. Figure 2-4 
 
 FROM COLD 
 WATER MAIN 
 
 AUTOMATIC 
 
 SHUT-OFF 
 
 VALVE 
 
 STORAGE 
 DHW PUMP 
 
 PREHEAT 
 DHW PUMP 1 - 
 
 l MIXING 
 X^VALVE 
 
 TO DHW 
 DISTRIBUTION 
 AND LOAD 
 
 AUXILIARY 
 
 HOT WATER 
 
 TANK 
 
 AUXILIARY ENERGY 
 INPUT TO DHW 
 
 Figure 2-4. Schematic Arrangement of a Solar Domestic Hot Water (DHW) 
 Subsystem 
 
2-7 
 
 is a schematic drawing showing a typical arrangement of components for 
 utilizing solar heat in a domestic hot water (DHW) system of either 
 type. Solar energy from a collector or a thermal storage unit is used 
 to preheat water supplied from the cold water main. Thermostatic con- 
 trols actuate the two pumps when the DHW preheat tank is colder than the 
 solar source so that heat can be transferred in the heat exchanger to 
 the DHW supply. Instead of the separate heat exchanger, coils of tubing 
 inside the DHW preheat tank may be used. A conventional hot water 
 heater supplements the solar supply as required. As hot water is used 
 in the building, water preheated by solar energy replaces the quantity 
 drawn from the auxiliary hot water tank. Gas or electricity is used to 
 raise and maintain the temperature of the preheated water at the desired 
 setting (e.g. , 140°F). 
 
 LIQUID SYSTEM COMPONENTS 
 
 In addition to the components of conventional heating systems, a 
 solar system requires a solar collector, thermal storage unit, DHW 
 preheat tank, some additional plumbing/sheet metal work, and a more 
 extensive control system. Of the additional solar components, the most 
 important is the solar collector. 
 
 Solar Collectors for Liquid Heating 
 
 A solar collector is a device to convert incident solar radiation 
 to useful energy, usually in the form of heated air or heated liquid. 
 Figures 2-5 and 2-6 show examples of two liquid-type solar collectors 
 used in solar heating and cooling systems. 
 
MOUNTING 
 BRACKET 
 
 2-8 
 
 ABSORBER PLATE 
 WITH 
 SELECTIVE SURFACE 
 
 COPPER TUBES 
 
 SILICONE RUBBER PADS 
 TO ISOLATE ABSORBER PLATE 
 FROM FRAME 
 I 
 TWO COVER GLASSES 
 
 GLASS SEAL 
 TO FRAME 
 
 STEEL FRAMING 
 
 INLET WATER 
 HEADER 
 
 SEMI-RIGID 
 INSULATION 
 
 PLUMBING FITTING 
 
 Figure 2-5. Typical Liquid-Heating Collector with Tubular Liquid 
 Passages 
 
 GLASS COVER 
 
 ABSORBER PLATE 
 
 REFLECTIVE SURFACE 
 
 LIQUID FLOW 
 PASSAGE 
 
 RIGID FOAM INSULATION 
 
 PIPING CONNECTION 
 AND MOUNTING 
 
 Figure 2-6. Liquid-Heating Collector with Flow Between Metal Plate* 
 
2-9 
 
 Each collector consists of an absorber plate (commonly a blackened 
 metal surface) which absorbs the incident solar radiation and increases 
 in temperature. Heat in the absorber plate then flows to a liquid which 
 circulates through passages in the plate and delivers the heat to other 
 parts of the system. As it collects energy, the absorber plate loses 
 some heat to the surroundings, so the collector is designed to reduce 
 these losses to the minimum practical level. 
 
 Heat may be lost upward and downward from the absorber plate by 
 radiation, conduction, and convection. Since the cost of the solar heat 
 supply depends directly on the total collector area required, reduction 
 of heat losses will permit use of less collector area and reduced cost. 
 Insulation beneath the absorber and transparent covers above it reduce 
 all three types of heat loss. Glass is opaque to thermal radiation 
 emitted from the absorber plate, and a glass cover can also reduce 
 convection losses due to air movement across the absorber. An air space 
 between the absorber plate and cover acts to reduce convection losses 
 between these two surfaces. 
 
 A special type of flat-plate collector comprises a glass tube 
 surrounding a flat or cylindrical absorbing surface. As shown in 
 Figures 2-7 and 2-8, a high vacuum inside the tube minimizes heat losses 
 from these collectors. There is no concentration of radiation in this 
 type, but efficiencies and delivery temperatures may be considerably 
 higher than usually obtained in conventional flat-plate collectors. 
 
 A concentrating or focusing collector gathers solar radiation 
 falling on a large area and focuses the energy onto a smaller absorber 
 area. Concentrating collectors can deliver heat at higher temperatures 
 
2-10 
 
 3 / 32 in. THICK 
 PYREX GLASS TUBE 
 
 ABSORBER SUPPORT. 
 CLIPS 
 
 % in. OD COPPER 
 TUBING 
 
 '/„ in THICK COPPER 
 ABSORBER PLATE 
 
 MOLDED PLASTIC MOUNTING 
 WITH MANIFOLD TUBES- 
 
 ABSORBER SUPPORT 
 CLIPS (6/ABSORBER) 
 
 %in TUBE SPACING 
 MOLDED PLASTIC MOUNTING 
 
 TYPICAL TUBE DETAIL 
 
 Figure 2-7. Corning Glass Company Evacuated Tube Collector 
 
 ABSORBER TUBE 
 
 .COVER 
 
 DELIVERY TUBE 
 
 SPRING SUPPORT 
 
 TIP -OFF 
 
 COVER TUBE 
 t = 0.92 
 
 SELECTING COATING 
 a = 0.86, € * 0.07 
 
 HERMETIC 
 SEAL 
 
 FEEDER TUBE 
 
 FLUID FLOW AREA 
 (SUPPLY) 
 
 VACUUM PRESSURE 
 P< I0" 4 torr 
 ABSORBER TUBE 
 
 FLUID FLOW (RETURN) 
 
 Figure 2-8. 
 
 Schematic of the Owens-Illinois Evacuated Tube Solar 
 Collector 
 
2-11 
 
 than flat-plate types and may therefore be used for steam generation and 
 other applications for which such temperatures are necessary. But if 
 this type is used for heat supply at the moderate temperatures needed 
 for space heating and hot water, collector area requirements are com- 
 parable to those of the flat-plate type but equipment costs are higher. 
 
 Thermal Storage Units 
 
 The absence of solar radiation at night and the need for continuous 
 space heating in cold weather, results in a requirement for storing 
 excess solar energy collected, but not needed, during sunny daylight 
 hours. The stored energy can then be used for meeting nighttime heating 
 demands. This energy storage requirement is most economically met by 
 transferring the excess heat to a mass of solid or liquid in an in- 
 sulated container. Numerous materials could be used, but because of 
 simplicity and economy, most commercial liquid solar systems utilize hot 
 water storage. 
 
 It is technically possible to store heat in scrap metal, melted 
 chemicals, waxes, rock, ceramic bricks, and other materials. Water has 
 a higher heat storage capacity than any other material, pound- for-pound, 
 unless melting of a solid is involved. It is also the cheapest heat 
 storage material, but the cost of a container must be considered. Heat 
 can readily be stored in water by increasing its temperature during the 
 day, then using the hot water for heat supply at night. 
 
 Several chemical salts and waxes can store heat by melting rather 
 than by increase in temperature. When the molten material again solidi- 
 fies, the stored heat is released for use. Because the heat stored by 
 
2-12 
 
 melting a substance is considerably greater than the heat involved in 
 changing the temperature of an equal mass of water fifty degrees F or 
 so, a phase-change heat storage unit can be much smaller than the other 
 types. However, because of economic disadvantages and technical diffi- 
 culties, phase-change storage materials are not ready for practical use 
 in solar heating and cooling systems. 
 
 Extensive studies and experiments have shown that for space heating 
 and domestic hot water supply, practical and economical heat storage 
 units should have a capacity sufficient for storing one day's solar 
 collection for use the following night. Larger storage capacities 
 provide only small additional gains, so the storage of sufficient heat 
 for use during one or more cloudy days is uneconomical. 
 
 AIR-HEATING SOLAR SYSTEMS 
 
 A BASIC SYSTEM 
 
 The main components and their primary functions in an air system 
 are the same as in a liquid collection and storage system. This can be 
 seen by comparing Figure 2-9 with Figure 2-1. An important character- 
 istic of the air system in comparison with the liquid type is the direct 
 supply of heat from the collector to the living space. Whereas liquid 
 collection and storage systems may involve heat distribution either as 
 hot air or as hot water, air is always used for distribution when it is 
 also the collection medium. Auxiliary heat is nearly always supplied as 
 a supplement or boost in air systems (Figure 2-9), but in liquid systems 
 having hot water distribution (Figure 2-1), the auxiliary is in parallel 
 rather than in series with the solar supply. 
 
2-13 
 
 BLOWER 
 
 AUTOMATIC 
 DAMPER 
 
 SOLAR 
 
 HEAT 
 
 STORAGE 
 
 UNIT 
 
 It 
 
 AUXILIARY 
 HEATER AND 
 FAN (FURNACE) 
 
 HEAT 
 
 DISTRIBUTION 
 
 SYSTEM 
 
 Figure 2-9. Schematic Diagram of an Air-Heating Solar System 
 (Simplified) 
 
 The most economical and effective type of heat storage for an air 
 system is a rock-filled bin through which air is circulated and in which 
 heat is transferred to and from egg-sized pebbles or crushed rock. This 
 key component serves not only as a heat storage unit but also as a heat 
 exchanger during the storing cycle and as a heat exchanger during the 
 transfer of stored heat to air being supplied to the rooms. The use of 
 a pebble bed, as shown in a subsequent module, results in beneficial 
 temperature stratification in the storage unit and a substantially 
 higher solar collector efficiency than if transfer to hot water storage 
 were attempted. 
 
 SYSTEM OPERATION 
 
 A common type of air-heating solar system is shown in Figure 2-10. 
 The components include (1) air-heating solar collector, (2) pebble-bed 
 
2-14 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY 
 " FURNACE 
 
 WARM AIR 
 TO BUILDING 
 HEATING LOAD 
 
 TO DHW 
 LOAD 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 RETURN AIR 
 
 BACK- DRAFT 
 DAMPERS 
 
 FROM BUILDING 
 
 Figure 2-10. Air-Heating Solar System 
 
 heat storage unit to and from which heat is transferred by circulating 
 air through the bed, (3) control unit which includes the sensors and 
 control logic necessary to collect and store solar heat when available 
 and to automatically maintain comfort conditions at all times, (4) air 
 handler comprising automatic dampers, filters, and blower, (5) solar hot 
 water heater consisting of an air-to-water heat exchanger and a preheat 
 storage tank connected to an auxiliary hot water heater, and (6) warm- 
 air furnace to provide auxiliary heat when storage or collector tempera- 
 tures are insufficient to meet demands. 
 
 As air flows from one end of the collector to the other, its 
 temperature normally rises from about 70 degrees to about 130 to 150 
 degrees (F) during the mid-part of the day. Whenever heating is needed 
 
2-15 
 
 during sunny periods, warm air is supplied to the rooms directly from 
 the collector via the auxiliary furnace. Cool air from the building is 
 returned to the collector for reheating. 
 
 When heat is not needed in the building, solar- heated air is routed 
 through the storage unit, thereby heating the pebbles; cool air, usually 
 at 70°F, returns from the pebble bed to the collector for reheating. 
 Temperature stratification in the pebble bed assures maximum heat re- 
 covery from the collector. 
 
 When the sun is not shining, heat is delivered to the rooms by 
 circulating air from the building through the pebble bed. Because of 
 temperature stratification in the storage unit, this mode supplies heat 
 to the rooms at the highest available temperature. The system automati- 
 cally provides auxiliary heating from fuel or electricity when the solar 
 supply is insufficient to meet requirements. 
 
 SERVICE WATER HEATING 
 
 Service hot water can be heated by use of an air-to-water heat 
 exchanger in the hot air duct from the collector. When solar-heated air 
 is being delivered to storage, heat is also being supplied to the hot 
 water system by operation of the water pump. The temperature of the air 
 passing through the water heating coil is thus usually reduced by a 
 degree or two. Other coil locations have been used, but this position 
 has proved to be the most satisfactory. So that solar-heated water can 
 be available in the summer when no space heating is needed, a by-pass 
 duct is opened and air returns to the collector without passage through 
 storage or the rooms. 
 
2-16 
 
 SYSTEM COMPONENTS 
 
 Solar Collectors for Air Heating 
 
 Solar air collectors resemble the liquid heating types and differ 
 primarily in the design of the fluid passages in contact with the ab- 
 sorber plate. There may also be a difference in absorber plate mate- 
 rials, steel or aluminum normally being used in air collectors, whereas 
 corrosion considerations usually dictate use of copper or stainless 
 steel in liquid types. Figures 2-11 and 2-12 show two commercial types 
 of air collectors, one featuring internal manifolds for air distribution 
 to and from an array of numerous panels, and the other employing a 
 perforated absorber surface. Glazing, bottom insulation, and metal box 
 are similar to those used in the liquid types. 
 
 Numerous variations in the design of solar air collectors have been 
 used. Corrugated, finned, perforated and other modified absorber plate 
 forms have been tested. The most widely used type of air collector 
 contains a smooth black absorber plate beneath which air is circulated 
 in a space about one-half inch high. 
 
 Heat Storage in Air Systems 
 
 Because of low cost, high heat transfer effectiveness, and wide- 
 spread availability, gravel or crushed rock is nearly always used for 
 heat storage in air-heating solar systems. An insulated rectangular bin 
 is usually constructed in a basement or a utility area in the building. 
 The bin walls may be of concrete, masonry, or wood, and the top is 
 usually of wood. Clean aggregate normally used in concrete, screened to 
 a 3/4- inch to 1^-inch size range, is supported on wire mesh above spaced 
 concrete blocks or steel frames on the bin bottom. Depths of 5 to 7 
 
2-17 
 
 GLASS COVER 
 
 PORTS 
 
 MANIFOLD 
 
 Figure 2-11. Air Collector with Ducts Beneath Absorber and Internal 
 Manifolds (Exploded View) 
 
 BLACK METAL 
 MESH ABSORBER 
 
 AIR OUTLET 
 INSULATION 
 
 AIR INLET 
 
 Figure 2-12. Air Collector with Perforated Absorber Plate 
 (Exploded View) 
 
2-18 
 
 feet are typical, and air supply and withdrawal openings are provided in 
 the top and bottom plenum spaces. Figure 2-13 shows a cut-away view of 
 a pebble bed in a wood bin. 
 
 HOT AIR 
 CONNECTION 
 
 COLD AIR 
 CONNECTION 
 
 WIRE SCREEN 
 SUPPORTED 
 ON STEEL 
 FRAME. 
 
 in. CONCRETE 
 AGGREGATE 
 
 RIGID INSULATION 
 
 Figure 2-13. Pebble-Bed Heat Storage Unit 
 
 Heated air supplied to the top of a pebble bed from a solar 
 collector passes down through the bed and leaves the bottom essentially 
 at the rock temperature in the lowest portion of the bed. Air returning 
 to the collector has thus been fully cooled and its useful heat content 
 has been transferred to pebbles usually in the upper part of the bed. 
 
2-19 
 
 AUXILIARY HEATERS 
 
 HYDRONIC SYSTEMS 
 
 During cloudy periods and on mid-winter nights, the solar system is 
 usually unable to meet all of the heat needs of the building. In a 
 liquid system, a conventional hot water boiler (Figure 2-14) may be 
 provided to supply part or all of the heating requirements during these 
 periods. If the temperature in the solar storage tank is too low to 
 maintain the preset building temperature, the auxiliary boiler automati- 
 cally supplies hot water to the distribution system. When a hot water 
 boiler is used for auxiliary heat supply, it is used in parallel, not in 
 series, with the solar supply. It is therefore an alternate heat source 
 rather than a "booster", so that auxiliary will not partially feed back 
 to solar storage. 
 
 SOLAR 
 HEAT 
 
 (STORAGE 
 
 OR 
 COLLECTOR) 
 
 AUTOMATIC 
 VALVE 
 
 <$> 
 
 AUXILIARY 
 BOILER 
 
 HOT WATER 
 TO HEATING 
 LOAD 
 
 ENERGY INPUT 
 
 <3- 
 
 (GAS, ELECTRICITY, etc.) 
 
 RETURN 
 
 \ 
 
 PUMP 
 
 Figure 2-14. Typical Use of Auxiliary in Liquid (Hydronic) 
 Distribution System 
 
2-20 
 
 AIR FURNACES 
 
 If the building is provided with a warm-air heating system, and if 
 solar heat is supplied from either liquid or air collectors, an air 
 furnace is usually used for auxiliary heat. Figure 2-10 shows auxiliary 
 use in all-air systems, and Figure 2-15 shows a liquid-to-air heat ex- 
 changer and warm-air auxiliary furnace in a solar liquid system. 
 Electricity or any type of fuel may be supplied to the furnace. Aux- 
 iliary heat may also be provided by a heat pump. 
 
 Although the auxiliary heater is usually called upon to supply 
 only part of the total space heating demand, there will be occasions 
 when no solar heat is available from the collector or storage. Full 
 design capacity must therefore be provided so that comfort can be 
 
 maintained without solar supply during the coldest weather. 
 
 WARM AIR 
 TO ROOMS 
 
 WARM 
 
 AIR 
 
 FURNACE 
 
 SOLAR 
 
 THERMAL 
 
 STORAGE 
 
 TANK 
 
 ^> 
 
 A/WVi 
 
 VVsAAJ 
 
 FUEL OR 
 
 ELECTRICITY 
 
 HEAT 
 
 TRANSFER 
 
 COIL 
 
 RETURN AIR 
 FROM ROOMS 
 
 Figure 2-15. Solar Heat from Liquid System to Warm Air 
 Distribution System 
 
2-21 
 
 HEAT DISTRIBUTION 
 
 In "hydremic" systems, hot water can be piped from storage or 
 auxiliary boiler to coils imbedded in floors or ceilings (radiant 
 heating) or to "radiators", fan-coil units, or baseboard strip heaters 
 in individual rooms. The operating temperature of most baseboard hot 
 water heaters is about 180°F, which is too high for use with typical 
 solar systems. But if additional heating surface is provided, as for 
 example, with double rows of baseboard tubes, lower temperatures may be 
 usefully employed, and solar-heated water can be supplied at suitable 
 temperatures. 
 
 Forced warm air distribution is commonly used with all types of 
 solar heating systems. In liquid collection and storage systems, hot 
 water from the solar storage tank is pumped to a heating coil (finned- 
 tube exchanger) as illustrated in Figure 2-15, and circulating air is 
 heated as it passes through the coil. Figure 2-10 shows that in all-air 
 systems, warm air from collector or storage is delivered through conven- 
 tional distribution ducts via the auxiliary furnace in which additional 
 heat is supplied if needed. 
 
 AUTOMATIC CONTROLS 
 
 To control the temperature in a conventionally heated home, the 
 homeowner needs only to set a thermostat. The same is true in a house 
 with a well-designed solar heating system. However, controls for solar 
 heating and cooling are more complex than in a conventional system, 
 because they must operate collector and storage pumps and blowers, 
 
2-22 
 
 automatic valves and dampers, as well as the conventional equipment. To 
 illustrate the principles, a schematic diagram of a control assembly for 
 a liquid-heating solar system for space and domestic water is shown in 
 Figure 2-16. 
 
 Pressure 
 ♦ Relief Valve 
 
 STORAGE 
 TANK 
 
 DIFFERENTIAL 
 THERMOSTAT 
 
 PUMP NO. 5jT 
 COLD WATER V -^ ^iL 
 
 SUPPLY / / V f 
 
 DIFFERENTIAL 
 THERMOSTAT^ 
 
 ^XJPUMP NO. 3 
 
 HEAT TO 
 ROOMS 
 
 VALVE 
 
 i PUMP NO. 4 
 
 PRE- HEAT 
 TANK 
 
 ^ S4 
 
 HOT 
 WATER 
 HEATER 
 
 _ SERVICE HOT 
 WATER 
 
 *S3 IS COMBINATION 
 TEMPERATURE SENSOR 
 AND 2 -STAGE THERMOSTAT 
 
 Figure 2-16. Typical Controls for a Liquid-Heating Solar System 
 
 In nearly all solar heating systems, a differential thermostat 
 senses the difference in temperature between collector outlet and stor- 
 age. When this difference is more than a preset number of degrees, the 
 circulating pumps are operated and solar heat is stored. A pressure 
 relief valve protects the system from excessive pressure which might 
 otherwise develop if there is circulation failure during a sunny period. 
 
2-23 
 
 Supply of heat to a building is usually controlled by a two-stage 
 thermostat, the normal setting actuating pumps and fans which circulate 
 solar heated air or water to the rooms. If the room temperature con- 
 tinues to drop, a second (lower temperature) contact point in the ther- 
 mostat actuates the supply of fuel or electricity to the auxiliary 
 heater. 
 
 Preheating of service water is controlled by a differential 
 thermostat which senses the difference in temperature between the solar 
 storage tank and the preheat tank. At a difference of more than a few 
 degrees, circulation pumps are operated and heat is transferred from the 
 main storage to the preheat tank. A "high set" thermostat (limit con- 
 trol) may be used to prevent too high a temperature in the preheat tank 
 by interrupting power to the circulation pumps. 
 
 Numerous controllers for solar space heating systems are 
 commercially available, and many varieties of control circuits and 
 methods are being used. Design of control systems requires directions 
 from the manufacturers of the control components and experience in their 
 proper integration and adjustment. 
 
 SOLAR COOLING 
 
 There are several possible methods for cooling with solar energy. 
 These include absorption refrigeration (lithium bromide-water and 
 ammonia-water systems), Rankine-cycle vapor-compression, and desiccant- 
 evaporative cooler combinations. Only the lithium-bromide absorption 
 type is commercially available, and its operation with solar heat has 
 been almost entirely in experimental installations. Although not solar 
 
2-24 
 
 operated, heat pumps are sometimes used in solar heating systems for 
 auxiliary heat supply and for conventional cooling with electric power. 
 An absorption cooling system in which solar-heated water is the 
 energy source is illustrated in Figure 2-17. Solar cooling by this and 
 other methods is complex and expensive, so it is currently in an 
 experimental status. Cooling machines that can be operated with hot 
 water at 160°F to 200°F are commercially available in sizes from 3 tons 
 to over 25 tons of cooling capacity. Chilled water, at 40°F to 45°F, is 
 produced and supplied to one or more fan-coil units in the air 
 circuit. Air is cooled, dehumidified, and distributed to the rooms. 
 Heat is rejected from the system in cooling water which is recirculated 
 through a cooling tower. 
 
 
 SOLAR 
 
 STORAGE 
 
 TANK 
 
 AIR 
 
 I 
 
 COOLING 
 TOWER 
 
 «G- 
 
 ABSORP- 
 TION 
 CHILLEFl 
 
 AUXILIARY 
 BOILER 
 
 <S> 
 
 t I 
 
 AIR TO 
 ROOMS 
 
 <P-°-f 
 
 VWV-i 
 
 t 
 
 COOLING 
 COIL 
 
 HEATING 
 COIL 
 
 AIR FROM 
 ROOMS 
 
 Figure 2-17. Solar Heating and Cooling System 
 
2-25 
 
 Other experimental methods of solar cooling include conventional 
 vapor compression driven by power generated in an on-site engine sup- 
 plied with steam or organic vapor from a solar collector/boiler. Desic- 
 cant (air-drying) systems in which room air is dehumidified and the 
 solid or liquid drying agent is regenerated by solar heat are also being 
 investigated. None of these systems is at present technically or 
 economically practical. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 3 
 
 SOLAR RADIATION 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
3-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 LIST OF TABLES . ... 
 
 GLOSSARY OF TERMS 
 
 LIST OF SYMBOLS 
 
 OBJECTIVES 
 
 INTRODUCTION 
 
 SOLAR CONSTANT 
 
 EXTRATERRESTRIAL RADIATION 
 VARIATIONS IN TERRESTRIAL RADIATION 
 
 MONTHLY VARIATIONS .... 
 
 DAILY VARIATIONS .... 
 
 HOURLY VARIATIONS .... 
 
 REGIONAL VARIATIONS .... 
 SOLAR RADIATION DATA FOR DESIGN PURPOSES 
 
 DIMENSIONS AND CONVERSION FACTORS FOF 
 
 HORIZONTAL RADIATION DATA 
 
 RADIATION ON TILTED SURFACES . 
 
 EFFECT OF COLLECTOR ORIENTATION 
 CALCULATIONS FOR SYSTEM DESIGN 
 EXAMPLE PROBLEMS 
 
 EXAMPLE PROBLEM 1 . . . . 
 Solution ..... 
 Alternate Solution to Problem 1 
 
 
 
 Page 
 
 
 3-iii 
 
 . 
 
 3-v 
 
 
 3-vi 
 
 
 3-vii 
 
 , # 
 
 
 3-1 
 
 • 
 
 
 3-1 
 
 ■ 
 
 
 3-2 
 
 • 
 
 
 3-3 
 
 • 
 
 
 3-3 
 
 • 
 
 
 3-4 
 
 • 
 
 
 3-5 
 
 • 
 
 
 3-6 
 
 • 
 
 
 3-7 
 
 • 
 
 
 3-7 
 
 ERGY AND POWER . 
 
 3-7 
 
 • 
 
 
 3-9 
 
 • 
 
 
 3-9 
 
 • 
 
 
 3-12 
 
 • 
 
 
 3-13 
 
 • 
 
 
 3-16 
 
 • 
 
 
 3-16 
 3-16 
 
 
 
 3-17 
 
3-ii 
 
 EXAMPLE PROBLEM 2 . 
 
 Solution . 
 
 Alternate Solution to Problem 2 
 
 REFERENCES 
 
 APPENDIX 
 
 3-18 
 3-18 
 3-19 
 3-21 
 A3-1 
 
3—i i i 
 
 LIST OF FIGURES 
 
 F- 
 
 igure 
 
 3- 
 
 ■1 
 
 3- 
 
 ■2 
 
 3- 
 
 ■3 
 
 3- 
 
 ■4 
 
 3-5 
 
 3-6 
 3-7 
 
 3-8 
 3-9 
 
 Page 
 
 Spectrum of Solar Irradiance at the Earth's Surface . 3-2 
 
 Atmospheric Effects on Solar Radiation Reaching Earth . 3-4 
 
 Energy Intercepted by a Unit-Width Horizontal Surface . 3-5 
 
 Monthly Variation of Average Daily Radiation on a 
 
 Horizontal Surface, Boulder, Colorado .... 3-5 
 
 Hourly Record of Total Solar Radiation on a Horizontal 
 
 Surface on Clear Days in Fort Collins, Colorado . . 3-6 
 
 Effect of Tilted Surface on Energy Intercepted . . 3-10 
 
 Variation of the Sun's Position Relative to Horizontal 
 
 and Tilted Surfaces ........ 3-11 
 
 Effect of Collector Orientation ..... 3-12 
 
 Solar Radiation on Horizontal and Tilted Surfaces . . 3-13 
 
 
 
 
 LIST 
 
 OF FIGURES 
 
 IN APPENDIX 
 
 
 A3-1 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation < 
 
 ^Langleys) 
 
 , January 
 
 A3-15 
 
 A3-2 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation < 
 
 ^Langleys) 
 
 , February 
 
 A3-15 
 
 A3-3 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 ^Langleys) 
 
 , March . 
 
 A3-16 
 
 A3-4 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 'Langleys) 
 
 , April . 
 
 A3-16 
 
 A3-5 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 ^Langleys) 
 
 ., May 
 
 A3-17 
 
 A3-6 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 ^Langleys) 
 
 , June . 
 
 A3-17 
 
 A3-7 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 'Langleys) 
 
 , July . 
 
 A3-18 
 
 A3-8 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation I 
 
 ^Langleys) 
 
 , August 
 
 A3-18 
 
 A3-9 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation l 
 
 [Langleys) 
 
 , September . 
 
 A3-19 
 
 A3-10 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation ( 
 
 [Langleys) 
 
 , October 
 
 A3-19 
 
 A3-11 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation I 
 
 [Langleys) 
 
 , November 
 
 A3-20 
 
 A3-12 
 
 Mean 
 
 Daily 
 
 Solar 
 
 Radiation I 
 
 [Langleys) 
 
 , December 
 
 A3-20 
 
3-iv 
 
 A3-13 
 A3- 14 
 A3-15 
 A3-16 
 A3-17 
 A3- 18 
 A3-19 
 A3-20 
 A3-21 
 A3-22 
 A3-23 
 A3-24 
 A3-25 
 A3-26 
 A3-27 
 A3-28 
 A3-29 
 A3-30 
 A3-31 
 A3-32 
 A3-33 
 A3-34 
 A3-35 
 A3-36 
 A3-37 
 A3-38 
 A3-39 
 A3-40 
 
 Ti 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 T 
 
 List of Figures (Continued) 
 It Correction Factor for 25° Latitude 
 It Correction Factor for 30° Latitude 
 It Correction Factor for 35° Latitude 
 It Correction Factor for 40° Latitude 
 It Correction Factor for 45° Latitude 
 
 It Correcti 
 
 It Correcti 
 
 It Correcti 
 
 It Correcti 
 
 on Factor for 50° Latitude 
 
 on Factor for 55° Latitude 
 
 on Factor for 25° Latitude 
 
 on Factor for 30° Latitude 
 
 It Correction Factor for 35° Latitude 
 
 It Correction Factor for 40° Latitude 
 
 It Correction Factor for 45° Latitude 
 
 It Correction Factor for 50° Latitude 
 
 It Correction Factor for 55° Latitude 
 
 It Correction Factor for 25° Latitude 
 
 It Correction Factor for 30° Latitude 
 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 It Correcti 
 
 on Factor for 35° Latitude 
 on Factor for 40° Latitude 
 on Factor for 45° Latitude 
 on Factor for 50° Latitude 
 on Factor for 55° Latitude 
 on Factor for 25° Latitude 
 on Factor for 30° Latitude 
 on Factor for 35° Latitude 
 on Factor for 40° Latitude 
 on Factor for 45° Latitude 
 on Factor for 50° Latitude 
 
 It Correction Factor for 55° Latitude 
 
 10° T 
 15° 1 
 20° T- 
 25° T- 
 30° Ti 
 35° T' 
 40° Ti 
 25° " 
 30° ' 
 35° Ti 
 40° Ti 
 45° 7 
 50° Ti 
 55° " 
 40° 7 
 45° 1! 
 50° 1 
 55° T: 
 60° T 
 65° Ti 
 70° Ti 
 
 "ilt . . A3-21 
 
 "ilt . . A3-22 
 
 "ilt . . A3-23 
 
 ilt . . A3-24 
 
 "ilt . . A3-25 
 
 ilt . . A3-26 
 
 'ilt . . A3-27 
 
 "ilt . . A3-28 
 
 "ilt . . A3-29 
 
 ilt . . A3-30 
 
 ilt . . A3-31 
 
 "ilt . . A3-32 
 
 "ilt . . A3-33 
 
 ilt . . A3-34 
 
 "ilt . . A3-35 
 
 ilt; . . A3- 36 
 
 ilt . . A3-37 
 
 "ilt . . A3-38 
 
 "ilt . . A3-39 
 
 "ilt . . A3-40 
 
 "ilt . . A3-41 
 
 Vertical Tilt . A3-42 
 
 Vertical Tilt . A3-43 
 
 Vertical Tilt . A3-44 
 
 Vertical Tilt . A3-45 
 
 Vertical Tilt . A3-46 
 
 Vertical Tilt . A3-47 
 
 Vertical Tilt . A3-48 
 
3-v 
 LIST OF TABLES 
 
 Table Page 
 
 3-1 Monthly Variations in Energy on a Horizontal Surface for 
 
 Selected Cities in the United States .... 3-7 
 
 3-2 Energy and Power Units ....... 3-8 
 
 3-3 Conversion Factors for Energy and Power .... 3-8 
 
 LIST OF TABLES IN APPENDIX 
 
 A3-1 I Monthly Average Daily Extraterrestrial Radiation on a 
 
 Horizontal Surface ........ A3-1 
 
 A3-2 Radiation and Other Data for 81 Locations in the United 
 
 States A3-3 
 
 A3-3 Ratio of Monthly Average Daily Radiation on a Tilted Surface 
 
 to that on a Horizontal Surface, R for K. = . 30 . . A3-9 
 
 A3-4 Ratio of Monthly Average Daily Radiation on a Tilted Surface 
 
 to that on a Horizontal Surface, R or K. = .40 . . A3-10 
 
 A3-5 Ratio of Monthly Average Daily Radiation on a Tilted Surface 
 
 to that on a Horizontal Surface, R for R. - .50 . . A3-11 
 
 A3-6 Ratio of Monthly Average Daily Radiation on a Tilted Surface 
 
 to that on a Horizontal Surface, R for K = .60 . . A3-12 
 
 A3-7 Ratio of Monthly Average Daily Radiation on a Tilted Surface 
 
 to that on a Horizontal Surface, R for K = .70 . . A3-13 
 
3-vi 
 
 GLOSSARY OF TERMS 
 
 Azimuth Deviation in angle from due south. 
 
 Beam Radiation Radiation reaching the earth's surface from the 
 
 solar disc. 
 
 Btu British Thermal Unit, the quantity of heat required 
 
 to raise the temperature of one pound of water one 
 degree Fahrenheit. 
 
 Calorie The quantity of heat required to raise the 
 
 temperature of one gram of water one degree 
 Centigrade. 
 
 Declination Position of the sun relative to the equatorial plane 
 
 at solar noon. 
 
 Diffuse Radiation Radiation reaching the earth's surface from 180 
 
 degree hemisphere, excluding the beam radiation. 
 
 Direct Radiation Radiation reaching the earth's surface from the 
 
 solar disc. 
 
 Extraterrestrial Solar radiation outside the earth's atmosphere. 
 Radiation 
 
 Horizontal Surface Surface that is tangent to the earth's surface at 
 
 any point, and any surface that is parallel to the 
 tangent surface. 
 
 Langley Measure of solar radiation intensity. 
 
 Solar Constant Solar Radiation intensity on a surface normal to the 
 
 sun's rays at the mean earth-sun distance, 428 Btu/ 
 (hr-ft 2 ) 
 
 Solar Radiation Portion of total radiation which is useful for solar 
 
 heating and cooling systems. 
 
 Solar Radiation Time rate of delivery of solar radiation. 
 Flux 
 
 Tilted Surface Tilted with respect to the horizontal. 
 
3-vii 
 
 LIST OF SYMBOLS 
 
 D Average daily diffuse radiation for a month 
 
 T„ Monthly average daily total radiation on a horizontal surface, 
 h Btu/(dayft 2 ) 
 
 I Solar constant, 428 Btu/(hr-ft 2 ) 
 sc 
 
 I Extraterrestrial radiation on a horizontal surface at the 
 outer limits of earth's atmosphere, Btu/(hr*ft 2 ) 
 
 T T Monthly averaged daily radiation on a tilted surface, Btu/ 
 1 (dayft 2 ) 
 
 K. Fraction of solar energy which penetrates through the earth's 
 atmosphere on daily average 
 
 n Number of days from January 1 
 
 R Fraction of average daily radiation on tilted surface compared 
 to a horizontal surface 
 
 R n Ratio of the average daily beam radiation on a tilted surface 
 to that on a horizontal surface 
 
 'D 
 
 s Collector tilt angle from horizontal, degrees 
 
 T Temperature, °F 
 
 t Time variable 
 
 id Sunset hour angle, degrees from solar noon 
 
 6 Solar declination, position of the sun relative to the 
 equatorial plane at solar noon, degrees 
 
 § Latitude angle, degrees (north is plus) 
 
 p Reflectivity of material or ground surface 
 
3-1 
 
 OBJECTIVES 
 
 The objective in this module is to present methods for calculation 
 of solar radiation incident on a tilted collector surface by use of 
 solar radiation data on a horizontal surface. With the information in 
 this module the trainee should be able to: 
 
 1. Recognize the factors which affect the variability of solar 
 radiation at the earth's surface. 
 
 2. Estimate mean daily solar radiation for each month of the 
 year. 
 
 3. Convert solar radiation data from one set of units to another. 
 
 4. Determine the solar radiation intensity on a collector surface 
 at any tilt and orientation. 
 
 INTRODUCTION 
 
 Energy is radiated from the sun as a result of thermonuclear 
 reactions which take place within its core. Violent action that accom- 
 panies the thermonuclear reactions leads to particulate emission from 
 the sun and the high surface temperatures result in electromagnetic 
 radiation (or more simply, radiant energy) emission outward through 
 space. The particulate emission consists of electrons and protons and 
 is commonly called "solar wind". The electromagnetic radiation is 
 commonly termed "solar radiation" and is the form of energy with which 
 we are concerned in this module. 
 
 The electromagnetic radiation consists of a wide spectrum of wave- 
 lengths and energetic intensities as shown in Figure 3-1. Almost half 
 of the solar energy received on earth is in the band of visible light, 
 
3-2 
 
 I 2 
 
 Wavelength, X (/im) 
 
 Figure 3-1. Spectrum of Solar Irradiance at the Earth's Surface 
 
 and nearly all of the other half consists of the near infrared wave- 
 lengths. A small portion is attributable to ultraviolet and other short 
 wave length energy radiation, most of which is filtered out by the 
 earth's atmosphere. The intensity of solar energy varies with latitude, 
 altitude, time of day and time of year. Figure 3-1 shows a "smoothed" 
 spectral distribution (narrow absorption bands due to carbon dioxide, 
 water vapor, and ozone in the atmosphere have been averaged into nearby 
 wavelengths) of solar energy received at sea level, under "standard" 
 atmospheric conditions known as air mass 1.0. 
 
 SOLAR CONSTANT 
 
 The solar radiation flux (time rate of delivery of solar energy) 
 varies inversely with distance from the sun, and since the earth is in 
 an elliptical orbit about the sun, the energy flux reaching the outer 
 limits of the earth's atmosphere varies from about 410 to 440 Btu/ 
 (ft 2 *hr). At the mean earth-sun distance, the energy flux is called the 
 
3-3 
 
 solar constant, I , and its magnitude is 428 Btu/(ft 2 «hr), equal to 
 1.35 KW/m 2 . 
 
 EXTRATERRESTRIAL RADIATION 
 
 Solar radiation at the outer limits of the earth's atmosphere is 
 called extraterrestrial radiation, I . The extraterrestrial radiation 
 on a plane which is parallel to, and directly above, a horizontal plane 
 on the earth's surface will vary with respect to latitude and time of 
 year. The monthly average daily extraterrestrial radiation, I , on a 
 horizontal surface is calculated for each month at various latitudes and 
 presented in Table A3-1 in the appendix to this module. 
 
 VARIATIONS IN TERRESTRIAL RADIATION 
 
 As the solar rays penetrate the earth's atmosphere, radiation is 
 scattered, absorbed, and reflected by the atmospheric constituents such 
 as carbon dioxide, oxygen, ozone, water vapor and particulate matter in 
 the atmosphere as shown in a schematic representation in Figure 3-2. 
 Some of the energy is reflected back into outer space at the outer 
 fringes of the atmosphere and still more is reflected from the tops of 
 clouds. As much as 30 percent of the extraterrestrial radiation may not 
 reach the earth's surface on a clear day. Solar radiation which pene- 
 trates the atmosphere without being reflected or scattered is called 
 direct, or beam radiation. Diffuse radiation reaches the earth's sur- 
 face by reflection from particulate matter and clouds in the atmosphere. 
 At a particular point on the ground, therefore, diffuse radiation ar- 
 rives from clouds and the entire sky. 
 
3-4 
 
 UPPER 
 ATMOSPHERE 
 
 DUST 
 
 (SCATTERING) 
 
 . ^ ^ \ ^ V V ^ \ V ' V V V V ' s V V ^ i, \ V l, \ V V V ^ 's \ \ \ \ \ v s s v x 
 DIFFUSE RADIATION DIRECT RADIATION EARTH 
 
 Figure 3-2. Atmospheric Effects on Solar Radiation Reaching Earth 
 
 MONTHLY VARIATIONS 
 
 The mean daily radiation on a horizontal surface, I H , varies from 
 month-to-month and with geographic location, due to seasonal changes in 
 weather and changing angular relationship between the sun and earth's 
 surface. In the winter, the sun is lower in the sky than in the summer, 
 and the resulting smaller angle between the sun and a horizontal surface 
 reduces the amount of radiation intercepted by the surface, as shown in 
 Figure 3-3(A). In the summer, the sun is higher above the horizon (at 
 noon) than in winter and a larger amount of energy is intercepted by a 
 horizontal surface as shown in Figure 3-3(B). 
 
 An example of the variation in the monthly average daily radiation 
 on a horizontal surface is shown in Figure 3-4 for Boulder, Colorado. 
 It is noted that the average daily radiation in June and July is about 
 twice that in January. 
 
3-5 
 
 SOLAR RADIATION 
 12 "UNITS" 
 
 SOLAR RADIATION 
 12 "UNITS" 
 
 (A) LOW SUN ANGLE, WINTER 
 4 "RADIATION UNITS" 
 INTERCEPTED 
 
 (B) HIGH SUN ANGLE, 
 SUMMER 
 
 6 "RADIATION UNITS" 
 INTERCEPTED 
 
 Figure 3-3. Energy Intercepted by a Unit-Width Horizontal Surface 
 
 2000 
 
 -g 1000 
 
 CO 
 
 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 
 
 Figure 3-4. Monthly Variation of Average Daily Radiation on a Horizontal 
 Surface, Boulder, Colorado (From the Climatic Atlas of the 
 United States) 
 
 DAILY VARIATIONS 
 
 There are wide variations in total daily radiation on a horizontal 
 surface largely as a result of clouds. On overcast days when the total 
 radiation is largely diffuse, there may be only two or three hundred 
 
3-6 
 
 Btu/ft 2 for the entire day with the intensity so low that a solar system 
 could not collect useful heat. On sunny days, two to three thousand 
 Btu/ft 2 may be received. 
 
 HOURLY VARIATIONS 
 
 Hourly variations in total solar radiation are a result of the 
 earth's rotation about its own axis. Early morning sun is at a very low 
 angle and the solar rays must penetrate a "thick" atmospheric layer. 
 Maximum radiation occurs at noon, when the sun is at the highest angle 
 above the horizon and the radiation encounters a minimum thickness of 
 the atmosphere. 
 
 Hourly variations of solar radiation on a horizontal surface, 
 measured in Fort Collins, Colorado, on clear days are shown in Figure 
 3-5. Clouds would, of course, create random variations in solar inten- 
 sity and the total radiation would be less than on clear days. 
 
 300 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6/ 
 
 /75 
 
 
 
 
 
 
 
 
 
 
 
 
 250 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4/26/75 
 
 
 
 
 
 
 
 
 ~ 200 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 150 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1/19/75 ""*\ 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 \ ! 
 
 5 ( 
 
 
 r t 
 
 i < 
 
 J 1 
 
 1 
 
 1 1 
 
 2 
 
 
 > - 
 
 5 A 
 
 \ I 
 
 5 i 
 
 > 7 
 
 t 
 
 Time of Day 
 
 Figure 3-5. Hourly Record of Total Solar Radiation on a Horizontal 
 Surface on Clear Days in Fort Collins, Colorado (Data 
 from Solar House I) 
 
3-7 
 
 REGIONAL VARIATIONS 
 
 To emphasize regional variations of solar radiation, the monthly 
 average daily solar radiation at selected cities in the United States is 
 listed in Table 3-1 for four months which represent the four seasons of 
 the year. The variations are due to different latitudes as well as to 
 weather conditions. 
 
 Table 3-1 
 
 Monthly variations in Energy on a Horizontal Surface 
 for Selected Cities in the United States 
 [Btu/(ft 2 -day)] 
 
 City 
 
 Latitude 
 
 December 
 
 March 
 
 June 
 
 September 
 
 Chicago, IL 
 
 41° 
 
 354 
 
 838 
 
 1690 
 
 1155 
 
 i Tucson, AZ 
 
 32° 07' 
 
 1172 
 
 1993 
 
 2601 
 
 2122 
 
 Washington, DC 
 
 38° 51' 
 
 632 
 
 1255 
 
 2081 
 
 1446 
 
 ! 
 
 Miami, FL 
 
 25° 47' 
 
 1292 
 
 1829 
 
 1992 
 
 1647 
 
 Fairbanks, AK 
 
 64° 49' 
 
 66 
 
 860 
 
 1971 
 
 700 
 
 Los Angeles, CA 
 
 34° 03' 
 
 912 
 
 1641 
 
 2259 
 
 1892 , 
 
 SOLAR RADIATION DATA FOR DESIGN PURPOSES 
 
 DIMENSIONS AND CONVERSION FACTORS FOR ENERGY AND POWER 
 
 The intensity of solar radiation is expressed in several different 
 dimensions. In this manual, British Thermal Units (Btu), foot, and hour 
 are used, but other dimensions may be encountered. Thus, the relation- 
 ships between units are given in Table 3-2 and conversion factors are 
 listed in Table 3-3. 
 
3-8 
 
 Table 3-2 
 Energy and Power Units 
 
 Abbreviation 
 
 Unit 
 
 Energy Density 
 Btu/ft 2 
 kJ/m 2 
 Langley (cal/cm 2 ) 
 
 British Thermal Units per square ft 
 Kilojoules per square meter 
 Calories per square centimeter 
 
 Power 
 Btu/(ft 2 -hr) 
 
 kJ/(m 2 -hr) 
 
 Langley/min 
 
 W/m 2 
 
 British Thermal Units per square ft 
 per hour 
 
 Kilojoules per square meter per 
 hour 
 
 Calories per square centimeter per 
 minute 
 
 Watts per square meter 
 
 Table 3-3 
 Conversion Factors for Energy and Power 
 
 To Convert into Btu/ft 2 
 
 To Convert into Btu/(hr-ft 2 ) 
 
 Multiply By 
 
 Multiply By 
 
 Langleys 3.69 
 
 Langleys/min 221 
 
 kJ/m 2 . 088 
 
 kJ/m 2 -hr .088 
 
 
 W/m 2 . 316 
 
3-9 
 
 HORIZONTAL RADIATION DATA 
 
 The principal source of solar radiation data for the United States 
 is the National Weather Service Climatic Data Center at Asheville, North 
 Carolina. Presently there are 86 stations throughout the United States 
 and West Indies that are recording total radiation on a horizontal 
 surface. At five stations the direct component is also measured. Of 
 the 86 stations, 67 have their data processed for daily total only, and 
 hourly data are processed at 19 stations. The estimated errors in the 
 recorded data range from ± 5 percent to ± 30 percent, as reported by 
 Jessup (Ref. 1). 
 
 Monthly average daily total radiation on horizontal surfaces (from 
 Ref. 2) for 81 locations in the United States and Canada is listed in 
 Table A3-2 of the Appendix. Using these data, maps showing the monthly 
 average daily radiation on a horizontal surface for each month of the 
 year were drawn by the National Weather Service. The maps, printed in 
 the Climatic Atlas of the United States, are reproduced in Figures A3-1 
 through A3-12 for the months of January through December respectively. 
 The radiation units on the maps are Langleys per day and should be 
 multiplied by the conversion factor, 3.69, to change the units to 
 Btu/(ft 2 -day). 
 
 RADIATION ON TILTED SURFACES 
 
 When designing solar systems, it is advantageous to tilt the 
 collectors to be perpendicular to the sun's rays. The increased amounts 
 of solar radiation intercepted by a collector that is tilted, compared 
 to the same collector in a horizontal position, are illustrated in 
 Figure 3-6. When the collector is perpendicular to the incoming radia- 
 tion, the additional energy intercepted is a maximum as seen in Figure 
 
3-10 
 
 3-6(B). For any other angle, less solar energy is intercepted as seen 
 in Figure 3-6(C). A collector which follows the sun across the sky so 
 that the rays are always perpendicular to the surface intercepts the 
 maximum amount of energy during the day. However, for many types of 
 collectors, tracking is not practical, and is particularly unsuitable 
 for residential solar heating systems. An alternative arrangement to a 
 tracking collector is a collector array at a fixed tilt to intercept the 
 maximum amount of radiation during a selected period of time, say 
 September through May for a space heating system or during the entire 
 year for a domestic water-heating system. 
 
 I H , RADIATION 
 INTERCEPTED BY A 
 HORIZONTAL COLLECTOR 
 
 I H , ADDITIONAL 
 RADIATION INTERCEPTED 
 BY A TILTED COLLECTOR 
 
 1 
 
 (A) COLLECTOR TILT ANGLE 0° (B) COLLECTOR TILT ANGLE 45° (Q COLLECTOR TILT ANGLE 75° 
 
 Figure 3-6. Effect of Tilted Surface on Energy Intercepted 
 
 To maximize solar energy collection during the heating season, the 
 plane of the collector should be tilted at an angle greater than lati- 
 tude. The reason is illustrated in Figure 3-7. The declination of the 
 
3-11 
 
 sun, which is the angle between the plane of the equator and the sun at 
 solar noon, 6, varies from zero degrees on September 21 and March 21, to 
 -23° 45' on December 21 and +23° 45' on June 21, as shown in Figure 
 3-7(a). Thus a collector tilt, s, which is greater than the latitude 
 angle, 0, is more nearly perpendicular to the solar rays from September 
 through March as illustrated in Figure 3-7(b). To maximize summer 
 collection, the collector should be tilted at an angle less than lati- 
 tude, and if collection is desired throughout the year, a tilt angle 
 nearly equal to the latitude is appropriate. The exact tilt angle for a 
 given location will depend on climatic conditions, but a general rule is 
 to tilt the collectors at latitude plus 15 degrees for a space heating 
 system and at the latitude angle for a domestic water heating system. 
 
 June 2 
 
 September 21 
 March 21 
 
 December 21 
 
 sr 23° 45 
 
 Horizonta 
 
 Latitude 
 Angle, <p 
 
 (a) Position of Sun Relative to 
 a Horizontal Plane at Equinoxes 
 and Solstices 
 
 September 21 
 March 21 
 
 Latitude 
 Angle, <p 
 
 (b) Collector Tilted at Angles 
 
 Greater than Latitude Maximizes 
 Solor Energy Collection During 
 the Heating Season 
 
 Figure 3-7. Variation of the Sun's Position Relative to Horizontal and 
 Tilted Surfaces 
 
3-12 
 
 The total solar radiation intercepted by a tilted collector is not 
 only the direct beam radiation as implied in Figure 3-7. There may be a 
 significant amount of diffuse radiation available depending upon cli- 
 matic conditions and the reflectivity of surfaces in "front" of the 
 collectors. Although a portion of the hemispherical diffuse radiation 
 is "cut off" by a tilted collector, reflected radiation from the fore- 
 ground may more than offset the reduction of total diffuse sky 
 radiation. 
 
 EFFECT OF COLLECTOR ORIENTATION 
 
 Because the arc of the sun is symmetrical about solar noon, the 
 preferred orientation of the collector is due south. Any other collec- 
 tor orientation (non-zero azimuth angle) will decrease the total energy 
 incident on the collector surface during the day. However, deviations 
 either east or west by as much as 30 degrees (two hours) will decrease 
 the total daily solar radiation by less than 5 percent as shown in 
 Figure 3-8. An azimuth angle larger than 30 degrees will noticeably 
 affect the solar system. In Figure 3-8, s is the optimum tilt angle. 
 
 o 
 
 D 
 
 U_ 
 
 c 
 o 
 
 .0 
 
 0.9 
 
 o 
 
 c 0.8 
 
 i_ 
 
 o 
 0.7 
 
 
 
 
 
 
 
 
 
 
 Horiz. 
 
 
 
 
 
 
 
 
 
 
 — S - 
 
 - 45° 
 
 
 
 
 
 
 
 
 
 
 — So- 
 
 - 30° 
 
 
 
 
 
 
 
 
 ert-^ 
 
 
 — So- 
 — So 
 
 - 15° 
 
 
 
 
 
 
 
 V 
 
 
 ^-So- 
 
 1- 15° 
 H 30° 
 
 0.6 
 
 10 20 30 40 50 60 70 80 90 100 110 
 
 South . . .. . . East, West 
 
 Azimuth Angle 
 
 Figure 3-8. Effect of Collector Orientation 
 
3-13 
 
 CALCULATIONS FOR SYSTEM DESIGN 
 
 The monthly average daily solar radiation on a tilted surface that 
 is facing south, I T , (zero azimuth) is the quantity needed to select 
 the collector area of a solar heating system. The quantity, Ij, is 
 calculated from the mean daily horizontal radiation, I H , with a conver- 
 sion factor R that is calculated for a specific location. 
 
 The quantities needed to calculate I T are illustrated in Figure 3-9, 
 and Equation (3-1) is to be used. 
 
 I sc [solar Constant, 428 Btu/(ft 2 • hr)l 
 
 Monthly Average Daily Extraterrestrial 
 Radiation on a Horizontal Surface 
 
 >>?>>/>WWV^& 
 
 ^TT^^^^^^^mr 
 
 Monthly Average Daily 
 Total Radiation on a 
 Horizontal Surface 
 
 Diffuse 
 
 Collector 
 
 Diffuse 
 
 Collector 
 , s Tilt An gle 
 
 Monthly Average Daily 
 Total Radiation on a 
 Tilted Surface 
 
 K. = 
 
 R 
 
 Terrestrial 
 Extraterrestrial 
 
 Tilted 
 
 Horizontal 
 
 _±H_ 
 
 Figure 3-9. Solar Radiation on Horizontal and Tilted Surfaces 
 
3-14 
 
 I T = R • I H (3-1) 
 
 where 
 
 I,, is determined from Table A3-2 or radiation maps of Figures A3-1 
 through A3-12 
 
 R is calculated from Equation (3-2), or interpolated from Tables 
 A3-3 through A3-7, or read from graphs of Figures A3-13 
 through A3-40. 
 
 r = (1 - L) R d + L (32SOS-S) + p (!£§§-!) (3-2) 
 
 where 
 
 s is collector tilt in degrees 
 
 p is ground reflectance. A value of 0.25 may be representative for 
 green grass, 0.2 for old concrete and crushed rock, and 0.1 
 for bituminous parking lot surface 
 
 — is determined from Equation (3-3), and 
 T H 
 
 R . is determined from Equation (3-5). 
 
 —■ = 1.3903-4.0273 K t + 5.532 K t 2 - 3.100 K t 3 , ... (3-3) 
 
 and 
 
 K. = -P- (3-4) 
 
 T o 
 
3-15 
 
 cos ((|>-s) cos 6 sin u) ' + uj" sin (<Jrs) sin 6 
 
 p = s s (3-5) 
 
 d " cos ty cos 6 sin uj + uj * sin <)> sin 6 
 
 in which, 
 
 uj ' is the smaller value of [uj or cos (tan(4>-s) tanS)] 
 
 uj " is uj ' expressed in radians 
 s s r 
 
 <)) is latitude angle, degrees 
 
 s is collector tilt angle, degrees 
 
 8 is declination estimated from Equation (3-6), degrees 
 
 uj is sunset hour angle calculated by Equation (3-7), degrees 
 
 uj * is sunset hour angle expressed in radians 
 
 5 = 23.45 sin [360(^~)] (3.6) 
 
 in which, 
 
 n is the day of the year counted from January 1 
 
 uj = cos (-tan <\> tan5) (3-7) 
 
 The calculation of the radiation on a tilted surface, Ij, by 
 Equations (3-2) through (3-7) can be time consuming (and confusing), so 
 it is more convenient to use a table of R values and even more conveni- 
 ent to read R values from graphs. Because the value of R depends on 
 many variables, R values not listed in Tables A3-3 through A3-7 must be 
 interpolated from the tabular values (for different K.), latitude, 
 collector tilt, and month of year. Interpolation of R values is some- 
 what easier with the graphs of Figures A3-13 through A3-40. Values of 
 K. for 81 cities are listed for each month in Table A3-2, and for loca- 
 tions that are not listed, estimates need to be made, either from near- 
 by locations or by reading the solar radiation maps for I H and the 
 
3-16 
 
 appropriate value of I from Table A3-1 and solving Equation (3-4). The 
 extraterrestrial radiation may also be calculated from Equation (3-8) 
 
 ! o = h J T ^c^ ' 033 cos ( Hr )] [cos ♦ cos 6 sin ^s + 
 o 
 
 w 3?q sin (f) sin 6] dt (3-8) 
 
 EXAMPLE PROBLEMS 
 
 EXAMPLE PROBLEM 1 
 
 Determine the average daily radiation for the month of January on a 
 collector surface that is tilted at an angle of 51 degrees in Las Vegas, 
 Nevada. 
 
 Solution 
 
 Step 1. From Table A3-2 
 
 Read: L = 1035.8 Btu/(ft 2 -day) 
 
 R t = 0.654 
 Latitude = 36° 05' N 
 Tilt = Latitude + 15° 
 Step 2. From Table A3-6 (for K. = 0.6), and tilt = latitude + 15°, 
 Read: Latitude 35° R = 1.76 
 Latitude 40° R = 2.02 
 Step 3. Calculate for Latitude 36° 05' (36.08°) 
 
 R = ( 2 -^33 76 ) x (36.08-35) + 1.76 = 1.82 
 
3-17 
 
 Step 4. From Table A3-7 (for K. = 0.7), and tilt = latitude + 15 ( 
 Read: Latitude 35° R = 1.86 
 Latitude 40° R = 2.15 
 Step 5. Calculate for Latitude 36° 05' 
 
 R = ( 2 -^qI^ 86 ) x (36.08-35) + 1.86 = 1.92 
 Step 6. Calculate for R t = 0.654 
 
 R = ( 1 q 92 "^ 2 ) x (0.654-0.6) + 1.82 = 1.87 
 Step 7. I T = R • I H 
 
 = 1.87 x 1035.8 = 1937 Btu/(ft 2 -day) ANSWER 
 
 Alternate Solution to Problem 1 
 Step 1. From Table A3-2 
 
 Read: I H = 1035.8 Btu/(ft 2 -day) 
 K t = 0.654 
 
 Latitude = 36° 05' N 
 Step 2. Calculate 
 
 Latitude - tilt = 36° - 51° = -15° 
 or, Tilt = Latitude + 15° 
 Step 3. From Figure A3-29 (Latitude 35°, Tilt 50°) 
 
 Read for K t =0.654, R = 1.81 
 Step 4. From Figure A3-30 (Latitude 40°, Tilt 55°) 
 
 Read for K t =0.654, R = 2.09 
 Step 5. Interpolate for latitude = 36° 05" (36.08°) 
 R = ( 2 'll~-l' b 81 ) x (36.08-35) + 1.81 = 1.87 
 
 (compare with Step 6, previous solution, 1.87) 
 Step 6. L = R • L 
 
 = 1.87 x 1035.8 = 1937 Btu/(ft 2 -day) ANSWER 
 
3-18 
 
 EXAMPLE PROBLEM 2 
 
 Determine the average daily radiation for the month of January on a 
 collector surface that is tilted at an angle of 45 degrees for a solar 
 heating system in Kansas City, Missouri. 
 
 Solution 
 
 Step 1. In Table A3-2 note that Kansas City, MO is not listed. 
 Step 2. Find from Figure A3-1 
 
 I H = 190 Langleys/day = 190 x 3.69 = 701 Btu/(ft 2 -day) 
 Latitude = 39.5° 
 Step 3. Calculate K. 
 From Table A3-1 
 
 Latitude 35° I = 1590 Btu/(ft 2 -day) 
 Latitude 40° I = 1324 Btu/(ft 2 -day) 
 Interpolate for Latitude 39.5° 
 
 I Q = ( 13 4qI35 9 ° ) * (39.5-40) + 1324 = 1351 Btu/(ft 2 -day) 
 
 h = =~ = 1351 = °- 519 - 
 o 
 
 Step 4. Calculate (latitude - tilt) 
 
 Latitude - tilt = (39.5 - 45) = -5.5° 
 or, Tilt = Latitude +5.5° 
 Step 5. From Figure A3-29 (for latitude 35°, tilt = latitude + 15°) 
 Read: for R t =0.519, R = 1.67 
 
 From Figure A3-30 (for latitude 40°, tilt = latitude + 
 15°) for K t = 0.519, R = 1.92 
 
3-19 
 
 Interpolate for latitude 39.5° 
 
 R = C 1 '^"^ 67 ) x (3.95-35) + 1.67 = 1.90 
 Step 6. From Figure A3-22 (for latitude 35°, tilt = latitude) 
 Read: for L = 0.519, R = 1.57 
 
 From Figure A3-23 (for latitude 40°, tilt = latitude) 
 for K t = 0.519, R = 1.79 
 Interpolate for latitude 39.5° 
 
 R = &lll\s 57 ) x (39.5-35) + 1.57 = 1.77 
 
 o 
 
 Step 7. Interpolate for collector tilt = latitude + 5.5 
 R = ( 1,9 °5o' 77 ) x (5.5°) + 1.77 = 1.82 
 
 Step 8. Calculate Ij 
 
 I T = r • i H 
 
 = (1.82)(701) = 1276 Btu/(ft 2 -day) ANSWER 
 
 Alternate Solution to Problem 2 
 
 Step 1. Find from Figure A3-1 
 
 I H = 190 Langleys/day = 190 x 3.69 = 701 Btu/(ft 2 -day) 
 Latitude = 39.5° 
 
 Step 2. Calculate K. 
 
 From Table A3-1: Latitude 35° I = 1590 Btu/(ft 2 -day) 
 
 Latitude 40° I = 1324 Btu/(ft 2 -day) 
 
 Interpolate for Latitude 39.5 
 
 o 
 
 I = ( 15 40-35 24 ) x (40-39-5) + 1324 = 1351 Btu/(ft 2 -day) 
 R t = f=l35l = - 519 
 
 
 
3-20 
 
 Step 3. Calculate R from Equations (3-2) through (3-7) 
 
 Use p = 0.2; n = 15; s = 45° 
 
 Result R = 1.83 
 
 (compare with 1.82 from previous method) 
 Step 4. Calculate Ij 
 
 I T = 1.83 x 701 = 1283 Btu/(ft 2 -day) ANSWER. 
 
3-21 
 
 REFERENCES 
 
 1. Jessup, E:, "A Brief History of the Solar Radiation Program", 
 Report and Recommendations of the Solar Energy Data Workshop, 
 November 29-30, 1973. Report No. NSF-RANN-74-062, NOAA, September 
 1974. 
 
 2. Liu, B. Y. H. , and Jordan, R. C. , (1977), "Availability of Solar 
 Energy for Flat-Plate Solar Heat Collectors", Chapter V, Applica- 
 tions of Solar Energy for Heating and Cooling of Buildings. ASHRAE 
 GRP 170 edited by Jordan and Liu, ASHRAE, Inc., New York, New York. 
 
 3. Klein, S. A., Beckman, W. A., and Duffie, J. A., "A Design 
 Procedure for Solar Heating Systems". Presented by International 
 Solar Energy Society Meeting, Los Angeles, California, July/August 
 1975. 
 
 4. Liu, B. Y. H. , and Jordan, R. C. , (1963) "A Rational Procedure for 
 Predicting a Long-Term Average Performance of Flat-Plate Collec- 
 tors", Solar Energy , Volume 7, No. 2. 
 
 5. Liu, B. Y. H. , and Jordan, R. C, (1960) "The Interrelationship 
 and Characteristic Distribution of Direct, Diffuse, and Total Solar 
 Radiation." Solar Energy , Volume 4, No. 3, pp. 1-19. 
 
 6. Duffie, J. A., and Beckman, W. A., (1974) Solar Energy Thermal 
 Processes , John Wiley and Sons, New York, New York. 
 
 7. National Bureau of Standards, Intermediate Minimum Property 
 Standards for Solar Heating and Domestic Hot Water Systems. Report 
 No. NBSIR 77-1226, March 1977. 
 
A3-1 
 
 APPENDIX 
 
A3-2 
 
 Table A3-1 
 
 I , Monthly Average Daily Extraterrestrial Radiation on a Horizontal 
 Surface Btu/(ft 2 -day) 
 
 Location 
 
 Jan 
 
 Feb 
 
 Mar Apr 
 
 May Jun 
 
 Jul 
 
 Aug 
 
 Sep 
 
 Oct 
 
 Nov 
 
 Dec 
 
 20 
 
 2349 
 
 2671 
 
 3019! 3301 
 
 i 
 
 3421 
 
 3445 
 
 3423 
 
 3332 
 
 3106 
 
 2763 
 
 2421 
 
 2246 
 
 25 
 
 2103 
 
 2474 
 
 2891 
 
 3266 
 
 3463 
 
 3524 
 
 3485 
 
 3329 
 
 3013 
 
 2588 
 
 2192 
 
 1995 
 
 30 
 
 1851 
 
 2260 
 
 2740 
 
 3206 
 
 3482 
 
 3581 
 
 3526 
 
 3303 
 
 2877 
 
 2395 
 
 1950 
 
 1735 
 
 35 
 
 1590 
 
 2030 
 
 2570 
 
 3124 
 
 3479 
 
 3619 
 
 3546 
 
 3254 
 
 2759 
 
 2184 
 
 1698 
 
 1468 
 
 40 
 
 1324 
 
 1788 
 
 2380 
 
 3019 
 
 3454 
 
 3637 
 
 3545 
 
 3183 
 
 2600 
 
 1950 
 
 1438 
 
 1194 
 
 45 
 
 1056 
 
 1535 
 
 2172 
 
 2892 
 
 3409 
 
 3636 
 
 3525 
 
 3090 
 
 2421 
 
 1720 
 
 1174 
 
 931 
 
 50 
 
 719 
 
 1275 
 
 1948 
 
 2746 
 
 3346 
 
 3621 
 
 3489 
 
 2979 
 
 2225 
 
 1470 
 
 910 
 
 669 
 
 55 
 
 535 
 
 1011 
 
 1769 
 
 2582 
 
 3209 
 
 3596 
 
 3441 
 
 2856 
 
 2012 
 
 1212 
 
 651 
 
 422 
 
 60 
 
 299 
 
 747 
 
 1459 
 
 2403 
 
 3185 
 
 3571 
 
 3389 
 
 2709 
 
 1784 
 
 950 
 
 405 
 
 200 
 
A3-3 
 
 Table A3-2 
 Radiation and Other Data for 81 Locations 
 
 in the United States* 
 
 Jan 
 
 Feb 
 
 Mar 
 
 Apr 
 
 May 
 
 Jun 
 
 Jul 
 
 Aug Sep Oct Nov Dec 
 
 ALASKA 
 
 Annette Is hi 236.2 
 
 Lat,55°02'N K t 0.427 
 
 El. 110 ft t a 35.8 
 
 Barrow Tu 13.3 
 
 Lat. 71'20'N K t 
 
 El. 22 ft t a -13.2 
 
 Bethel Tj 14 2' 4 
 
 Lat. 60°47'N K t 0.536 
 
 El. 125 ft t a 9.2 
 
 Fairbanks Tj 66 
 
 Lat. 64°49'N K t 0.639 
 
 El. 436 ft t a -7.0 
 
 Hatanuska Tu 119.2 
 
 Lat. 6T30'N K t 0.513 
 
 El. 180 ft t a 13.9 
 
 ALBERTA 
 
 Edmonton Tu 331.7 
 
 Lat53"35'N 1CV 0.529 
 
 El. 2219 ft t a 10.4 
 
 ARKANSAS 
 
 Little Rock T^ 704.4 
 
 Lat. 34°44'N Kt 0.424 
 
 El. 265 ft t a 44.6 
 
 ARIZONA 
 
 Phoenix T^ 1126.6 
 
 Lat. 33°26'N K t 0.65 
 
 El. 1112 ft t a 54.2 
 
 Tucson Jh 1171.9 
 
 Lat32°07'N K t 0.648 
 
 El. 2556 ft t a 53.7 
 
 CALIFORNIA 
 
 Davis hi 599.2 
 
 Lat. 38°33'N K t 0.416 
 
 El. 51 ft t a 47.6 
 
 Fresno T^ 712.9 
 
 Lat. 36°46'N K t 0.462 
 
 El. 331 ft t a 47.3 
 
 Inyokern Tu 1148.7 
 
 Lat. 35°39'N K t 0.716 
 
 El. 2440 ft t a 47.3 
 
 Los Angeles, (WBO) Ih 911.8 
 
 Lat. 34°03'N K t 0.538 
 
 El. 99 ft t a 57.9 
 
 Los Angeles, (WBAS) ~U\ 930.6 
 
 Lat. 33°56'N K t 0.547 
 
 El. 99 ft t a 56.2 
 
 Riverside Tj 999.6 
 
 Lat. 33°57'N K t 0.589 
 
 El. 1020 ft t a 55.3 
 
 Santa Marl a Tu gs3 8 
 
 Lat. 34°54'N K t 0.595 
 
 El. 238 ft t a 54.1 
 
 COLORADO 
 
 Grand Junction Tu, 848 
 
 Lat. 39°07'N K t 0.597 
 
 El. 4849 ft t 26.9 
 
 a 
 
 Grand Lake Tu 735 
 
 Lat. 40°15'N K t 0.541 
 
 El. 8389 ft t a 18.5 
 
 428.4 
 0.415 
 37.5 
 
 883.4 
 0.492 
 39.7 
 
 1357.2 
 0.507 
 x4.4 
 
 1634.7 
 0.484 
 51.0 
 
 1638.7 
 0.441 
 56.2 
 
 1632.1 
 0.454 
 58.6 
 
 1269.4 
 0.427 
 59.8 
 
 962 
 
 0.449 
 
 54.8 
 
 454.6 
 0.347 
 48.2 
 
 220.3 
 0.304 
 41.9 
 
 152 
 
 0.361 
 
 37.4 
 
 143.2 
 0.776 
 -15.9 
 
 713.3 
 0.773 
 -12.7 
 
 1491.5 
 0.726 
 2.1 
 
 1883 
 0.553 
 20.5 
 
 2055.3 
 0.533 
 35.4 
 
 1602.2 
 0.448 
 41.6 
 
 953.5 
 0.377 
 40.0 
 
 428.4 
 0.315 
 31.7 
 
 152.4 
 
 0.35 
 
 18.6 
 
 22.9 
 2.6 
 
 -8.6 
 
 404.8 
 0.557 
 11.6 
 
 1052.4 
 0.704 
 14.2 
 
 1662.3 
 0.675 
 29.4 
 
 1711.8 
 0.519 
 42.7 
 
 1698.1 
 0.458 
 55.5 
 
 1401.8 
 0.398 
 56.9 
 
 938.7 
 0.336 
 54.8 
 
 755 
 
 0.406 
 
 47.4 
 
 430.6 
 0.432 
 33.7 
 
 164.9 
 0.399 
 19.0 
 
 83 
 
 0.459 
 
 9.4 
 
 283.4 
 0.556 
 0.3 
 
 860.5 
 0.674 
 13.0 
 
 1481.2 
 0.647 
 32.2 
 
 1806.2 
 0.546 
 50.5 
 
 1970.8 
 0.529 
 62.4 
 
 1702.9 
 0.485 
 63.8 
 
 1247.6 
 0.463 
 58.3 
 
 699.6 
 0.419 
 
 47.1 
 
 323.6 
 0.416 
 29.6 
 
 104.1 
 0.47 
 5.5 
 
 20.3 
 
 0.458 
 
 -6.6 
 
 345 
 
 0.503 
 
 21.0 
 
 27.4 
 
 1327.6 
 0.545 
 38.6 
 
 1628.4 
 0.494 
 50.3 
 
 1727.6 
 0.466 
 57.6 
 
 1526.9 
 0.434 
 60.1 
 
 1169 
 0.419 
 58.1 
 
 737.3 
 
 0.401 
 50.2 
 
 373.8 
 0.390 
 37.7 
 
 142.8 
 0.372 
 22.9 
 
 56.4 
 
 0.364 
 
 13.9 
 
 652.4 
 0.585 
 14 
 
 1165.3 
 0.624 
 26.3 
 
 1541.7 
 0.564 
 42.9 
 
 1900.4 
 0.558 
 55.4 
 
 1914.4 
 0.514 
 61.3 
 
 1964.9 
 0.549 
 66.6 
 
 1528 
 0.506 
 63.2 
 
 1113.3 
 0.506 
 54.2 
 
 704.4 
 0.504 
 44.1 
 
 413.6 
 0.510 
 26.7 
 
 245 
 
 0.492 
 
 14.0 
 
 974.2 
 0.458 
 48.5 
 
 1335.8 
 0.496 
 56.0 
 
 1669.4 
 0.513 
 65.8 
 
 1960.1 
 0.545 
 73.1 
 
 2091.5 
 0.599 
 76.7 
 
 2081.2 
 0.566 
 85.1 
 
 1938.7 
 0.574 
 84.6 
 
 1640.6 
 0.561 
 78.3 
 
 1282.6 
 0.552 
 67.9 
 
 913.6 
 
 0.484 
 54.7 
 
 701.1 
 0.463 
 46.7 
 
 1514.7 
 0.691 
 58.8 
 
 1967.1 
 0.716 
 64.7 
 
 2388.2 
 0.728 
 72.2 
 
 2709.6 
 0.753 
 80.8 
 
 2781.5 
 0.745 
 89.2 
 
 2450.5 
 0.667 
 94.6 
 
 2299.6 
 0.677 
 92.5 
 
 2131.3 
 .722 
 87.4 
 
 1688.9 
 0.708 
 75.8 
 
 1290 
 0.657 
 63.6 
 
 1040.9 
 0.652 
 56.7 
 
 1453.8 
 0.646 
 57.3 
 
 62.3 
 
 2434.7 
 0.738 
 69.7 
 
 78.0 
 
 2601.4 
 0.698 
 87.0 
 
 2292.2 
 0.625 
 90.1 
 
 2179.7 
 0.640 
 87.4 
 
 2122.5 
 0.710 
 84.0 
 
 1640.9 
 0.672 
 73.9 
 
 1322.1 
 0.650 
 62.5 
 
 1132.1 
 0.679 
 56.1 
 
 945 
 
 0.490 
 52.1 
 
 1504 
 0.591 
 56.8 
 
 1959 
 0.617 
 63.1 
 
 2368.6 
 0.662 
 69.6 
 
 2619.2 
 0.697 
 75.7 
 
 2565.6 
 0.697 
 81 
 
 2287.8 
 0.687 
 79.4 
 
 1856.8 
 0.664 
 76.7 
 
 1288.5 
 0.598 
 67.8 
 
 795.6 
 0.477 
 57 
 
 550.5 
 0.421 
 48.7 
 
 1116.6 
 0.551 
 53.9 
 
 1652.8 
 0.632 
 59.1 
 
 2049.4 
 0.638 
 65.6 
 
 2409.2 
 0.672 
 73.5 
 
 2641.7 
 0.703 
 80.7 
 
 2512.2 
 0.682 
 87.5 
 
 2300.7 
 0.686 
 84.9 
 
 1897.8 
 0.665 
 78.6 
 
 1415.5 
 0.635 
 68.7 
 
 906.6 
 0.512 
 57.3 
 
 616.6 
 
 0.44 
 48.9 
 
 1554.2 
 0.745 
 53.9 
 
 2136.9 
 0.803 
 59.1 
 
 2594.8 
 0.8 
 65.6 
 
 2925.4 
 0.815 
 73.5 
 
 3108.8 
 0.830 
 80.7 
 
 2908.8 
 0.790 
 87.5 
 
 2759.4 
 0.820 
 84.9 
 
 2409.2 
 0.834 
 78.6 
 
 1819.2 
 0.795 
 68.7 
 
 3170.1 
 0.743 
 57.3 
 
 1094.4 
 0.742 
 48.9 
 
 1223.6 
 0.568 
 59.2 
 
 1640.9 
 0.602 
 61.8 
 
 1866.8 
 0.571 
 64.3 
 
 2061.2 
 0.573 
 67.6 
 
 2259 
 
 0.605 
 70.7 
 
 2428.4 
 0.66 
 75.8 
 
 2198.9 
 0.648 
 76.1 
 
 1891.5 
 0.643 
 74.2 
 
 1362.3 
 0.578 
 69.6 
 
 1053.1 
 0.548 
 65.4 
 
 877.8 
 0.566 
 60.2 
 
 1284.1 
 0.596 
 56.9 
 
 1729.5 
 0.635 
 59.2 
 
 1948 
 0.595 
 61.4 
 
 2196.7 
 0.610 
 64.2 
 
 2272.3 
 0.608 
 66.7 
 
 2413.6 
 0.657 
 69.6 
 
 2155.3 
 0.635 
 70.2 
 
 1898.1 
 0.641 
 69.1 
 
 1372.7 
 
 0.574 
 66.1 
 
 1082.3 
 0.551 
 62.6 
 
 901.1 
 0.566 
 58.7 
 
 1335 
 0.617 
 57.0 
 
 1750.5 
 0.643 
 60.6 
 
 1943.2 
 0.594 
 65.0 
 
 2282.3 
 0.635 
 69.4 
 
 2492.6 
 0.667 
 74.0 
 
 2443.5 
 0.665 
 81.0 
 
 2263.8 
 0.668 
 81.0 
 
 1955.3 
 0.665 
 78.5 
 
 1509.6 
 0.639 
 71.0 
 
 1169 
 0.606 
 63.1 
 
 979.7 
 0.626 
 57.2 
 
 1296.3 
 0.613 
 55.3 
 
 1805.9 
 0.671 
 57.6 
 
 2067.9 
 0.636 
 59.5 
 
 2375.6 
 0.661 
 61.2 
 
 2599.6 
 0.695 
 63.5 
 
 2540.6 
 0.690 
 65.3 
 
 2293.3 
 0.678 
 65.7 
 
 1965.7 
 0.674 
 65.9 
 
 1566.4 
 0.676 
 64.1 
 
 1169 
 0.624 
 60.8 
 
 943.9 
 0.627 
 56.1 
 
 1210.7 
 0.633 
 35.0 
 
 1622.9 
 0.643 
 44.6 
 
 2002.2 
 0.632 
 55.8 
 
 2300.3 
 0.643 
 66.3 
 
 2645.4 
 0.704 
 75.7 
 
 2517.7 
 0.690 
 82.5 
 
 2157.2 
 0.65 
 79.6 
 
 1957.5 
 0.705 
 71.4 
 
 1394.8 
 0.654 
 58.3 
 
 969.7 
 
 0.59 
 
 42.0 
 
 793.4 
 0.621 
 
 31.4 
 
 1135.4 
 0.615 
 23.1 
 
 1579.3 
 0.637 
 28.5 
 
 1876.7 
 0.597 
 39.1 
 
 1974.9 
 0.553 
 48.7 
 
 2369.7 
 0.63 
 56.6 
 
 2103.3 
 0.572 
 62.8 
 
 1708.5 
 0.516 
 61.5 
 
 1715.8 
 0.626 
 55.5 
 
 1212.2 
 0.583 
 45.2 
 
 775.6 
 0.494 
 30.3 
 
 660.5 
 0.542 
 22.6 
 
 *Taken from Applications of Solar Energy for Heating and Cooling of 
 Buildings, ASHRAE [2]. 
 
DISTRICT OF COLUMBIA 
 
 Washington (WBCO) T^ 
 
 Lat. 38°51'N Kt 
 
 El. 64 ft t a 
 
 FLORIDA 
 
 Apalachicola J_n 
 
 Lat. 29°45'N K t 
 
 El. 35 ft ta 
 
 Gainesville Tj 
 
 Lat. 29°39'N Kt 
 
 El. 165 ft t a 
 
 Miami Tu 
 
 Lat. 25°47'N K t 
 
 El- 9 ft t a 
 
 Tampa Jh 
 
 Lat. 27°55'N Kt 
 
 El. 11 ft t a 
 
 GEORGIA 
 
 Atlanta T^ 
 
 Lat. 33°39'N Kt 
 
 El. 976 ft t a 
 
 Griffin Tj 
 
 Lat. 33°15'N Kt 
 
 El. 980 ft t, 
 
 IDAHO 
 
 Boise J_h 
 
 Lat. 43°34'N Kt 
 
 El. 2844 ft t a 
 
 ILLINOIS 
 
 Lemont T^ 
 
 Lat. 41°40'N K t 
 
 El. 595 ft t 
 
 INDIANA 
 
 Indianapolis Iu 
 
 Lat. 39°44'N K t 
 
 El. 793 ft t 
 
 KANSAS 
 
 Dodge City I>| 
 
 Lat. 37°46'N Kt 
 
 El. 2592 ft t, 
 
 KENTUCKY 
 
 Lexington 1# 
 
 Lat. 38°02'N Kt 
 
 El. 979 ft t a 
 
 LOUISIANA 
 
 Lake Charles lu 
 
 Lat. 30°13'N K t 
 
 El. 12 ft t a 
 
 MAINE 
 
 Caribou Tu 
 
 Lat. 46°52'N K t 
 
 El. 628 ft t a 
 
 Portland Tj 
 
 Lat. 43°39'N Kt 
 
 El. 63 ft t a 
 
 MANITOBA 
 
 Winnipeg J^ 
 
 Lat. 49°54'N K 
 
 El. 786 ft t u 
 
 MASSACHUSETTS 
 
 Blue Hill Tj 
 
 Lat. 42"13'N Kt 
 
 El. 629 ft t„ 
 
 A3-4 
 
 Table A3-2 (continued) 
 
 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 
 
 Boston 
 
 Lat. 42°22'N 
 
 El. 29 ft t 
 
 t 
 
 632.4 
 0.445 
 38.4 
 
 901.5 
 0.470 
 39.6 
 
 1255 
 0.496 
 48.1 
 
 1600.4 
 0.504 
 57.5 
 
 1846.8 
 0.516 
 67.7 
 
 2080.8 
 0.553 
 76.2 
 
 1929.9 
 0.524 
 79.9 
 
 1712.2 
 0.516 
 77.9 
 
 1446.1 
 0.520 
 72.2 
 
 1083.4 
 0.506 
 60.9 
 
 763.5 
 0.464 
 50.2 
 
 594.1 
 0.460 
 40.2 
 
 1107 
 0.577 
 57.3 
 
 1378.2 
 0.584 
 59.0 
 
 1654.2 
 0.576 
 62.9 
 
 2040.9 
 0.612 
 69.5 
 
 2268.6 
 0.630 
 76.4 
 
 2195.9 
 0.594 
 81.8 
 
 1978.6 
 0.542 
 83.1 
 
 1912.9 
 0.558 
 
 83.1 
 
 1703.3 
 0.559 
 80.6 
 
 1544.6 
 0.608 
 73.2 
 
 1243.2 
 0.574 
 63.7 
 
 982.3 
 0.543 
 58.55 
 
 1036.9 
 0.535 
 62.1 
 
 1324.7 
 0.56 
 63.1 
 
 1635 
 0.568 
 67.5 
 
 1956.4 
 0.587 
 72.8 
 
 1934.7 
 0.538 
 79.4 
 
 1960.9 
 0.531 
 83.4 
 
 1895.6 
 0.519 
 83.8 
 
 1873.8 
 0.547 
 84.1 
 
 1615.1 
 0.529 
 82 
 
 1312.2 
 0.515 
 75.7 
 
 1169.7 
 0.537 
 67.2 
 
 919.5 
 0.508 
 62.4 
 
 1292.2 
 
 0.604 
 71.6 
 
 1554.6 
 0.616 
 72.0 
 
 1828.8 
 0.612 
 73.8 
 
 2020.6 
 0.600 
 77.0 
 
 2068.6 
 0.578 
 79.9 
 
 1991.5 
 0.545 
 82.9 
 
 1992.6 
 0.552 
 84.1 
 
 1890.8 
 0.549 
 84.5 
 
 1646.8 
 0.525 
 83.3 
 
 1436.5 
 0.534 
 80.2 
 
 1321 
 0.559 
 75.6 
 
 1183.4 
 0.588 
 72.6 
 
 1223.6 
 0.605 
 64.2 
 
 1461.2 
 0.600 
 65.7 
 
 1771.9 
 0.606 
 68.8 
 
 2016.2 
 0.602 
 74.3 
 
 2228 
 0.620 
 79.4 
 
 2146.5 
 0.583 
 83.0 
 
 1991.9 
 0.548 
 84.0 
 
 1845.4 
 0.537 
 84.4 
 
 1687.8 
 0.546 
 82.9 
 
 1493.3 
 0.572 
 77.2 
 
 1328.4 
 0.590 
 69.6 
 
 1119.5 
 0.589 
 65.5 
 
 848 
 
 0.493 
 
 47.2 
 
 1080.1 
 0.496 
 49.6 
 
 1426.9 
 0.522 
 
 55.9 
 
 1807 
 0.551 
 65.0 
 
 2618.1 
 0.561 
 73.2 
 
 2002.6 
 0.564 
 80.9 
 
 2002.9 
 0.545 
 82.4 
 
 1898.1 
 0.559 
 81.6 
 
 1519.2 
 0.515 
 77.4 
 
 1290.8 
 0.543 
 66.5 
 
 997.8 
 0.510 
 54.8 
 
 751.6 
 0.474 
 47.7 
 
 889.6 
 0.513 
 48.9 
 
 1135.8 
 0.517 
 51.0 
 
 1450.9 
 0.528 
 59.1 
 
 1923.6 
 0.586 
 66.7 
 
 2163.1 
 
 0.601 
 74.6 
 
 2176 
 0.583 
 81.2 
 
 2064.9 
 0.562 
 83.0 
 
 1961.2 
 0.578 
 82.2 
 
 1605.9 
 0.543 
 78.4 
 
 1352.4 
 0.565 
 68 
 
 1073.8 
 0.545 
 57.3 
 
 781.5 
 0.487 
 49,4 
 
 518.8 
 
 0.446 
 29.5 
 
 884.9 
 0.533 
 36.5 
 
 1280.4 
 0.548 
 45.0 
 
 1814.4 
 0.594 
 53.5 
 
 2189.3 
 
 0.619 
 62.1 
 
 2376.7 
 0.631 
 69.3 
 
 2500.3 
 0.684 
 79.6 
 
 2149.4 
 0.660 
 77.2 
 
 1717.7 
 0.656 
 66.7 
 
 1128.4 
 0.588 
 56.3 
 
 678.6 
 
 0.494 
 42.3 
 
 456.8 
 
 0.442 
 33.1 
 
 (590) 
 
 (0.464) 
 28.9 
 
 879 
 
 0.496 
 
 30.3 
 
 1255.7 
 
 0.520 
 39.5 
 
 1481.5 
 0.477 
 49.7 
 
 1866 
 0.525 
 59.2 
 
 2041.7 
 0.542 
 70.8 
 
 1990.8 
 0.542 
 75.6 
 
 1836.9 
 0.559 
 74.3 
 
 1469.4 
 0.547 
 67.2 
 
 1015.5 
 0.506 
 57.6 
 
 (639) 
 
 (0.433) 
 43.0 
 
 (531) 
 
 (0.467 
 
 30.6 
 
 526.2 
 
 0.380 
 31.3 
 
 797.4 
 0.424 
 33.9 
 
 1184.1 
 
 0.472 
 43.0 
 
 1481.2 
 0.47 
 54.1 
 
 1828 
 0.511 
 
 64.9 
 
 2042 
 0.543 
 74.8 
 
 2039.5 
 0.554 
 79.6 
 
 1832.1 
 
 0.552 
 77.4 
 
 1513.3 
 
 0.549 
 70.6 
 
 1094.4 
 0.520 
 59.3 
 
 662.4 
 0.413 
 44.2 
 
 491.1 
 0.391 
 33.4 
 
 953.1 
 0.639 
 33.8 
 
 1186.3 
 0.598 
 38.7 
 
 1565.7 
 0.606 
 46.5 
 
 1975.6 
 
 0.618 
 57.7 
 
 2126.5 
 
 0.594 
 66.7 
 
 2459.8 
 0.655 
 77.2 
 
 2400.7 
 0.652 
 83.8 
 
 2210.7 
 0.663 
 82.4 
 
 1841.7 
 0.654 
 73.7 
 
 1421 
 0.650 
 61.7 
 
 1065.3 
 0.625 
 46.5 
 
 873.8 
 0.652 
 36.8 
 
 36.5 
 
 38.8 
 
 47.4 
 
 1834.7 
 
 0.575 
 57.8 
 
 2171.2 
 0.606 
 67.5 
 
 76.2 
 
 2246.5 
 0.610 
 79.8 
 
 2064.9 
 0.619 
 78.2 
 
 1775.6 
 0.631 
 72.8 
 
 1315.8 
 0.604 
 61.2 
 
 47.6 
 
 681.5 
 0.513 
 38.5 
 
 899.2 
 0.473 
 55.3 
 
 1145.7 
 0.492 
 58.7 
 
 1487.4 
 0.521 
 63.5 
 
 1801.8 
 0.542 
 70.9 
 
 2080.4 
 0.578 
 77.4 
 
 2213.3 
 0.597 
 83.4 
 
 1968.6 
 0.538 
 84.8 
 
 1910.3 
 0.558 
 85.0 
 
 1678.2 
 0.553 
 81.5 
 
 1505.5 
 0.597 
 73.8 
 
 1122.1 
 
 0.524 
 62.6 
 
 875.6 
 
 0.494 
 56.9 
 
 497 
 
 0.504 
 
 11.5 
 
 861.6 
 0.579 
 12.8 
 
 1360.1 
 0.619 
 24.4 
 
 1495.9 
 0.507 
 37.3 
 
 1779.7 
 0.509 
 51.8 
 
 1779.7 
 0.473 
 61.6 
 
 1898.1 
 0.522 
 67.2 
 
 1675.6 
 0.527 
 65.0 
 
 1254.6 
 0.506 
 56.2 
 
 793 
 0.455 
 
 44.7 
 
 415.5 
 0.352 
 31.3 
 
 398.9 
 0.470 
 16.8 
 
 565.7 
 
 0.482 
 23.7 
 
 874.5 
 
 0.524 
 24.5 
 
 1329.5 
 0.569 
 34.4 
 
 1528.4 
 0.500 
 44.8 
 
 1923.2 
 0.544 
 55.4 
 
 2017.3 
 0.536 
 65.1 
 
 2095.6 
 0.572 
 
 71.1 
 
 1799.2 
 0.554 
 69.7 
 
 1428.8 
 0.546 
 61.9 
 
 1035 
 0.539 
 51.8 
 
 591.5 
 0.431 
 40.3 
 
 507.7 
 0.491 
 28.0 
 
 488.2 
 
 0.601 
 3.2 
 
 835.4 
 0.636 
 7.1 
 
 1354.2 
 0.661 
 21.3 
 
 1641.3 
 0.574 
 40.9 
 
 1904.4 
 0.550 
 55.9 
 
 1962 
 0.524 
 65.3 
 
 2123.6 
 0.587 
 71.9 
 
 1761.2 
 0.567 
 69.4 
 
 1190.4 
 0.504 
 58.6 
 
 767.5 
 0.482 
 45.6 
 
 444.6 
 0.436 
 25.2 
 
 345.4 
 0.503 
 10.1 
 
 555.3 
 0.445 
 28.3 
 
 797 
 
 0.458 
 
 28.3 
 
 1143.9 
 0.477 
 36.9 
 
 1438 
 0.464 
 46.9 
 
 1776.4 
 0.501 
 58.5 
 
 1943.9 
 0.516 
 67.2 
 
 1881.5 
 0.513 
 72.3 
 
 1622.1 
 0.495 
 70.6 
 
 1314 
 0.492 
 64.2 
 
 941 
 0.472 
 
 54.1 
 
 592.2 
 0.406 
 43.3 
 
 482.3 
 0.436 
 31.5 
 
 505.5 
 0.410 
 31.4 
 
 738 
 
 0.426 
 
 31.4 
 
 1067.1 
 0.445 
 39.9 
 
 1355 
 0.438 
 49.5 
 
 1769 
 0.499 
 60.4 
 
 1864 
 0.495 
 69.8 
 
 1860.5 
 0.507 
 74.5 
 
 - 1570.1 
 0.480 
 73.8 
 
 1267.5 
 0.477 
 66.8 
 
 896.7 
 0.453 
 57.4 
 
 535.8 
 0.372 
 46.6 
 
 442.8 
 0.400 
 34.9 
 
MASSACHUSETTS (Contd. ) 
 
 East Wareham Tu 
 
 Lat. 4T46'N K t 
 
 El. 18 ft t a 
 
 MICHIGAN 
 
 East Lansing Tu 
 
 Lat. 42°44'N K t 
 
 El. 856 ft t a 
 
 Sault Ste. Marie In 
 
 Lat. 46°28'N K t 
 
 El. 724 ft t a 
 
 MINNESOTA 
 
 St. Cloud Tj 
 
 Lat. 45°35'N K t 
 
 El. 1034 ft t a 
 
 MISSOURI 
 
 Columbia Jh 
 
 Lat. 38°58'N K t 
 
 El. 785 ft t a 
 
 MONTANA 
 
 Glasgow I 
 
 Lat. 48°13'N K 
 
 El. 2277 ft t 
 
 Great Falls Tu 
 
 Lat. 47°29'N K t 
 
 El. 3664 ft t a 
 
 NEBRASKA 
 
 Lincoln Jjj 
 
 Lat. 40°51'N K t 
 
 El. 1189 ft t a 
 
 NEVADA 
 
 Ely h 
 
 Lat. 39°17'N Kt 
 
 El. 6262 ft t, 
 
 Las Vegas Tj 
 
 Lat. 36°05'N K t 
 
 El. 2162 ft ta 
 
 NEW JERSEY 
 
 Seabrook Tu 
 
 Lat. 39°30'N Kt 
 
 El. 100 ft t a 
 
 NEW MEXICO 
 
 Albuquerque Jn 
 
 Lat. 35°03'N K t 
 
 El. 5314 ft t a 
 
 NEW YORK 
 
 Ithaca Tu 
 
 Lat. 42°27'N K t 
 
 El. 950 ft t a 
 
 iW 
 
 New York I 
 
 Lat. 40°46'N KV 
 
 El. 52 ft t a 
 
 Sayvllle Tu 
 
 Lat. 40°30'N K? 
 
 El. 20 ft t a 
 
 Schenectady Tu 
 
 Lat. 42°50'N K t 
 
 El. 217 ft t a 
 
 Upton Tu 
 
 Lat. 40°52'N K t 
 
 El. 75 ft t a 
 
 NORTH CAROLINA 
 
 Greensboro Tu 
 
 Lat. 36°05'N Kt 
 
 El. 891 ft t a 
 
 A3-5 
 
 Table A3-2 (continued) 
 
 Jan Feb Mar Apr May Jun Jul Aug Sep Oct 
 
 504.4 
 0.398 
 32.2 
 
 762.4 
 0.431 
 31.6 
 
 1132.1 
 0.469 
 39.0 
 
 1392.6 
 0.449 
 48.3 
 
 1704.8 
 0.480 
 58.9 
 
 1958.3 
 0.520 
 67.5 
 
 1873.8 
 0.511 
 74.1 
 
 1607.4 
 0.489 
 72.8 
 
 1363.8 
 0.508 
 65.9 
 
 996.7 
 0.496 
 56 
 
 636.2 
 0.431 
 46 
 
 521 
 
 0.461 
 
 34.8 
 
 425.8 
 
 0.35 
 
 26.0 
 
 739.1 
 0.431 
 26.4 
 
 1086 
 0.456 
 35.7 
 
 1249.8 
 0.406 
 48.4 
 
 1732.8 
 0.489 
 59.8 
 
 1914 
 0.508 
 70.3 
 
 1884.5 
 0.514 
 74.5 
 
 1627.7 
 0.498 
 72.4 
 
 1303.3 
 0.493 
 65.0 
 
 891.5 
 0.456 
 53.5 
 
 473.1 
 0.333 
 40.0 
 
 379.7 
 0.349 
 29.0 
 
 488.6 
 0.490 
 16.3 
 
 843.9 
 0.560 
 16.2 
 
 1336.5 
 0.606 
 25.6 
 
 1559.4 
 0.526 
 39.5 
 
 1962.3 
 0.560 
 52.1 
 
 2064.2 
 0.549 
 61.6 
 
 2149.4 
 0.590 
 67.3 
 
 1767.9 
 0.554 
 66.0 
 
 1207 
 
 0.481 
 57.9 
 
 809.2 
 0.457 
 46.8 
 
 392.2 
 0.323 
 33.4 
 
 359.8 
 0.408 
 21.9 
 
 632.8 
 0.595 
 13.6 
 
 976.7 
 0.629 
 16.9 
 
 1383 
 0.614 
 29.8 
 
 1598.1 
 0.534 
 46.2 
 
 1859.4 
 0.530 
 58.8 
 
 2003.3 
 0.533 
 68.5 
 
 2087.8 
 0.573 
 74.4 
 
 1828.4 
 0.570 
 71.9 
 
 1369.4 
 0.539 
 62.5 
 
 890.4 
 0.490 
 50.2 
 
 545.4 
 0.435 
 32.1 
 
 463.1 
 0.504 
 18.3 
 
 651.3 
 0.458 
 32.5 
 
 941.3 
 0.492 
 36.5 
 
 1315.8 
 0.520 
 45.9 
 
 1631.3 
 0.514 
 57.7 
 
 1999.6 
 0.559 
 66.7 
 
 2129.1 
 0.566 
 75.9 
 
 2148.7 
 0.585 
 81.1 
 
 1953.1 
 0.588 
 79.4 
 
 1689.6 
 0.606 
 71.9 
 
 1202.6 
 0.562 
 61.4 
 
 839.5 
 0.510 
 46.1 
 
 590.4 
 0.457 
 35.8 
 
 572.7 
 0.621 
 13.3 
 
 965.7 
 0.678 
 17.3 
 
 1437.6 
 0.672 
 31.1 
 
 1741.3 
 0.597 
 47.8 
 
 2127.3 
 0.611 
 59.3 
 
 2261.6 
 0.602 
 67.3 
 
 2414.7 
 0.666 
 76 
 
 1984.5 
 0.630 
 73.2 
 
 1531 
 0.629 
 61.2 
 
 997 
 
 0.593 
 
 49.2 
 
 574.9 
 0.516 
 31.0 
 
 428.4 
 0.548 
 18.6 
 
 524 
 
 0.552 
 
 25.4 
 
 869.4 
 0.596 
 27.6 
 
 1369.7 
 0.631 
 35.6 
 
 1621.4 
 0.551 
 47.7 
 
 1970.8 
 0.565 
 57.5 
 
 2179.3 
 0.580 
 64.3 
 
 2383 
 0.656 
 73.8 
 
 1986.3 
 0.627 
 71.3 
 
 1536.5 
 0.626 
 60.6 
 
 984.9 
 0.574 
 51.4 
 
 575.3 
 0.503 
 38.0 
 
 420.7 
 0.518 
 29.1 
 
 712.5 
 0.542 
 27.8 
 
 955.7 
 0.528 
 32.1 
 
 1299.6 
 0.532 
 42.4 
 
 1587.8 
 0.507 
 55.8 
 
 1856.1 
 0.522 
 65.8 
 
 2040.6 
 0.542 
 76.0 
 
 2011.4 
 0.547 
 82.6 
 
 1902.6 
 0.577 
 80.2 
 
 1543.5 
 0.568 
 71.5 
 
 1215.8 
 0.596 
 59.9 
 
 773.4 
 0.508 
 43.2 
 
 643.2 
 0.545 
 31.8 
 
 871.6 
 0.618 
 27.3 
 
 1255 
 0.660 
 32.1 
 
 1749.8 
 0.692 
 39.5 
 
 2103.3 
 0.664 
 48.3 
 
 2322.1 
 0.649 
 57.0 
 
 2649 
 0.704 
 65.4 
 
 2417 
 0.656 
 74.5 
 
 2307.7 
 0.695 
 72.3 
 
 1935 
 0.696 
 63.7 
 
 1473 
 0.691 
 52.1 
 
 1078.6 
 0.658 
 39.9 
 
 814.8 
 
 0.64 
 
 31.1 
 
 1035.8 
 0.654 
 47.5 
 
 1438 
 0.697 
 53.9 
 
 1926.5 
 0.728 
 60.3 
 
 2322.8 
 0.719 
 69.5 
 
 2629.2 
 0.732 
 78.3 
 
 2799.2 
 0.746 
 88.2 
 
 2524 
 0.685 
 95.0 
 
 2342 
 0.697 
 92.9 
 
 2062 
 0.716 
 85.4 
 
 1602.6 
 0.704 
 71.7 
 
 1190 
 0.657 
 57.8 
 
 964.2 
 0.668 
 50.2 
 
 591.9 
 0.426 
 39.5 
 
 854.2 
 0.453 
 37.6 
 
 1195.6 
 0.476 
 43.9 
 
 1518.8 
 0.481 
 54.7 
 
 1800.7 
 0.504 
 6a. 9 
 
 1964.6 
 0.522 
 74.1 
 
 1949.8 
 0.530 
 79.8 
 
 1715 
 0.517 
 77.7 
 
 1445.7 
 0.524 
 69.7 
 
 1071.9 
 0.508 
 61.2 
 
 721.8 
 0.449 
 48.5 
 
 522.5 
 0.416 
 39.3 
 
 1150.9 
 0.704 
 37.3 
 
 1453.9 
 0.691 
 43.3 
 
 1925.4 
 0.719 
 50.1 
 
 2343.5 
 0.722 
 59.6 
 
 2560.9 
 0.713 
 69.4 
 
 2757.5 
 0.737 
 79.1 
 
 2561.2 
 0.695 
 82.8 
 
 2387.8 
 0.708 
 80.6 
 
 2120.3 
 0.728 
 73.6 
 
 1639.8 
 0.711 
 62.1 
 
 1274.2 
 0.684 
 47.8 
 
 1051.6 
 0.704 
 39.4 
 
 434.3 
 0.351 
 27.2 
 
 755 
 
 0.435 
 
 26.5 
 
 1074.9 
 0.45 
 36 
 
 1322.9 
 0.428 
 48.4 
 
 1779.3 
 0.502 
 59.6 
 
 2025.8 
 0.538 
 68.9 
 
 2031.3 
 0.554 
 73.9 
 
 1736.9 
 0.530 
 71.9 
 
 1320.3 
 0.497 
 64.2 
 
 918.4 
 0.465 
 53.6 
 
 466.4 
 0.324 
 41.5 
 
 370.8 
 0.337 
 29.6 
 
 539.5 
 0.406 
 35.0 
 
 790.8 
 0.435 
 34.9 
 
 1180.4 
 0.480 
 43.1 
 
 1426.2 
 0.455 
 52.3 
 
 1738.4 
 0.488 
 63.3 
 
 1994.1 
 0.53 
 72.2 
 
 1938.7 
 0.528 
 76.9 
 
 1605.9 
 0.486 
 75.3 
 
 1349.4 
 0.500 
 69.5 
 
 977.8 
 0.475 
 59.3 
 
 598.1 
 0.397 
 48.3 
 
 476 
 
 0.403 
 
 37.7 
 
 602.9 
 0.453 
 35 
 
 936.2 
 0.511 
 34.9 
 
 1259.4 
 0.510 
 43.1 
 
 1560.5 
 0.498 
 52.3 
 
 1857.2 
 0.522 
 63.3 
 
 2123.2 
 0.564 
 72.2 
 
 2040.9 
 0.555 
 76.9 
 
 1734.7 
 0.525 
 75.3 
 
 1446.8 
 0.530 
 69.5 
 
 1087.4 
 0.527 
 59.3 
 
 697.8 
 0.450 
 48.3 
 
 533.9 
 0.447 
 37.7 
 
 488.2 
 0.406 
 24.7 
 
 753.5 
 0.441 
 24.6 
 
 1026.6 
 0.433 
 34.9 
 
 1272.3 
 
 0.413 
 48.3 
 
 1553.1 
 0.438 
 61.7 
 
 1687.8 
 0.448 
 70.8 
 
 1662.3 
 0.454 
 76.9 
 
 1494.8 
 0.458 
 73.7 
 
 1124.7 
 0.426 
 64.6 
 
 820.6 
 0.420 
 53.1 
 
 436.2 
 0.309 
 40.1 
 
 356.8 
 0.331 
 28.0 
 
 583 
 
 0.444 
 
 35.0 
 
 872.7 
 0.483 
 34.9 
 
 1280.4 
 0.522 
 43.1 
 
 1609.9 
 0.514 
 52.3 
 
 1891.5 
 0.532 
 63.3 
 
 2159 
 0.574 
 72.2 
 
 2044.6 
 0.557 
 76.9 
 
 1789.6 
 0.542 
 75.3 
 
 1472.7 
 0.542 
 69.5 
 
 •1102.6 
 0.538 
 59.3 
 
 686.7 
 0.448 
 48.3 
 
 551.3 
 0.467 
 37.7 
 
 743.9 
 0.469 
 42.0 
 
 1031.7 
 0.499 
 44.2 
 
 1323.2 
 0.499 
 51.7 
 
 1755.3 
 0.543 
 60.8 
 
 1988.5 
 0.554 
 69.9 
 
 2111.4 
 0.563 
 78.0 
 
 2033.9 
 0.552 
 80.2 
 
 1810.3 
 0.538 
 78.9 
 
 1517.3 
 0.527 
 73.9 
 
 1202.6 
 0.531 
 62,7 
 
 908.1 
 0.501 
 51.5 
 
 690.8 
 0.479 
 43.2 
 
NORTH CAROLINA (Contd.) 
 
 Hatteras Tu, 
 
 Lat. 35°13'N K t 
 
 El. 7 ft ta 
 
 NORTH DAKOTA 
 
 Bismarck Tu 
 
 Lat. 46°47'N K t 
 
 El. 1660 ft t a 
 
 OHIO 
 
 Cleveland T^ 
 
 Lat. 41°24'N ft 
 
 El. 805 ft t a 
 
 Columbus Tu 
 
 Lat. 40°00'N K t 
 
 El. 833 ft t a 
 
 OKLAHOMA 
 
 Oklahoma City Tu 
 
 Lat. 35°24'N ft 
 
 El. 1304 ft U 
 
 Stillwater Iu, 
 
 Lat. 36°09'N K t 
 
 El. 910 ft t. 
 
 ONTARIO 
 
 Ottawa 
 
 Lat. 45°20'N K 
 
 Ah 
 
 El. 339 ft tj 
 
 Toronto Tu 
 
 Lat. 43°41'N K t 
 
 El. 379 ft tg 
 
 OREGON 
 
 Astoria Tu 
 
 Lat. 46°12'N K t 
 
 El- 8ft ^ 
 
 Medford lu 
 
 Lat. 42°23'N K t 
 
 El. 1329 ft tg 
 
 PENNSYLVANIA 
 
 State College T^ 
 
 Lat. 40°48'N K t 
 
 El. 1175 ft tj 
 
 RHODE ISLAND 
 
 Newport J_h 
 
 Lat. 41°29'N ft 
 
 El. 60 ft t a 
 
 SOUTH CAROLINA 
 
 Charleston Iu 
 
 Lat. 32°54'N K t 
 
 El. 46 ft t^ 
 
 SOUTH DAKOTA 
 
 Rapid City Tu 
 
 Lat. 44°09'N K t 
 
 El. 3218 ft ta 
 
 TEXAS 
 
 Brownsville Tu 
 
 Lat. 25°55'N ft 
 
 El. 20 ft t a 
 
 El Paso Tu 
 
 Lat. 31°48'N ft 
 
 El. 3916 ft t a 
 
 Fort Worth Tu 
 
 Lat. 32°50'N ft 
 
 El. 544 ft t. 
 
 A3-6 
 
 Table A3-2 (continued) 
 
 Apr May Jun Jul Aug Sep Oct Nov Dec 
 
 891.9 
 0.546 
 49.9 
 
 1184.1 
 0.563 
 49.5 
 
 1590.4 
 0.593 
 54.7 
 
 2128 
 0.655 
 61.5 
 
 2376.4 
 0.661 
 69.9 
 
 2438 
 0.652 
 77.2 
 
 2334.3 
 0.634 
 80.0 
 
 2085.6 
 0.619 
 79.8 
 
 1758.3 
 0.605 
 76.7 
 
 1337.6 
 0.58 
 67.9 
 
 1053.5 
 0.566 
 59.1 
 
 798.1 
 0.535 
 51.3 
 
 587.4 
 0.594 
 12.4 
 
 934.3 
 0.628 
 15.9 
 
 1328.4 
 0.605 
 29.7 
 
 1668.2 
 0.565 
 46.6 
 
 2056.1 
 0.588 
 48.6 
 
 2173.8 
 0.579 
 67.9 
 
 2305.5 
 0.634 
 76.1 
 
 1929.1 
 0.606 
 73.5 
 
 1441.3 
 0.581 
 61.6 
 
 1018.1 
 0.584 
 49.6 
 
 600.4 
 0.510 
 31.4 
 
 464.2 
 0.547 
 18.4 
 
 466.8 
 0.361 
 30.8 
 
 681.9 
 0.383 
 30.9 
 
 1207 
 
 0.497 
 39.4 
 
 1443.9 
 0.464 
 50.2 
 
 1928.4 
 0.543 
 62.4 
 
 2102.6 
 0.559 
 72.7 
 
 2094.4 
 0.571 
 77.0 
 
 1840.6 
 0.559 
 75.1 
 
 1410.3 
 0.524 
 68.5 
 
 997 
 
 0.491 
 
 57.4 
 
 526.6 
 0.351 
 44.0 
 
 427.3 
 0.371 
 32.8 
 
 486.3 
 0.356 
 32.1 
 
 746.5 
 0.401 
 33.7 
 
 1112.5 
 0.447 
 42.7 
 
 1480.8 
 0.470 
 53.5 
 
 1839.1 
 0.515 
 64.4 
 
 (2111) 
 (0.561) 
 74.2 
 
 2041.3 
 0.555 
 78 
 
 1572.7 
 0.475 
 75.9 
 
 1189.3 
 0.433 
 70.1 
 
 919.5 
 0.441 
 58 
 
 479 
 
 0.302 
 
 44.5 
 
 430.2 
 0.351 
 34.0 
 
 938 
 
 0.580 
 40.1 
 
 1192.6 
 0.571 
 45.0 
 
 1534.3 
 0.576 
 53.2 
 
 1849.4 
 0.570 
 63.6 
 
 2005.1 
 0.558 
 71.2 
 
 2355 
 0.629 
 80.6 
 
 2273.8 
 0.618 
 85.5 
 
 2211 
 0.565 
 85.4 
 
 1019.2 
 0.628 
 77.4 
 
 1409.6 
 0.614 
 66.5 
 
 1085.6 
 0.588 
 52.2 
 
 897.4 
 0.608 
 43.1 
 
 763.8 
 0.484 
 41.2 
 
 1081.5 
 0.527 
 45.6 
 
 1463.8 
 0.555 
 53.8 
 
 1702.6 
 0.528 
 64.2 
 
 1879.3 
 C.523 
 71.6 
 
 2235.8 
 0.596 
 81.1 
 
 2224.3 
 0.604 
 85.9 
 
 2039.1 
 0.607 
 85.9 
 
 1724.3 
 0.599 
 77.5 
 
 1314 
 0.581 
 67.6 
 
 991.5 
 0.548 
 52.6 
 
 783 
 
 0.544 
 
 43.9 
 
 539.1 
 0.499 
 
 14.6 
 
 852.4 
 0.540 
 15.6 
 
 1250.5 
 0.554 
 27.7 
 
 1506.6 
 0.502 
 43.3 
 
 1857.2 
 0.529 
 57.5 
 
 2084.5 
 0.554 
 67.5 
 
 2045.4 
 0.560 
 71.9 
 
 1752.4 
 0.546 
 69.8 
 
 1326.6 
 0.521 
 61.5 
 
 826.9 
 0.450 
 48.9 
 
 458.7 
 0.359 
 35 
 
 408.5 
 0.436 
 19.6 
 
 451.3 
 0.388 
 26.5 
 
 674.5 
 0.406 
 26.0 
 
 1088.9 
 0.467 
 34.2 
 
 1388.2 
 0.455 
 46.3 
 
 1785.2 
 0.506 
 58 
 
 1941.7 
 0.516 
 68.4 
 
 1968.6 
 0.539 
 73.8 
 
 1622.5 
 0.500 
 71.8 
 
 1284.1 
 0.493 
 64.3 
 
 835 
 
 0.438 
 
 52.6 
 
 458.3 
 0,336 
 40.9 
 
 352.8 
 0.346 
 30.2 
 
 338.4 
 0.330 
 41.3 
 
 607 
 
 0.397 
 
 44.7 
 
 1008.5 
 0.454 
 46.9 
 
 1401.5 
 0.471 
 51.3 
 
 1838.7 
 0.524 
 55.0 
 
 1753.5 
 0.466 
 59.3 
 
 2007.7 
 0.551 
 62.6 
 
 1721 
 0.538 
 63.6 
 
 1322.5 
 0.526 
 62.2 
 
 780.4 
 0.435 
 55.7 
 
 413.6 
 0.336 
 48.5 
 
 295.2 
 0.332 
 43.9 
 
 435.4 
 0.353 
 39.4 
 
 804.4 
 0.464 
 45.4 
 
 1259.8 
 0.527 
 50.8 
 
 1807.4 
 0.584 
 56.3 
 
 2216.2 
 0.625 
 63.1 
 
 2440.5 
 0.648 
 69.4 
 
 2607.4 
 0.710 
 76.9 
 
 2261.6 
 0.689 
 76.4 
 
 1672.3 
 0.628 
 69.6 
 
 1043.5 
 0.526 
 58.7 
 
 558.7 
 0.384 
 47.1 
 
 346.5 
 0.313 
 40.5 
 
 501.8 
 0.381 
 31.3 
 
 749.1 
 0.413 
 31.4 
 
 1106.6 
 0.451 
 39.8 
 
 1399.2 
 0.448 
 51.3 
 
 1754.6 
 0.493 
 63.4 
 
 2027.6 
 0.539 
 71.8 
 
 1968.2 
 0.536 
 75.8 
 
 1690 
 0.512 
 73.4 
 
 1336.1 
 0.492 
 66.1 
 
 1017 
 0.496 
 55.6 
 
 580.1 
 0.379 
 43.2 
 
 4443.9 
 0.376 
 32.6 
 
 565.7 
 0.438 
 29.5 
 
 856.4 
 0.482 
 32.0 
 
 1231.7 
 0.507 
 39.6 
 
 1484.8 
 0.477 
 48.2 
 
 1849 
 0.520 
 58.6 
 
 2019.2 
 0.536 
 67.0 
 
 1942.8 
 0.529 
 73.2 
 
 1687.1 
 0.513 
 72.3 
 
 1411.4 
 0.524 
 66.7 
 
 1035.4 
 0.512 
 56.2 
 
 656.1 
 0.44 
 46.5 
 
 527.7 
 0.460 
 34.4 
 
 946.1 
 0.541 
 53.6 
 
 1152.8 
 0.521 
 55.2 
 
 1352.4 
 0.491 
 60.6 
 
 1918.8 
 0.584 
 67.8 
 
 2063.4 
 0.574 
 74.8 
 
 2113.3 
 0.567 
 80.9 
 
 1649.4 
 0.454 
 82.9 
 
 1933.6 
 0.569 
 82.3 
 
 1557.2 
 0.525 
 79.1 
 
 1332.1 
 0.554 
 69.8 
 
 1073.8 
 0.539 
 59.8 
 
 952 
 
 0.586 
 
 54.0 
 
 687.8 
 0.601 
 24.7 
 
 1032.5 
 0.627 
 27.4 
 
 1503.7 
 0.649 
 34.7 
 
 1807 
 0.594 
 48.2 
 
 2028 
 0.574 
 58.3 
 
 2193.7 
 0.583 
 67.3 
 
 2235.8 
 0.612 
 76.3 
 
 2019.9 
 0.622 
 75.0 
 
 1628 
 0.628 
 64.7 
 
 1179.3 
 0.624 
 52.9 
 
 763.1 
 0.566 
 38.7 
 
 590.4 
 0.588 
 29.2 
 
 1105.9 
 0.517 
 63.3 
 
 1262.7 
 0.500 
 66.7 
 
 1505.9 
 0.505 
 70.7 
 
 1714 
 0.509 
 76.2 
 
 2092.2 
 0.584 
 81.4 
 
 2288.5 
 0.627 
 85.1 
 
 2345 
 0.650 
 86.5 
 
 2124 
 0.617 
 86.9 
 
 1774.9 
 0.566 
 84.1 
 
 1536.5 
 0.570 
 78.9 
 
 1104.8 
 0.468 
 70.7 
 
 982.3 
 0.488 
 65.2 
 
 1247.6 
 0.686 
 47.1 
 
 1612.9 
 0.714 
 53.1 
 
 2048.7 
 0.730 
 58.7 
 
 2447.2 
 0.741 
 67.3 
 
 2673 
 0.743 
 75.7 
 
 2731 
 0.733 
 84.2 
 
 2391.1 
 0.652 
 84.9 
 
 2350.5 
 0.669 
 83.4 
 
 2077.5 
 0.693 
 78.5 
 
 1704.8 
 0.695 
 69.0 
 
 1324.7 
 0.647 
 56.0 
 
 1051.6 
 0.626 
 48.5 
 
 936.2 
 0.530 
 48.1 
 
 1198.5 
 0.541 
 52.3 
 
 1597.8 
 0.577 
 59.8 
 
 1829.1 
 0.556 
 68.8 
 
 2105.1 
 0.585 
 75.9 
 
 2437.6 
 0.654 
 84.0 
 
 2293.3 
 0.624 
 87.7 
 
 2216.6 
 0.653 
 88.6 
 
 1880.8 
 0.634 
 81.3 
 
 1476 
 0.612 
 71.5 
 
 1147.6 
 0.576 
 58.8 
 
 913.6 
 0.563 
 50.8 
 
TEXAS (Contd.) 
 
 Midland T^ 
 
 Lat. 31°56'N K* 
 
 El. 2854 ft t a 
 
 San Antonio Tu 
 
 Lat. 29°32'N K t 
 
 El 794 ft t, 
 
 TENNESSEE 
 
 Nashville Tu 
 
 Lat. 36°07'N K t 
 
 El. 605 ft tg 
 
 Oak Ridge Tjh 
 
 Lat. 36-01'N Kt 
 
 El. 905 ft t, 
 
 UTAH 
 
 Salt Lake City In 
 
 Lat. 40°46'N K 
 
 El. 4227 ft t 
 
 t 
 ■•a 
 
 WASHINGTON 
 
 Seattle-Tacoma Tu 
 
 Lat. 47°27'N K t 
 
 El. 386 ft t a 
 
 Seattle Tu 
 
 Lat. 47°36'N K t 
 
 El. 14 ft t a 
 
 Spokane Tu 
 
 Lat. 47°40'N K 
 
 El. 1968 ft t 
 
 WISCONSIN 
 
 A3-7 
 
 Table A3-2 (continued) 
 
 Feb Mar Apr May Oun Jul Aug Sep Oct Nov Dec 
 
 1066.4 
 0.587 
 47.9 
 
 1345.7 
 0.596 
 52.8 
 
 1784.8 
 0.638 
 60.0 
 
 2036.1 
 0.617 
 68.8 
 
 2301.1 
 0.639 
 77.2 
 
 2317.7 
 0.622 
 83.9 
 
 2301.8 
 0.628 
 85.7 
 
 2193 
 0.643 
 85.0 
 
 1921.8 
 0.642 
 73. 9 
 
 1470.8 
 0.600 
 70.3 
 
 1244.3 
 0.609 
 56.6 
 
 1023.2 
 0.611 
 49.1 
 
 1045 
 0.541 
 53.7 
 
 1299.2 
 0.550 
 58.4 
 
 1560.1 
 0.542 
 65.0 
 
 1664.6 
 0.500 
 72.2 
 
 2024.7 
 0.563 
 79.2 
 
 2250* 
 0.62 
 
 85.0 
 
 2364.2 
 0.647 
 87.4 
 
 2185.2 
 0.637 
 87.8 
 
 1844.6 
 0.603 
 82.6 
 
 1487.4 
 0.584 
 74.7 
 
 1104.4 
 0.507 
 63.3 
 
 954.6 
 0.528 
 56.5 
 
 589.7 
 0.373 
 42.6 
 
 907 
 
 0.440 
 
 45.1 
 
 1246.8 
 0.472 
 52.9 
 
 1662.3 
 0.514 
 63.0 
 
 1997 
 0.556 
 71.4 
 
 2149.4 
 0.573 
 80.1 
 
 2079.7 
 0.565 
 83.2 
 
 1862.7 
 0.554 
 81.9 
 
 1600.7 
 0.556 
 76.6 
 
 1223.6 
 0.540 
 65.4 
 
 823.2 
 0.454 
 52.3 
 
 614.4 
 0.426 
 44.3 
 
 604 
 
 0.382 
 
 41.9 
 
 895.9 
 0.435 
 44.2 
 
 1241.7 
 0.471 
 51.7 
 
 1689.6 
 0.524 
 61.4 
 
 1942.8 
 0.541 
 69.8 
 
 2066.4 
 0.551 
 77.8 
 
 1972.3 
 0.536 
 80.2 
 
 1795.6 
 0.534 
 78.8 
 
 1559.8 
 0.542 
 74.5 
 
 1194.8 
 0.527 
 62.7 
 
 796.3 
 
 0.438 
 50.4 
 
 610 
 
 0.422 
 
 42.5 
 
 622.1 
 
 0.468 
 29.4 
 
 986 
 
 0.909 
 
 36.2 
 
 1301.1 
 0.529 
 44.4 
 
 1813.3 
 0.579 
 53.9 
 
 63.1 
 
 71.7 
 
 81.3 
 
 79.0 
 
 1689.3 
 0.621 
 68.7 
 
 1250.2 
 0.610 
 57.0 
 
 42.5 
 
 552.8 
 
 0.467 
 34.0 
 
 282.6 
 0.296 
 42.1 
 
 520.6 
 
 0.355 
 45.0 
 
 992.2 
 0.456 
 48.9 
 
 1507 
 0.510 
 54.1 
 
 1881.5 
 0.538 
 59.8 
 
 1909.9 
 0.508 
 64.4 
 
 2110.7 
 0.581 
 68.4 
 
 1688.5 
 0.533 
 67.9 
 
 1211.8 
 0.492 
 63.3 
 
 702.2 
 
 0.407 
 56.3 
 
 386.3 
 0.336 
 48.4 
 
 239.5 
 0.292 
 
 44.4 
 
 252 
 
 0.266 
 
 38.9 
 
 471.6 
 0.324 
 42.9 
 
 917.3 
 0.423 
 46.9 
 
 1375.6 
 0.468 
 51.9 
 
 1664.9 
 0.477 
 58.1 
 
 1724 
 0.459 
 62.8 
 
 1805.1 
 0.498 
 67.2 
 
 1617 
 0.511 
 66.7 
 
 1129.1 
 
 0.459 
 61.6 
 
 638 
 
 0.372 
 
 54.0 
 
 325.5 
 0.284 
 45.7 
 
 218.1 
 0.269 
 41.5 
 
 446.1 
 0.478 
 26.5 
 
 837.6 
 0.579 
 31.7 
 
 1200 
 
 0.556 
 40.5 
 
 1864.6 
 
 0.602 
 
 49.2 
 
 2104.4 
 0.603 
 57.9 
 
 2226.5 
 
 0.593 
 64.6 
 
 2479.7 
 0.684 
 73.4 
 
 2076 
 
 0.656 
 71.7 
 
 1511 
 0.616 
 62.7 
 
 844.6 
 0.494 
 51.5 
 
 486.3 
 0.428 
 37.4 
 
 279 
 
 0.345 
 30.5 
 
 564.6 
 
 0.40 
 
 21.8 
 
 812.2 
 
 0.478 
 24.6 
 
 1232.1 
 0.522 
 35.3 
 
 1455.3 
 0.474 
 49.0 
 
 1745.4 
 0.493 
 61.0 
 
 2031.7 
 0.540 
 70.9 
 
 2046.5 
 0.559 
 76.8 
 
 1740.2 
 0.534 
 74.4 
 
 1443.9 
 0.549 
 65.6 
 
 993 
 
 0.510 
 
 53.7 
 
 555.7 
 0.396 
 37.8 
 
 495.9 
 0.467 
 25.4 
 
 786.3 
 
 0.65 
 
 20.2 
 
 1146.1 
 0.672 
 26.3 
 
 1638 
 
 0.691 
 34.7 
 
 1988.5 
 0.647 
 45.5 
 
 2114 
 0.597 
 56.0 
 
 2492.2 
 0.662 
 65.4 
 
 2438.4 
 0.665 
 74.6 
 
 2120.6 
 0.649 
 72.5 
 
 1712.9 
 0.647 
 61.4 
 
 1301.8 
 0.666 
 48.3 
 
 837.3 
 0.589 
 33.4 
 
 694.8 
 0.643 
 23.8 
 
 Madison L. 
 
 Lat. 43°08'N K t 
 
 El. 866 ft t g 
 
 WYOMING 
 
 Lander T^ 
 
 Lat. 42°48'N K t 
 
 El. 5370 ft t. 
 
 *0r1g1nal values incorrect. Values estimated from insolation maps. 
 
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A3-15 
 
 MEAN DAILY SOLAR RADIATION ^Lai 
 JANUARY 
 
 Figure A3-1. Mean Daily Solar Radiation (Langleys), January 
 
 ;j ^^.v.^-..^MEAN DAILY SOLAR RADIATION 
 
 Figure A3-2. Mean Daily Solar Radiation (Langleys), February 
 
A3-16 
 
 Figure A3-3. Mean Daily Solar Radiation (Langleys), March 
 
 MEAN "DAILY SOLAR RADIATION (Lang leys)' 
 APRIL 
 
 Figure A3-4. Mean Daily Solar Radiation (Langleys), April 
 
A3-17 
 
 Figure A3-5. Mean Daily Solar Radiation (Langleys), May 
 
 Figure A3-6. Mean Daily Solar Radiation (Langleys), June 
 
A3-18 
 
 MEAN^DAILY SOLAR RADIATION (Langleys )\ 
 
 -■f-ra»r Ul 1 
 
 Figure A3-7. Mean Daily Solar Radiation (Langleys), July 
 
 7JMEAN DAILY SOLAR RADIATION (Langleys) 
 
 Figure A3-8. Mean Daily Solar Radiation (Langleys), August 
 
A3-19 
 
 SsA-~. ~TiEAN DAILY SOLAR RADIATION 
 
 Figure A3-9. Mean Daily Solar Radiation (Langleys), September 
 
 7(^ : -v.--. J ft % PrMEAN_DAILY SOLAR RADIATION 
 
 Figure A3-10. Mean Daily Solar Radiation (Langleys), October 
 
A3 -20 
 
 Figure A3-11. Mean Daily Solar Radiation (Langleys), November 
 
 -Je* 
 
 Figure A3-12. Mean Daily Solar Radiation (Langleys), December 
 
A3-21 
 
 JULY 
 
 K. 
 
 Figure A3-13. Tilt Correction Factor for 25° Latitude, 10° Tilt 
 
A3-22 
 
 1.4 
 
 1.3 
 
 LATITUDE = 30° 
 TILT= LATITUDE^ 
 
 TILT=!5 
 
 1.0 
 
 0.9 
 
 K, 
 
 Figure A3-14. Tilt Correction Factor for 30° Latitude, 15° Tilt 
 
A3-23 
 
 0.9 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3- 15. Tilt Correction Factor for 35° Latitude, 20° Tilt 
 
.8 
 
 1.7 
 
 1.6 
 
 1.5 
 
 .4 
 
 1.3 
 
 .2 
 
 .0 
 
 0.9 
 
 A3-24 
 
 LATITUDE=40 
 
 _TILT= LATITUDES 
 TILT=25°„ . L -^_b: 
 
 — MAY 
 
 JUL 
 
 J UN 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K< 
 
 Figure A3- 16. Tilt Correction Factor for 40° Latitude, 25° Tilt 
 
A3-25 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K< 
 
 Figure A3- 17. Tilt Correction Factor for 45° Latitude, 30° Tilt 
 
A3-26 
 
 03 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3- 18. Tilt Correction Factor for 50° Latitude, 35° Tilt 
 
A3-27 
 
 ^Zf-~Z 
 
 4.0 
 
 LAT1TUDEa55l< 
 
 T 1LT= L ATJJUDE--J5^ 
 TlLTr_4 d ^F^r 
 
 
 3.5 
 
 T^l 
 
 DEC 
 
 3.0 
 
 R 2.5 
 
 2.0 
 
 .5 
 
 1.0 
 
 AUG 
 tMAY_ 
 : JUL 
 
 J UN 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3- 19. Tilt Correction Factor for 55° Latitude, 40° Tilt 
 
A3-28 
 
 0.9 
 
 0.8 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-20. Tilt Correction Factor for 25° Latitude, 25° Tilt 
 
A3-29 
 
 
 LATITUDE =30° 
 
 TJ LT = LATI TUDE ^ ^ 
 
 TILT= 30° 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-21. Tilt Correction Factor for 30° Latitude, 30° Tilt 
 
A3-30 
 
 R 
 
 Figure A3-22. Tilt Correction Factor for 35° Latitude, 35° Tilt 
 
A3-31 
 
 3EE£EHEE&I DEC 
 
 0.7 
 
 K< 
 
 Figure A3-23. Tilt Correction Factor for 40° Latitude, 40° Tilt 
 
A3-32 
 
 2.8 
 2.6 
 2.4 
 2.2 
 
 ^LATITUDE =4S* ~-r 
 
 XILT= LATITUDE^ 
 TILT = 45^^ r ^ 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3-24. Tilt Correction Factor for 45° Latitude, 45° Tilt 
 
A3-33 
 
 3.6 
 
 3.4 
 
 3.2 
 
 3.0 
 
 2.8 
 
 2.6 
 
 2.4 
 
 R 2.2 
 
 2.0 
 
 1.8 
 
 1.6 
 
 1.2 
 
 1.0 
 
 0.8 
 
 0.6 
 0.4 
 
 - r •■"-[-• - 
 
 
 LATITUDE =50° 
 
 
 DEC 
 
 TILT= LATITUDE 
 TILT=50°__:__ 
 
 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-25. Tilt Correction Factor for 50° Latitude, 50° Tilt 
 
A3-34 
 
 
 5.0 
 
 LATITUDE* 55l°L 
 
 TILT* LATITUDE! 
 _TILT=-55° ^ 
 
 4.0 
 
 3.0 
 
 2.0 
 
 1.0 
 
 0.0 
 
 Figure A3-26. Tilt Correction Factor for 55° Latitude, 55° Tilt 
 
A3-35 
 
 0.9 
 
 0.8 
 
 0.7 
 
 JUN 
 
 0.3 
 
 Figure A3-27. 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Tilt Correction Factor for 25° Latitude, 40° Tilt 
 
A3-36 
 
 R 
 
 K, 
 
 Figure A3-28. Tilt Correction Factor for 30° Latitude, 45° Tilt 
 
A3-37 
 
 0.7 
 
 K, 
 
 Figure A3-29. Tilt Correction Factor for 35° Latitude, 50° Tilt 
 
A3 -38 
 
 2.6 
 
 2.4 
 
 2.2 
 
 2.0 
 
 I .8 
 
 R 1.6 
 
 I .4 
 
 1.2 
 
 1.0 
 
 0.8 
 
 0.6 
 
 0.4 
 
 LAT1TUDE=l4Q ° ^B^ 
 
 TILT= LATITUDE 4 
 TILT=55 ° ^ 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-30. Tilt Correction Factor for 40° Latitude, 55° Tilt 
 
A3-39 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-31. Tilt Correction Factor for 45° Latitude, 60° Tilt 
 
A3 -40 
 
 4.0 
 
 3.5 
 
 3.0 
 
 2.5 
 
 2.0 
 
 1.0 
 
 0.5 
 
 LATITUDE=.5Q° 
 
 
 TILT= LATITUDE +15° 
 
 TILTv65 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3-32. Tilt Correction Factor for 50° Latitude, 65° Tilt 
 
A3-41 
 
 5.0 
 
 4.0 
 
 3.0 
 
 2.0 
 
 1.0 
 
 0.0 
 
 DE^ 
 
 -LATITUDE 
 
 rr-^APR 
 
 — AUG 
 = MAY 
 
 — JUL 
 — -JUN 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3-33. Tilt Correction Factor for 55° Latitude, 70° Tilt 
 
A3-42 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3-34. Tilt Correction Factor for 25° Latitude, Vertical Tilt 
 
A3-43 
 
 R 1.0 
 
 MAY 
 
 JUL 
 
 0.4 
 
 0.5 
 
 K 
 
 Figure A3-35. Tilt Correction Factor for 30° Latitude, Vertical Tilt 
 
A3 -44 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-36. Tilt Correction Factor for 35° Latitude, Vertical Tilt 
 
A3-45 
 
 =^ftUG 
 MAY 
 JUL 
 J UN 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K, 
 
 Figure A3-37. Tilt Correction Factor for 40° Latitude, Vertical Tilt 
 
A3 -46 
 
 MAY 
 JUbH 
 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-38. Tilt Correction Factor for 45° Latitude, Vertical Tilt 
 
A3-47 
 
 4.0 
 
 3.5 
 
 3.0 
 
 2.5 
 
 R 2.0 
 
 1.5 
 
 0.5 
 
 0.0 
 
 _j_ 
 
 
 \- :,:: 
 
 JUL 
 JUN 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-39. Tilt Correction Factor for 50° Latitude, Vertical Tilt 
 
A3-48 
 
 6.0 
 
 5.0 
 
 4.0 
 
 3.0 
 
 2.0 
 
 0.0 
 
 0.3 
 
 0.4 
 
 0.5 
 
 0.6 
 
 0.7 
 
 K 
 
 Figure A3-40. Tilt Correction Factor for 55° Latitude, Vertical Tilt 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 4 
 
 SOLAR COLLECTORS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
4-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 LIST OF SYMBOLS 
 
 Page 
 4- i i i 
 4-iv 
 4-v 
 
 OBJECTIVES 4-1 
 
 INTRODUCTION 4-1 
 
 TYPICAL SOLAR COLLECTORS 4-2 
 
 TYPICAL LIQUID COLLECTOR 4-2 
 
 TYPICAL AIR COLLECTOR 4-3 
 
 BASIC PRINCIPLES 4-4 
 
 HEAT LOSSES FROM COLLECTOR 4-7 
 
 SOLAR ENERGY ABSORPTION 4-9 
 
 SELECTIVE SURFACES 4-12 
 
 COLLECTOR PERFORMANCE 4-13 
 
 CONVENIENT PERFORMANCE EQUATION 4-13 
 
 HEAT RECOVERY FACTOR 4-14 
 
 COLLECTOR TEMPERATURE PATTERNS 4-15 
 
 COLLECTOR EFFICIENCY 4-17 
 
 Typical Collector Characteristics .... 4-20 
 
 Collector Characteristics Presented with Different 
 
 Temperature Base ....... 4-22 
 
 Comparison of Liquid and Air Collector Performance. 4-25 
 
 CORROSION PROTECTION FOR LIQUID COLLECTORS .... 4-28 
 
 CORROSION BY OXIDATION 4-28 
 
4-ii 
 
 CORROSION BY ION EXCHANGE 
 
 CORROSION BY GALVANIC ACTION . 
 
 CORROSION BY CREVICING 
 
 EROSION OF CONDUITS .... 
 FREEZE PROTECTION FOR LIQUID COLLECTORS . 
 
 ETHYLENE GLYCOL ADDITIVE . 
 
 ORGANIC FLUIDS FOR FREEZE PROTECTION 
 
 COLLECTOR ARRAYS 
 
 REFERENCES 
 
 Page 
 4-29 
 4-31 
 4-32 
 4-33 
 4-33 
 4-33 
 4-35 
 4-35 
 4-41 
 
4-iii 
 
 LIST OF FIGURES 
 
 n Liquid- and 
 
 Figure 
 
 4-1 Liquid-Heating Solar Collector 
 
 4-2 Air-Heating Solar Collector 
 
 4-3 Definition Sketch for Equation 4-1 
 
 4-4 Comparison of Typical Temperatures 
 Air-Heating Solar Collectors . 
 
 4-5 Typical Collector Performance Curve 
 
 4-6 Measured Solar Collector Efficiencies of 
 
 Several Collectors ....... 
 
 4-7 Comparison of Liquid and Air Collectors Based on 
 Measured Performance (points shown are for air 
 collector operating at 2 cfm/ft 2 . 
 
 4-8 Results of Performance Calculations 
 
 4-9 Specific Heat of Aqueous Ethylene Glycol Solutions. 
 
 4-10 Density of Aqueous Ethylene Glycol Solutions . 
 
 4-11 Viscosity of Aqueous Ethylene Glycol Solutions 
 
 4-12 Definition Sketch for Fluid Flow Distribution 
 Through a Solar Collector Array . 
 
 4-13 Typical Arrangement of Internally Manifolded 
 Collector Modules in an Array . 
 
 Page 
 4-3 
 4-4 
 4-6 
 
 4-16 
 4-19 
 
 4-21 
 
 4-25 
 4-28 
 4-36 
 4-36 
 4-37 
 
 4-39 
 
 4-39 
 
4-iv 
 
 LIST OF TABLES 
 
 Table Page 
 
 4-1 Collector Performance Parameters .... 4-23 
 
 4-2 Comparison of Typical Solar Heating Systems 
 
 Employing Liquid and Air Collectors . . . 4-27 
 
 4-3 Some Inhibitors Suitable for Use in Aqueous 
 
 Solar Collector Fluids 4-30 
 
 4-4 Galvanic Order of Some Common Metals . . . 4-31 
 
 4-5 Concentration of Ethylene Glycol Required for 
 
 Freeze Protection ....... 4-34 
 
 4-6 Some Physical Properties of Dowtherm J and 
 
 Therminol 55 ....... 4-37 
 
4-v 
 
 LIST OF SYMBOLS 
 
 2 
 A Overall collector area or absorber area, ft 
 c ' 
 
 c Specific heat of fluid, Btu/(lb-°F) 
 
 C Heat capacity flow rate = mc , Btu/(hr*°F) 
 
 F R Heat recovery factor, a correction factor in the_col lector 
 performance equation when T. is used instead of t 
 
 2 
 I Solar insolation, Btu/(hr*ft ) 
 
 I Extraterrestrial radiation on a horizontal surface at the 
 outer limits of earth's atmosphere, Btu/(hr«ft 2 ) 
 
 Ij Solar radiation on the outer cover of a tilted collector 
 per unit area, Btu/(hr*ft 2 ) 
 
 m Fluid mass flow rate, lb/hr 
 
 Q Useful heat delivered by the collector, Btu/hr 
 
 T Atmospheric temperature, °F 
 a 
 
 T. Fluid temperature at the inlet to the collector, °F 
 
 f Average temperature of the upper surface of the absorber 
 p plate, °F 
 
 U, Overall heat loss coefficient from the collector per unit 
 collector area or absorber area, Btu/(hr*ft 2 *°F) 
 
 a Absorptance of solar radiation by the absorber plate, no 
 dimension 
 
 rt Collector efficiency, useful heat delivered by the collector 
 divided by the total solar radiation incident on the 
 collector 
 
 t Transmittance of solar radiation through the covers, no 
 dimensions 
 
 (ia) n Transmittance absorptance product when beam radiation is 
 normal to the plane of the collector cover 
 
 n 
 
4-1 
 
 OBJECTIVES 
 
 At the end of this module, the trainee should be able to: 
 
 1. Identify and describe the purpose of each component of a solar 
 collector. 
 
 2. Compare the performance of various collectors. 
 
 3. Describe methods of preventing corrosion and freezing of 
 collectors. 
 
 4. Describe the use of various fluids in collectors. 
 
 5. Recognize effect of system design on collector performance. 
 
 6. Explain the factors contributing to solar collector 
 durability. 
 
 INTRODUCTION 
 
 Collectors may be divided into two classes, liquid- heating and 
 air-heating solar collectors. A common design for both types consists 
 of an absorber plate, with black surface coating, contained in a metal 
 frame box with one or more transparent covers above the absorber plate. 
 The covers are transparent to incoming solar radiation and relatively 
 opaque to outgoing (long-wave) radiation. The principal purpose of 
 transparent covers is to reduce heat losses. Insulation is placed 
 beneath the absorber plate to reduce heat losses through the back of the 
 collector. A special collector design uses a vacuum jacket around the 
 absorber to reduce conduction and convection heat losses. 
 
4-2 
 
 Nearly all practical systems for solar space heating and hot water 
 heating involve flat-plate collectors. They are easy to install, re- 
 quire no moving parts, and have reasonable prospects for reliable and 
 durable operation. Some types of concentrating collectors are being 
 tested in experimental situations, but their cost is much higher than 
 the flat-plate types, and there is not sufficient information available 
 at the present time to evaluate the practicality of concentrating 
 collector systems. 
 
 TYPICAL SOLAR COLLECTORS 
 
 TYPICAL LIQUID COLLECTOR 
 
 A partially sectioned diagram of a typical flat-plate liquid solar 
 collector is shown in Figure 4-1. The drawing shows a commercially 
 manufactured collector comprising a glass-covered metal box containing 
 an absorber plate to which an array of tubes is attached and beneath 
 which insulation is provided. A liquid is pumped through the collector 
 tubes and manifolds for heating. Typical collector dimensions are 6.5 
 feet by 3.0 feet. The space between glass covers is about one-half inch 
 and the inner glass cover is about one inch above the absorber plate. 
 Two to four inches of insulation such as heat-resistant fibrous glass 
 are commonly used below the absorber plate. Metal is probably the best 
 material for absorber plates, and good thermal contact is required 
 between the absorber plate and the tubes through which the liquid is 
 transported. Volumetric flow rate is typically 0.02 gal/(min«ft ) of 
 collector surface area. 
 
4-3 
 
 MOUNTING 
 BRACKET 
 
 ABSORBER PLATE 
 WITH 
 SELECTIVE SURFACE 
 
 COPPER TUBES 
 
 SILICONE RUBBER PADS 
 TO ISOLATE ABSORBER PLATE 
 FROM FRAME 
 I 
 TWO COVER GLASSES 
 
 GLASS SEAL 
 TO FRAME 
 
 INLET WATER 
 HEADER 
 
 STEEL FRAMING 
 
 SEMI-RIGID 
 INSULATION 
 
 PLUMBING FITTING 
 
 Figure 4-1. Liquid-Heating Solar Collector 
 
 TYPICAL AIR COLLECTOR 
 
 A sketch of a typical air-heating solar collector is shown in 
 Figure 4-2. The principal difference between air- and liquid-heating 
 collectors is the size and configuration of the fluid conduits. The 
 figure shows three wide air passages directly beneath the absorber 
 plate. Air therefore flows in contact with nearly the entire absorber 
 surface, through channels about one-half inch high, at a sufficient 
 velocity for effective heat transfer. The design shown also has an 
 internal manifold for air distribution to the three channels of the 
 collector panel. Volumetric flow rate is typically 2 cfm/ft of 
 collector surface area. 
 
4-4 
 
 METAL FRAME BOX 
 
 TRANSPARENT 
 COVERS 
 
 ABSORBER PLATE 
 
 INSULATION 
 AIR PASSAGES 
 
 INTERNAL MANIFOLD 
 
 Figure 4-2. Air-Heating Solar Collector 
 
 BASIC PRINCIPLES 
 
 A solar collector is a device for converting the energy in solar 
 radiation to heat in a fluid. This conversion is accomplished by ab- 
 sorbing the solar radiation on a broad, thin metal surface which is in 
 contact with a stream of liquid or gas. Absorption of solar energy 
 causes the temperature of the metal surface to rise so that the tempera- 
 ture of the fluid increases as it moves past the surface. 
 
 Under steady conditions, the useful heat delivered by the solar 
 collector is equal to the energy absorbed in the metal surface minus the 
 heat losses from that surface directly and indirectly to the surround- 
 ings. This principle can be stated in the relationship: 
 
4-5 
 
 Useful 
 
 Area 
 
 Solar 
 
 Heat 
 
 heat = 
 
 of 
 
 radiation - 
 
 ■ losses 
 
 gain 
 
 absorber 
 
 absorbed 
 
 
 or rewriting in equation form, 
 
 where 
 
 (4-1) 
 
 Q is useful heat delivered by the collector, Btu/hr 
 
 2 
 A is total collector area, ft 
 c 
 
 Ij is the solar energy received on the upper surface of 
 the sloping collector per unit area, Btu/(hr*ft 2 ) 
 
 x is fraction of the incoming solar radiation which 
 reaches the absorbing surface, no dimensions 
 
 a is fraction of the solar energy reaching the surface 
 which is absorbed, absorptivity, no dimensions 
 
 U. is the overall heat loss coefficient, Btu/(hr*ft 2 «°F) 
 transferred to the surroundings from each square foot of 
 exposed collector surface per degree difference between 
 average collector surface temperature and the surrounding 
 air temperature 
 
 T is average temperature of the upper surface of the 
 absorber plate, °F 
 
 T is atmospheric temperature, °F 
 
 A diagrammatic representation of the terms in this relationship is shown 
 in Figure 4-3. 
 
4-6 
 
 \ 
 
 :^ 
 
 © 
 
 CONVECTION LOSS 
 
 RADIATION 
 LOSS 
 
 ABSORPTION 
 
 REFLECTION 
 
 BOTTOM OF 
 COLLECTOR 
 
 LATION 
 
 CONDUCT!- 
 
 FLUID PASSAGE 
 
 ABSORBED ENERGY = A c I T ra 
 EFFECTIVE HEAT LOSS = A c U L ( T p -T Q ) 
 
 Figure 4-3. Definition Sketch for Equation 4-1 
 
4-7 
 
 HEAT LOSSES FROM COLLECTOR 
 
 In order that the performance of a solar collector can be as high 
 as economically practical, the design and operating factors which can 
 maximize the value of the first term on the right-hand side of Equation 
 (4-1) and can minimize the value of the second term are selected. In 
 other words, the greater the energy absorption in the metal surface and 
 the lower the heat loss from that surface, the higher will be the useful 
 recovery. If a bare metal plate serves as the collector, and with 
 typical values of 2 to 10 Btu/(hr«ft 2 *°F) for the coefficient of heat 
 transfer to the atmosphere, U. , the rates of heat loss will be so large 
 that an absorber plate temperature 25 to 50 degrees above atmospheric 
 
 temperature would be the maximum achievable under typical full solar 
 
 2 
 radiation of 300 Btu/(hr«ft ). Under these conditions no useful heat 
 
 would be delivered from the collector because the heat loss would be 
 equal to the solar heat absorbed, leaving nothing for useful delivery. 
 To reduce the rate of heat loss occurring by radiation and 
 convection, one or more transparent surfaces, such as glass, can be 
 placed above the metal surface. The glass will transmit as much as 90 
 percent of the incident solar radiation and it will greatly reduce the 
 heat loss coefficient, U, . The reduction in U. is due to the suppres- 
 sion of convection losses from the absorber plate by the relatively 
 stagnant air layer between the absorber plate and the glass, and by 
 intercepting the long-wave, thermal radiation emitted by the hot metal 
 surface because glass is opaque to the long-wave radiation. The heat 
 loss coefficient can be reduced to 1 or 2 Btu/(hr«ft « F) by the use of 
 one glass cover. Similar benefits can be realized by use of certain 
 transparent plastic materials. 
 
4-8 
 
 Further reduction in the heat loss coefficient can be realized by 
 using a second transparent surface with an air space between the two 
 surfaces. Two relatively stagnant air barriers to convection loss are 
 then present, as well as two surfaces impeding radiation loss. Coeffi- 
 cients in the range of 0.7 Btu/(hr*ft '°F) are typically then obtained. 
 
 Radiation losses can be reduced by other techniques, such as by 
 reducing the radiation-emitting characteristics of the heat absorbing 
 surface. This measure is discussed in the section pertaining to the 
 solar radiation absorbing characteristics of the surface. Thermal 
 radiation emitted by the absorber plate may also be reduced by reflect- 
 ing it downward from the lower glass cover by applying an infrared- 
 reflecting coating on the glass. An optically transparent, very thin 
 layer of tin oxide or indium oxide deposited on the glass will reduce 
 radiation loss by reflecting it back to the absorber plate. This coat- 
 ing absorbs a small fraction of the solar radiation, however, so the 
 reduced thermal loss is largely off-set by reduced solar energy input to 
 the absorber plate. 
 
 Significant losses can occur from the side and back of the 
 collector unless insulation is used. It is advisable to use a high- 
 temperature insulation adjacent to the back side of the absorber plate 
 layered with a lower temperature insulation to provide the required 
 resistance to heat flow. The total R value of the insulation should 
 be at least 10 for medium- temperature flat-plate collectors. 
 
 A transparent honeycomb of thin plastic film can also suppress 
 radiation loss if interposed between the absorber plate and the lower 
 glass cover. Convection loss suppression also can be achieved, leading 
 to improvement of overall efficiency. Low- to moderate-priced plastic 
 
4-9 
 
 film does not appear to have sufficient resistance to damage by high 
 collector-plate temperatures, however, so this technique has not been 
 commercially utilized. 
 
 The foregoing discussion has been concerned with methods for 
 reducing U. , the heat loss coefficient, to the lowest practical level. 
 By so doing, the total heat loss is minimized and collector efficiency 
 is increased. It is evident from Equation (4-1) that losses also de- 
 crease as the difference between plate temperature and air temperature 
 decreases. The ambient (outside) air temperature is an uncontrollable 
 factor, of course, but the fact that it varies with time and with geo- 
 graphic location means that collector efficiency will also be dependent 
 upon these factors. It is clear, also, that a collector will be more 
 efficient at lower plate temperatures than at high temperatures. Plate 
 temperature is dependent largely on the way the collector is operated, 
 that is, by the temperature of the fluid being circulated in contact 
 with the plate, the rate of fluid circulation, and the type of fluid. 
 Fluid temperature depends on conditions elsewhere in the system, whereas 
 the other factors depend on the collector design and the operating 
 conditions. 
 
 SOLAR ENERGY ABSORPTION 
 
 In Equation (4-1), the first term is the solar energy absorbed in 
 the absorbing surface, which depends upon the solar energy incident on 
 the tilted surface of the collector and is affected by collector orien- 
 tation, as outlined in Module 3. This climatic variable can be measured 
 or derived from tables of averages, and if not already converted, can be 
 calculated for the proper collector position. 
 
4-10 
 
 The transmissivity of the glass, i, is a function of the quality of 
 the glass and the angle at which the solar radiation reaches the glass. 
 At normal incidence (solar beam perpendicular to the glass surface), one 
 sheet of ordinary window glass reflects about eight percent of the solar 
 radiation. Two sheets of glass with air space between reflect about 15 
 percent. Impurities in the glass, principally iron, result in some 
 radiation absorption; typical glasses 1/8 inch in thickness absorb one 
 to five percent per sheet. Glass with reasonably low iron content may 
 absorb about two percent per sheet, so at normal incidence, the total 
 transmission of two sheets of glass can be approximately 80 percent. 
 The value of t is, therefore, 0.8. 
 
 Because the beam radiation from the sun strikes the collector at an 
 angle which varies throughout the day, as well as seasonally, a weighted 
 mean transmissivity is somewhat lower than this normal -incidence value. 
 Precise calculations can be made, but a satisfactory approximation for a 
 single-glazed collector can be based on a 10 percent average reflection 
 loss and a suitable absorption loss dependent on glass quality. Assum- 
 ing two percent absorption, an average transmissivity, x, of a single 
 sheet could be about 0.88. In a double-glazed collector, an effective 
 transmission coefficient of 0.78 could be obtained with good quality 
 glass. 
 
 If plastics are used for the transparent surfaces, transmission 
 coefficients could be appreciably different, depending upon the char- 
 acteristics of the plastics. Some have transmissivities moderately 
 higher than glass, whereas others show lower values. 
 
 Methods for reducing the reflectivity of glass surfaces have been 
 developed. Metallic films formed by vapor deposition are commonly used 
 
4-11 
 
 as lens coatings in photographic equipment. These interference layers 
 are too costly for use in solar collectors. Another process involves a 
 delicate etching of the glass surface by acid treatment, producing 
 essentially a slightly porous silica surface. Solar reflectivities as 
 low as 1 to 2 percent can be obtained under carefully controlled condi- 
 tions. Total transmissivity of a double-glazed collector can thereby be 
 increased to values above 90 percent. The cost-effectiveness of this 
 substantial improvement in performance has yet to be established. 
 
 The solar absorptivity of the radiation-receiving surface, a, is 
 dependent on the optical property of the materials exposed to solar 
 radiation. Surfaces which appear black to the eye have high absorptiv- 
 ity for the visible portion of the solar spectrum, and usually also are 
 good absorbers for the infrared portion of the solar radiation. Carbon 
 black, numerous oxides, and most black paints have absorptivities above 
 0.95, that is, they absorb 95 percent of the solar radiation reaching 
 the surface. The remainder of the solar radiation is reflected upwards 
 through the glazing. The overall efficiency of the collector is strong- 
 ly dependent on the absorptivity of this surface. 
 
 The most common types of absorber surfaces are heat-resistant black 
 paints, usually applied by spraying, followed by curing with heat to 
 eliminate solvents and to secure permanence. These surfaces must be 
 capable of prolonged exposure to temperatures of 300°F to 400°F in 
 double-glazed collectors, without appreciable deterioration or outgas- 
 sing. In a recently developed solar air collector, sheet steel coated 
 with black porcelain enamel (applied to the steel as a sprayed-on frit 
 and fused to the surface in a furnace) is achieving successful 
 application. 
 
4-12 
 
 SELECTIVE SURFACES 
 
 Most surfaces that are good absorbers for solar radiation are also 
 good radiators of heat. If, for example, a surface has an absorptivity 
 of 0.95 for solar radiation, it will normally radiate heat at a rate 
 about 95 percent of that of a "perfect" radiator. Certain combinations 
 of surfaces, known as selective surfaces, are capable of absorbing solar 
 radiation effectively, while at the same time radiating heat at a low 
 rate. Most selective surfaces are composed of a very thin black metal- 
 lic oxide on a bright metal base. The black oxide coating is thick 
 enough to act as a good absorber, with an absorptivity as high as 0.95, 
 but it is essentially transparent to long-wave thermal radiation emitted 
 by an object at a temperature of several hundred degrees F. Because 
 bright metals have low emissivity for thermal radiation, that is, are 
 poor heat radiators, and the thin oxide coating is transparent to such 
 radiation, the combination is a poor heat radiator. As a result, the 
 radiation loss from this type of surface is considerably lower than from 
 a conventional, non-selective surface. The overall heat loss coeffi- 
 cient for the collector, U, , has a lower value when a selective surface 
 is used. 
 
 The most successful and stable selective surface developed to date 
 is made by electroplating a layer of nickel on the absorber plate, then 
 electrodepositing an extremely thin layer of chromium oxide on the 
 nickel substrate. Nickel oxide coatings have also been used, but they 
 are less resistant to damage from moisture. Coatings of copper oxide on 
 bright copper and nickel have similar properties, but temperature sta- 
 bility is limited. The most effective selective surfaces have solar 
 absorptivities near 0.95 and thermal emissivities near 0.1. 
 
4-13 
 
 COLLECTOR PERFORMANCE 
 
 CONVENIENT PERFORMANCE EQUATION 
 
 Having now recognized the principal design factors affecting 
 collector performance, specifically those related to heat loss control 
 and those involving the absorption of solar radiation, we now can see 
 from Equation (4-1) that if the numerical values of all the terms are 
 known, the rate of useful heat recovery, Q , can be calculated. In 
 addition to the design characteristics of the collector discussed above, 
 the three operating conditions, solar radiation, average absorber-plate 
 temperature, and ambient temperature must be known. With the exception 
 of plate temperature, these terms can readily be measured or obtained 
 from tables or charts. Absorber-plate temperature, however, is seldom 
 known, nor can it be easily determined. It is affected by the other 
 collector operating conditions and, most critically, by the temperature 
 of the fluid being supplied to the collector. 
 
 In an operating system comprising collector, storage, and space 
 being heated, the temperature of the fluid in storage can be calculated 
 or assumed until confirmed. This fluid is supplied to the collector and 
 strongly controls the absorber-plate temperature in Equation (4-1). In 
 a typical liquid collector, average plate temperatures usually are 10 to 
 20 degrees above inlet liquid temperature and, in air collectors, the 
 temperature difference is 30 to 50 degrees. As a convenience, there- 
 fore, Equation (4-1) can be modified by substituting inlet fluid temper- 
 ature for the average plate temperature, if a correction factor is 
 applied to the resulting useful heat determination. The resulting 
 equation is 
 
4-14 
 
 "u " f A^ l l ra " U L (T i " V ] (4 ' 2) 
 
 where 
 
 T. is the temperature of the fluid entering the collector 
 
 F R is a correction factor or "heat recovery factor", having a 
 
 value between and 1.0, such that the useful heat recovery 
 
 calculated by Equation (4-2) is equal to that calculated by 
 
 Equation (4-1). 
 
 HEAT RECOVERY FACTOR 
 
 The heat recovery factor, F R , can be interpreted as the ratio of 
 the heat actually recovered to that which would be recovered if the 
 collector plate were operating at a temperature equal to that of the 
 entering fluid. This temperature equality would theoretically be pos- 
 sible if the fluid were circulated at such a high rate through the 
 collector that there would be a negligible rise in the temperature of 
 the fluid passing through the collector, and the heat transfer coeffi- 
 cient were so high that the temperature difference between the absorber 
 surface and the fluid would be negligible. 
 
 In Equation (4-2), the temperature of the inlet fluid is dependent 
 on the characteristics of the complete solar heating system and the heat 
 demand of the building. F R , however, is affected only by the collector 
 characteristics and the fluid flow rate through the collector. As 
 indicated above, the numerical value of F R would be 1.0 if the entering 
 fluid temperature and the average plate temperature were the same. 
 
4-15 
 
 COLLECTOR TEMPERATURE PATTERNS 
 
 The better the heat transfer coefficient between the metal plate 
 and the fluid, the more nearly the fluid temperature will approach the 
 plate temperature at any one position in the collector, hence the higher 
 will be the value of F R . Similarly, the greater the fluid circulation 
 rate, the smaller will be the temperature change from inlet to outlet 
 and the closer will be the inlet fluid temperature to the average plate 
 temperature. Figure 4-4 shows a typical temperature pattern in a solar 
 heater being supplied with liquid at 130 degrees. Liquid leaves the 
 collector at about 150 degrees, the collector-plate temperature is about 
 10 degrees above the liquid temperature throughout the collector, and 
 the average plate temperature is about 150 degrees. If typical values 
 of the collector parameters are substituted in Equations (4-1) and 
 (4-2), it will be found that using 130°F as inlet fluid temperature in 
 Equation (4-2) instead of 150°F as the average plate temperature in 
 Equation (4-1) would necessitate use of a heat recovery factor, F R , of 
 about 0.9 to obtain the correct value of Q . If the coefficient of heat 
 transfer between the collector plate and the liquid is lower, or if a 
 lower fluid circulation rate is used, the value of F R would be slightly 
 less. 
 
 A temperature pattern in a typical air-heating collector operating 
 with an air supply from the space being heated or from the cold end of a 
 pebble-bed storage unit at 70°F is also shown in Figure 4-4. Full sun 
 and a practical air circulation rate of about 2 cfm per square foot of 
 collector are assumed in the example. An air temperature rise of about 
 60 to 80 degrees would occur under these conditions, which is much 
 higher than in the liquid case because of the lower specific heat for 
 air. The mass flow rate is about the same as that of the liquid 
 
4-16 
 
 
 
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4-17 
 
 (measured as pounds per hour, for example) for suitable pressure loss 
 conditions. Rather than a moderate 10-degree difference between plate 
 and fluid temperatures, as in the liquid case, the air collector is 
 characterized by a 30- to 50-°F temperature driving force. The much 
 lower heat transfer coefficient from the plate to the air is responsible 
 for this difference. Under the conditions chosen, the average plate 
 temperature would be about 150 degrees, approximately the same as that 
 estimated for the liquid system. Use of Equation (4-2) with an inlet 
 temperature of 70 degrees results in a heat recovery factor, F R , typi- 
 cally about 0.7 for the air collector. Characteristically, solar air 
 heaters having heat transfer surfaces approximately equal to the solar 
 absorbing area show heat recovery factors substantially below those 
 achieved in liquid collectors. However, as shown below, this difference 
 must not be interpreted as superiority of one over the other when used 
 in suitably designed systems. 
 
 COLLECTOR EFFICIENCY 
 
 Equation (4-2) may be rewritten as an efficiency of solar 
 collection, n, c > that is, the ratio of useful heat delivery divided by 
 the total solar radiation, by dividing both sides of the equation by I T 
 and by A . Equation (4-3) is the result. 
 
 (T, " T ) 
 
 n„ = 
 
 u c curl a i ( collector\ rn OA 
 
 t . F D xa - F n U. [ r ] - **• • (4-3) 
 
 IjA R R L L I T J vefficiency/ v J 
 
 For a given collector operating at a constant fluid circulation rate, 
 A , Fn, , a, and U. are nearly constant regardless of solar and tempera- 
 ture conditions. Assuming that they are constant, Equation (4-3) repre- 
 sents a straight line on a graph of efficiency versus T. - T /I T 
 
 a as 
 
4-18 
 
 shown in Figure 4-5. The characteristics of this line are an intercept 
 (the intersection of the line with the vertical efficiency axis) equal 
 to the numerical value of F R xa and a "slope" of the line, that is, the 
 vertical scale change divided by the horizontal scale change, which is 
 equal to F R U.. If experimental data on collector heat delivery at 
 various temperatures and solar conditions are plotted on a graph with 
 efficiency as the vertical axis and T. - T /I-p as the horizontal axis, 
 the best straight line through the data points is a complete representa- 
 tion of the collector performance over its entire operating range. 
 Experimental data are normally taken for collectors with the 
 collector tilted to be perpendicular to the solar beam radiation. 
 
 Therefore, F D xa from performance curves is labeled F D (xa) where (xa) 
 R r K n n 
 
 indicates that the beam radiation is perpendicular to the plane of the 
 collector cover. 
 
 The point at which the line intersects the vertical axis 
 corresponds to the fluid inlet temperature being the same as the ambient 
 temperature, and collector efficiency is at its maximum. Where the line 
 intersects the horizontal axis, collection efficiency is zero. This 
 situation corresponds to such a low radiation level or such a high 
 temperature of the fluid supply to the collector that heat losses are 
 equal to solar absorption and no useful heat is delivered from the 
 collector. At this point, the temperature of the absorber plate is 
 equal to T., and is the maximum possible at the particular levels of 
 ambient temperature and solar radiation. It is commonly referred to as 
 stagnation temperature of the collector. 
 
 In a solar heating system employing a non-freezing liquid and a 
 heat exchanger for transfer of energy to storage, it is convenient 
 
4-19 
 
 1.0 
 0.9 
 0.8 
 0.7 
 
 o0.6 
 
 £ 0.5 
 
 "o 
 
 £ 0.4 
 til 
 
 B 0.3 
 
 o 
 
 o 0.2 
 
 0.0 
 
 VV'Wl 
 
 (Ti-Tj 
 
 i 'a 
 
 (Eq. 4-3) 
 
 F_{ra) (Intercept) =0.7 
 K n 
 
 Experimental Data (Hypothetical in this Illustration) 
 
 0.7 
 
 Slope = F D U, = - : =— = 0.93 
 
 0.75 
 
 J L 
 
 0.0 0.1 0.2 0.3 0.4 0.5 
 
 T; -T 
 
 0.6 0.7 0.8 0.9 1.0 
 
 i ' a 
 
 /hr-ft 2 °F\ 
 \ Btu / 
 
 Figure 4-5. Typical Collector Performance Curve 
 
4-20 
 
 to modify the heat recovery factor, F R , so that it includes the 
 exchanger and so that storage tank temperature may be substituted for T. 
 in Equation (4-3). This adjusted factor, F R , is less than F R by the 
 ratio of efficiencies obtainable with and without the exchanger. Its 
 actual value can be determined by use of F R , the characteristics of the 
 heat exchanger, and the liquid flow rates through the exchanger. The 
 procedure for its determination is outlined in Module 7. For air col- 
 lectors and for drain-back liquid collectors, no adjustment in F R is 
 required. 
 
 Typical Collector Characteristics 
 
 Efficiencies of several types of collectors tested in the NASA 
 Lewis Research Center are shown in Figure 4-6. Collectors 1 and 2 are 
 seen to have the highest efficiencies, but final selection also depends 
 on costs, durability, appearance, and so on. Collector 1 appears to 
 have the best performance of all those compared in Figure 4-6 if nor- 
 mally operated at conditions represented by the left-hand side of the 
 graph. Such conditions are low operating temperatures or high solar 
 radiation. Near the right-hand side of the graph, however, collector 2 
 is more efficient than collector 1, where high inlet collector tempera- 
 tures or low solar radiation prevail. It is evident that some collec- 
 tors are better than others in some temperature and radiation ranges, 
 whereas a reversal can occur at different conditions. 
 
 A graph such as Figure 4-6 for comparing a particular collector 
 with others of similar type can be useful in selecting suitable equip- 
 ment. Collector manufacturers usually provide such data. Of equal 
 value are dependable data on the quantities F R (ia) and F R U. . Knowledge 
 
.0 
 
 0.9 
 
 4-21 
 
 Tj - Fluid Temperature at Inlet, °F 
 
 Outdoor Air Temperature, 
 
 I T - Solar Radiation on Tilted Collector, "o" r 
 1 lit • hn 
 
 0.4 0.6 
 T; -T„ 
 
 I- 
 
 0.8 1.0 
 (hrft 2o F) 
 
 BTU 
 
 Figure 4-6. 
 
 Measured Solar Collector Efficiencies of Several 
 
 Collectors (Number label on graph refers to Reference Number 
 
 in Table 4-1) 
 
4-22 
 
 of those two factors is equivalent to having the graphical relationship. 
 Table 4-1 contains this information for the same collectors shown in 
 Figure 4-6 plus other commercially available collectors. 
 
 Collector Characteristics Presented with Different Temperature Base 
 
 The collector efficiency curves of Figures 4-5 and 4-6 and the 
 
 characteristic values of F R U. and F r (toO listed in Table 4-1 apply 
 
 specifically when the abscissa (horizontal axis) on the efficiency graph 
 
 is expressed as the parameter (T. - T )/I T . Collector performance may 
 
 i a 
 
 be correlated with other collector temperatures, and various parameters 
 are used for the abscissa of the collector efficiency curve. Two other 
 parameters that are commonly used are: (1) [T. + T /2 - T ]/I-p and (2) 
 (T - T )/I T , where T is collector outlet fluid temperature. In the 
 first parameter, (T. + T )/2 is used instead of T. on the premise that 
 an average of the inlet and exit temperatures more nearly represents the 
 average plate temperature as expressed in Equation (4-1). It is also 
 sometimes argued that the fluid temperature measured at the collector 
 exit is more representative of collector performance because it is more 
 indicative of the value or intensity of the heat collected. If the 
 collector temperatures are "well behaved" as illustrated in Figure 4-6, 
 it really makes little difference whether T-, (T. + T )/2, or T is used 
 
 J 110 
 
 in the parameter to express collector efficiency. However, the heat 
 recovery factor, F R , will differ for each case. 
 
 When either (T. + T )/2 or T is used in the abscissa of the 
 collector efficiency curve, corrections can be made to F R , hence to 
 F R (ta) and F R U. . That is, the values of F R (xa) and F R U. that will 
 
4-23 
 
 Table 4-1 
 Collector Performance Parameters* 
 
 Ref. 
 No. 
 
 Manufacturer 
 
 F R (xcO n 
 
 F R U L 
 (Btu/ft 2 h°F) 
 
 Type 
 
 1 
 
 Honeywell (NASA) 
 
 0.863 
 
 0.715 
 
 Liquid 
 
 2 
 
 Owens-Illinois 
 
 0.447** 
 
 0.206** 
 
 Liquid or Air 
 
 3 
 
 Miromit 
 
 0.724 
 
 0.947 
 
 Liquid 
 
 4 
 
 Beasley 
 
 0.600 
 
 0.759 
 
 Liquid 
 
 5 
 
 Revere 
 
 0.716 
 
 0.964 
 
 Liquid 
 
 6 
 
 Barber 
 
 0.816 
 
 1.204 
 
 Liquid 
 
 7 
 
 PPG 
 
 0.632 
 
 0.930 
 
 Liquid 
 
 8 
 
 Solar Products 
 
 0.600 
 
 1.057 
 
 Liquid 
 
 9 
 
 Solaron 
 
 0.516 
 
 0.516 
 
 Air 
 
 10 
 
 Rocky Mountain 
 
 0.679** 
 
 0.789** 
 
 Liquid or Air 
 
 11 
 
 General Electric 
 
 0.639 
 
 0.614 
 
 Liquid 
 
 12 
 
 LeRC 
 
 0.745 
 
 0.820 
 
 Liquid 
 
 13 
 
 InterTechnology 
 
 0.650 
 
 0.610 
 
 Liquid 
 
 14 
 
 Southwest Std 
 
 0.672 
 
 0.794 
 
 Liquid 
 
 15 
 
 Sunworks 
 
 0.650 
 
 0.789 
 
 Liquid 
 
 16 
 
 Trantor 
 
 0.700 
 
 0.830 
 
 Liquid 
 
 *From graphical presentation by Johnson, S.M. , and Simons, F.F. (1976) 
 "Comparison of Flat-Plate Collector Performance Obtained Under Con- 
 trolled Conditions in a Solar Simulator". Lewis Research Center, 
 NASA, Cleveland, Ohio. Presented at Annual ISES Meeting, Winnipeg, 
 Manitoba, Canada. 
 
 ** 
 
 Numerical values apply to liquid collectors. 
 
4-24 
 
 later be used in design calculations will be on the uniform basis, 
 as if the parameter (T. - T a )/Ij were used to express the collector 
 efficiency curve. 
 
 The corrections are as follows: 
 
 1. When (T. + T )/2 is used, 
 
 10 
 
 Fn(ta) [corrected] = F R (ia) [uncorrected] x 
 
 1 + 
 
 < F rV A c 
 2C_ 
 
 2. 
 
 Within the terms in the bracket, F R U. is the uncorrected 
 
 value and C is the collector fluid capacitance rate, 
 
 C = mc (Btu/hr-°F) 
 c p 
 
 When T is used, 
 o 
 
 F R (xa) [corrected] = F R (ia) [uncorrected] x 
 
 1 + 
 
 W\K 
 
 and 
 
 F R U, [corrected] = F R U. [uncorrected] x 
 
 1 + 
 
 tf^a; 
 
 where the terms in the brackets are defined under item (1) above. 
 
 It should be noted that the mass flow rate and fluid capacitance 
 rate through air collectors can significantly influence the collector 
 performance discussed in the following section. The correction proce- 
 dures cannot be applied for a flow rate that is different from that used 
 to obtain the experimental data. 
 
4-25 
 
 Comparison of Liquid and Air Collector Performance 
 
 Efficiency relationships for a widely used air collector operating 
 at two different air circulation rates and a liquid collector (collector 
 10 from Table 4-1) are shown in Figure 4-7. Whereas flow rate 
 
 Liquid Collector #10 
 
 O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 
 T;-Tn ft-hr-°F 
 
 I T Btu 
 
 Figure 4-7. Comparison of Liquid and Air Collectors Based on Measured 
 Performance (points shown are for air collector operating 
 at 2 cfm/ft 2 ) 
 
 does not significantly affect the efficiency of a liquid collector, it 
 is evident that air flow rate has a substantial influence on air collec- 
 tor performance. Although even greater efficiencies can be achieved 
 
 with higher air flow rates, the larger pressure drop and power require- 
 
 2 
 ments to circulate air at rates above 2 cfm/ft force a compromise 
 
 between collector efficiency and power consumption. As seen from Figure 
 
4-26 
 
 4-7, the liquid collector is more efficient than the air collector 
 (toward the left-hand side) at the same inlet temperature, ambient 
 temperature, and solar radiation level. It is important to recognize, 
 however, that in space heating systems, liquid and air collectors nor- 
 mally operate at very different inlet temperatures so that air collec- 
 tors usually operate at conditions substantially nearer the left side of 
 the graph than do the liquid type. The net result is comparable operat- 
 ing efficiency of the two collectors when assembled in typical space 
 heating systems. The foregoing comparison leads to the conclusion 
 that whereas similar types of collectors such as flat-plate liquid 
 heaters can be compared by means of a graph such as Figure 4-6, compari- 
 sons cannot be drawn in this way between different types. A second 
 conclusion is that since the conditions at which the collector must 
 operate depend on system conditions, particularly storage temperature, 
 comparative evaluation requires attention to the other components in the 
 system and their effect on collector performance. 
 
 Table 4-2 contains a step-by-step summary comparison of air and 
 liquid types of collectors. Typical air and water heaters are compared 
 at a high solar radiation level and at a fairly low solar intensity. 
 Characteristic designs and operating conditions have been assumed. 
 
 The results of the two calculations are shown in Figure 4-8 in 
 graphical form. It may be noted that at the high solar radiation level, 
 300 Btu/(hr*ft 2 ), the two collectors have identical (50 percent) effi- 
 ciency, and at the lower solar level, 150 Btu/(hr*ft 2 ), the air collec- 
 tor (operating at the characteristically low return air temperature) has 
 an efficiency substantially greater than the liquid collector. 
 
4-27 
 
 Table 4-2 
 
 Comparison of Typical Solar Heating Systems 
 Employing Liquid and Air Collectors 
 
 Liquid 
 
 Air 
 
 0.9 
 
 0.7 
 
 0.75 
 
 0.75 
 
 0.85 
 
 0.85 
 
 0.95 
 
 0.95 
 
 0.73 
 
 0.57 
 
 0.68 
 
 0.53 
 
 Performance Relationship : 
 Collection Efficiency: 
 
 jrh - f r « " f r u l <~4r^ 
 
 C I I 
 
 Design Characteristics : 
 
 Heat Recovery Factor F R 
 Heat Loss Coefficient U. 
 Cover Transmission t 
 Plate Absorptivity a 
 
 F R (T0,) n 
 F R U L 
 
 Operating Conditions : 
 
 Atmospheric Temperature T , °F 30 30 30 30 
 
 a 
 
 Fluid Inlet Temperature T.,°F 130 130 70 70 
 Solar Radiation L, Btu/(hr-ft 2 ) 300 150 300 150 
 Fluid Flow Rate, gpm/ft 2 , cfm/ft 2 0.02 0.02 2.0 2.0 
 
 (T. - T a )/I T 0.333 0.666 0.133 0.266 
 
 ■ a i 
 
 Calculated Performance : 
 
 F R U L< T i " V'*T 
 
 F R to, - F R U L (T r T a )/I T 
 
 Collection Efficiency, % 
 Computed Outlet Temperature, °F 
 
 0.23 
 
 0.46 
 
 0.07 
 
 0.14 
 
 0.50 
 
 0.27 
 
 0.50 
 
 0.43 
 
 50 
 
 27 
 
 50 
 
 43 
 
 145 
 
 138 
 
 134 
 
 125 
 
4-28 
 
 0.8 
 
 0.6 
 
 £ 0.4 
 
 c 
 
 o 
 
 r 0.2 
 
 LU 
 
 
 
 0.73 
 
 I 
 
 ^=0.68= F R U L 
 
 Air Slope 
 
 =0.53=F 'U, 
 
 0.133 I 0.333 I 
 
 Lj • " X ■ I ' ' ' ' L 
 
 0.2 0.4 0.6 0.8 1.0 
 T, -T a 
 
 Figure 4-8. Results of Performance Calculations 
 
 CORROSION PROTECTION FOR LIQUID COLLECTORS 
 
 Corrosion is a major problem that concerns not only collectors but 
 the entire liquid-heating solar system. It is of particular concern in 
 collectors with aluminum absorber plates and systems with aluminum 
 pipes. There are several forms of corrosion that are of concern. These 
 include pitting by oxidation and ion exchange, galvanic corrosion, 
 crevice corrosion, and erosion. 
 
 CORROSION BY OXIDATION 
 
 Oxidation of metals can be eliminated by removing the dissolved 
 oxygen in the heat transfer liquid and preventing exposure of the liquid 
 to the atmosphere. This can be accomplished in closed systems. While 
 initially there will be free oxygen in the liquid, metal in the closed 
 loop system will react with the oxygen and remove it from the liquid. 
 
4-29 
 
 The amount of initial oxidation is not of practical concern. In 
 drain-down systems, when fresh air is admitted repeatedly into the 
 system, oxidation is a concern. If drain-down collectors are used, the 
 collector tubing should have high resistance to oxidation. Copper and 
 some types of stainless steel have been found reasonably satisfactory in 
 such usage. 
 
 CORROSION BY ION EXCHANGE 
 
 Heavy metal ions in the collector fluid (and elsewhere in the 
 system) can cause pitting. Pitting is aggravated by the presence of 
 dissolved chloride ions which may originate from the water supply or 
 from soldering fluxes in the piping. Heavy metal ions may result from 
 corrosion of other parts of the system or may be present naturally in 
 the water supply. 
 
 Ion exchange and consequent pitting may be effectively prevented by 
 addition of a small amount of corrosion inhibitor to the transport 
 liquid. Some chemicals that are commonly used as inhibitors are listed 
 in Table 4-3. 
 
 It is particularly important that a corrosion inhibitor be added to 
 systems involving antifreeze solutions in water. The most commonly used 
 antifreeze is ethylene glycol. A 50 percent solution by volume of 
 ethylene glycol in water will provide freezing protection down to about 
 -30°F with a boiling point of about 230°F. At high temperatures the 
 glycol can break down to form glycol ic acid. This decomposition is 
 accelerated by dissolved oxygen in the system. The resulting acid will 
 reduce the pH of the transport medium and tend to accelerate corrosion. 
 Therefore a solar system that has a glycol antifreeze in the fluid 
 
4-30 
 
 Table 4-3 
 
 Some Inhibitors Suitable for Use in Aqueous Solar 
 Collector Fluids* 
 
 Inhibitor 
 
 Function 
 
 Suitability 
 
 Water 
 
 Glycol Solution 
 
 Sodium Tetraborate 
 Na 2 B 4 y • 5H 2 
 
 Buffer, protects Fe 
 
 7 
 
 V 
 
 Sodium 
 
 Mercaptobenziothiazole 
 (Na MBT) C ? H 4 NH 2 Na 
 
 Cu alloy inhibitor 
 
 V 
 
 V 
 
 Sodium Metasilicate 
 Na 2 S 2 4 • 9H 2 
 
 General inhibitor 
 for Cu, Fe, Al 
 
 V 
 
 V 
 
 Sodium Orthophosphate 
 Na 3 P0 4 • 12H 2 
 
 Protects Fe, Al 
 
 V 
 
 V 
 
 Sodium Nitrate 
 Na N0 3 
 
 Protects Fe, Al , and 
 solder 
 
 V 
 
 V 
 
 Sodium Orthoarsenate 
 Na 3 A S0 4 • 12H 2 
 
 General inhibitor 
 Most effective on Al 
 
 V 
 
 . V 
 
 Chromates (Na, K, etc) 
 
 General inhibitor 
 for Al , Fe, and Cu 
 
 V 
 
 X 
 
 *J.M. Popplewell, "Corrosion Prevention in Aluminum Solar Systems", 
 Paper 170, Corrosion/77, San Francisco, California, March 1977. 
 
 Notes: 
 
 (1) Many other inhibitors suitable for solar service are 
 available. This table lists a few of the more common 
 ones only. 
 
 (2) V = Suitable 
 
 ? = 
 
 Questionable 
 
 X = Unsuitable 
 
4-31 
 
 should be periodically monitored in order to avoid corrosion problems. 
 The pH should be measured regularly and if it deviates more than one pH 
 unit from the original value of the fresh solution, the system should be 
 drained and a new solution should be used. The pH of the original 
 solution can vary with the particular application but is normally 
 recommended to exceed 10. 
 
 CORROSION BY GALVANIC ACTION 
 
 Galvanic corrosion occurs when two dissimilar metals are joined in 
 an electrolyte. The more noble metal acts as a cathode and is protected 
 by the less noble metal, which acts as an anode and will be consumed. 
 The galvanic relationship between various metals is listed in Table 4-4. 
 
 Table 4-4 
 
 Galvanic Order of Some Common Metals* 
 (Electrode Potential is for Sea Water) 
 
 Metal 
 
 Electrode Potential 
 wrt H z 
 
 (Volts) 
 
 Magnesium 
 
 -1.45 
 
 
 Zinc 
 
 -0.80 
 
 
 Aluminum 
 
 -0.53 
 
 
 Iron 
 
 -0.50 
 
 
 Carbon steel 
 
 -0.40 
 
 
 Lead 
 
 -0.30 
 
 
 Tin 
 
 -0.25 
 
 
 Copper 
 
 -0.08 
 
 
 Stainless steel 
 
 +0.07 
 
 
 (type 304) 
 
 
 
 Platinum 
 
 +0.40 
 
 
 *N.D. Tomashov, Theory of Corrosion and Protection of Metals , MacMillan, 
 1966. 
 
4-32 
 
 Although the data were generated for sea water, the metals have the same 
 order of activity in a different electrolyte. It is clear from the data 
 that if copper and aluminum are coupled, the copper will act as a 
 cathode and corrosion will be accelerated on the aluminum. 
 
 The best protection against galvanic corrosion is to avoid contact 
 between dissimilar metals. Dielectric couplers (rubber hose) may be 
 used to join two dissimilar metals in the plumbing of a solar system. 
 However, it is important to note that different alloys of the same 
 material may have significantly different electrolytic potentials, and 
 care should be taken to ensure that plumbing fittings are of the same 
 alloy as the pipe. 
 
 CORROSION BY CREVICING 
 
 Crevice corrosion is similar to pitting corrosion and results in 
 rapid loss of metal inside a crevice. The crevice can be the result of 
 bad fittings, leaky gaskets, scale deposits, blockages, or unusual flow 
 patterns. The crevice represents a restricted area where an occluded 
 cell may develop. The mechanism of crevice corrosion is that oxygen is 
 rapidly depleted inside the cell, thereby creating an anode. If there 
 is abundant supply of oxygen outside the crevice, then the area outside 
 the crevice can serve as a cathode. The small area inside the crevice 
 will become active and rapid corrosion can occur. 
 
 Crevice corrosion is perhaps a more difficult type of corrosion to 
 avoid than the previously mentioned corrosion types. The best procedure 
 is to attempt to eliminate crevices through good design, good installa- 
 tion, and filtering to remove any debris that could lead to a blockage. 
 
4-33 
 
 EROSION OF CONDUITS 
 
 Erosion corrosion is the result of mechanical removal of the pro- 
 tective film provided by an inhibitor, and it is most likely to occur 
 when high flow rates and turbulent flow conditions exist. It is aggra- 
 vated by the entrainment of air and debris. 
 
 Control of the flow rate is the best way to avoid metal erosion. A 
 general rule of thumb is to maintain flow rates less than 6 feet per 
 second. It is also recommended that a filter be used to remove debris 
 from the circulating liquid. 
 
 FREEZE PROTECTION FOR LIQUID COLLECTORS 
 
 ETHYLENE GLYCOL ADDITIVE 
 
 Experience indicates that an ethylene glycol concentration of 10 to 
 20 percent is adequate to prevent pipe and tubing from bursting when 
 exposed to temperatures well below the freezing point of the mixture. 
 If the liquid in the system is static and flow at lower temperatures is 
 not required, glycol concentrations as high as indicated in freezing 
 point tables are not necessary. But pipes leading to a collector must 
 be protected from freezing so that flow is always possible. Otherwise, 
 the liquid in the collector may boil even in midwinter and, if the 
 connecting pipes are frozen, flow cannot occur. Increased pressure in 
 the absorber tubes caused by boiling could burst thin tubes. 
 
 Adequate freeze protection for a water collector can be obtained 
 with antifreeze concentrations that are less than those required in an 
 automobile radiator, as the purpose of the antifreeze is to prevent 
 damage to the collector, but not necessarily to prevent the formation 
 
4-34 
 
 of ice crystals. In Table 4-5, the temperatures and percent ethylene 
 glycol concentration in water (by volume) will result in a slushy 
 
 Table 4-5 
 
 Concentration of Ethylene Glycol Required for 
 Freeze Protection 
 
 Percent Ethylene Glycol 
 by Volume in 
 Water 
 
 Minimum Temperature 
 for Freeze 
 Protection, °F* 
 
 
 
 32 
 
 5 
 
 26 
 
 10 
 
 16 
 
 15 
 
 2 
 
 20 
 
 -18 
 
 c Flow will not be possible below these temperatures 
 
 condition which, while very dense, does not result in damage to the 
 absorber tubes. If the corrosion inhibitor additive in the antifreeze 
 is to be effective, the minimum glycol concentration should be about 30 
 percent. For complete freeze protection in the most severe climates, 
 ethylene glycol concentrations of 50 percent are usually recommended. 
 In the presence of air, ethylene glycol degrades more readily than 
 without air. A portion of the degradation product results in an acidic 
 solution which promotes corrosion. If simultaneous exposure to oxygen 
 and elevated temperatures of the ethylene glycol solution cannot be 
 avoided, then the temperatures must be moderated. The allowable maximum 
 temperature depends upon the degree of aeration and the desired service 
 life of the solution. A temperature of 250°F may be acceptable when the 
 
4-35 
 
 only source of air is a vent or vacuum breaker line. Antioxidants are 
 helpful in some applications. 
 
 The specific heat, density, and viscosity of aqueous ethylene 
 glycol solutions vary with concentration and temperature. Of particular 
 importance is the reduction of heat capacity and increase in viscosity 
 of the mixture as concentration is increased and temperature is de- 
 creased. The effects on the properties of the fluid mixtures are shown 
 in Figures 4-9 through 4-11. In the absence of more detailed informa- 
 tion, properties for mixture concentrations different from those shown 
 will necessarily require some interpolative estimations. 
 
 ORGANIC FLUIDS FOR FREEZE PROTECTION 
 
 ( R) 
 Dowtherm J^-^is an organic fluid which has a low freezing point and 
 
 is also non-corrosive toward all metals or alloys commonly used in solar 
 
 systems, such as steel, copper, aluminum, and stainless steel alloys. 
 
 ($) (r) 
 
 The physical properties of Dowtherm J^; as well as Therminol 55 v ~', are 
 
 CRJ 
 listed in Table 4-6. Therminol 55^-^is probably not adequate as a non- 
 freezing fluid in cold climates. Silicone oils, although expensive, are 
 stable, odorless, non-corrosive, and have no freezing or boiling 
 problems. 
 
 COLLECTOR ARRAYS 
 
 The previous sections concerned individual collector modules or 
 panels, and, in general, several modules are required in a solar system 
 to provide the energy to meet the heating needs. Collector modules may 
 
4-36 
 
 70 • 
 
 1 0.66 
 
 o 
 
 C 0.64 
 
 9, 0.62 
 
 059 
 56 
 0.54 
 
 o 
 
 tf<v. 
 
 S5* 
 
 gC 
 
 GOV 
 
 60 80 100 120 140 160 ISO 
 LIQUID TEMPERATURE, °F 
 
 200 220 240 
 
 Figure 4-9. Specific Heat of Aqueous Ethylene Glycol Solutions 
 
 20 
 
 40 60 80 100 120 140 160 
 
 LIQUID TEMPERATURE, °F 
 
 180 200 220 
 
 Figure 4-10. Density of Aqueous Ethylene Glycol Solutions 
 
4-37 
 
 40 80 120 160 200 
 
 LIQUID TEMPERATURE, »F 
 
 240 
 
 Figure 4-11. Viscosity of Aqueous Ethylene Glycol Solutions 
 
 Table 4-6 
 Some Physical Properties of Dowtherm J^and Therminol 55^ 
 
 Property 
 
 Dowtherm J® 
 
 Therminol 55 ^ 
 
 Operating temperature range, °F 
 
 -100 to 575 
 
 -5 to 600 
 
 Pour point, °F 
 
 — 
 
 -40 
 
 Boiling point, °F 
 
 358 
 
 635 
 
 Flash point, °F 
 
 145 
 
 355 
 
 Fire point, °F 
 
 155 
 
 410 
 
 Auto ignition temperature, °F 
 
 806 
 
 675 
 
4-38 
 
 be assembled in parallel and in series to form a complete array. An 
 important consideration is a design by which nearly equal flow through 
 each collector can be obtained. Liquid-heating solar collectors may be 
 arranged as shown in Figure 4-12 with headers at the top and bottom of 
 the array. Satisfactory flow distribution is realized if the headers 
 are large enough for the head loss (pressure drop) from the bottom to 
 the top of each collector (column) to be above 95 percent of the total 
 head loss from A to B. 
 
 An arrangement for an array of air-heating collectors is shown in 
 Figure 4-13. The main manifold ducts are sized in accordance with the 
 volumetric air flow rates and, in the scheme shown, the manifolds within 
 the collectors are used as "headers". The specific arrangement depends 
 upon the design of the collector. 
 
 Collector arrays, for both liquid- and air-heating systems, should 
 be leak tested during or immediately after assembly. While leaks in 
 liquid systems are easy to detect, leaks in air systems are not as 
 readily located. Care in the installation of collectors, pipes, and 
 ducts, is essential. The cost of labor for careful assembly is a small 
 fraction of the cost of labor for disassembly and making repairs. 
 
 Joints in piping, particularly from the headers to the collector 
 modules, may be made with flexible hoses. Because neoprene or rubber 
 hoses require periodic replacement, the design should make replacement 
 convenient. Other piping connections and valve locations should be 
 given similar consideration. Connections from the headers to the ab- 
 sorber plates of liquid collectors cannot usually be rigid couplings 
 because of thermal expansion and contraction of the plates and headers. 
 A number of manufacturers recommend all-metal connections (for 
 
4-39 
 
 Top r 
 
 Solar 
 Collectors 
 
 •if 
 
 4 
 
 Header 
 
 B 
 
 l\ 
 
 -a- 
 
 Jr-ir 
 
 T 
 
 ii- 
 
 ■ir 
 
 -A- 
 
 -iA 
 
 r^i 
 
 Bottom 
 
 Header 
 
 Figure 4-12. Definition Sketch for Fluid Flow Distribution Through 
 a Solar Collector Array 
 
 Arrows Indicate 
 Direction of 
 Air Flow 
 
 Connections 
 
 To Collector 
 
 Manifold Ducts 
 
 Solar Heated Air : *;; 
 
 From the Collectors 
 Air to the Collecto 
 
 j 
 
 Figure 4-13. Typical Arrangement of Internally Manifolded Collector 
 Modules in an Array 
 
4-40 
 
 durability) to the solar panels, with sufficient flexibility in piping 
 and manifolding to permit expansion and contraction. Air collector 
 modules may be connected by flexible ducting or by gasketed ports. 
 
 
4-41 
 
 REFERENCES 
 
 1. Dickinson, W.S., Neifert, R.D., Lof, G.O.G., and Winn, C.B., 
 (1975). "Performance Handbook for Solar Heating Systems". 
 Presented at the 1975 International Solar Energy Society Congress, 
 University of California at Los Angeles, California. 
 
 2. Oonk, R.L., Lof, G.O.G., and Shaw, L.E., (1976). "A Method of 
 Comparing Flat-Plate Air and Liquid Solar Collectors for Use in 
 Space Heating Applications". Presented at the 1976 International 
 Solar Energy Conference, Winnipeg, Manitoba, Canada. 
 
 3. Klein, S.A. , Beckman, W.A. , and Duffie, J. A., (1975). "A Design 
 Procedure for Solar Heating Systems". Presented at the 1975 
 International Solar Energy Society Congress, University of 
 California at Los Angeles, California. 
 
 4. Johnson, S.M. and Simon, F.F., (1976). "Comparison of Flat-Plate 
 Collector Performance Obtained Under Controlled Conditions on a 
 Solar Simulator". Presented at the 1976 International Solar Energy 
 Society Annual Meeting of the American Section, Lewis Research 
 Center, Cleveland, Ohio. 
 
 5. Palerman, L.D., (1959). "The Physical Properties and Behavior of 
 Ethylene and Propylene Glycol and Their Water Mixtures". Presented 
 at the Annual Meeting of the American Society of Heating and Air 
 Conditioning Engineers, Incorporated, Philadelphia, January 26-29. 
 
 6. Private communication with D.J. Fulginiti, Antifreeze Marketing 
 Consumer Products Division, Fabrics and Finishes Department, E.I. 
 DuPont De Nemours and Company, Incorporated, Wilmington, Delaware, 
 19898. 
 
 7. Ward, J.C. and Lof, G.O.G. , (1976). "Long-Term (18 Years) Perfor- 
 mance of a Residential Solar Heating System". Solar Energy , Vol. 
 18, No. 4, pp. 301-308. 
 
 8. Duffie, J. A. and Beckman, W.A. , (1974). S olar Energy Thermal 
 Processes , John Wiley and Sons, New York. 
 
 9. Popplewell, J.M. (1977). "Corrosion Prevention in Aluminum Solar 
 Systems", Paper 170, Corrosion/77, San Francisco, California, March 
 1977. 
 
 10. Tomashov, N.D., (1966). Theory of Corrosion and Protection of 
 Metals, MacMillan and Company. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 5 
 
 HEATING AND COOLING LOAD ANALYSES 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
5-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 5-iii 
 
 LIST OF TABLES 5-iii 
 
 GLOSSARY OF TERMS 5-iv 
 
 LIST OF SYMBOLS 5-v 
 
 OBJECTIVE 5-1 
 
 INTRODUCTION 5-1 
 
 HEAT LOSSES 5-2 
 
 HEAT TRANSMISSION THROUGH BUILDING ENVELOPE ... 5-2 
 
 TRANSMISSION COEFFICIENTS 5-3 
 
 Example 5-1 - Frame Wall (2x4 studs) . . . 5-4 
 
 Example 5-2 - Frame Wall (2x6 studs) . . . 5-5 
 
 Example 5-3 - Solid Masonry Wall .... 5-5 
 
 Example 5-4 - Masonry Walls ..... 5-6 
 
 Example 5-5 - Basement Wall ..... 5-6 
 
 Example 5-6 - Insulated Ceiling, 6 inches . . 5-7 
 
 Example 5-7 - Insulated Ceiling, 9 inches . . 5-7 
 
 Example 5-8 - Floor ....... 5-8 
 
 Example 5-9 - Floor ....... 5-8 
 
 Example 5-10 - Basement Walls and Floor . . . 5-9 
 
 Example 5-11 - Pitched Roofs (Heat Flow Up) . . 5-9 
 
 HEAT LOSS BY INFILTRATION 5-9 
 
 DESIGN TEMPERATURES 5-11 
 
5-ii 
 
 
 
 
 
 
 
 Page 
 
 Temperatures c 
 
 )f Unheated Spaces . 
 
 5-11 
 
 Attic Temperature ...... 
 
 5-11 
 
 Example 5-12 - 
 Shingled Roof 
 
 ■ Attic Temp< 
 
 jratui 
 
 "e foi 
 
 r a W( 
 
 )od 
 
 5-12 
 
 Unheated 
 
 Garage 
 
 
 
 
 
 5-13 
 
 HEATING LOAD . 
 
 • 
 
 
 
 
 
 5-13 
 
 HEAT GAINS 
 
 • 
 
 
 
 
 
 5-15 
 
 TRANSMISSION . 
 
 • 
 
 
 
 
 
 5-15 
 
 INFILTRATION . 
 
 • 
 
 
 
 
 
 5-16 
 
 OCCUPANCY . 
 
 
 
 
 
 
 5-17 
 
 SOLAR EQUIPMENT 
 
 
 
 
 
 
 5-17 
 
 LATENT HEAT 
 
 
 
 
 
 
 5-17 
 
 COOLING LOAD . 
 
 
 
 
 
 
 5-17 
 
 EXAMPLE . 
 
 • 
 
 
 • 
 
 . 
 
 5-18 
 
 WORKSHEET FOR HEAT LOAD 
 
 CALCULATIONS 
 
 • 
 
 • 
 
 5-25 
 
 COOLING LOAD WORKSHEET 
 
 . 
 
 • 
 
 • 
 
 5-27 
 
 APPENDIX . 
 
 
 
 
 
 
 A5-1 
 
5-iii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 5-1 Example Residential Building ..... 5-20 
 
 A5-1 to Degree Day Maps ....... A5-23 to 
 
 A5-12 A5-34 
 
 LIST OF TABLES 
 
 Table Page 
 
 5-1 Description of Materials ...... 5-21 
 
 A5-1 Surface Conductances and Resistances for Air Films. A5-2 
 
 A5-2 Resistance Values for Air Spaces .... A5-2 
 
 A5-3 Resistance Values for Building Materials . . A5-3 
 
 A5-4 U Factors for Windows and Patio Doors 
 
 Btu/(hr)(ft 2 )(°F) A5-4 
 
 A5-5 U Factors for Solid Doors Btu/(hr)(ft 2 )(°F) . . A5-5 
 
 A5-6 Air Changes for Average Residential Conditions . A5-5 
 
 A5-7 Design Equivalent Temperature Differences (°F) . A5-6 
 
 A5-8 Design Heat Gains Through Windows Btu/(hr)(ft 2 ) . A5-7 
 
 A5-9 Shade Line Factors (5 hour average, 1 August) . A5-8 
 
 A5-10 Heating Degree Days and Design Outdoor 
 
 Temperature ........ A5-9 
 
5-iv 
 
 GLOSSARY OF TERMS 
 
 Cooling Load 
 Conductance 
 
 Design Equivalent 
 Temperature Differen- 
 tial 
 
 Heat Gains 
 
 Heat Loss 
 
 Heat Transmission 
 Losses 
 
 Heating Load 
 Infiltration Gain 
 
 Infiltration Loss 
 
 R value 
 U value 
 
 Rate of heat removal from a building to 
 maintain constant indoor temperature. 
 
 Expresses the ease or difficulty of materials 
 to conduct heat from the high temperature side 
 to the low temperature side. 
 
 Temperature differential between outdoor and 
 indoor temperature adjusted for effects of sur- 
 face absorptance of solar energy and radiation. 
 
 Rate of heat flow into a building per unit 
 time, usually one hour. 
 
 Rate of heat flow out of a building per unit 
 time, usually one hour. 
 
 Heat loss. 
 
 Rate of heat supply to a building to maintain 
 constant indoor temperature. 
 
 Infiltration of hot air into a building which 
 must be cooled to the comfort level of the 
 building air. 
 
 Infiltration of cold air into a building which 
 must be heated to the comfort level of the 
 building air. 
 
 Thermal resistance of materials to flow of 
 heat. 
 
 Heat transfer coefficient for material. 
 
5-v 
 LIST OF SYMBOLS 
 
 2 
 A Area of heat transfer surface, ft 
 
 f. Air film conductance for still air on inside surface of the 
 1 building, Btu/(hr)(ft 2 )(°F) 
 
 f Air film conductance for moving air on outside surface of the 
 building, Btu/(hr)(ft 2 )(°F) 
 
 Q Heat flow rate, Btu/hr 
 
 2 
 R Thermal resistance of building materials, (hr)(ft )(°F)/Btu 
 
 2 
 R. Thermal resistance of inside air film, (hr)(ft )(°F)/Btu 
 
 2 
 R Thermal resistance of outside air film, (hr)(ft )(°F)/Btu 
 
 R. Total thermal resistance for composite building components, 
 (hr)(ft 2 )(°F)/Btu 
 
 T. Design inside temperature, °F 
 
 T« Design garage temperature, °F 
 
 T Design outdoor temperature, °F 
 
 U Heat transfer coefficient, Btu/(hr)(ft 2 )(°F) 
 
 U Q Overall heat transfer coefficient, Btu/(hr)(ft 2 )(°F) 
 
 3 
 V Volume change of air in the rooms per hour, ft /hr 
 
 W- Humidity ratio of indoor air, dimensionless 
 
 W Humidity ratio of outdoor air, dimensionless 
 
5-1 
 
 OBJECTIVE 
 
 The objective of this module is to present methods for estimating 
 heat losses and gains in buildings. From the information contained in 
 this module the trainee should be able to: 
 
 1. Determine heat transmission coefficients. 
 
 2. Compute heat transmission losses. 
 
 3. Compute the heating load of a building. 
 
 4. Compute the cooling load of a building. 
 
 INTRODUCTION 
 
 Proper sizing of space heating and air-conditioning equipment 
 requires knowledge of heating and cooling loads in a building. This 
 applies to solar systems as well as conventional equipment. Oversizing 
 of conventional space-conditioning equipment which has been prevalent in 
 the past, especially for residential buildings, leads to inefficient 
 operation. On the other hand, undersizing is not acceptable from a 
 standpoint of comfort. Oversizing of solar systems is not advisable 
 because of high initial cost, but undersizing may not provide signifi- 
 cant savings of conventional fuels. It is therefore important to make 
 accurate calculations of heating and cooling loads for proper sizing of 
 solar as well as conventional equipment. 
 
5-2 
 
 HEAT LOSSES 
 
 Heat transmission losses, or more simply heat losses, from 
 buildings occur in two significant ways: (1) transmission losses 
 through walls, floor, ceiling, glass and other surfaces and (2) infil- 
 tration losses through cracks and crevices in the walls and through open 
 doors and windows. 
 
 HEAT TRANSMISSION THROUGH BUILDING ENVELOPE 
 
 The rate of heat flow, Q, into or out of a building enclosure 
 depends upon the surface area, A, an overall heat transfer coefficient, 
 U, and the air temperature difference between the inside, T., and out- 
 side, T . Expressed in equation form: 
 
 Q = UA(Ti " V (Btu/hr) ( 5 -V 
 
 The overall heat transfer coefficient, often called the U factor , 
 
 is the reciprocal of the total thermal resistance, R T , and is expressed 
 
 as 
 
 and 
 
 U = 1- [Btu/(hr-ft 2 -°F)] (5-2) 
 
 R T 
 
 R T = R, + R + R + R. + ... + R (5-3) 
 
 12 3 4 n 
 
 where the R Factors Rl' R 2' etc ' ' are individual resistances of the wall 
 components. 
 
 Heat is transferred from inside air to the inside wall surface 
 through a thin film of air adjacent to the wall surface. This air film 
 has a resistance, R., which is the reciprocal of the film conductance, 
 f., and may be determined by 
 
5-3 
 
 R i = 77 • (5 " 4) 
 
 Similarly, there is a thin air film at the outside surface, with con- 
 ductance f , which provides some resistance to heat flow. The resis- 
 o r 
 
 tance of the outside air film, R , is 
 
 R o = f • < 5 " 5 > 
 
 o 
 
 Surface conductances and resistances for air films for interior and 
 exterior surfaces, in winter and summer, are tabulated in Table A5-1 of 
 the Appendix to this module. The winter values are based on wind velo- 
 city of 15 mph and summer values are based on wind velocity of 7 mph. 
 
 Dead air spaces between walls offer thermal resistance. The 
 resistance values are tabulated in Table A5-2 for 3/4-inch and 4-inch 
 spaces for winter and summer conditions. For spaces between 3/4 inch 
 and 4 inches, values may be interpolated. 
 
 Thermal resistances of common building materials are tabulated in 
 Table A5-3. U factors for windows and patio doors are listed in Table 
 A5-4, and U factors for solid doors with and without storm doors are in 
 Table A5-5. The values in these tables correspond with more complete 
 tables listed in Chapter 20, ASHRAE Handbook of Fundamentals (1972). 
 
 TRANSMISSION COEFFICIENTS 
 
 The procedure for determining the overall heat transmission 
 coefficients, U, for typical wall, roof, ceiling and floor construction 
 is presented in this section. The values of R for materials and compo- 
 nents are found in Tables A5-1 through A5-5. U factors for composite 
 construction are determined in the following examples and U factors for 
 other types of construction may be calculated by following these 
 examples. 
 
5-4 
 
 Example 5-1 - Frame Wall (2x4 studs) 
 
 ITEM 
 
 1. Outside film (15 mph wind, winter) 
 
 2. Siding, wood (h x 8 lapped) 
 
 3. Sheathing (h inch regular) 
 
 4. Insulation batt (3-3% inch) 
 
 5. Gypsum wall board (h inch) 
 
 6. Inside surface (winter) 
 
 Total Resistance, Rj 
 U = 1/R T 
 
 0. 
 
 17 
 
 0. 
 
 81 
 
 1. 
 
 32 
 
 11. 
 
 00 
 
 0. 
 
 45 
 
 
 
 68 
 
 14.43 
 0.07 
 
 The calculated U factor applies to the area between 2x4 studs. 
 Because the resistance to heat flow through the 2x4 stud is different 
 from the insulation, a correction is sometimes considered. However, the 
 correction is usually small, amounting to less than the accuracy of the 
 R values, and therefore unnecessary. 
 
5-5 
 
 Example 5-2 - Frame Wall (2x6 studs) 
 From Example 5-1 
 
 R T 
 
 Replace 3^- inch insulation, subtract 
 
 Add 5^-inch insulation 
 
 New R T 
 
 U = 1/R T 
 Difference in U from Example 1 
 Percent Difference from 2x4 wall 
 
 14.43 
 
 11.00 
 
 3.43 
 19.00 
 
 22.43 
 
 0.04 
 
 0.03 
 
 43 percent 
 
 There is 43-percent reduction in heat loss for a 2 x 6 wall as 
 compared with a 2 x 4 wall with correspondingly thicker insulation in the 
 2 x 6 wall. 
 
 Example 5-3 - Solid Masonry Wall 
 
 ITEM 
 
 1. Outside film ( 15 mph wind, winter) 
 
 2. Face brick (4 inch) 
 
 3. Common brick (4 inch) 
 
 4. Air space (3/4 inch) 
 Gypsum board (h inch) 
 Inside surface 
 
 Total Resistance, Rj 
 U = 1/R T 
 
 ^^ 
 
 R 
 
 0.17 
 0.44 
 0.80 
 1.28 
 0.45 
 0.68 
 3.82 
 0.26 
 
5-6 
 
 Example 5-4 - Masonry Walls 
 
 ITEM 
 
 1. Outside surface (15 mph) 
 
 2. Face brick (4 inch) 
 
 3. Cement mortar (h inch) 
 
 4. Cinder block (8 inch) 
 
 5. Air space (3/4 inch) 
 
 6. Gypsum board (h inch) 
 
 7. Inside surface 
 
 Total Resistance, FL- 
 
 U = 1/R-r 
 
 0.17 
 0.44 
 0.10 
 1.72 
 1.28 
 0.45 
 0.68 
 4.84 
 0.21 
 
 12 3 4 5 6 7 
 
 Example 5-5 - Basement Wall 
 
 ITEM 
 
 1. Concrete wall (8 inch) 
 
 2. Insulation batt (2 inch) 
 
 3. Gypsum board (h inch) 
 
 4. Inside surface 
 Total Resistance, R-p 
 U = 1/R, 
 
 _R 
 
 0.64 
 7.00 
 0.45 
 0.68 
 8.77 
 0.11 
 
 I 2 3 4 
 
5-7 
 
 Example 5-6 - Insulated Ceiling, 6 inches 
 
 ITEM 
 
 1. Inside surface 
 
 2. Insulation batt (6 inch) 
 
 3. Gypsum board (h inch) 
 
 4. Inside surface 
 
 Total Resistance, Ry 
 U = 1/R T 
 
 
 
 68 
 
 19. 
 
 00 
 
 
 
 45 
 
 0. 
 
 68 
 
 20.81 
 0.05 
 
 Example 5-7 - Insulated Ceiling, 9 inches 
 
 ITEM 
 
 1. Inside surface 
 
 2. Insulation (9 inch) 
 
 3. Gypsum board (h inch) 
 
 4. Inside surface 
 
 Total Resistance, R T 
 
 U = 1/R T 
 Percent decrease of U with 9- inch insulation over 
 6-inch insulation, 20 percent 
 
 R 
 
 0.61 
 24.00 
 
 0.45 
 
 0.61 
 25.67 
 
 0.04 
 
5-8 
 
 Example 5-8 - Floor 
 
 ITEM 
 
 1. Top surface 
 
 2. Linoleum or tile 
 
 3. Felt 
 
 4. Plywood (5/8 inch) 
 
 5. Wood subfloor (3/4 inch) 
 
 6. Air space 
 
 7. Acoustic ceiling tile (3/4 inch) 
 
 8. Surface 
 
 Total Resistance, Rj 
 U = 1/R, 
 
 0.61 
 0.05 
 0.06 
 0.78 
 0.94 
 0.85 
 1.89 
 0.61 
 5.79 
 0.17 
 
 I 2 3 4 5 6 7 8 
 
 Example 5-9 - Floor 
 
 ITEM 
 
 1. Carpet and fibrous pad 
 
 2. Plywood (3/4 inch) 
 
 3. Insulation (9 inch) 
 
 4. Surface (still air) 
 
 Total Resistance, R, 
 U = 1/R, 
 
 R 
 
 2.08 
 
 0.93 
 
 24.00 
 
 0.61 
 
5-9 
 
 Example 5-10 - Basement Walls and Floor 
 
 A heat transfer coefficient, U, for basement walls and floors of 
 0.10 Btu/(hr«ft '°F) is generally conservative because (dry) earth adds 
 to overall thermal resistance. A ground temperature equal to the ground 
 water temperature (generally 45°F to 55°F) is appropriate for use as the 
 outside temperature in Equation (5-1). 
 
 Example 5-11 - Pitched Roofs (Heat Flow Up) 
 
 ITEM R 
 
 1. Outside surface (15 mph) 0.17 
 
 2. Asphalt shingle roofing 0.44 
 
 3. Building paper 0.06 
 
 4. Plywood deck (5/8 inch) 0.78 
 
 5. Inside surface 0.61 
 
 Total Resistance, R T 2.06 
 
 U = 1/R T 0.49 
 
 HEAT LOSS BY INFILTRATION 
 
 There are two methods for estimating infiltration losses, the 
 "crack" method and the "air change" method. Of the two methods, the 
 air change method is simpler and easier to use and is the one discussed 
 in this module. Details of the crack method are explained in the 
 
5-10 
 
 ASHRAE Handbook of Fundamentals (1972). In either method, the objective 
 is to determine the amount of heat required to raise the temperature of 
 cold air which enters a building through cracks, open windows, and 
 doors, to room temperature. 
 
 The volume of cold air expected to enter a building through cracks 
 during a one-hour period depends on such factors as wind direction and 
 speed, pressure differences inside and outside the building, whether 
 there are storm windows and doors or air locks on outdoor entrances. 
 The entering volume of cold air may be expressed in terms of the volume 
 of the room or the building interior and the number of air changes per 
 hour. The average air changes for rooms with various fenestrations 
 listed in Table A5-6 are in accordance with Chapter 19, ASHRAE Handbook 
 of Fundamentals (1972). 
 
 From the air change rate the contribution to the heating load by 
 infiltration is calculated from 
 
 Q = 0.018 V (T- - T Q ) (5-6) 
 
 3 
 where V is the volume change per hour (ft /hr) and Q is the increase in 
 
 heating load, Btu/hr. 
 
 When moisture is added to air to maintain winter comfort 
 
 conditions, heat will be required to evaporate water which adds to the 
 
 building heating load. The added heating load is: 
 
 Q = 79.5 V (Wi " V (5 " 7) 
 
 u w- 4-u •4T-14.+- 4. /4T4.3/. x ,,. is humidity ratio of 
 where V is the infiltration rate (ft /hr), Wi J 
 
 indoor air, and W is humidity ratio of outdoor air. 
 o 
 
5-11 
 
 DESIGN TEMPERATURES 
 
 The "design" indoor temperature, T. , in Equation (5-1) is somewhat 
 arbitrary, with 70°F commonly used for heating load calculations. When 
 the procedure for heat load calculations was developed during the 1940's 
 and early 50' s to size natural gas furnaces, the design indoor tempera- 
 ture was 75°F. With modern building construction practices and 
 materials a lower indoor temperature may be used. The lower indoor 
 temperature leads to smaller design heat loss rates and smaller 
 furnaces. 
 
 The design outdoor temperature, T , is based on a statistical 
 analysis of the hourly temperature readings in December, January, and 
 February. For residential buildings a temperature is selected such that 
 99 percent of the time during those months, the air temperature is 
 higher than that value. For non-residential buildings a 97.5 percent 
 temperature is recommended. Design temperatures for residential build- 
 ing calculations are listed for various cities in Table A5-10 in the 
 Appendix. 
 
 Temperatures of Unheated Spaces 
 
 Attic Temperature - The attic temperature is determined from a 
 
 steady-state balance of heat flow into and out of the attic. Heat flow 
 
 into the attic is from the ceiling; heat flow out is through the roof 
 
 surfaces and end walls. The general formula for determining attic 
 
 temperature is: 
 
 A U T + T (A U +AU) 
 t - c c c o v r r w w y >£ ft \ 
 
 'at AU+AU+AU ^~ o; 
 
 c C V V WW 
 
5-12 
 
 where 
 
 at 
 
 A. 
 
 A 
 
 w 
 
 w 
 
 is attic temperature, °F 
 is room temperature, °F 
 
 is outside temperature, °F 
 
 2 
 is ceiling area, ft 
 
 2 
 is roof area, ft 
 
 2 
 is roof wall area, ft 
 
 is ceiling U factor, Btu/(hr)(ft 2 )(°F) 
 
 is roof U factor, Btu/(hr)(ft 2 )(°F) 
 
 is wall U factor, Btu/(hr)(ft 2 )(°F) 
 
 Example 5-12 - Attic Temperature for a Wood Shingled Roof 
 
 Calculate attic temperature for a wood shingled roof with the 
 given dimensions. T is -9°F, T is 68°F. See Example 5-6 for 
 ceiling U factor, U = 0.05. See Example 5-11 for roof U factor, 
 U = 0.49. For Example 5-1 a wall with no insulation has a U 
 
 factor of: 
 
 R-p from Example 5-1 
 Subtract insulation 
 Subtract gypsum board 
 
 Total Resistance, Rj 
 
 U w = 1/R T 
 
 14.43 
 
 -11.00 
 
 - 0.45 
 
 2.98 
 
 0.34 
 
 Calculated Area: 
 
 w 
 
 30 x 50 = 1500 ftT 
 
 V2 x 15 x 50 x 2 = 2120 ft 2 
 
 30 x 15 x h x 2 = 450 
 
5-13 
 
 t ~ (1500)(0.05)(68) + (-9)[(2120)(0.49) + (450)(0.34)] 
 'at (1500)(0.5) + (2120)(0.49) + (450)(0.34) 
 
 T 5100 - 10,726 . 9 q or 
 
 'at ~ 75 + 1039 + 153 *•*■-• 
 
 When ventilation is provided, at 0.5 cfm per square foot of 
 ceiling, the attic temperature must be reduced from those calculated in 
 Example 5-12. Thus, the attic temperature approaches outdoor tempera- 
 ture. Attic temperature may be assumed to be the outdoor temperature 
 with well- insulated ceilings without significant error in heat loss 
 calculation . 
 
 i 
 
 Unheated Garage - With similar detailed calculations it can be 
 shown that the temperature in an unheated garage is nearly equal to the 
 mean of the indoor and outdoor temperatures. Since the garage tempera- 
 ture is subject to large changes, a simple calculation to estimate the 
 garage temperature is satisfactory, and T~ is used in Equation 5-1 in 
 place of T . An unheated garage temperature may be estimated from 
 
 T G = ° 2 n . (5-9) 
 
 HEATING LOAD 
 
 An example heat loss calculation is presented for a house in Fort 
 Collins, Colorado. The building and plans are shown in Figure 5-1, and 
 the description of materials is given in Table 5-1. The windows in all 
 bedrooms are 3' x 4 1 , double hung, single pane, wood sash with storm 
 windows having 3- inch air space. The window in the bathroom is 2' x 2' , 
 
5-14 
 
 double hung, single pane, wood sash with storm window. The window in 
 the living room is 4' x 8 1 , wood sash, double glass with ^-inch air 
 space. The window in the kitchen is 2.5 1 x 4 1 double hung, single pane, 
 wood sash with storm window. The window in the breakfast nook is 3 1 x 
 4 1 double glass, wood sash with Vinch air space. The 6' x 6 1 sliding 
 patio door in the family room is double-glass wood frame with ^-inch air 
 space. The basement windows are IV x IV and will be ignored in this 
 calculation. Bathrooms and kitchen are ventilated. 
 
 A worksheet is used to facilitate heat load calculations. The 
 design winter temperature for Fort Collins, Colorado, is not listed in 
 Table A5-10, but is taken to be -9°F. The design indoor temperature is 
 chosen to be 68°F. The total heat loss rate from the building using the 
 design temperatures is 53,215 Btu per hour (see page 2 of worksheet). 
 
 Heating loads for each month of the year may be calculated from the 
 heat loss rate and information on the average number of degree days in 
 the month. A degree-day is the difference between 65°F and the average 
 temperature during a 24-hour period, where average temperature is the 
 mean of the high and low temperature. Thus if the average temperature 
 for a 24-hr period is 64°F, there would be one degree-day for that day. 
 The sum of the degree days for each day of the month results in the 
 total degree days for the month, and the sum of the degree days in each 
 month results in the annual degree-days. Monthly and annual degree days 
 for a number of cities in the United States are listed in Table A5-10. 
 Maps of heating degree days are also provided in Figures A5-1 through 
 A5-12 and may be used for locations that are not tabulated in Table 
 A5-10. 
 
5-15 
 
 To calculate monthly and annual heating loads, calculate the unit 
 heating load for the building, 0™, from Equation (5-10) 
 
 Qnn - n — . He , at Los ^ Rat * . x 24(Btu/DD) (5-10) 
 
 X DD Design Temperature Diff. v ' v ' 
 
 For the example building, the unit heating load is 
 
 Q D D = 5 68 2 - 5 (-9) 4 = 16590 Btu/DD 
 
 and using the annual heating degree days for Denver, from Table A5-10, 
 the annual heating load for the building, L, is 
 
 L - 16590 x 6283 = 104.2 MMBtu 
 
 where MMBtu is an abbreviation for million Btu. 
 
 Using the calculations performed above, the furnace for the 
 building should have a heat output capability of about 55,000 Btuh. It 
 will be noted that the contractor has specified a hot water heating 
 system with a 120-150 Btuh capability which is 2.5 to 3 times the re- 
 quired capacity, and leads generally to inefficient water boiler opera- 
 tion because of excessive on-off cycling for short intervals of opera- 
 tion at lowered efficiency. 
 
 HEAT GAINS 
 
 TRANSMISSION 
 
 Heating of air inside a building takes place by radiation and 
 conduction from building surfaces and by infiltration of warm air into 
 conditioned space. The detailed procedure for calculating heat gains 
 into a building is quite complex, taking into account the thermal and 
 optical properties of the building materials, time of day, day of the 
 year, solar radiation intensity, etc. The procedure described in this 
 
5-16 
 
 module is based on a simplified method using a design equivalent 
 temperature difference (DETD). 
 
 Heat gain is then computed by: 
 
 Q = UA(DETD) (5-11) 
 
 where 
 
 Q is rate of heat gain, Btu/hr 
 
 A is area of surface, ft 
 
 U is heat transmission coefficient, Btu/(hr*ft *°F) 
 
 DETD is design equivalent temperature difference. 
 
 The DETD's for three design outdoor temperatures are listed in 
 Table A5-7. U factors for typical construction may be computed in the 
 manner shown in Examples 5-1 through 5-11. Heat gain through windows 
 depends upon exposure to the sun and will differ for different window 
 orientations as listed in Table A5-8. No credit is given for shade line 
 below an overhang in the table. When a permanent overhang is provided, 
 the shaded window may be treated as a north-facing window. Average 
 shade lines below an overhang for various latitudes and window orienta- 
 tions are given in Table A5-9. The overhang width multiplied by the 
 shade factor determines the average effective shadow lines below the 
 level of the overhang. Data are for August 1, averaged over 5 hours. 
 
 INFILTRATION 
 
 Infiltration in the summer is less than in winter because the 
 
 temperature difference and wind velocity are usually less. Air changes 
 
 per hour for the summer are listed in Table A5-6. Sensible heat gain is 
 
5-17 
 
 determined by Equation (5-7) and latent heat gain by Equation (5-8). 
 Residential cooling loads are almost always based only on sensible heat 
 gains. 
 
 OCCUPANCY 
 
 Heat gain from human occupancy in a residence is usually assumed to 
 be about 300 to 400 Btu per hour per person. For normally equipped 
 kitchens, heat gains from electrical appliances may amount to 1200 Btuh 
 although larger values may be applicable for homes with many appliances. 
 
 SOLAR EQUIPMENT 
 
 Heat gains (losses) from solar equipment in a residence, such as 
 storage tanks, motors, heated pipes and ducts, will add to the cooling 
 
 load. The heat gain could be significant from water storage tanks if 
 
 the insulation is inadequate and the equipment room is not vented. A 
 
 heat gain equivalent to the kitchen load, 1200 Btuh, may be assumed if 
 the solar storage tank is used during the summer. 
 
 LATENT HEAT 
 
 A latent heat load of 30 percent of the sensible heat load is 
 generally applicable for residential buildings. 
 
 COOLING LOAD 
 
 The distinction between maximum heat gain rate and cooling load is 
 important in selecting the size of air-conditioning equipment. There 
 are relatively few days each season with high heat gains, and a partial 
 load condition exists for many hours during a season. Thus, cooling 
 
5-18 
 
 equipment sized on the basis of maximum heat gain rate would be 
 oversized, and would not perform efficiently because of intermittent 
 cycling. Equipment should be designed to operate continuously for 
 several hours a day in the warmest months. 
 
 EXAMPLE 
 
 The cooling load for the house of Figure 5-1 is calculated as shown 
 in the Cooling Load Worksheet, pages 5-27 and 5-28. The outdoor design 
 temperature is 89°F (not listed in Table A5-10 for Fort Collins). The 
 indoor design temperature is 75°F. The U factors for walls, ceiling and 
 door are the same as for winter conditions. Refinements in U factors 
 were not made in these computations although the R factors in air films 
 in Tables A5-1 and A5-2 would result in slightly different R factors. 
 
 The overhangs over the south-facing windows effectively reduce the 
 heat transfer rates to values equivalent to the north-facing windows, 
 and there are no east- and west-facing windows. No credit is taken for 
 shades or drapes over the windows. 
 
 The temperature in the garage was assumed to be the mean between 
 indoor and outdoor design temperatures, and the design equivalent tem- 
 perature differences (DETD) given in Table A5-7 were interpolated for 
 the design outdoor temperature of 89°F. 
 
 The total cooling load for the building is calculated to be 18,621 
 Btuh. This low cooling load is a result of low design outdoor tempera- 
 ture in Fort Collins, 89°F, and a building which is insulated properly 
 with shading over windows. The values used apply for average summer 
 conditions, so on days when temperatures reach 95°F, greater cooling 
 
5-19 
 
 capacity is required. If not provided, interior temperature will rise 
 above the desired setting. But if the air-conditioner is sized for the 
 outdoor design temperature of 89°F, it will operate continuously in hot 
 weather, and temperature excursions inside the building should not be 
 large. 
 
5-20 
 
 JBBLSggRABgfl 
 
 2078+f z -2 flo 
 plus 1182 f t 2 - Base 
 
 3 26 ft 2 
 
 Colonial two-story with all the neces- 
 sary size and luxury for a large or 
 growing family • Four Bedrooms and 
 Two Baths on the Second Floor • 
 Large Entry With Open Stairway • 
 Spacious Living Room • Formal Din- 
 ing Room • U-Shape Kitchen With 
 Eating Space • Family Room With 
 Fireplace Located Next To Kitchen 
 • Full Unfinished Basement • Two 
 Car Garage • Paneling 
 
 3 ft. overhang 
 32.' _ 
 
 TFlhw 
 
 £ 
 
 Ii> 
 
 '""(J 
 
 
 PANTRY 
 
 ■ 2 -_ 
 
 O - 
 
 CD 
 
 2*r 
 
 286 
 
 m 
 
 - 54' 
 a— "~^ 
 
 32 
 
 -i FUTURE 
 • ' '"f\\ BATH 
 
 u 
 
 H 
 
 FURNACE 
 
 CZZIO 
 
 Si'i 
 
 II 
 
 H 
 
 i 
 
 FULL BASEMENT 
 
 - 3i' 
 
 *Roof Overhang 3 ft. 
 
 
 Figure 5-1. Example Residential Building 
 
 PLAN 809 
 
5-21 
 
 Table 5-1 
 
 THA Yum JOOS 
 VA rare. 26-1 Sl> 
 Rat. 1/74 
 
 D fropot*d Construction 
 □ Uod«r Construction 
 Property addnu , 
 
 klNHIWl 0« MUM lOullU C*«UO~>laf 
 
 IIHllv MUmO UkuwtUallO* 
 far Weeraie rv|UMt mi tirh*i ra*Mi. ferra 
 Mir be •eearaire' aluae »a~.« Me gteple 
 tf«W#>J«»4 dK*iIi |»|~hl« in •tigUsI <**«*. 
 
 DESCRIPTION OF MATERIALS no. 
 
 See— A iff 1*4 
 MB Ne. M-HOOU 
 
 it! E Em3 WMa . Va7 
 
 Ory. 
 
 Srtrfo. 
 
 Mortpofjor or Sponior 
 
 (Na«-I 
 
 Confrorior or 8t/l'rdtr Rarrran Hnmp« Tt> 
 
 (Na— r) 
 
 INSTRUCTIONS 
 
 1. For additional information an how this form It to be aubroJtted. 
 a_abaf of cootee. etc.. •♦« we inacructione applicable to the FHA 
 Application for Mortgage Ineurance or VA Reo^ieel for Determination of 
 Reaaonable Value, mm the caae tray ba. 
 
 2- Deecnbe all meteriala and equipment to ba uaed, whether or not 
 ahowr. on tha drawtrura, °y marking an I Ln aach appropriate check-boa 
 and entering the Information called for m aecti apaca. If apaoa la 
 Inadequate, enter "See rruac" and deaenbr undar Hem 77 or on an 
 attached aheet. THE USE OF PAINT CONTAJfflNG MORE THAN FrVE- 
 TUfTH- OF OKI PERCENT LEAD OY VFJCHT IS HHOinnTtD. 
 
 3^ Wort not apecifically aaambad or anown will not ba c<— aidered 
 
 unlaaa — <aiired. than the minimum acceptable will ba aeeumed. Work 
 eaceedinf minimum rsoairementa cannot ba coneldered unleee apaaflcaJly 
 deecnbe_ 
 
 *• Include no allemetee. "or etaiaJ" phraaaa. or contradictory ueme- 
 (Conaldarauon of a — queet for acceptance of aubauruta materia— or 
 exaiipmentle not thereby precluded.) 
 
 5. Include elgnaruree required at lha and of thit form. 
 
 a. The conto-ucuun oh. II ba completed in compllanca with tha rettled 
 d/awtno and ecwclficationa, aa amended duruii procaaama, Tha ape-fice- 
 •Jone include thia Daacnpnon of Matanala and applicable kUrumum Pro- 
 P*ny 9 1 *n«i» ni a. 
 
 I. IXCAVATlONi 
 
 Bearing aoj. type 
 
 3. FOUNOATIONSi 
 Feaxlnp: cone rata mU 
 
 Clnv 
 
 _._. 
 
 Mratifth pal 2S00M 
 
 .enema 
 
 Faundailan wall: material 
 
 laorrlar foundation wall material 
 
 Calumm: malarial and ilari aeo plans 
 
 Cl/den: material and naet «r»a plan*. 
 
 Baaemeni arKnuaca areaway ____________ 
 
 WaurprocAof hot «p rav ftephalt 
 
 Tar milt i 
 
 Party bundailoa wall 
 
 Reinforcing , 
 Reinforcing , 
 
 **HW 
 
 see plans 
 
 Pirn: malarial and reinforcing 80fl plana 
 
 Silli: malarial 
 
 Window araawa- _Bfl plans 
 
 Footing draiaa QflXLfl 
 
 proucuoa 
 
 Baaemeni— u (pace: ground cover . 
 Special (Mindauoaa 
 
 55lf felt 
 
 Inaulailon . 
 
 .. fbundation ^r-Lbird screen 
 
 Addiiiooal iaJormaiion: 
 
 3. CHlMNfYSi 
 
 Maicrial wntal 
 
 riua lining: macahal 
 
 Prafabricated f»«aar tnd net) . 
 Heater Aua liar Si 
 
 FircpUcc Aua im 3L I . D - 
 
 Venu ^nflrrWiaf Ji{r/- gat or oil healer ^^^^_____^____— 
 
 Additional information: _^_^___^__^_^_„^_________„__ 
 
 4. HWPIACES: 
 
 Type: Q tolid fuel, □ gat-buminf; Q circulator f m*Ju *»4 no) . 
 rirrpUce: facing Ryir-lr l/>Tiriir ■ Un.ng auitfl] 
 
 water heater . 
 
 Aah dump and clean^ut 
 
 haanh . 
 
 hrirk 
 
 . . mantel ttTinrl 
 
 AddiUonal Inbrmatlon: Hunt i lnrny Marlr \23 Mnrlal ^O^fS. 
 
 S. IXmiO* WALUi 
 
 Waod frama: wood grade, and •prcict W.C. CfniT f \r 
 
 •naalhiaf i n a..1 b«o r rl j thklmeu Jai! ; width . 
 
 MU, W00( 
 
 «WiwrUa. 
 Sauce* 
 
 . ; grade . 
 . i grade . 
 
 Ihlckn 
 
 type — 
 
 typa. 
 ; Lath 
 
 Q Corner bracing. Building paper or (ell ^________^___- 
 
 I CD aoltdi □ tpacad * a. c, Q diagonal; 
 
 i llae ; mpoaure *, Culenlng g_aV . Beai 1 6 
 
 i tiae ' eapoture *, (aliening Q il 1 " n t J 1 6 
 
 lb. 
 
 Maaonry vtnmt 
 
 Slllt. 
 
 U»iaU n a n *) 
 
 Maaonry: O >alid Q bead Q ttuccoed; total wall thicaneu . 
 
 Backup malarial 
 
 Door -lb Window i.IU 
 
 Interior auriecee. dampprooring, coara a/ ______ 
 
 A—diuonal loformalion: _________ 
 
 "; lacing thlcLneaa . 
 m l thlekneat 
 
 ; weight . 
 
 Bate flaihmg raatfta — 
 facing maierial ______ 
 
 bonding . 
 
 Lia-la 
 
 Baae Aa thing . 
 
 furring 
 
 —urrior pairoing: maiar— I J o n ag Blai r »*. X .» r i.o r pai nt 
 
 Cable wall conatrucuon: JQ tame al main walla, Q other coniiructioa 
 
 •. FIOOC; FILAMJNO: 
 
 Jo-u. wood, grade, and ipecin -W_G_ — e onst i — r-iT° ,hc ' 
 
 _; number of coait J 
 
 ; bridging — J^^J. 
 
 anchon LM- } at— 
 _ . ihKkneaa ___ 
 
 CoaoTW slab. _) baarm enl Aoor, O f\ru Aoor; Q ground aupponed; Q aclf-auopordne;; mm S Caok 
 
 nmtonmi 6 / 6-1 0/ 1 UVF : inluUtion . membrane p<> 1 y M T-O t h ft ne) 
 
 grawl ; ih«:k_a_ — 4_ 
 
 Ptl lander alab: nu i— al , 
 
 Addufe—tJ iataar - laiioni 
 
 7. SUtFlOOtlNOl (Oatcnba vndwrflooring for tp+uol floor* unoW mam 2 1 .) 
 Malarial: grade and •peeart 1 / 4 '' t U flg a n d | f » » V t 
 
 -f*«- 
 
 -e^- 
 
 Laid: Q Aral floor; _) arcond Aoor; Q ailK . 
 
 . tq. A-l Q duuronal; QQ rta>> ejurlca. Additional laformaiMei: 
 
 I. P)N|(H PlCOeiNO. 'Wood* only. Oatcnbo oikmt Hnuh Roofing undwr .ham 21.) 
 
 Pint Hoar 
 
 Ank Baor_ 
 Additional Infer— ia 
 FHAfw— TtVrt 
 
 .e.,. » 
 
 rcai ni 1 
 
5-22 
 
 Table 5-1 (continued) 
 
 DESCRIPTION OP MATERIALS 
 
 ». PARTITION PSAMINOi 
 
 ftrucU wood, |rade, and ipecta — DL£ rnuU fix tiat tad f— ^ 7ri * 7il " " r 
 
 AddMonai t-fa""-" Rearing Wa I 1 «. • ?t4 fl 1 ft" n c 
 
 ia CBUNO FJUMJNOt 
 
 OUrfr. 
 
 Joott: wood, fradr, tad tpacjc* Other _ 
 
 AdtMofuJ WoftnlbM: tinier ( m affarhaM dfil) 
 
 II. SOOP PRAMINOt 
 
 RjlUn: wood, grade, and ip>cir« Ran 
 
 Additional Information: fruit (ma att;mhfld i J • t m Jl 1 ) 
 
 II KOOflNOi 
 
 ■ridfUc. 
 
 (tot dauil): erad* tad ipodn . 
 
 45 ° pitch 
 
 •haethlaf,: wood, grttir, and •p~' L - 1," P II plyvonri 
 
 lUoAaf Aaphalt ; n»d« 21St 
 
 U.dorUy_E«j4 
 
 Built-up rooAnf ____________^__________ 
 
 FWhine: material -ply. TiTll 
 
 Additional U/ormtuon: 
 
 , | (3 "•Hi O »p«o«d . 
 
 .i tim. 
 
 . i weijht «r talchocat _J^£_ 
 . ; MBbir of pllet _^___ 
 . i |t(i or wrlejht J£_ 
 
 ,| ilea 
 
 ; •urfadaf material . 
 
 .1 fcattwW y a U , n n U i 
 
 -• D ptvtl ttope; O «°*w fuarde 
 
 19, OVTTIU AND DOWNSPOUTSi 
 
 Gurtm: material C3lv . 
 
 DbwnipouU: material C a 1 V ■ 
 
 .i |<p or wo)rhi_3a}_ 
 .; (»(• tr waiahl,^. 
 
 .; ilat — ^a_ 
 
 use. 
 
 . i thana . 
 . ; thapa . 
 
 m o ulded 
 
 Downapouu connected to: Q Storm trwer; Q tanitary arwer; Q dry-wau. (J] Splaah blocka: matrruu tad uc . 
 Additional Information: ; 
 
 14. LATH AND PIASTER 4 
 
 Ltd) O "till, O ceiling!: material . 
 
 «Ory-waO J] wtili, Qfceilinp material gyp bd 
 Joiat ircttm«at f ap» 
 
 .; weight or thickneu _ 
 ; thjckoae. 
 
 Plaiter: cotts . 
 
 Aniih . 
 
 Anuh. 
 
 ttXLm g 
 
 15. DECORATING: (Paint, wallpap". •*., 
 
 Wall f(uaM Matuuj. amo AmJotnoM 
 
 Ctajwa fiaon Mtmui /u»d Amjc«no»i 
 
 Kitchen . 
 ■ait 
 
 Other. 
 
 ( 1) prima fl(2) a n a m »l sea t s 
 
 fl) coat rubber has* 
 
 Add.llorjl Information: applies only t n f<m<.ht»H prog* (l«a pl?nf) 
 
 14. INTERIOR DOORS AND T8IM: 
 
 Doon: i yr WQQd flush 
 
 material — m a h o g a ny 
 
 thkkr.ru 
 
 t - 3/6 L 
 
 Dm trim: type_ Sj LULfi : nvturuiwh Ira pi nn BtM; «rp« S, lino ; material t^Ktte pine — • *"*-5'y 
 
 *•»■= *»n f ill. C2J CQ a tS U a ln 1 in™ ( 1 ) pr i m a , (3) mhhhH eo a t s 
 
 Other trim '•»•«#. (yar •«/ ***/»«,) winrtnu «il]«- fr.r^j^p 
 
 Additional inibrmtiion: ClfUBT. At\C\T\ ' BCtjJ H - fcld/lfJUVrod 
 
 17. WINDOWS: General Aluminum Corp. TARTAR teu. 321-4316 
 
 window. : type sliding 
 
 CUm: r .dr — in a ul^t e d 
 
 Trim; typ> 
 
 "«••» -Scries WOO 
 
 m * ,e ™' — alumi n u m 
 
 taih thicknraj . 
 
 ■ ; O aul> wrighu; Q baltaca. lypc . 
 . ; tanritl 
 
 brad Raahinf . 
 
 Ptiai. 
 
 . ; number cottt. 
 
 Wctlbrntrippinf: type 
 
 Scrtcai: D lull; j*J half; type 
 
 taktmcat wlndowc type fil idlng 
 
 Sprcitl wlndowt 
 
 Additional IrJbrmtiion: 
 
 mtteruj , 
 
 icnu cloth mttrrial. 
 tcroBoa, ni.mh*^ all 
 
 Storm tath. number. 
 
 ; Storm uih, number . 
 
 II. ENTRANCES AND EXTERIOR DSTAIU 
 
 Main rniranc* door: mtlrrUI Mghpgfln/ 
 
 Other cntrtnos doon: mtteritl 
 
 Fir 
 
 lhacknen . 
 
 Head lUihlni 8 alv - mcta ^ 
 
 Streea doon: ihk knew _!__". number 1 
 
 Combination worm and icrorn doom ihkknnt « "\ number 
 
 •Kutwn: D Klnatd: Q (Ued. Rallinj* 
 
 Kittarior miUwork: |rade tn<i tpeciet __i___________ 
 
 Addioontl I r» formation ^ — __- 
 
 select 
 
 _; width Tfr" ; thlcancM ) J/5-" Frame: material r| . irtacaneei . a_li 
 
 .; width 32 ' ; thicanra L_3jl8." Frame: material " ; thicknew " 
 
 W<atherurippia|: type , uodkx _^__^____^^______ 
 
 ; tcroia cloth mtteritl A^ ^J Storm doon: thicknrM ", aumbrr ____„_ 
 
 •crotn cloth malarial . 
 
 -** 
 
 , Ataa lovren. 
 
 Palu. 
 
 Dumber coau . 
 
 If. CABIHTTS AND INTERIOR DHAIU Manufactured by Alpine cabinet Co. see 
 
 Km-hen cabinru, wall unin material Timnnrh ; fo 1 n . ; Uneal bet at thalvci xOaXie ; ,Mlf width __XI^_ 
 
 tara uakt: mtwriil ; country loo f ti rm I r a , tdfina cn^ T 
 
 Back and and tpltah forq}c3 rinlth of cabinru wnrtrl grain ulnyl ; aumbar coau 
 
 dodltlaa cabiarut make ____^______^^_^___^_____^__^ 
 
 Odor cabtneu tad built-in lurnliun) . 
 Additional inbrmauon 
 
 JO. STAIRS: 
 
 hath VftnlHrx poi- plane 
 
 
 Tu«a 
 
 Kat«M 
 
 ■now 
 
 H*<aaatt 
 
 otahartti 
 
 
 Maurtal 
 
 Tkktaao 
 
 MaMflrte. 
 
 TkWkara 
 
 nil 
 
 Urn 
 
 Maurkd 
 
 Sua 
 
 Mawwol 
 
 lur 
 
 ttomrr»1 
 
 fir 
 
 S/4 
 
 pi pp 
 
 \fi. 
 
 w <~ f \r 
 
 ?»P 
 
 
 1" 
 
 W I . 
 
 1/1" 
 
 M+x* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Dieaopearinf: makr tnrl modri 
 Addioaaai uuarmatian: 
 
5-23 
 
 Table 5-1 (continued) 
 
 11. SKOAL ROOKS AND WAINSCOT i 
 
 
 Location 
 
 Matuual, Onoe. boaoaa, Vxu, C<u>4, Ira 
 
 Thuwm ■ 
 
 MATUMi 
 
 UaIUM 
 
 U.oeanjooa 
 Miruiu 
 
 1 
 
 KUrlwa 
 
 Arms t ran? or ciin.il 
 
 
 |-iihho r 
 
 
 1 
 
 M.Ik 
 
 
 
 II 
 
 '| 
 
 c 
 
 entry 
 
 •i 
 
 
 •1 
 
 
 
 other 
 
 Carpet ffinHhrd ar»,i<; nnly) ( s «« attachoil) 
 
 
 
 ,, 
 
 
 
 
 
 
 
 t 
 
 Location 
 
 kferuuxk, Coum. ituu. Cat. lun, G*ae. Ire 
 
 Heienr 
 
 HUOMT 
 
 O-x. Tvie 
 
 (ho. FuHtl 
 
 I 
 
 •Uik 
 
 Ceramic tile 
 
 7 ?" 
 
 63" 
 
 72" 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 IIJ-P** 1 
 
 .; mmhw hnrf| Q Attached; «..i«*-ul chremtf 
 
 Bathroom uoruarWi (3 ReceMed; aaaicruvl rhrnmf 
 
 Addition*] l/uVmauor»: 
 
 ••ember b*^^ 
 
 33. KUMllNOi 
 
 Mni Fiktu.i iDtmrono. No 
 
 Bin*. 
 
 kir.-hf 
 
 Sr i gfl g 
 
 -J44U- 
 
 3 U3; 
 
 w hit e 
 
 Lavatory 
 
 Water cJoati . 
 Bathtub 
 
 hath 
 
 A mur , — S t a n da r d 
 
 S.Q 07 . D S 6 
 
 IP" Die ! 
 
 > ' .t> h i» f 
 
 M i l2 P B 
 
 Slower over lub~_ 
 
 Stall .newer A 
 
 Laundry rrayi 
 
 B r *8 S *- 
 
 3000 
 
 30x 6 
 
 A[J Outlaid rod ^Q Door Q Sho.tr pen: material 
 
 Water tupply: Q pubiic; Q communiry ij«em, □ individual (private ) rruem * 
 
 Sgwafe dWpo ti.1: fjQ public; Q communiry lyttem; Q individual (private) lyuern.tV 
 
 <rila» cw' anmar uWu-urW r>«*m w mnpliU dtttil m uptrmU sVeuna/ / mi iptt]fi mHmu attmdii^ m nnirmmii. 
 
 Houat drain (Irulde): Q can iroo; □ lilt; [J other _^£g Houee newer (ouuidt): Q cast iron, CJ ule ; D other 
 
 Water piping: O galvenired ateel; Q copper tubing; □ other Sill cockj, number __2 
 
 Domestic water healer: type H? i : maJta and mndel \ O 9mi th ; healing capacity 
 
 3$ 3 gph. 100" rta*. Storage tana malarial glatt li np A ; capacity _ 
 
 One aervice: Q uiillry company; fj liq. ptL |aj; ^ other ^ __„ 
 
 4JL_ gallona. 
 
 Oaj piping: Q cooking, JJ houat healing 
 
 Footing dralru connected to: □ 110*™ tewer; Q aeoltary erwer; Q dry well. Sump pump, make and model. 
 ___________^ ; cepacia; , ,_ ; dlacruu-gee law 
 
 Hot waterJ □ Stum, fj Vapor. Q One-pipe m«m. JQ Two-p«pe tyitem 
 atari. Q Convecton. Q Baseboard radiation. Make and model 
 
 Radiant pand: Q floor; Q wall; Q ceiling. Panel ccal: material 
 
 n Circulator. Q Rerun* pump. Make and model 
 
 Boiler: make and model ____ ________-_^__^_____^___— Oitput 
 
 Additional information 
 
 capaciry . 
 
 . Btuh.; net rating . 
 
 .gpm. 
 Bruh 
 
 Warm air: □ Gravity. "J Forced. Type et lyiicra _ 
 Duct maacriai: lupply aqlv. reruni . 
 
 Fumaca: make and model 
 AdditioruU inlbrmaiioa: 
 
 g tt U . 
 
 s&d>- ;j~o &y~«' 
 
 Iniuiauon. 
 
 l. » nn o w 
 
 . thickneu Q CXitaide air intake. 
 
 lnpnl«»» plant Blnh ■ nuiput iff pi Jn< Btuh 
 
 □ Space heater, Q floor fumaca; Q wail heaiar. Input. 
 
 . Bruh.; output 
 
 Btuh ; number units . 
 
 Make, model 
 
 Additional infornva»rn : 
 
 ComroU: make and typei . 
 Addilbonai information: 
 
 La nn oit 
 
 Fiatl: D Ce* 1 : D »'; D l«; Q Lq. pet pi; alectnc; Q other. 
 Adoluooai inlormauon: ___^ _^ _^__^ 
 
 „,. ; atorage capaary . 
 
 T\r\r<% •quipmeni rurnuhed Kpanuily: Q Cat bursar, coavanloa type. Q Stoker: hopper feed Q, bin feed Q 
 OU burner: □ proaure atomiaing; vaporiaiiyj _______^______^___^________^^_________ 
 
 Make and modal OoaUrol 
 
 Addhioaud UCorrruiuan: __________^_^___^______________^_________^__^_______ 
 
 Ikprtrk heeling tytlera: typ« 
 
 Addittoeul infarmailoo: _______________^____^__^__ 
 
 Input . 
 
 .went, . 
 
 . voiu, autpui . 
 
 Btuh. 
 
 Veaulatiag •quiprnenti aula Ua, makt and modd . 
 
 . . capacity . 
 
 kite bee taKaurt Can. make aad model 
 Other keedahg, veauiating. or cooling equipment 
 
 i . i i t axB i 3 6 
 
 34. aiCUiC WlUNOi 
 
 -Vrvica Q overhead: [3 underground. Panel. Q fuae boa; Q3 circuM-braakar; ""ka ElintOO 
 
 Viring Q conduit: Q armored cabie, QC nonmetalUe cable; Q ki^ob and rube; Q "«h»r 
 ipecial ouileo Q( r »' > f«: D "•*" heairr, Qixhrr Jryor 
 
 -AMFi top No. circuiu j r, 
 
 d L^ortaHI. Q Qwmea, Puaa-bunoa locauom front do or 
 
 Additional iaaWanauao: 
 
 33. UOKT1NO nXTUHIS. 
 
 Total number of Umiuiti «aa plant Total alio nance for Aatuna. typval laataUatioa, i IjQ . QQ 
 
 NanrypM^I wutaliauon . 
 Additional tnaomvattoa: 
 
 DESCRIPTION Of MATERIALS 
 
5-24 
 
 Table 5-1 (continued) 
 
 DESCRIPTION OP MATERIALS 
 
 OUlBf 
 
 Wilt. 
 Floor . 
 
 ifc 
 
 ?m 
 
 H 
 
 
 463 -mfsi 
 
 HAROWAIL frnoU, mor.no/, ond flniiVJ c.,.^., k-.,. ,«,„„.. k 
 
 Privacy lock ;tr master hd ir 
 
 2 - rage do o r,- m i oth.r ,i.„ ^ SSaS^ mrrnnrr daaxs inrlnilin g 
 
 
 by ti»ob/nh»d custom, or* tuppiitd by 
 
 T j rha a r LUsposaJ . lasiafce ratoi "iH rjar 
 "**»• - RBE 353 
 
 Hood. 
 
 Nautilus 
 
 Opt io n al f . r e pU ea KaafrUa*»g Ma*Jt U3 'l- tl d iqj u 
 
 °P*l » " a l Hn d . a .n a G a hin n r n.n.f.H r?T ; fl 0lla l I V AL 113Q 
 
 Matf on Ml form.; P '"oaoqt/of.. Alwoyt r.rV.nc. by ,'om numb.r fo corr.ipond fo n W mbor.n 
 
 Pr o v lJa h a t 
 
 i»p— waafc«vii_ — 
 
 - HO D Ut tKtWwm^f 
 
 — MQ-a+x-Wt— » o »- d ry»r 
 
 PORCHES: 
 
 see plan a- 
 
 THRACtS: 
 
 "see plain 
 
 OARAOtS: 
 
 arfarh^rl c»„ p], nf 
 
 WALKS AND DRIVIWAYS: " 
 
 C»rt»»w. r . width 1 7 ! , baar m.e«ri.l_ 4ea ««4 ; i»ic.««._4 "; .urf.cn, m.icri.1 
 
 Troni walk: width _JJ ■ ™™l_ wwwu _, thickr*.. __4_ -. fcn,|c. „.,,. Wldln 
 
 fcfp.: rrumrUI C OBCa Tf _; trwda ^U.-; rWra 6>l - Chrrk „.||, _ 
 
 ao n a r a to - 
 
 ; material 
 
 ; ihicknra . 
 
 . Inkknni . 
 
 OTHM ONSTO IMMOVIMINTOi 
 
 {S ^^ , JZ'Z'.r n "' m ' '"">"*"»»■ «*** '"- >v«n. < i. .»*< -....., ,„,„.„.„. „,,..,,. 
 
 lANOSCAPtNO, PLANTINO, AND PINIJH ORADINO, 
 T«o»l i ,„*.. qjj rrrml yMnt . Q lld , rardj . q w ytyl) ^ 
 
 I— « r^M, «4M, - .Anif^: Q front yard 3Brf j e j ; Q .id, r .rd. 
 
 r*»"l'nr O « •prrlnrtj arnj .hovn on drawmp. □ al Ukm: 
 5°**** trrea, o>ciduou». * ca&pcr. 
 
 . Tort behind main buikJina; 
 , Q mar yarrJ 
 
 . Low AoMiim, i/TTt. dVcKtuoua. 
 . H%hfrowtn| inruba. oVtiduoua, 
 . Moditam-frowtn, thruba. oVoduoua, 
 ■ l**1">"'»l ihruba, drcxtuoui 
 
 . £^«f gi rat lrr*l. 
 . t» c«g ioao ahnjba. 
 . Vln«. )- r oar 
 
 . B 4 B 
 
 ^^^o?:,^^ ^ """^ 5 *• "-""* ^ °" -^ - • p —- -'•' = -p— — - - 5 th. u.« - 
 
 21. .lantiarv 1Q7^ 
 
 S^fiaMurv . 
 
 PHA rWm 3O0S 
 
 VA hm Jo- uij 
 
 Stfn 
 

 
 5- 
 
 25 
 
 
 
 
 ; 
 
 WORKSHEET FOR HEAT LOAD CALCULATIONS 
 
 
 
 
 (for Example Building) 
 
 
 
 
 BUILDING SECTION 
 
 SIZE 
 
 NET 
 
 U 
 
 TEMP. 
 
 HEAT 
 
 TOTALS 
 
 
 OR 
 
 AREA OR 
 
 C0EFF. 
 
 DIFF. 
 
 LOSS 
 
 * 
 
 1 
 
 VOLUME 
 
 VOLUME 
 
 
 C68-C-9)] 
 
 * 
 
 
 BEDROOM 1 
 
 
 
 
 
 
 
 South wall 
 
 (15+3)x8 
 
 120 
 
 .07 
 
 77 
 
 647 
 
 
 East wal 1 
 
 13.5x8 
 
 108 
 
 .07 
 
 77 
 
 282 
 
 
 Windows (2) 
 
 3x4 
 
 24 
 
 .50 
 
 77 
 
 924 
 
 
 Infiltration 
 
 2/3x15x13.6x8 
 
 1088 
 
 .018 
 
 77 
 
 1508 
 
 3361 
 
 BEDROOM 2 
 
 
 
 
 
 
 
 East wall 
 
 14x8 
 
 112 
 
 .07 
 
 77 
 
 604 
 
 
 North wall 
 
 11x8 
 
 76 
 
 .07 
 
 77 
 
 410 
 
 
 Window 
 
 3x4 
 
 12 
 
 .50 
 
 77 
 
 462 
 
 
 Infiltration 
 
 2/3x11x11x8 
 
 645 
 
 .018 
 
 77 
 
 894 
 
 2370 
 
 BATHROOM 
 
 
 
 
 
 
 
 North wall 
 
 8x8 
 
 60 
 
 .07 
 
 77 
 
 323 
 
 
 Window 
 
 2x2 
 
 4 
 
 .50 
 
 77 
 
 154 
 
 
 Infiltration 
 
 3/4x7.5x11x8 
 
 495 
 
 .018 
 
 77 
 
 686 
 
 1163 
 
 BEDROOM 3 
 
 
 
 
 
 
 
 North wall 
 
 12x8 
 
 84 
 
 .07 
 
 77 
 
 453 
 
 
 West wall 
 
 10x8 
 
 80 
 
 .07 
 
 77 
 
 431 
 
 
 Wi ndow 
 
 3x4 
 
 12 
 
 .50 
 
 77 
 
 462 
 
 
 Infiltration 
 
 2/3x10x12x8 
 
 640 
 
 .018 
 
 77 
 
 887 
 
 2233 
 
 BEDROOM 4 & HALLWAY 
 
 
 
 
 
 
 
 West wall 
 
 16x8 
 
 128 
 
 .07 
 
 77 
 
 690 
 
 
 South wall 
 
 14x8 
 
 88 
 
 .07 
 
 77 
 
 474 
 
 
 Windows (2) 
 
 3x4 
 
 24 
 
 .50 
 
 77 
 
 924 
 
 
 Infiltration 
 
 2/3x14x16x8 
 
 1195 
 
 .018 
 
 77 
 
 1656 
 
 3744 
 
 LIVING ROOM 
 
 
 
 
 
 
 
 South wall 
 
 32x8 
 
 203 
 
 .07 
 
 77 
 
 1094 
 
 
 Door 
 
 3x7 
 
 21 
 
 .26 
 
 77 
 
 420 
 
 
 Window 
 
 4x8 
 
 32 
 
 .62 
 
 77 
 
 1528 
 
 
 East wall 
 
 13.5x8 
 
 108 
 
 .07 
 
 77 
 
 582 
 
 
 Infiltration 
 
 2/3x19x13.5x8 
 
 1368 
 
 .018 
 
 77 
 
 1896 
 
 5520 
 
 DINING ROOM 
 
 
 
 
 
 
 
 East wall 
 
 13.5x8 
 
 108 
 
 .07 
 
 77 
 
 582 
 
 
 North wall 
 
 11x8 
 
 88 
 
 .07 
 
 77 
 
 474 
 
 
 Infiltration 
 
 1/3x11x13.5x8 
 
 396 
 
 .018 
 
 77 
 
 549 
 
 1650 
 
5-26 
 
 WORKSHEET FOR HEAT LOAD CALCULATIONS 
 (for Example Building) 
 
 BUILDING SECTION 
 
 KITCHEN, BREAKFAST 
 
 North wall 
 Window 
 Window 
 Infiltration 
 
 FAMILY ROOM 
 
 North wall 
 Patio Door 
 West wall 
 South wall 
 Infiltration 
 
 HALL 
 
 West wall 
 Infiltration 
 
 BASEMENT 
 
 North wall 
 West wall 
 South wall 
 East wall 
 Floor 
 Floor 
 Infiltration 
 
 CEILING 
 
 Second floor 
 Family room 
 
 *Btuh 
 
 SIZE 
 
 OR 
 
 VOLUME 
 
 18x8 
 2.5x4 
 3.4 
 1x18x11x8 
 
 21.5x8 
 
 6x6 
 13x8 
 22x8 
 2x13x22x8 
 
 17x8 
 1x8x8x17 
 
 54x8 
 
 28x8 
 
 54x8 
 
 28x8 
 
 32x28 
 
 13x22 
 
 1/6x54x13x8+ 
 
 1/6x15x32x8 
 
 32x28 
 13x22 
 
 NET 
 AREA OR 
 VOLUME 
 
 122 
 
 10 
 
 12 
 
 1584 
 
 136 
 
 36 
 
 104 
 
 176 
 
 4576 
 
 136 
 1088 
 
 432 
 224 
 432 
 224 
 896 
 286 
 1576 
 
 896 
 286 
 
 U 
 COEFF. 
 
 07 
 50 
 50 
 018 
 
 07 
 58 
 20 
 52 
 018 
 
 TEMP. 
 
 DIFF. 
 
 E68-(-9)] 
 
 77 
 77 
 77 
 77 
 
 77 
 77 
 77 
 38 
 77 
 
 HEAT 
 
 LOSS 
 * 
 
 657 
 
 385 
 
 462 
 
 2195 
 
 733 
 1608 
 1602 
 3478 
 6342 
 
 .52 
 
 38 
 
 2687 
 
 .018 
 
 77 
 
 1508 
 
 .10 
 
 23 
 
 994 
 
 .10 
 
 23 
 
 515 
 
 .10 
 
 23 
 
 994 
 
 .10 
 
 23 
 
 515 
 
 .10 
 
 23 
 
 2061 
 
 .10 
 
 23 
 
 658 
 
 .018 
 
 77 
 
 2184 
 
 .04 
 
 77 
 
 2760 
 
 .04 
 
 77 
 
 681 
 
 Unit Heating Load = gfrfrfj x 24 = 16590 Btu/DD 
 Annual Heating Load = 16590 x 6283 = 104.2 MMBtu 
 
 TOTALS 
 * 
 
 3699 
 
 13763 
 
 4195 
 
 7921 
 
 3641 
 
 TOTAL HEAT LOSS RATE (Btuh) 53215 
 
5-27 
 
 COOLING LOAD WORKSHEET 
 (for Example Building) 
 
 BUILDING SECTION 
 
 SIZE 
 
 NET 
 
 U or UNIT 
 
 DETD 
 
 HEAT 
 
 TOTALS 
 
 
 OR 
 
 AREA OR 
 
 HEAT 
 
 
 GAIN 
 
 
 
 VOLUME 
 
 VOLUME 
 
 GAIN 
 
 
 
 
 BEDROOM 1 
 
 
 
 
 
 
 
 South wall 
 
 18x8 
 
 120 
 
 .07 
 
 19 
 
 160 
 
 
 East wal 1 
 
 13.5x8 
 
 1C8 
 
 .07 
 
 19 
 
 144 
 
 
 Windows (2) 
 
 3x4 
 
 24 
 
 27 
 
 
 648 
 
 
 Infiltration 
 
 1632 
 
 816 
 
 .018 
 
 14 
 
 205 
 
 1157 
 
 BEDROOM 2 
 
 
 
 
 
 
 
 East wall 
 
 14x8 
 
 112 
 
 .07 
 
 19 
 
 149 
 
 
 North wall 
 
 11x8 
 
 76 
 
 .07 
 
 19 
 
 101 
 
 
 Wi ndow 
 
 3x4 
 
 12 
 
 27 
 
 
 324 
 
 
 Infiltration 
 
 968 
 
 484 
 
 .018 
 
 14 
 
 122 
 
 696 
 
 BATHROOM 
 
 
 
 
 
 
 
 North wall 
 
 8x8 
 
 60 
 
 .07 
 
 19 
 
 80 
 
 
 Wi ndow 
 
 2x2 
 
 4 
 
 27 
 
 
 108 
 
 
 Infiltration 
 
 660 
 
 660 
 
 .018 
 
 14 
 
 166 
 
 354 
 
 BEDROOM 3 
 
 
 
 
 
 
 
 North wall 
 
 12x8 
 
 84 
 
 .07 
 
 19 
 
 112 
 
 
 West wall 
 
 10x8 
 
 80 
 
 .07 
 
 19 
 
 106 
 
 
 Window 
 
 3x4 
 
 12 
 
 27 
 
 
 324 
 
 
 Infiltration 
 
 960 
 
 480 
 
 .018 
 
 14 
 
 121 
 
 663 
 
 BEDROOM 4 AND HALLWAY 
 
 
 
 
 
 
 
 West wall 
 
 16x8 
 
 128 
 
 .07 
 
 19 
 
 170 
 
 
 South wall 
 
 14x8 
 
 88 
 
 .07 
 
 19 
 
 117 
 
 
 Windows (2) 
 
 3x4 
 
 24 
 
 27 
 
 
 648 
 
 
 Infiltration 
 
 1792 
 
 896 
 
 .018 
 
 14 
 
 226 
 
 1161 
 
 LIVING ROOM 
 
 
 
 
 
 
 
 South wall 
 
 32x8 
 
 203 
 
 .07 
 
 19 
 
 270 
 
 
 Door 
 
 3x7 
 
 21 
 
 .47 
 
 19 
 
 188 
 
 
 Wi ndow 
 
 4x8 
 
 32 
 
 21 
 
 
 672 
 
 
 East Wall 
 
 13.5x8 
 
 108 
 
 .15 
 
 11 
 
 178 
 
 
 Infiltration 
 
 2052 
 
 1026 
 
 .018 
 
 14 
 
 258 
 
 1566 
 
 DINING ROOM 
 
 
 
 
 
 
 
 East wall 
 
 13.5x8 
 
 108 
 
 .07 
 
 19 
 
 144 
 
 
 North wall 
 
 11x8 
 
 88 
 
 .07 
 
 19 
 
 117 
 
 
 Infiltration 
 
 1188 
 
 198 
 
 .018 
 
 14 
 
 50 
 
 311 
 
5-28 
 
 COOLING LOAD WORKSHEET 
 (for Example Building) 
 
 BUILDING SECTION 
 
 SIZE 
 
 NET 
 
 U or UNIT 
 
 DETD 
 
 HEAT 
 
 TOTALS 
 
 
 OR 
 
 AREA OR 
 
 HEAT 
 
 
 GAIN 
 
 
 
 VOLUME 
 
 VOLUME 
 
 GAIN 
 
 
 
 
 KITCHEN, BREAKFAST 
 
 
 
 
 
 
 
 North wal 1 
 
 1848 
 
 122 
 
 .07 
 
 19 
 
 162 
 
 
 Windows (2) 
 
 
 22 
 
 27 
 
 
 594 
 
 
 Infiltration 
 
 1584 
 
 1584 
 
 .918 
 
 14 
 
 399 
 
 1155 
 
 FAMILY ROOM 
 
 
 
 
 
 
 
 North wall 
 
 21.5x8 
 
 136 
 
 .07 
 
 19 
 
 180 
 
 
 West wal 1 
 
 13x8 
 
 104 
 
 .20 
 
 19 
 
 395 
 
 
 South wall 
 
 22x8 
 
 176 
 
 .52 
 
 7 
 
 640 
 
 
 Patio door 
 
 6x6 
 
 36 
 
 21 
 
 
 756 
 
 
 Infiltration 
 
 2288 
 
 2288 
 
 .018 
 
 14 
 
 577 
 
 2548 
 
 HALL 
 
 - 
 
 
 
 
 
 
 West wal 1 
 
 17x8 
 
 136 
 
 .52 
 
 7 
 
 495 
 
 
 Infiltration 
 
 1088 
 
 1088 
 
 .018 
 
 14 
 
 274 
 
 769 
 
 CEILING 
 
 
 
 
 
 
 
 Second floor 
 
 32x28 
 
 896 
 
 .04 
 
 39 
 
 1398 
 
 
 Family room 
 
 13x22 
 
 286 
 
 .04 
 
 39 
 
 446 
 
 1844 
 
 No load is calculated for 
 basement. No credit for 
 cool basement taken. 
 
 TOTAL 12224 
 
 4 occupants x 225 900 
 
 Kitchen appliances 1200 
 
 Total Sensible Heat Gain 14324 
 
 Latent Heat Gain (30%xl4324) 4297 
 
 Latent + Sensible Heat Gain 18621 
 
 Cooling Load, Btuh 18621 
 
A5-1 
 
 APPENDIX 
 
A5-2 
 
 Table A5-1 
 Surface Conductances and Resistances for Air Films 
 
 ITEMS 
 
 WINTER 
 
 SUMMER 
 
 f 
 
 R 
 
 f 
 
 R 
 
 INTERIOR SURFACES 
 
 
 
 
 
 Ceiling 
 
 1.63 
 
 0.61 
 
 1.08 
 
 0.92* 
 
 Sloped ceiling 45° 
 
 1.60 
 
 0.62 
 
 1.32 
 
 0.76* 
 
 Wal Is and windows 
 
 1.46 
 
 0.68 
 
 1.46 
 
 0.68 
 
 Floor 
 
 1.08 
 
 0.92 
 
 1.08 
 
 0.92 
 
 EXTERIOR SURFACES 
 
 
 
 
 
 Roofs, walls and windows 
 
 6.00 
 
 0.17+ 
 
 4.00 
 
 0.25 1 " 
 
 * Heat flow direction reversed from winter conditions 
 
 + 15 mph wind 
 
 + 
 
 7.5 mph wind 
 
 Table A5-2 
 Resistance Values for Air Spaces 
 
 ITEM 
 
 
 WINTER 
 
 SUMMER 
 
 \ Air Space 
 
 3/4" 
 
 4" 
 
 3/4" 
 
 4" 
 
 Flat roof 
 Wall 
 
 1.02 
 1.28 
 
 1.12 
 1.16 
 
 0.87 
 1.01 
 
 0.94 
 1.01 
 
A5-3 
 
 Table A5-3 
 Resistance Values for Building Materials 
 
 TYPE AND MATERIAL 
 
 R 
 
 TYPE AND MATERIAL 
 
 R 
 
 BUILDING BOARD 
 
 
 
 SIDING 
 
 
 Asbestos-cement: 
 
 1/8" 
 
 0.03 
 
 Asbestos-cement 
 
 0.21 
 
 
 1/4" 
 
 0.06 
 
 Wood shingles, 16" 
 
 0.87 
 
 Gypsum: 
 
 3/8" 
 
 0.32 
 
 Wood bevel ,1/2x8 
 
 0.81 
 
 
 1/2" 
 
 0.45 
 
 Wood bevel 3/4 x 10 
 
 1.05 
 
 Plywood: 
 
 1/4" 
 
 0.31 
 
 Wood plywood, 3/8 
 
 0.59 
 
 
 3/8" 
 
 0.47 
 
 Aluminum or steel 
 
 0.61 
 
 
 1/2" 
 
 0.62 
 
 Insulating Board: 
 
 
 
 3/4" 
 
 0.93 
 
 3/8" normal 
 
 1.82 
 
 Insulating Board 
 
 25/32" 
 
 2.06 
 
 3/8" foiled 
 
 2.96 
 
 Regular 
 
 1/2" 
 
 1.32 
 
 
 
 Laminated Paper 
 
 3/4" 
 
 1.50 
 
 FINISH FLOORING 
 
 
 Acoustic Tile 
 
 1/2" 
 
 1.25 
 
 
 
 
 3/4" 
 
 1.89 
 
 Carpet and fibrous pad 
 
 2.08 
 
 Hardboard 
 
 3/4" 
 
 0.92 
 
 Carpet and rubber pad 
 
 1.23 
 
 Particle Board 
 
 5/8" 
 
 0.82 
 
 Cork tile, 1/8" 
 
 0.28 
 
 Wood Subfloor 
 
 3/4" 
 
 0.94 
 
 Terrazzo, 1" 
 
 Tile, asphalt, linoleum, 
 
 0.08 
 
 MASONRY 
 
 
 
 vinyl , rubber 
 Hardwood 
 
 0.05 
 0.08 
 
 Concrete 
 
 6" 
 
 0.48 
 
 
 
 
 18" 
 
 0.64 
 
 INSULATION 
 
 
 
 10" 
 
 0.80 
 
 
 
 Concrete Blocks, 
 
 
 
 Blanket and Batt: 2-2 3/4" 
 
 7.00 
 
 3 oval core 
 
 
 
 3-3 1/2" 
 
 11.00 
 
 Sand and Gravel 
 
 4" 
 
 0.71 
 
 5 1/4-6 1/2" 
 
 19.00 
 
 
 8" 
 
 1.11 
 
 Loose Fill 
 
 
 
 12" 
 
 1.28 
 
 Cellulose, per inch 
 
 3.70 
 
 Cinder 
 
 4" 
 
 1.11 
 
 Sawdust, per inch 
 
 2.22 
 
 
 8" 
 
 1.72 
 
 Perlite, per inch 
 
 2.70 
 
 
 12" 
 
 1.89 
 
 Mineral fibre 
 
 
 Lightweight 
 
 4" 
 
 1.50 
 
 (rock, slag, glass) 3" 
 
 9.00 
 
 
 8" 
 
 2.00 
 
 4 1/2" 
 
 13.00 
 
 
 12" 
 
 2.27 
 
 6 1/4" 
 
 19.00 
 
 Concrete Blocks, 
 
 
 
 7 1/2" 
 
 24.00 
 
 2 rect. core 
 
 
 
 Vermicul ite, per inch 
 
 2.20 
 
 Sand and Gravel 
 
 8" 
 
 1.04 
 
 
 
 Lightweight 
 
 8" 
 
 2.18 
 
 ROOFING 
 
 
 Common Brick 
 
 2" 
 
 0.40 
 
 
 
 
 4" 
 
 0.80 
 
 Asphalt 
 
 0.44 
 
 Face Brick 
 
 2" 
 
 0.22 
 
 Wood 
 
 0.94 
 
 
 4" 
 
 0.44 
 
 3/8" Built-up 
 
 Woods: oak, maple per inch 
 
 0.33 
 0.91 
 
 BUILDING PAPER 
 
 
 
 fir, pine, softwoods 
 per inch 
 
 1.25 
 
 15# felt 
 
 
 0.06 
 
 3/4" 
 
 0.94 
 
 i 
 
A5-4 
 
 Table A5-4 
 
 (J Factors for Windows and Patio Doors Btu/(hr*ft »°F) 
 
 
 
 DESCRIPTION 
 
 WINTER 
 
 SINGLE GLASS 
 
 
 Metal sash 
 
 Wood sash, 80% glass 
 
 1.13 
 0.02 
 
 DOUBLE GLASS: 
 
 
 1/4" Air Space 
 Metal sash 
 
 Wood sash, 80% glass 
 Wood sash, 60% glass 
 
 0.65 
 0.62 
 0.55 
 
 1/2" Air Space 
 Metal sash 
 Wood sash, 80% glass 
 
 0.70 
 0.49 
 
 TRIPLE GLASS 
 
 
 1/4" Air Space 
 Metal sash 
 Wood sash, 80% glass 
 
 0.56 
 0.45 
 
 STORM WINDOWS 
 
 
 1" to 4" Air Space 
 Wood 
 Metal 
 
 0.50 
 0.56 
 
 SLIDING PATIO DOORS 
 
 
 Single Glass 
 Wood frame 
 Metal frame 
 
 1.07 
 1.13 
 
 Double Glass, 1/2" Air Space 
 Wood frame 
 Metal frame 
 
 0.58 
 0.64 
 
A5-5 
 
 Table A5-5 
 
 U Factors for Solid Doors Btu/(hr-ft 2 -°F) 
 
 THICKNESS (IN) 
 
 WINTER 
 
 SUMMER 
 WITHOUT 
 STORM DOOR 
 
 WITHOUT 
 STORM DOOR 
 
 WITH STORM 
 DOOR, 50% GLASS 
 
 WOOD 
 
 METAL 
 
 1 
 1 h 
 
 l h 
 2 
 
 0.64 
 0.55 
 0.49 
 0.43 
 
 0.30 
 0.28 
 0.27 
 0.24 
 
 0.39 
 0.34 
 0.33 
 0.29 
 
 0.61 
 0.53 
 0.47 
 0.42 
 
 Table A5-6 
 Air Changes for Average Residential Conditions 
 
 KIND OF ROOM 
 
 AIR CHANGE PER HOUR 
 
 WINTER 
 
 SUMMER 
 
 Rooms with no windows or exterior 
 doors 
 
 Rooms with windows or exterior 
 doors on one side 
 
 Rooms with windows or exterior 
 doors on two sides 
 
 Rooms with windows or exterior 
 doors on three sides 
 
 Entrance halls and air locks 
 
 1/3 
 
 2/3 
 
 1 
 
 1 1/3 
 1 1/2 
 
 1/6 
 
 1/2 
 
 2/3 
 
 1 
 1 
 
A5-6 
 
 Table A5-7 
 Design Equivalent Temperature Differences (°F) 
 
 DESIGN OUTDOOR TEMPERATURE 
 
 85 
 
 95 
 
 105 
 
 TEMPERATURE RANGE DURING DAY 
 
 15-25 
 
 15-25 
 
 >25 
 
 >25 
 
 WALLS AND DOORS 
 
 Wood frame and doors 
 Masonry 
 
 CEILINGS AND ROOF 
 
 Under vented attic, 
 dark roof 
 
 Built-up roof (no ceiling), 
 light roof 
 
 FLOORS 
 
 Over unconditioned rooms 
 and open crawl space 
 
 Over basement, enclosed 
 crawl space 
 
 14 
 6 
 
 34 
 26 
 
 5 
 
 
 24 
 16 
 
 44 
 
 36 
 
 15 
 
 19 
 11 
 
 39 
 
 31 
 
 10 
 
 29 
 21 
 
 49 
 
 41 
 
 20 
 
A5-7 
 
 Table A5-8 
 
 Design Heat Gains Through Windows Btu/(hr«ft ) 
 
 OUTDOOR DESIGN TEMPERATURE 
 
 SINGLE PANE 
 
 DOUBLE PANE 
 
 85 
 
 95 
 
 105 
 
 85 
 
 95 
 
 105 
 
 NO AWNINGS OR INSIDE SHADING 
 
 
 
 
 
 
 
 North 
 
 23 
 
 31 
 
 38 
 
 19 
 
 24 
 
 28 
 
 Northeast; Northwest 
 
 56 
 
 64 
 
 71 
 
 46 
 
 51 
 
 55 
 
 East and West 
 
 81 
 
 89 
 
 96 
 
 68 
 
 73 
 
 77 
 
 Southeast; Southwest 
 
 70 
 
 78 
 
 85 
 
 59 
 
 64 
 
 68 
 
 South 
 
 40 
 
 48 
 
 55 
 
 33 
 
 38 
 
 42 
 
 WITH DRAPERIES OR VENETIAN 
 
 
 
 
 
 
 
 BLINDS 
 
 
 
 
 
 
 
 North 
 
 15 
 
 23 
 
 30 
 
 12 
 
 17 
 
 21 
 
 Northeast; Northwest 
 
 32 
 
 40 
 
 47 
 
 27 
 
 32 
 
 36 
 
 East and West 
 
 48 
 
 56 
 
 63 
 
 42 
 
 47 
 
 51 
 
 Southeast; Southwest 
 
 40 
 
 48 
 
 55 
 
 35 
 
 40 
 
 44 
 
 South 
 
 23 
 
 31 
 
 38 
 
 20 
 
 25 
 
 29 
 
 ROLLER SHADES, HALF DOWN 
 
 
 
 
 
 
 
 North 
 
 18 
 
 26 
 
 33 
 
 15 
 
 20 
 
 24 
 
 Northeast, Northwest 
 
 40 
 
 48 
 
 55 
 
 38 
 
 43 
 
 47 
 
 East and West 
 
 61 
 
 69 
 
 76 
 
 54 
 
 59 
 
 63 
 
 Southeast; Southwest 
 
 52 
 
 60 
 
 67 
 
 46 
 
 51 
 
 55 
 
 South 
 
 29 
 
 37 
 
 44 
 
 26 
 
 32 
 
 36 
 
 AWNINGS 
 
 
 
 
 
 
 
 North 
 
 20 
 
 28 
 
 35 
 
 13 
 
 18 
 
 22 
 
 Northeast; Northwest 
 
 21 
 
 29 
 
 36 
 
 14 
 
 19 
 
 23 
 
 East and West 
 
 22 
 
 30 
 
 37 
 
 14 
 
 19 
 
 23 
 
 Southeast; Southwest 
 
 21 
 
 29 
 
 36 
 
 14 
 
 19 
 
 23 
 
 South 
 
 21 
 
 28 
 
 35 
 
 13 
 
 18 
 
 22 
 
A5-8 
 
 Table A5-9 
 Shade Line Factors* (5 hour average, 1 August) 
 
 WINDOW ORIENTATION 
 
 LATITUDE 
 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 East and West 
 
 0.8 
 
 0.8 
 
 0.8 
 
 0.8 
 
 0.8 
 
 0.8 
 
 Southeast; Southwest 
 
 1.9 
 
 1.6 
 
 1.4 
 
 1.3 
 
 1.1 
 
 1.0 
 
 South 
 
 10.1 
 
 5.4 
 
 3.6 
 
 2.6 
 
 2.0 
 
 1.7 
 
 ^Multiply shade line factors by width of overhang to determine shadow 
 line below overhang. 
 
A5-9 
 
 Table A5-10 
 Heating Degree Days* and Design Outdoor Temperature 
 
 o 
 
 K 
 
 rs is lo 
 
 CO 
 
 CO CO CM 
 
 LO UD 
 
 1— 
 
 ID 
 
 co 
 
 CT> Cn CT> 
 
 cr> 
 
 is lo 00 
 
 IS CO 
 
 CT)U_ 
 
 
 
 
 
 
 
 
 
 
 •i— O 
 
 4- 
 
 <S\ CO CO 
 
 CM 
 
 LO LO CO 
 
 IS CM 
 
 CO 
 
 21 
 
 1— 1 t— 1 CM 
 
 CM 
 
 CM ^f LO 
 
 1 CO 
 
 cu 
 
 •— i 
 
 
 
 1 1 1 
 
 1 
 
 Q 
 
 s 
 
 
 
 
 
 
 _j 
 
 r-l CO O 
 
 I— 1 
 
 ■vTcri^csuDO^cn 
 
 LOCOLOCOi— lOllsCM 
 
 
 =a; 
 
 un is co 
 
 CTl 
 
 iO(£»rsiocna3U3N 
 
 o*3-ocoiscr>cocr> 
 
 
 ID 
 
 LO O LO 
 
 CM 
 
 cooncor- • co rs cm 
 
 ISCOr-ICMi— lr-IIOO 
 
 
 21 
 
 CM CO 1— 1 
 
 CM 
 
 orsocnoocne^'* 
 
 cni— ito«^-«cj-t— icncn 
 
 
 21 
 
 
 
 r— I CM 1 — IH r— 1 
 
 1—1 l—l 1 — 1 1— 1 1 — 1 
 
 
 <c 
 
 
 
 
 
 LU 
 
 000 
 
 
 
 LOr-ir^«sJ-CM<-H^-CM 
 
 t— iCOtOCOCOCOCOLO 
 
 
 21 
 
 
 
 HMLnCMOCTKd-W 
 
 COOCOLOISCMCnCO 
 
 
 zz> 
 
 
 
 cococncn^d-LO>^-CM 
 
 co«3-<ocMLors<o-st- 
 
 
 cr> en 
 
 
 
 CMOLOCOUDCMOLO 
 
 r-HC0rs00O<OIsCM 
 
 
 ^ 
 
 r-H 
 
 
 cncr>«3-isoa~>coLO 
 
 OISLO<^-COCOCOCO 
 
 
 < 
 
 
 
 LO<=3-^J-COCOrsCOLO 
 
 COIDOV0O1CA00VD 
 
 
 2: 
 
 
 
 I— 1 1— 1 
 
 l—l 
 
 . 
 
 00 00 CM 
 
 
 
 CnOO^COCOi— I^CO 
 
 O<O<*CM^-00L0CD 
 
 
 cu 
 
 on>* 
 
 en 
 
 rs^^-CMMTHDVO 
 
 1— itOLOCMi—icnoo^t- 
 
 
 Q_ 
 
 1— > «— i 
 
 
 co <o cn en 1— iCTicoo 
 
 COCTiLOi— ICOOOOCO 
 
 
 < 
 
 
 
 I— 1 1— 1 1— 1 I—l 
 
 r-H l—l t—l r-l 
 
 a 
 
 CO «3- 1— 1 
 
 CO 
 
 cocooorsLOc\jcocn 
 
 COt— lOCOOLOt-HCM 
 
 o 
 
 q; 
 
 CO CO ■— 1 
 
 r-l 
 
 Cn ^f" CO IS LO CM 1— 1 co 
 
 ISt— ICOLOISCOi— l-^t 
 
 lo 
 
 <e 
 
 CO «3" CM 
 
 CO 
 
 CM CO «3" «3" CO 1— 1 1— IN 
 
 o«?i-orsiscMOO 
 
 <o 
 0) 
 
 2: 
 
 
 
 
 
 . 
 
 CM IS CD 
 
 is 
 
 iONMOlOlOIDH 
 
 ococMisiocococn 
 
 to 
 
 CQ 
 
 uDino 
 
 r-l 
 
 r-icocococncocoo 
 
 rscocoi— itotOLOt-H 
 
 03 
 CO 
 
 LU 
 Ll_ 
 
 «3" LO CO s" 
 
 COOOCOCOLOOOCTl 
 
 ococnco<Oi— icno 
 
 
 
 . 
 
 CM ^i" LO 
 
 CO 
 
 ■HCftNtonrocncn 
 
 isocM^-cnooLocn 
 
 CO 
 
 21 
 
 tr> ct> 1— « 
 
 <d- 
 
 CO«^-r-HCOOLOCT>LO 
 
 coocr>cr>iscM^-co 
 
 >- 
 
 <X. 
 
 LO CO «vi- 
 
 LO 
 
 (OCnLOLOOIr-lCMCO 
 
 CMtOr-ICMOOCMOrH 
 
 < 
 
 ■"D 
 
 
 
 r-H MCMHHHtM 
 
 1— li— ICMCM1—I1— li—lr— 1 
 
 . 
 
 inmN 
 
 is 
 
 NCrtNrs*OC0H^ 
 
 LOUDISCMOISCM^J- 
 
 LU 
 
 O 
 
 LO CO LO 
 
 CM 
 
 tsCncOCOCOCMCMLO 
 
 COOCMCOCMCyi>^-<^- 
 
 LU 
 
 LU 
 
 LO CO CO 
 
 LO 
 
 LOC0COCOC0«-<CMCM 
 
 1— iCOi— iCMOOt— lOt-H 
 
 LU 
 
 Q 
 
 
 
 i—l CM CM r-l 1— 1 r-H CM 
 
 1— 1 1— 1 CM CM 1— 1 r-l i— It— 1 
 
 . 
 
 CO VO CO 
 
 
 
 «d-C0i— i«=3-s-corsco 
 
 1— lOCOr- ILOCO<0<0 
 
 O 
 
 > 
 
 CO CM r-H 
 
 CO 
 
 coroNrj-ooHHCo 
 
 CMCnCMCTiLOVOIscO 
 
 
 O 
 
 CO ^ CM 
 
 CO 
 
 c\irscy>cn«3-cnoco 
 
 tncMrsrsi^-cncocn 
 
 21 
 
 21 
 
 
 
 r-l 1— 1 t—l r-l r-H i—l 
 
 r-H i—l t—l l-H 
 
 . 
 
 co rs cm 
 
 CO 
 
 osowojpjHn 
 
 LOoocn^i-<vj-cM<vj-<o 
 
 1— 
 
 1— 
 
 CT> CM CM 
 
 CO 
 
 fOtOOOO'S-NODOlMOcj-cOO^OCOrH 
 
 < 
 
 O 
 
 I—l 
 
 
 cnLOLO«=i-orsisc\j 
 
 iscr>cMt— icncorsN 
 
 LU 
 
 in 
 
 O 
 
 
 
 l—l t—l r-l r-l 
 
 t—l r-H i—l 
 
 1— 
 
 CO CM O 
 
 
 
 COISLOISCMLOCNJCM 
 
 COCOCOCOCOCMr-l^- 
 
 _j 
 
 D_ 
 
 t— 1 
 
 
 rH CM O 00 H IM CVJ cj- 
 
 CQHCMrocnHON 
 
 i <c 
 
 LU 
 
 
 
 LOCOOO^COLOLOCO 
 
 <^-Lor^<o<o<OLO<=d- 
 
 i— 
 
 co 
 
 
 
 r-l 
 
 
 o 
 
 1— 
 
 
 
 
 
 
 . 
 
 000 
 
 
 
 ■HCOowxi-inrHMcoojujixnocniON 
 
 
 ej 
 
 
 
 cno«3-rscr>c\jcnco 
 
 cocM^-cocr>cors«^- 
 
 _3 
 
 r3 
 
 
 
 CMCMCOrsoO^-COCO 
 
 coco«=i-co^j-lo>^i-co 
 
 
 <C 
 
 
 
 
 
 >- 
 
 000 
 
 
 
 LOCMCOLOCns-COt-l 
 
 t— ICOt— lOOr-ILOISOO 
 
 ! o 
 
 _j 
 
 
 
 cj- rj- O CO H IS iO IS 
 
 Oi-icoocoorsco 
 
 21 
 
 ID 
 •"D 
 
 
 
 CMCM00rsCOs-COi— 1 
 
 COCOCOCM^UDLOCO 
 
 
 21 
 O 
 i — 1 
 
 I— 
 < 
 
 1— 
 
 
 
 T3 
 
 
 
 CO 
 
 
 
 03 
 
 c: 
 
 
 Q 
 
 E cu 
 
 >> 
 
 r— 
 
 O r— 
 
 
 21 
 
 03 r— 
 
 $- 
 
 cu to c/) 
 
 E 3 
 
 
 <c 
 
 ! sz 1 — 
 
 cu 
 
 en i-h >> ^£. 
 
 1— CU 03 
 
 
 
 < 
 
 OVi- 
 
 E 
 
 n3 <U IO ID C 
 
 03 3 -C Q_ 4-> 
 
 
 LU 
 
 2: 
 
 c > cu 
 
 < 
 
 S-+) 2S.r-CQ > nj 
 
 3(/)J3+> 03 03 
 
 
 h- 
 
 <c 
 
 •r- Wi — 
 
 O 4-» O CU CU O -Q 
 
 03 CU 03 4-> >>+-> 
 
 
 < 
 
 CO 
 
 E + J -»- 
 
 4-> CO 
 
 sz cu s- -i-> -c td td s- 
 
 (U D)N L (U C E 3 
 
 
 1— 
 
 «=c 
 
 i~ c: jd 
 
 c <! 
 
 O E i- S- +-> r— S-T- 
 
 CC4->OEt-<U-^ 
 
 
 CO 
 
 :_l 
 
 •1- 3 
 
 —I 
 
 cctarocuoofd 
 
 3-r-OOOo3^:o3 
 
 ,, 
 
 
 < 
 
 CQI2 
 
 2: < 
 
 <<Cfl£QCQOUU. 
 
 o^^5:zoow> 
 
 
 
 cu 
 
 
 
 S- 
 
 
 
 r$ 
 
 • 
 
 to 
 
 +-> 
 
 E 
 
 •1 — 
 
 03 
 
 -a 
 
 JT 
 
 S- 
 
 ■=c 
 
 +J 
 
 cu 
 
 ex 
 
 • 
 
 c: 
 
 F 
 
 > 
 
 rrj 
 
 <u 
 
 s- 
 
 JO. 
 
 +-> 
 
 O) 
 
 +-> 
 
 
 CO 
 
 
 JD 
 
 
 s- 
 
 r— 
 
 • 
 
 cu 
 
 3 
 
 '1 — 
 
 E 
 
 jQ 
 
 u 
 
 S- 
 
 
 CO 
 
 03 
 
 >> 
 
 
 s 
 
 S- 
 
 • 
 
 
 TD 
 
 > 
 
 cu 
 
 
 c 
 
 E 
 
 cu 
 
 LU 
 
 •1 — 
 
 E 
 
 
 +-> 
 
 
 fl 
 
 
 -t-> 
 
 cu 
 
 M- 
 
 
 
 
 
 
 M- 
 
 S- 
 
 
 
 
 O) 
 
 &9 
 
 
 F 
 
 en 
 
 &^ 
 
 E 
 
 en 
 
 l—l 
 
 
 
 "*— -* 
 
 >*— * 
 
 
 
 
 
 
 CM 
 
 CM 
 
 «t- 
 
 rs 
 
 IS 
 
 
 
 en 
 
 en 
 
 
 r-H 
 
 r-l 
 
 -(-> 
 
 
 
 sz 
 
 CO 
 
 CO 
 
 cu 
 
 1 — 
 
 1 — 
 
 F 
 
 rt3 
 
 03 
 
 4-> 
 
 +-> 
 
 4-> 
 
 S- 
 
 E 
 
 c 
 
 03 
 
 OJ 
 
 cu 
 
 ex 
 
 E 
 
 E 
 
 cu 
 
 03 
 
 03 
 
 Q 
 
 "U 
 
 •0 
 
 CO 
 
 . 
 
 M- 
 
 "4- 
 
 zo 
 
 O 
 
 O 
 
 *\ 
 
 .^ 
 
 ^»i 
 
 CO 
 
 O 
 
 O 
 
 a> 
 
 O 
 
 O 
 
 +j 
 
 jD 
 
 JZ\ 
 
 03 
 
 ■O 
 
 -O 
 
 +-> 
 
 c 
 
 c 
 
 CO 
 
 ra 
 
 03 
 
 
 DT 
 
 IC 
 
 -0 
 
 
 
 O) 
 
 LU 
 
 LU 
 
 +-> 
 
 <c 
 
 <C 
 
 •r— 
 
 cc 
 
 CU 
 
 c 
 
 zn 
 
 Zu 
 
 ^) 
 
 CO 
 
 CO 
 
 
 <c 
 
 < 
 
 O) 
 
 
 
 x: 
 
 M 
 
 tt 
 
 +-> 
 
 CO 
 
 CO 
 
 
 CO 
 
 CO 
 
 M- 
 
 
 
 O 
 
 S- 
 
 S- 
 
 
 cu 
 
 cu 
 
 CO 
 
 4-> 
 
 4-> 
 
 03 
 
 CD- 
 
 Q. 
 
 p — 
 
 OS 
 
 03 
 
 4-J 
 
 JZ 
 
 JZZ 
 
 < 
 
 C_) 
 
 CD 
 
 +J CU — 
 
 03 CO CU i- CU i- 
 
 E tO 1— 3 r— CU 
 
 •r- CJ> ^D -l-> JD 4-> 
 
 r— 1 — I 03 03 03 03 
 
 O H- i~ t— CU 
 
 •« CU S- 
 
 E CU E Q. E CD 
 
 O E O E O 
 
 L 3 L (D J. w 
 
 Lu <"3 U_ +J U_ •!— 
 
A5-10 
 
 Table A5-10 (continued 
 
 o 
 
 I=i 
 
 «=3- 
 
 CO CO 
 
 lo r-. 
 
 i— 1 
 
 . — 1 
 
 cn 
 
 cn 
 
 CO 
 
 NNHN<^ LO O COO LO 
 
 1— 
 
 5: 
 
 co 
 
 cn 
 
 O en 
 
 r-H 
 
 
 
 cn 
 
 cn 
 
 
 
 cncoococn co coco 00 
 
 
 ZD 
 
 
 1—1 
 
 1— < 
 
 r— 1 
 
 ■ — 1 
 
 
 
 ■ — 1 
 
 r-H i—l 
 
 CDLl_ 
 
 OO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■l— o 
 
 +- 
 
 
 
 1— 1 LO 
 
 cn cn 
 
 I-* 
 
 LO 
 
 cn 
 
 CM 
 
 1—1 
 
 COCXICOCOCM LO O CMCXI CM 
 
 CO 
 
 CD 
 
 Q 
 
 
 
 CO l-H 
 
 (XI 
 
 co 
 
 r-H 
 
 1 — 1 
 
 CM 
 
 co 
 
 COCOCMCO"^ CO CO ^3-"^- CO 
 
 3: 
 
 
 
 
 
 
 
 
 
 
 
 _l 
 
 (XI 
 
 LO CM 
 
 O (XI 
 
 r^ 
 
 CM 
 
 cn 
 
 CO 
 
 CvlNN 
 
 cococxir-ii— icxiOLOLOcocncnLOcxjr^ 
 
 
 «=C 
 
 LO 
 
 CO CO 
 
 CO 
 
 T— 1 
 
 cn 
 
 r-H 
 
 CO 
 
 CM CM O 
 
 ^•rJ-CTiHlDOJNOlHNOCIHin^ 
 
 
 rz> 
 
 1— 1 
 
 r~. co 
 
 co r^- cxi 
 
 CM 
 
 CM 
 
 LO 
 
 r-H CM LO 
 
 (0(D<*NONcominNrAj'vi-oom 
 
 
 2: 
 < 
 
 r^. 
 
 r-l •=* 
 
 r-H >=d- 
 
 r-H 
 
 co 
 
 CO 
 
 CM 
 
 CM «3" LO 
 
 r-4>^-CMi— ICMLOCMCOCMCM"^-r-ICOCMCXI 
 
 
 LU 
 
 
 
 O LO 
 
 O CD 
 
 O 
 
 
 
 O 
 
 O 
 
 O CO LO 
 
 coLOOcor-icnocoocor^cocOLOLO 
 
 
 Z^ 
 
 CO 
 
 i—l 
 
 
 
 
 
 
 co cn 
 
 r-HCO r-HCOLOCn«^- LOCOCMOCO 
 
 
 ZD 
 
 r— 1 
 
 
 
 
 
 
 
 i—l 
 
 CXI r-H CM i—l r-H r—l 
 
 
 r^ 
 
 O CO 
 
 CO CO 
 
 O 
 
 CM 
 
 cn 
 
 O 
 
 cr> ro r-» 
 
 HCM(DOOONOCOrsCM<d-<t'*(MCO 
 
 
 >- 
 
 co 
 
 LO 
 
 cn 
 
 
 CXI 
 
 
 
 r-i «3- cn 
 
 cor^LocnLO^-cocn'^t-ococO'— icnco 
 
 
 
 «* 
 
 1—1 
 
 
 
 
 
 
 i-l CO 
 
 CO 1— 1 CO •— 1 CM 1— 1 CM CXIr-HCM 
 
 . 
 
 i—( 
 
 LO O 
 
 LO t— 1 
 
 Cn 
 
 ^J- 
 
 CO 
 
 LO 
 
 LO CO CM 
 
 oocoococnLOLocncococococncncxi 
 
 
 or 
 
 LO 
 
 r^ co 
 
 r^- cn 
 
 CXI 
 
 *3" CM 
 
 O 
 
 O O CO 
 
 COCOLOCOr-ICMLO(OCOr-ICMCMr->.>^-C0 
 
 
 Q_ 
 
 CO 
 
 CO 
 
 (XI 
 
 
 I—l 
 
 i — 1 
 
 . — 1 
 
 r-l CO LO 
 
 1— l^-i—lr-l(XILOCMCOr-ICM>^-i— ICMCMCM 
 
 . 
 
 1— 1 
 
 r^ lo 
 
 (XI 1— 1 
 
 O 
 
 co >s}- 
 
 O 
 
 r--. cn r— i 
 
 cnLOcnr^cooococor- loocxicococo 
 
 
 
 c£ 
 
 . — 1 
 
 1— i >3- 
 
 CO 
 
 LO 
 
 CO 
 
 LO 
 
 co co cn 
 
 COCDr-HCOCOCOLOO^COCMOCOCMCO 
 
 LO 
 
 < 
 
 cn 
 
 CNJ CO 
 
 (XI CO 
 
 I—l 
 
 «* 
 
 «^r- 
 
 CO 
 
 (MIDN 
 
 CMLOCOCMCMr^CO«=a-COCOCOCMCOCOCO 
 
 CO 
 CD 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 . 
 
 l-H 
 
 CO l-H 
 
 «* 
 
 CO 
 
 < — 1 
 
 r^ co 
 
 •4-lOH 
 
 NOVDNCM<v|-OCVJOO(\lrHOMnCOO 
 
 LO 
 
 CQ 
 
 en 
 
 CNJ r- 1 
 
 "^ r-* 
 
 CXI 
 
 cn 
 
 r^ 
 
 CO 
 
 CO CO CO 
 
 NNOOlOCOOOIOJ'vtlO'taiON 
 
 re 
 
 LU 
 
 en 
 
 co r^ 
 
 co r^. 
 
 CM 
 
 LO 
 
 LO < 
 
 ro(ON 
 
 CM"^-"^-CMCor^-5i-co-=d-^t-cocxi(Ococo 
 
 CO 
 
 U_ 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 cn 
 
 «3" LO 
 
 r-H *3" 
 
 CO 
 
 r-H 
 
 CO 
 
 CO 
 
 CO <Sj" LO 
 
 COCOCOLOCMCOI^^t-LO«^-cX3COC0COCn 
 
 CO 
 
 21 
 
 co 
 
 r-. co 
 
 r^ lo 
 
 CO 
 
 co 
 
 LO 
 
 CXI 
 
 ^l- r~» co 
 
 (D^-CONNCOOJNOrHN>-iOir)Lf) 
 
 >- 
 
 ■=C 
 
 1— 1 
 
 •=d- co 
 
 •3- 
 
 CO 
 
 r^ 
 
 r~- 
 
 CO 
 
 LO CO CO 
 
 coLOLOcococnLO^-cocor^coLOcO"^- 
 
 O. 
 
 •"3 
 
 1 — 1 
 
 
 i— 1 
 
 
 
 
 
 
 
 . 
 
 CO 
 
 lo r^. 
 
 CD CO 
 
 cn 
 
 ■st 
 
 CO 
 
 T— • 
 
 CVJ KCD 
 
 1— •cncocO'— «cmi— lOLor^i— ir- icMcnt— 1 
 
 LU 
 
 (_> 
 
 1^. 
 
 1— I CT> 
 
 O O 
 
 1—1 
 
 O 
 
 r-H 
 
 CO 
 
 cn co 
 
 ocnLOoocnocooLor^cnLOcor^cn 
 
 LU 
 
 LU 
 
 <3- r-- 
 
 ^r 
 
 CO 
 
 r^-. 
 
 r~> 
 
 LO 
 
 uirvN 
 
 CO"=SrLOCMCMCn«^l-^-LOLOCOCXI^-CMCO 
 
 O 
 
 O. 
 
 r-H 
 
 
 r- 1 
 
 
 
 
 
 
 
 . 
 
 r^ 
 
 «vj- <n 
 
 t— 4 r-H 
 
 CO 
 
 O LO LO 
 
 cm co cn 
 
 N <t OllO O iO O r- ICOCOOCOCOLOO 
 
 Q 
 
 > 
 
 CO 
 
 CO 1^ 
 
 CO r-l 
 
 «3- 
 
 LO 
 
 CO 
 
 ^1- 
 
 cONr>. 
 
 r^ t— icoLococncDcni-tcococMOcor-^ 
 
 
 O 
 
 CO 
 
 (XI LO 
 
 (Xi r-~ 
 
 r-H 
 
 «* 
 
 "St 
 
 co 
 
 CM LO LO 
 
 1— KtroHr- icococMcoco"=^-t— iroHCvi 
 
 l-H 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO CM LO 
 
 LO LO 
 
 O 
 
 r— r>» 00 
 
 r^ co r-«. 
 
 cocnooococor^LOcot—icMr^cooco 
 
 f— 
 
 1— 
 
 LO 
 
 CXI <^- 
 
 00 «^- 
 
 
 CM 
 
 CM 
 
 r^ 
 
 ro-^^ 
 
 'tWN'tNOMOincoon'tLn'* 
 
 <c 
 
 O 
 
 LO 
 
 (XI 
 
 (XI 
 
 
 r— i 
 
 I — 1 
 
 
 CM CO 
 
 CO ^1" r—l CM CXl t— 1 1— 1 
 
 LU 
 
 zc 
 
 O 
 
 
 
 
 
 
 
 
 
 
 \— 
 
 T— 1 
 
 I-- 
 
 O CO 
 
 O 
 
 CM 
 
 cn 
 
 
 
 O CM O 
 
 COCOOCXICMCOLOCMOCMOLOOCncO 
 
 _j 
 
 a. 
 
 O 
 
 CNJ 
 
 
 
 r-H 
 
 
 
 >3- CM 
 
 lo r-i>^-cM"^-co i-hcoi—ico cn 
 
 <c 
 
 LU 
 
 C\J 
 
 
 
 
 
 
 
 r-H 
 
 CM i—l i—l 
 
 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r— 
 
 CD 
 
 CO 
 CO 
 
 
 
 
 
 O 
 
 O 
 
 
 
 
 
 OOO 
 LO 
 
 or--oocM>^-ocooooocooco 
 lo cm co lo co r— cn 
 
 _I 
 
 ZD 
 
 
 
 
 
 
 
 
 
 CM r-l 
 
 =3; 
 cc 
 
 < 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 CD 
 
 
 
 
 
 O 
 
 O 
 
 
 
 oo^oooocomrocxjoooiOHiooi 
 
 
 
 _J 
 
 <d" 
 
 
 
 
 
 
 
 CO 
 
 r^. cmcmloo co<-Hcn 
 
 7Z. 
 
 ZD 
 ■"D 
 
 
 
 
 
 
 
 
 
 CXI CM 
 
 2: 
 O 
 1— 1 
 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 <: 
 
 
 
 
 
 
 
 
 
 ra 
 
 
 1— 
 
 
 
 
 
 
 
 
 
 r— c: 
 
 
 CO 
 
 
 
 
 
 
 -M 
 
 
 XJ c 
 
 1— (J •!- 
 CO CD CO 1 — ra 
 
 
 O 
 
 
 
 
 
 JZ 
 
 
 
 <C 
 
 1— 
 
 -SZ CD ra ZJ O •!— ra *i— 
 
 
 Z^ 
 
 <+- 
 
 
 
 
 +-> 
 
 
 
 (O t— 1 
 
 CD >> 
 
 1 — 4-> cn<+_ +j ■«-» s- 
 
 
 <c 
 
 
 4- 
 
 +J 
 
 
 CO 
 
 •1 — 
 
 cc 
 
 C -21 
 
 •p- C 
 
 racuco s. n- c Ol Dl C Hi (O 
 
 
 
 <t 
 
 03 
 
 X +-> 
 
 3 
 
 < 
 
 E 
 
 
 ra a: 
 
 Cf- ra 
 
 ^. (Dcnra-ocarzjcDS-cDracos 
 
 
 LU 
 
 2^ 
 
 +-> 
 
 1- 
 
 c 
 
 CO 
 
 CO 
 
 QJ 
 
 -^ 
 
 CO D_C_) 
 
 CraOCQCXIC: 1 — ECDt-S- 
 
 
 h- 
 
 O 
 
 CO 
 
 rz 
 
 r— 
 
 z^ 
 
 
 1 — 
 
 4_ U_ 
 
 S- 
 
 ra-^C =a;cOra+ J CQrO- f ZiiDLL.rar0 
 
 
 <t 
 
 r-j 
 
 CD 
 
 CD to 
 
 O CO 
 
 at <=C 
 
 +-> 
 
 +-> 
 
 ra 1 — 1 
 
 CD -C CD 
 
 -QCDtOCT) > — C 5--0 4->+J 
 
 
 1— 
 
 ►— 1 
 
 m 
 
 O O) 
 
 co sz 
 
 S g 
 
 S- 
 
 +J 
 
 X —1 
 
 -i^ co zj 
 
 i-s-cDcco •-^•r--aoc:cccc 
 
 
 CO 
 
 ct 
 
 1 — 
 
 -£Z S- 
 
 ZJ -r- 
 
 =3 a: 
 
 
 
 •f— 
 
 a) <; 
 
 ra -i- 1 — 
 
 ZJZJS-OO-rJroOCDrarararararO 
 
 
 
 <C 
 
 Li_ 
 
 a. o_ 
 
 1— 3: 
 
 >- < 
 
 Lu 
 
 _l 
 
 1— cz> 
 
 CQ CQ CQ 
 
 CQ LU U l_JZOaCC(/)l/)(/)(/)CO(/) j 
 
A5-11 
 
 Table A5-10 (continued) 
 
 o 
 
 K 
 
 ^f- O C\J LO LO 
 
 co 
 
 CO 
 
 «^-«^J-LOCDLOi— lisOCMLOCMCM 
 
 1— 
 
 ST 
 O 
 
 00 cx> en en en 
 
 CTl CTl 00 
 
 en 
 
 cnencncncncncncncncncn 
 
 cnu_ 
 
 
 
 
 
 
 
 
 
 
 •i— o 
 
 4- 
 
 r-» t- 1 cm co lo 
 
 ^f 1— 1 LO 
 
 CM 
 
 CMCOCnLOLOLOCOCriLOLOO 
 
 to 
 
 z: 
 
 !—) 1 1 1 
 
 
 r-H 
 
 COCOCMLOCOi^-COCMCMCO«^- 
 
 CD 
 
 1—4 
 
 1 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 _l 
 
 Ol CO CO rHCM 
 
 NWN 
 
 
 
 coencMcncOT-ii— iLocoLococo 
 
 
 «=C 
 
 CM C\J CO «=f <£> 
 
 ■— 1 r^ en 
 
 CO 
 
 Or>-^J-COOLO'<|-LOLOCOCOLO 
 
 
 O 
 
 lo <^- cm lo *3r 
 
 LO r-1 CO 
 
 cr> 
 
 cocO'cj-cmt— iloi— ir^-^-«^-LOCM 
 
 
 < 
 
 CO LO LO LO Lf> 
 
 LO LO LO 
 
 <3- 
 
 i—l r-H r-H r— 1 
 
 UJ 
 
 CO «!*■ LO <— 1 LO 
 
 r>. ^t- lo 
 
 LO 
 
 000000000000 
 
 
 2: 
 
 LO CO LO CSJ i-H 
 
 CM CM <^J- 
 
 
 
 
 O 
 
 i—l 
 
 
 
 
 
 O 
 
 
 
 
 ^ 
 
 
 OCTlCO©'* 
 
 00 r- lo 
 
 CM 
 
 000000000000 
 
 
 >- 
 
 <^hoo<-s 
 
 r-^ «h- 
 
 I—l 
 
 
 
 < 
 
 ■=3" CO CM 1— 1 1— 1 
 
 CM 1— 1 CM 
 
 I—l 
 
 
 . 
 
 LO C\J 00 r-» <X> 
 
 O LO CO 
 
 r^. 
 
 COLOOi— IOOOLOLOLOOO 
 
 
 CrT 
 
 CXl CO LO CO CM 
 
 1— 1 en <^- 
 
 00 
 
 CO i-H CM CO CO 
 
 
 
 LO LO LO CO *5j- 
 
 LO «3" LO 
 
 CO 
 
 
 . 
 
 O CO r-^ CTl CM 
 
 CO CTt r-H 
 
 LO 
 
 oocM^i-cncncnLOcocMCMi— 1 
 
 o 
 
 cc 
 
 CM CT> CO CM t^ 
 
 moiN 
 
 CO 
 
 co<=3-Lor--. en ocooooo 
 
 LO 
 
 <=C 
 
 OC0C0ISN 
 
 CO CO CO 
 
 r^ 
 
 r-H r-H r-H r-H t-H CM r-H 
 
 LO 
 CD 
 
 2: 
 
 I-H 
 
 
 
 
 . 
 
 CM CO CO r^ f-H 
 
 LO r-H r-H 
 
 ■3- 
 
 OOrHVOrHlflVDLON^DCO'i - 
 
 c/j 
 
 OQ 
 
 lo co co r^ 
 
 lo lo en 
 
 r~- 
 
 LOcno^co^-coLor-^co^-LO 
 
 TCS 
 
 UJ 
 
 f-H CTl CTl CTl CO 
 
 en cti 
 
 CO 
 
 CM r-H 1— 1 CM I-H 1— 1 CM CM T-H 
 
 CO 
 
 u_ 
 
 r-H 
 
 r-H 
 
 
 
 . 
 
 lo 00 cm en LO 
 
 en en r^ 
 
 
 
 r^cOLOCMOLOLOOOLOCMr^ 
 
 CO 
 
 ^ 
 
 NMCOOCO 
 
 NOOl 
 
 CO 
 
 "*"^-^OO^CnmcvlONOCO 
 
 >- 
 
 <: 
 
 «3" *—i •— • cm 
 
 O CM CD 
 
 en 
 
 CO CM 1— 1 CO i-H CM^j-COCM 
 
 Q 
 
 ra 
 
 1— 1 1— 1 1— 1 i—l 1— 1 
 
 I — 1 I—l I— I 
 
 
 
 . 
 
 O CM LO CO LO 
 
 lo en «— i 
 
 r-* 
 
 cni— icnoco-^-ococoOi— ilo 
 
 UJ 
 
 O 
 
 CM CO CO i-l CO 
 
 CO i—l 1— • 
 
 CM 
 
 1— li— IOi— ICMLO"=J-CT>LOLOr^LO 
 
 UJ 
 
 UJ 
 
 «3- f— 1 en 
 
 en i—i 
 
 en 
 
 COCMt-HCO r-H 1— 1 CO CO r-H 
 
 o 
 
 Q 
 
 1— 1 r-H t— 1 1— 1 
 
 i—l r-H 
 
 
 
 . 
 
 LO LO a* LO 
 
 IfiHCO 
 
 CO 
 
 coLO>vj-"v]-or~^ocMLOcoOLO 
 
 O. 
 
 > 
 
 LO CM t-H CO LO 
 
 I— 1 I— 1 «3- 
 
 CO 
 
 Lor--CM^- lo r-.cncnLO 
 
 
 O 
 
 OCOCONts 
 
 LO r^ LO 
 
 LO 
 
 i—l r-H r-H i-H 
 
 O 
 
 ~ZL 
 
 I-H 
 
 
 
 
 . 
 
 CT> LO CO CO LO 
 
 I^CMI^ 
 
 
 
 LooocMOOOoencooo 
 
 J— 
 
 \— 
 
 CO LO CM r-i CM 
 
 r-» «3- 
 
 r-~ 
 
 r-H r-H r-H CM 
 
 <c 
 
 O 
 
 LO «sj- ^f- CO CO 
 
 CO CO CO 
 
 CM 
 
 
 UJ 
 
 O 
 
 
 
 
 
 zn 
 
 r— 
 
 01 cm r- «vj- 
 
 U3UIIN 
 
 I—l 
 
 000000000000 
 
 _i 
 
 Q_ 
 
 r». co t— 1 co lo 
 
 lo en co 
 
 LO 
 
 
 <c 
 
 UJ 
 
 CM t-H i—l 
 
 
 
 
 i— 
 o 
 
 00 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 • 
 
 en lo en 
 
 O LO CM 
 
 
 
 000000000000 
 
 
 
 
 CT» CM 
 
 I-H 
 
 
 
 _J 
 
 O 
 
 
 
 
 
 <c 
 
 <C 
 
 
 
 
 
 2: 
 
 
 
 
 
 
 >- 
 
 LO CTl LO O CD 
 
 000 
 
 
 
 000000000000 
 
 o 
 
 _l 
 
 LO 
 
 
 
 
 ■^. 
 
 
 
 
 
 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 1 
 
 to 
 
 
 
 
 
 f— 
 
 O) 
 
 
 
 JC 
 
 
 <c 
 
 £Z C 
 
 
 
 
 
 
 f— 
 
 •1- 
 
 
 
 JZ 03 
 
 
 00 
 
 Q- +■> 1— 
 
 
 
 ra u a> a) 
 
 1 — n3 1 — JZ O) CQ 
 
 
 Q 
 
 00 u 
 
 +-> 
 
 c 
 
 O CD to 1 — U CU 
 
 
 ^ 
 
 c <_> 
 
 s_ c 
 
 
 
 ocas-T- <o n3L0 £ 
 
 
 <c 
 
 
 
 O ZJ M 
 
 CD d) UJ 
 
 +-> 
 
 •1— (1) > -P "O QJ 1 — to 1 — 
 
 
 
 Q 
 
 IOT3 O I— 
 
 a. i- > 0; 
 
 en ex. 
 
 rio^cwcmoOfl no 
 
 
 UJ 
 
 ■=c 
 
 to (O S- O O 
 
 cu to <c 
 
 C Q 
 
 u cs a) fl T3or o_ 
 
 
 1— 
 
 a; 
 
 O S- CJ-Di — UJ 
 
 ct>m- re :s 
 
 •r— 1 — 1 
 
 fOO w3i — -r C 18 <d Id 
 
 
 <c 
 
 
 
 E > c .a z: 
 
 TJ +■> < 
 
 E CC 
 
 1 — 4->4->-i<: OJ E n> 1^1 — Q.4-> 
 
 
 1— 
 
 _J 
 
 ra 1— c <a a> z: 
 
 •r- J_ S — 1 
 
 ■— O 
 
 rO >> S- O >>-^ (O 1— C r— E *^ 
 
 
 00 
 
 
 
 r— O CD S_ 13 
 
 i_ <o cd uj 
 
 •r- _l 
 
 aiooioQJiO'ri.jjioioii) 
 
 
 
 
 
 <UQOQ- O 
 
 caiz 
 
 3 U_ 
 
 cCQU.'-D^-JSIOQ-f— J— 31 
 
A5-12 
 
 Table A5-10 (continued) 
 
 o 
 
 e 
 
 CD 
 
 CO 
 
 CO CO 
 
 co r^ 
 
 CO 
 
 
 CO 
 
 00 
 
 «3- 
 
 =cr «3- <sf cm 
 
 co 
 
 CO 
 
 CO CO CM 
 
 1— 
 
 co 
 
 CX> 
 
 cn 
 
 cn cr> 
 
 on cn 
 
 cn 
 
 
 CTi 
 
 cn 
 
 cn 
 
 cn cy> cr> cn 
 
 cn 
 
 cn 
 
 CTt CTi 0~> 
 
 CT>U_ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •i— o 
 
 -f— 
 
 r^ 
 
 CO 
 
 CO 
 
 CO CO 
 
 <tf 
 
 
 <=3- 
 
 CO 
 
 CO 
 
 rorvCMrv 
 
 1— 1 
 
 CO 
 
 O O CM 
 
 oo 
 
 21 
 
 < — 1 
 
 1 — 1 
 
 CM CM 
 
 CM i—l 
 
 CM 
 
 
 
 
 1 
 
 1 1 1 1 
 
 1 
 
 
 1 
 
 CD 
 
 i — i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 CTi 
 
 cn 
 
 r^» ro 
 
 CO CO 
 
 cn 
 
 cn 
 
 on co 
 
 O CM 
 
 CO 
 
 i-H CO CO CO 
 
 cn 
 
 co 
 
 lo o~i cn 
 
 
 <C 
 
 CM 
 
 CO 
 
 Cn 00 
 
 CO CM 
 
 1 — 1 
 
 CM 
 
 r^ 
 
 CO «n1- 
 
 ro 
 
 CM CO O CM ro CM 
 
 CO 
 
 a> ro 
 
 
 ZD 
 
 cn 
 
 cn 
 
 co ro 
 
 r-H CO 
 
 co co 
 
 co <3- 
 
 r^ co 
 
 
 
 CO 1— 1 «=t O CO 
 
 •3- 
 
 "5fr 
 
 CM CO <3- 
 
 
 21 
 21 
 
 CM 
 
 CM 
 
 CM CM 
 
 CM CO 
 
 r-H 
 
 1—1 
 
 CO CO 
 
 co co 
 
 r^. 
 
 CO CO CO CO CO 
 
 co 
 
 <* 
 
 CO CO CO 
 
 
 UJ 
 
 CD 
 
 O 
 
 
 
 O CD 
 
 O 
 
 O 
 
 i-H CM 
 
 CM 
 
 1 — 1 
 
 CD co cn co 
 
 00 
 
 
 
 <y> cn 
 
 
 21 
 
 
 
 
 
 
 
 00 cn 
 
 o~> cn 
 
 ■=d- 
 
 <3- co ro co 
 
 I— 1 
 
 
 CO CO CO 
 
 
 ZD 
 
 
 
 
 
 
 
 1 — 1 
 
 1—1 
 
 1— 1 
 
 
 
 
 
 
 ■"D 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CM 
 
 CO 
 
 
 
 «vf 
 
 O 
 
 O 
 
 CO i— i 
 
 co cn 
 
 cn 
 
 t~- 1— 1 cn co co 
 
 CO 
 
 co 
 
 on r^. cn 
 
 
 >- 
 
 C\J 
 
 CM 
 
 
 ro 
 
 
 
 >=j- cn 
 
 CO CO 
 
 1— t 
 
 "=t i-h 00 CO CO 
 
 CO 
 
 co 
 
 00 r-^ ro 
 
 
 2: 
 
 
 
 
 
 
 
 CM CO 
 
 CO CM 
 
 ro 
 
 CM i-H 1— 1 CM 
 
 1— 1 
 
 
 t— 1 1— 1 CM 
 
 . 
 
 1 — 1 
 
 CO 
 
 O CO 
 
 ro r-» 
 
 co 
 
 CO 
 
 CO r-l 
 
 r^- co 
 
 CO 
 
 CO O O CO CD 
 
 ■^1- 
 
 r-^ 
 
 i-H CM CO 
 
 
 q: 
 
 *t 
 
 CO 
 
 cn cn 
 
 co r^. 
 
 **■ 
 
 ro 
 
 co co 
 
 CO CM 
 
 CO 
 
 cn co co cm i-h 
 
 co 
 
 CO 
 
 r^» co cm 
 
 
 o_ 
 
 1 — 1 
 
 i—i 
 
 
 1—1 
 
 
 
 ■=*• co 
 
 CO «* 
 
 co 
 
 i-H "=i- «3- «v)- CO 
 
 CO 
 
 CM 
 
 «=d- "=3- co 
 
 . 
 
 I-H 
 
 h* 
 
 O CO 
 
 CO CO 
 
 ■* 00 
 
 CM CO 
 
 r^. «^- 
 
 cn 
 
 cr> CD 00 cr> 1— 1 
 
 cn 
 
 
 
 CD cn ro 
 
 
 
 ct: 
 
 CO 
 
 ro 
 
 CO CO 
 
 en co 
 
 CO 
 
 
 
 CM CO 
 
 cn 
 
 
 
 ro cn i-h ^j- co 
 
 CO 
 
 CM 
 
 cn co 
 
 CO 
 
 <c 
 
 <=t «5 
 
 CO CO 
 
 cm -^r 
 
 CM 
 
 CM 
 
 r^ 
 
 i—l CO 
 
 cn 
 
 co 00 on co cn 
 
 r~» 
 
 CO 
 
 00 00 en 
 
 CO 
 
 s 
 
 
 
 
 
 
 
 i-H 
 
 1 — 1 
 
 
 
 
 
 
 cn 
 
 cn 
 
 cn ^j- 
 
 co r^. 
 
 CO 
 
 CO 
 
 •^f- cn 
 
 i-H CO 
 
 CO 
 
 <h,- co r^. co 
 
 r-^ 
 
 00 cn 
 
 CO 
 
 CQ 
 
 CM 
 
 CM 
 
 <=i- co 
 
 CD r-^ 
 
 CO 
 
 O 
 
 co ^i- 
 
 cn i—i 
 
 CO 
 
 co <* cm ro 
 
 CO 
 
 CO 
 
 cm ^- r^ 
 
 03 
 
 UJ 
 
 co 
 
 co 
 
 "vf ■>)" 
 
 <3- co 
 
 CO 
 
 CO 
 
 C0 CM 
 
 CM OD 
 
 
 
 CO O i-H O i-H 
 
 cn 
 
 r~- 
 
 on 
 
 CD 
 
 U_ 
 
 
 
 
 
 
 
 1 — 1 
 
 i — 1 
 
 1 — 1 
 
 1— 1 i—H i— 1 i— 1 
 
 
 
 i-H i-H 
 
 . 
 
 C\J 
 
 cn 
 
 cn cm 
 
 CO 
 
 h- 
 
 "3- 
 
 ro co 
 
 oro<^ 
 
 co cn <^- co co 
 
 CO 
 
 CO 
 
 CO CO r-l 
 
 CO 
 
 "y 
 
 ^1- 
 
 CO 
 
 <^j- CO 
 
 1-1 
 
 co 
 
 cn 
 
 1— i CO 
 
 O CO 
 
 CM 
 
 CO CD i-H r—l CO 
 
 ro 
 
 co 
 
 r^ i-h cm 
 
 >- 
 
 < 
 
 co 
 
 CD 
 
 co co 
 
 co r^ 
 
 <tf 
 
 CO 
 
 i—1 CO 
 
 CO O 
 
 CO 
 
 00 CM ro CM CO 
 
 r-H 
 
 on 
 
 i-H ■— 1 CM 
 
 < 
 
 ra 
 
 
 
 
 
 
 
 i—l t-H 
 
 r-l r-l 
 
 i— 1 
 
 1 — 1 i-H i-H 1 — 1 
 
 i-H 
 
 
 r-H i-H i-H 
 
 . 
 
 C\J 
 
 co 
 
 CM CO 
 
 CM t— 1 
 
 hs 
 
 CO 
 
 r^- 
 
 CM CO 
 
 CO 
 
 1— 1 co i-h ro i-h 
 
 ro 
 
 CO 
 
 CO i-H CO 
 
 UJ 
 
 CD 
 
 CO 
 
 CM 
 
 co <^- 
 
 
 
 CO 
 
 CO 
 
 «-H 1^ 
 
 CO CO 
 
 CO 
 
 cn 1— 1 co <— • cm 
 
 CM 
 
 cn 
 
 CO CO CM 
 
 LU 
 
 UJ 
 
 CO 
 
 CO 
 
 LO CO 
 
 co r-» 
 
 <d- 
 
 CO 
 
 O CO 
 
 >=j- cn 
 
 r— 1 
 
 [^ i-H i-H i-H CM 
 
 O 
 
 co 
 
 1— 1 O ■— 1 
 
 cc 
 
 CD 
 UJ 
 
 en 
 
 
 
 
 
 
 
 1 — 1 I— 1 
 
 i — 1 
 
 i—l 
 
 i — 1 i-H i-H i-H 
 
 i-H 
 
 
 1 — 1 r-H i-H 
 
 . 
 
 co 
 
 «tf 
 
 CO CO 
 
 r^ «* 
 
 ■3- co 
 
 CM CO 
 
 r-» co 
 
 O 
 
 ron^- con 
 
 CO 
 
 CO 
 
 co co r^ 
 
 CD 
 
 > 
 
 
 
 < — 1 
 
 ro ro 
 
 cn r^. 
 
 CM 
 
 cn 
 
 cn co 
 
 co 
 
 O 
 
 1— 1 co r^ co co 
 
 cn 
 
 
 
 00CMN 
 
 
 
 
 <**■ 
 
 •=3" 
 
 ro ro 
 
 CM *3- 
 
 
 i-H 
 
 r-*. 
 
 ■— 1 r^- 
 
 cn 
 
 co 1-^ p~- r^» co 
 
 CO 
 
 co 
 
 r^ r^ r^ 
 
 CD 
 
 21 
 i — i 
 
 21 
 
 
 
 
 
 
 
 1—1 
 
 i — 1 
 
 
 
 
 
 
 . 
 
 co 
 
 NCON 
 
 T— 1 1—1 
 
 r^ 
 
 CO 
 
 CO CO 
 
 CO CO 
 
 CO 
 
 ^j- CO CO CO 
 
 i-H 
 
 
 
 00 CO CM 
 
 h- 
 
 r— 
 
 I— 1 
 
 CM 
 
 r~^ co 
 
 r~» co 
 
 <3" CM 
 
 i-H CM 
 
 ^r 
 
 0-1 
 
 co cm ro CM 
 
 cn 
 
 CM 
 
 NHN 
 
 < 
 
 c_> 
 
 r-H 
 
 1— 1 
 
 
 i—t 
 
 
 
 «^1- CO 
 
 CO «3" 
 
 <3- 
 
 ■— 1 ro ro co "3- 
 
 CM 
 
 CM 
 
 co ro co 
 
 UJ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 CM 
 
 CO O CD 
 
 O «* 
 
 
 
 
 
 CM O 
 
 CM CO 
 
 CM 
 
 CO rHCftN^- 
 
 CVJ 
 
 CO 
 
 CO O i-H 
 
 _i 
 
 D_ 
 
 I— 1 
 
 i— 1 
 
 
 CM 
 
 
 
 CO 1^ 
 
 CO CM 
 
 r-» 
 
 co 00 cn 00 i-h 
 
 1^- 
 
 CO 
 
 cn i-h 
 
 < 
 
 UJ 
 
 
 
 
 
 
 
 •-1 CM 
 
 CM i-H 
 
 i—i 
 
 i— 1 
 
 
 
 i-H r-H 
 
 r— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 O 
 
 O 
 
 CD O 
 
 
 
 
 
 O ^1- 
 
 O O 
 
 
 
 cn co cn 
 
 
 
 O 
 
 cn co 
 
 
 CD 
 
 
 
 
 
 
 
 CO «3 
 
 
 
 
 
 
 _i 
 
 ZD 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■=c 
 
 <C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 c£ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 
 
 
 
 O CD 
 
 
 
 
 
 O CO 
 
 CO CD 
 
 
 
 CO 
 
 
 
 O 
 
 000 
 
 o 
 
 _] 
 
 
 
 
 
 
 
 i—» 
 
 i-H 
 
 
 
 
 
 
 21 
 
 ZD 
 
 •"D 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1— i 
 
 
 
 
 
 
 
 
 3: 
 
 
 
 
 
 
 
 h- 
 
 
 
 
 
 
 
 zs. 
 
 SI 
 
 
 
 
 
 
 
 << 
 
 
 
 
 
 
 
 CO 
 
 CM 
 
 
 
 
 
 
 
 h- 
 
 
 
 
 
 
 
 «^- 
 
 "3- 
 
 
 
 
 
 
 
 CO 
 
 
 
 
 
 
 CU 
 
 00 
 
 00 
 
 
 
 -0 
 
 
 00 
 
 
 Q 
 
 
 
 
 
 
 1 — 
 
 t— 
 
 r— 
 
 
 
 ,— 
 
 CD 
 
 (U r— -O 
 
 
 21 
 
 
 
 
 
 
 1 — 
 
 1 — 
 
 t— 
 
 
 
 
 CU 
 
 1 — 
 
 C O C 
 
 
 <C 
 
 
 
 
 CO 
 
 
 sz 
 
 • 1 — 
 
 03 
 
 03 C 
 
 r— CO 
 
 -a 
 
 •r— 
 
 1 — 
 
 >> a. cu 
 
 
 
 <: 
 
 
 03 
 
 03 ZS 
 
 
 03 
 
 > 
 
 u_ 
 
 U- 
 
 r— I—l 
 
 O 5- 
 
 M- <C 
 
 • 1 — 
 
 03 03 CQ 
 
 
 UJ 
 
 1— H 
 
 CO 
 
 4J 
 
 +-> -O 
 
 
 c 
 
 00 
 
 
 4-> 
 
 cu 
 
 rjid) (O 
 
 cn 21 
 
 > 3 C 
 
 
 h- 
 
 CD 
 
 c 
 
 C 
 
 co E 
 
 C 
 
 c 
 
 03 O 
 
 CU 
 
 O 00 
 
 -»-> -21 
 
 O 03 C T- 14- 
 
 c <C 
 
 00 
 
 03 JZ 
 
 
 «a: 
 
 ce: 
 
 CU 
 
 03 
 
 =3 =3 
 
 O CU 
 
 03 
 
 E zc 
 
 00 JZ 
 
 JZ •!— 
 
 03 >—t 
 
 S- U T- S_ Jxi 
 
 •1— 1 — 1 
 
 C 
 
 +-> •!- +-> 
 
 
 1— 
 
 
 
 sz 
 
 1 — 
 
 CT>t — 
 
 E 
 
 > 
 
 O <c 
 
 •r- 03 
 
 03 2 
 
 O _l 
 
 •1- •!- ■ OO 
 
 S- CD 
 
 03 
 
 S-T33 
 
 
 CO 
 
 UJ 
 
 +-> 
 
 +J 
 
 ZS O 
 
 03 
 
 03 
 
 JZ CD 
 
 -0 
 
 "O CU 
 
 O —J 
 
 03 JZ O CU O 
 
 D_ 21 
 
 > 
 
 O C O 
 
 
 
 CD 
 
 <<<u 
 
 2: cn 
 
 co 
 
 (— 1-. 
 
 CQ 1 — 1 
 
 l—l _i 
 
 D_ 1—1 
 
 oosq-q: 
 
 CO i—i 
 
 UJ 
 
 U_ r-l CO 
 
A5-13 
 
 Te*ble A5-1Q (continued) 
 
 o 
 
 R 
 
 LO LO OO CO 1— 1 
 
 CTi CTi 
 
 CTi CM 
 
 CO <cj- 
 
 CO 
 
 l-~ 
 
 CO LO CO 
 
 cn 
 
 LO CO 
 
 1— 
 
 ID 
 
 Cn CT> CT> CT> CTl 
 
 CTi Ol 
 
 CTl O 
 r-H 
 
 CTi CTl 
 
 CD 
 
 CT. 
 
 CTl CTl cn 
 
 cn 
 
 CO CO 
 
 E 
 
 cnu_ 
 
 •1— o 
 
 OO 
 
 
 
 
 
 
 
 
 
 
 +- 
 
 <* N HOCM 
 
 CO CM 
 
 CO LO 
 
 CO CO 
 
 00 
 
 LO 
 
 LO CTl CM 
 
 CM 
 
 CO LO 
 
 in 
 
 2: 
 
 1 1 1— 1 1— 1 1— 1 
 
 1 
 
 
 
 
 CM 
 
 CM CM CO 
 
 CM 
 
 I— t 1 
 
 CD 
 
 1 — 1 
 
 1 1 1 
 
 
 
 
 
 
 
 
 1 
 
 Q 
 
 3: 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 ^■(XHOHO 
 
 CTi 00 <— ' 
 
 CM O 
 
 •st CO 
 
 O 
 
 1 — 1 
 
 >3- cn lo 
 
 ■^r 
 
 r~- i-h 
 
 
 < 
 
 <*orvLnoj 
 
 r»- CO «d" 
 
 CO CM 
 
 CO CO 
 
 CO 
 
 CM 
 
 CO CM LO 00 
 
 CO 
 
 CO t—* 
 
 
 ID 
 
 i-H CO CO 01 CO 
 
 <sj- CTl r— 1 
 
 1— 1 CD 
 
 CM CO 
 
 CO 
 
 CTi 
 
 LO CD "^ CO 
 
 r-H 
 
 r^. lo 
 
 
 2: 
 < 
 
 co co r~- co r^ 
 
 LO >=j- CO 
 
 LO ■5J- 
 
 LO «3" 
 
 ■^r 
 
 r-H 
 
 r-H r-H r-H i-H CM 
 
 cn r^ 
 
 
 
 
 
 
 
 
 
 
 
 LU 
 
 CO CTl CO Cn ^f" 
 
 00 CTl CM 
 
 CM CO 
 
 "vf O 
 
 CTi 
 
 O 
 
 OOOO 
 
 CD 
 
 CO r—t 
 
 
 2: 
 
 co co r-^ co lo 
 
 T-i <* 
 
 1— 1 
 
 CM 
 
 
 
 
 
 CO t-H 
 
 
 
 
 
 
 
 
 
 
 
 
 i-H r-H 
 
 
 •"3 
 
 
 
 
 
 
 
 
 
 
 
 r^ t— 1 <sj- CT> 
 
 Cn "sT CO 
 
 ■=3- r-. 
 
 CTi LO 
 
 LO 
 
 O 
 
 OOOO 
 
 
 
 CO CM 
 
 
 >- 
 
 r-^ i-H co «— 1 CM 
 
 •vf CM CO 
 
 CM CO 
 
 <3" O 
 
 
 
 
 
 
 co r*». 
 
 
 •=C 
 
 rHCMCMMCM 
 
 1— 1 1— 1 CM 
 
 t— 1 
 
 r-H 1— 1 
 
 t-H 
 
 
 
 
 ^j- CO 
 
 
 21 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO CTi CO CO t-H 
 
 cm ^1- r-^ 
 
 
 
 O LO 
 
 LO 
 
 CT. 
 
 co r-~ cn cn 
 
 i-H 
 
 CO LO 
 
 
 a: 
 
 CM 00 «=T CO CO 
 
 MtlO 
 
 CO 1^ 
 
 CTi CM 
 
 r-H 
 
 CO 
 
 CO CM CO CO 
 
 CO 
 
 lo r-^ 
 
 
 a. 
 
 «Sj- «r4- LO >=t LO 
 
 CO CO LO 
 
 CO CM 
 
 CO CO 
 
 CO 
 
 
 
 
 CO CO 
 
 
 ■=c 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CTi (^ CO CTi CO 
 
 <— 1 CTi ^f 
 
 CM LO 
 
 CO LO 
 
 CM 
 
 O 
 
 CO r-H LO CM 
 
 ** 
 
 CO CM 
 
 o 
 
 a: 
 
 LO CO CM CO CVJ 
 
 CO <— 1 CO 
 
 CM ^f 
 
 LO CO 
 
 CO 
 
 CO 
 
 ONOicn 
 
 
 
 ti- 
 
 LO 
 
 < 
 
 CO CTl O CTi O 
 
 r-* r-~ co 
 
 1^ CO 
 
 r-^ co 
 
 CO 
 
 CM 
 
 CM T-H i-H r-H 
 
 CO 
 
 ro 
 
 CO 
 
 2: 
 
 1— 1 t— 1 
 
 
 
 
 
 
 
 
 T-H T—\ 
 
 . 
 
 CM CO «st CO «— 1 
 
 CO O LO 
 
 CO «^j- 
 
 CO CO 
 
 CO 
 
 r-H 
 
 ■=3- CO <d" CO 
 
 CO 
 
 O CM 
 
 (/> 
 
 CQ 
 
 ^•^ocncM 
 
 CO "vf LO 
 
 cn 
 
 CTi «— 1 
 
 t-H 
 
 CO 
 
 cnnisin 
 
 CM 
 
 r^ co 
 
 03 
 
 LU 
 
 O rHM HM 
 
 CTi CO CT 
 
 00 CO 
 
 00 CO 
 
 00 
 
 CO 
 
 CM CM CM CM 
 
 ■St 
 
 «3" r-H 
 
 CD 
 
 U_ 
 
 
 
 
 
 
 
 
 
 r-H i-H 
 
 
 . 
 
 CTi CO O LO O 
 
 CO 1— 1 CO 
 
 CM CO 
 
 LO CO 
 
 
 
 r-H 
 
 cn co t-h co 
 
 CM 
 
 cn 
 
 oo 
 
 s: 
 
 lo cn cvj co co 
 
 CO LO CO 
 
 CM CM 
 
 CO "St 
 
 CO 
 
 r-» 
 
 CD CTl CO CO 
 
 LO 
 
 cn co 
 
 >- 
 
 <a; 
 
 cm ro^t^>* 
 
 1— 1 1— 1 
 
 .-1 
 
 O CTl 
 
 CTi 
 
 ■=3- 
 
 •=J- CM CO CO 
 
 LO 
 
 CO CO 
 
 < 
 
 rs 
 
 1— 1 r- 1 t— 1 «— 1 T-H 
 
 I-H t — If — 1 
 
 1— 1 r-H 
 
 r— 1 
 
 
 
 
 
 T-H i-H 
 
 . 
 
 uihso^d 
 
 CO CTi CO 
 
 O LO 
 
 CO CM 
 
 O 
 
 . — 1 
 
 cn «3- i-H cm 
 
 r<- 
 
 LO LO 
 
 LU 
 
 
 
 CO CO CO ^J- CTi 
 
 WCON 
 
 CO 
 
 CO O 
 
 CTi 
 
 CO 
 
 CO t-H «3- CM 
 
 r-~ 
 
 CO r-H 
 
 UJ 
 
 LU 
 
 1— 1 CO CM CM CM 
 
 O CTi O 
 
 CTi CTi 
 
 cn en 
 
 co 
 
 >=t 
 
 CO CM CO CO 
 
 "St 
 
 LO CM 
 
 a: 
 
 CD 
 Ul 
 
 O 
 
 1— 1 r— 1 r-H r— 1 1— 1 
 
 I— 1 I— 1 
 
 
 
 
 
 
 
 T-H T-H 
 
 . 
 
 CO f^- CO 1-^ CTi 
 
 LO CO O 
 
 CM 00 
 
 CTi CTi 
 
 CT. 
 
 CO 
 
 CO CO O CM 
 
 r>» 
 
 >=t r-^ 
 
 Q 
 
 > 
 
 CO CO CD CO CD 
 
 O CO 1— t 
 
 r^ i-h 
 
 CO 
 
 O 
 
 r-~ 
 
 i-h cn t-h cn 
 
 CTi 
 
 •sd- O 
 
 
 O 
 
 1-^ 00 CTi 00 CT» 
 
 r--- co co 
 
 CO CO 
 
 CO CO 
 
 CO 
 
 CM 
 
 CM CM t-h 
 
 CM 
 
 00 
 
 cd 
 
 >— 1 
 
 z: 
 
 
 
 
 
 
 
 
 
 T-H 
 
 . 
 
 CM CO O CTi 00 
 
 CO 1— » «— * 
 
 O CTi 
 
 t-l CTi 
 
 00 
 
 CO 
 
 i-h cn cn 
 
 r^ 
 
 CM CO 
 
 h- 
 
 »— 
 
 CM CO LO CO CM 
 
 r^ lo 00 
 
 r-~ cm 
 
 CTi CO 
 
 <3- 
 
 LO 
 
 CO i-H i-H 
 
 "St 
 
 CO 
 
 < 
 
 O 
 
 CO CO «s*" CO -=3- 
 
 CM CM CO 
 
 CM CM 
 
 CM CM 
 
 CM 
 
 
 
 
 CO LO 
 
 LU 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 CO CTi CO CO CO 
 
 rscoH 
 
 r^ co 
 
 LO •* "3" 
 
 
 
 OOOO 
 
 
 
 CO LO 
 
 _l 
 
 D_ 
 
 CTi CTi LO CD CO 
 
 LO CO 00 
 
 LO CO 
 
 r~» lo 
 
 LO 
 
 
 
 
 CO CTi 
 
 <c 
 
 LU 
 
 I— 1 1— 1 1— 1 
 
 
 
 
 
 
 
 
 CO T-H 
 
 j— 
 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 h- 
 
 CD 
 
 O CTi 1— • CTi CTi 
 CO t-H 
 
 CD O CO 
 
 
 
 
 
 O 
 
 
 
 OOOO 
 
 
 
 LO CO 
 r-H LO 
 
 _l 
 
 Z3 
 
 
 
 
 
 
 
 
 
 i-H 
 
 •=C 
 
 <c 
 
 
 
 
 
 
 
 
 
 
 2: 
 52 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 O O CM O CM 
 
 000 
 
 
 
 
 
 CD 
 
 
 
 OOOO 
 
 
 
 CO CM 
 
 
 
 _J 
 
 1—1 1— t 
 
 
 
 
 
 
 
 
 r^. i-h 
 
 z: 
 
 •"3 
 
 
 
 
 
 
 
 
 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
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 i — 
 
 c • • s- 2^: 
 
 1 — 
 
 (O dJ > 
 
 r— 1— 
 
 1 — to CQ 
 
 fOCi-S-fOOt — >« 
 
 -* >> 
 
 to c c 
 
 
 CO 
 
 1— 1 
 
 
 
 ra -t-> -»-> a. 
 
 •r™ 
 
 1— s- fa 
 
 <D f0 
 
 •1- T- UJ 
 
 S-'r-oOEOrO UJ 
 
 
 rC CU t- 
 
 
 
 2: 
 
 
 
 ^ CO CO co 2: 
 
 cqcocdix^sz s: 
 
 o_izzoto> s: 
 
 LU UJ 
 
 _i cc 3 
 
A5-16 
 
 Table A5-10 (continued) 
 
 o 
 
 K 
 
 1—1 
 
 r-H 
 
 ^j- CM 
 
 CO CM r-H LO 
 
 r-H r-H 0«^"r— ICOr— IOO 
 
 1— 
 
 Z3 
 
 en 
 
 CTl 
 
 cd cn 
 
 CD OlOOl 
 i—l 
 
 CDCD CDCDCDCDCDCDCD 
 
 cnu. 
 
 co 
 
 
 
 
 
 
 
 
 
 
 
 
 •I— o 
 
 +- 
 
 1 — 1 
 
 <* 
 
 <— 1 CM 
 
 >3- CM CO ■=!- 
 
 r-HCM LOr-lr^CMCMLOCM 
 
 00 
 
 2: 
 
 r-H 
 
 1—1 
 
 I— 1 T— 1 
 
 i—l 1 r-H T— 1 
 
 1 1 r— 1 r-H r— 1 II 
 
 <D 
 
 1 — 1 
 
 1 
 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 1 
 
 ro r^ 
 
 CM 
 
 cn 
 
 CO CO CO CO LO 
 
 LOCOt-HCMi-HCDi— ICOCDCO 
 
 
 <C 
 
 CO «"H 
 
 1 — 1 
 
 LO CO 
 
 <3" LO cm cn 
 
 r-»00LOCOr^t— lr-H«H-LOLO 
 
 
 =5 
 
 ro 00 
 
 CO 
 
 co cd 
 
 co r-H cm r^- r^ 
 
 C0C\J"*OC0CM03N^0rv 
 
 
 21 
 
 r-» ro 
 
 "St 
 
 «3- *3- 
 
 <3" CO CO CO CO 
 
 cor-^cor^>^-LO'^rcococo 
 
 
 ^Z 
 
 t— 1 
 
 
 
 
 
 
 < 
 
 
 
 
 
 
 LU 
 
 LO CO 
 
 LO 
 
 O CM 
 
 O r-H CO O O 
 
 LOCDLOOOCDCMCOOOCDLO 
 
 
 z; 
 
 p*. 
 
 . — 1 
 
 r-H 
 
 CM CO 
 
 >^-CD«^-r-^ r-H "vfco«:Hr 
 
 
 ID 
 
 CO 
 
 
 
 
 
 
 "-3 
 
 
 
 
 
 
 
 CO 
 
 co 
 
 CO •— 1 
 
 r-H CO r-H r—1 1"^ 
 
 CDCOCDCDCOr>»<d-CDr— 100 
 
 
 >• 
 
 CD CO 
 
 ro 
 
 i—l CM 
 
 CO CO CO CO 
 
 COi-HC\JCMr-ICOCMr-.r-H*3- 
 
 
 < 
 
 2: 
 
 csj en 
 
 1 — 1 
 
 r-H i—l 
 
 r-H CO 
 
 CMCOCMCOr— Ir— Ir— ICMCMCM 
 
 . 
 
 CO O 
 
 O 
 
 i— < cd 
 
 CO CTl CO r-H r-H 
 
 ^■iflfOLncoorj-Ncoo 
 
 
 cc 
 
 CO CO 
 
 CM 
 
 co en 
 
 CO CM ^1- O CO 
 
 lO "^ ■* >* O CO rH Oi <^- N 
 
 
 d. 
 
 CO CM 
 
 <3~ 
 
 CO CO 
 
 CM ^ LO CM CM 
 
 LOCOLOCO<=a-«*"^-LOLOLO 
 
 
 < 
 
 r-H 
 
 
 
 
 
 . 
 
 CO CM 
 
 ■ — 1 
 
 CD CO 
 
 IT) N^-HH 
 
 CMLOCDCD0100^1-O"=l- 
 
 o 
 
 C£ 
 
 CO LO 
 
 ■3" 
 
 CM LO 
 
 CD «3r CO CO CO 
 
 CD«^-«HrCOCOr-HLOr— ir^O 
 
 lo 
 
 <C 
 
 CO 
 
 r-^ 
 
 r-« r-» 
 
 lo r^. co «3- lo 
 
 moaioNcosowo 
 
 CO 
 CD 
 
 2: 
 
 t— 1 1— 1 
 
 
 
 
 r-H r-H r-H 1— 1 
 
 . 
 
 *H- CO 
 
 CO 
 
 CO LO 
 
 CO CM >^- r-H LO 
 
 CO>^-r-HLOLOLOCDCOi-HO 
 
 to 
 
 CO 
 
 CO CO 
 
 •^f- 
 
 r^ co 
 
 1— 1 «=J- 
 
 uimco'tconrspjco"* 
 
 rC 
 
 LU 
 
 r-H CO 
 
 co 
 
 CO 00 
 
 r^ co cn co co 
 
 1— Ir— ICDr— ICOCnOOr— Ir-Hr-H 
 
 OQ 
 
 u_ 
 
 1 — 1 1— 1 
 
 
 
 
 I — 1 1 — 1 r-H r-H r-H r-H r-H 
 
 . 
 
 co 
 
 CO 
 
 CO CD 
 
 O CO CO O i—l 
 
 <—ir^ocococDco«3-cot-i 
 
 CO 
 
 ■Zl 
 
 LO CO 
 
 CO 
 
 co 00 
 
 co co t-h <h- cn 
 
 H N 01 li) CO CM is ro CO In 
 
 >- 
 
 < 
 
 CO CO 
 
 CD 
 
 cn en 
 
 cn cn r-H co r^. 
 
 COCMi— ICMCDOCDCMCMCM 
 
 < 
 
 •D 
 
 T— i 1— 1 
 
 
 
 1 — 1 
 
 r— 1 r-H 1— 1 1— 1 r-H 1 — Ir-Hi— 1 
 
 . 
 
 O CM 
 
 O 
 
 r-H **" 
 
 co cn co co cr> 
 
 ^j-^j-r-^cocMcor-^LOcnco 
 
 LlI 
 
 C_) 
 
 «3" «3" 
 
 CO 
 
 CM CM 
 
 co cn ^r cm 
 
 CDCOOLOOCOCOCMLOLO 
 
 LU 
 
 LU 
 
 cm r^ 
 
 CO 
 
 cn cn 
 
 COCOOCON 
 
 r— Ir-Hr— Ir-HCDCDOOr— It- Ir— 1 
 
 cc 
 
 CD 
 
 LU 
 
 O 
 
 1— i i—i 
 
 
 
 r-H 
 
 r-H r-H r-H r-H r-H r-H r-H 
 
 . 
 
 CM r-H 
 
 cn 
 
 CO CO 
 
 cm cn lo co lo 
 
 r^.ocMr»o«3-oor^co«3- 
 
 Q 
 
 > 
 
 CM «H- 
 
 ^f- 
 
 r^ r^ 
 
 •=3- CD cm r-»- CM 
 
 rvHrON^uJwj-Wrj- 
 
 
 O 
 
 CO CO 
 
 LO 
 
 LO LO 
 
 CO CO CO LO LO 
 
 NODNNLninmrsNN 
 
 CD 
 
 i— i 
 
 ^ 
 
 r-H 
 
 
 
 
 
 . 
 
 ir> r^ 
 
 . — 1 
 
 00 -=d- 
 
 cn r-H cm co 
 
 Or-HCOOCOCOCOLOCMLO 
 
 i— 
 
 r— 
 
 CD LO 
 
 LO 
 
 «3- CO 
 
 CM r-H CO O CO 
 
 «^-r^.O"vl-CO>=l-C\Jr-HCMr-H 
 
 <c 
 
 CD 
 
 LO 
 
 CM 
 
 CM CM 
 
 CM CO <=3" CM r-H 
 
 ■^l-«^-«^- , =d-CMCMCM^-^l-'vJ- 
 
 LU 
 
 O 
 
 1— i 
 
 
 
 
 
 1— 
 
 r^ 
 
 CD 
 
 r-~ 
 
 CM CO CO CO CO 
 
 coHHHO^OMonoj 
 
 _j 
 
 o. 
 
 rs cm 
 
 CO 
 
 CO LO 
 
 r-H CO CM r-H 
 
 COO<3-«3-COCOCnJCMCMCO 
 
 <c 
 
 LU 
 
 •-h r-» 
 
 
 
 r-H 
 
 r-H CM r-H r-H r-H r-H r-H 
 
 r— 
 o 
 
 r— 
 
 CO 
 
 
 
 
 
 
 . 
 
 O CO 
 
 O 
 
 
 
 O CO CO O CD 
 
 CDLOCOr^OOOr-lCMCO 
 
 
 
 
 LO CO 
 
 
 
 CM 
 
 r-H CO CM CO CO CM CM 
 
 _I 
 
 =3 
 
 LO 
 
 
 
 
 
 
 <c 
 
 
 
 
 
 
 >- 
 
 CO CO 
 
 O 
 
 
 
 O O CD O O 
 
 OCMOCDOOOCDOCO 
 
 O 
 
 _1 
 
 cn 
 
 
 
 
 CM r-H 
 
 
 ■"3 
 
 •3- 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 1 — 1 
 
 
 
 
 
 • 
 
 
 r— 
 
 • 
 
 
 
 
 ^ — .^-^ r-^ 
 
 
 ■=c 
 
 >> 
 
 
 
 
 Q. O -!-> 
 
 
 r— 
 
 LU 
 
 10 
 
 >> 
 
 
 
 «=C o. c 
 
 
 CO 
 
 oi 
 
 -Q 
 
 +-> 
 
 
 
 — — -s*: t—i 
 
 
 
 1 — 1 
 
 O 
 
 •1— 
 
 
 a> >> 
 
 J- >> 
 
 
 Q 
 
 ;n 
 
 >- 
 
 O 
 
 O 
 
 rs 4-> 
 
 C C ro >> ro "U 
 
 
 ^ 
 
 CO 
 
 LU 
 
 
 
 
 cr •!- 
 
 OO Q. T3 t- S_ ro 
 
 
 «=c 
 
 Q_ 
 
 jt co 
 
 (_> 
 
 1—4 
 
 $- CD ^ 
 
 +->+-> cu ~o CD +-> CU 
 
 
 
 S 
 
 T3 to a; 
 
 "1 
 
 C X 
 
 0) E r— DC 
 
 SEOr— ES-+->OC0 
 
 
 LU 
 
 < 
 
 S- ro LU 
 
 +J 
 
 -^£ O LU 
 
 ZJ O r— i- O 
 
 >>r0tOi — (OCrOcoaj^ 
 
 
 h- 
 
 nz 
 
 O 12 --3 
 
 c 
 
 s- -t-> 2: 
 
 CT4-> c a> CU >- 
 
 err fi s. in 3 <u c 
 
 
 <: 
 
 
 U 
 
 ra 
 
 <o e 
 
 rs >> O 3 > 
 
 ro CD CDM- 4-> ^ CD -c: CU ro 
 
 
 1— 
 
 3: 
 
 C • 3 
 
 
 Scu 3: 
 
 -Q <TJ +-> O0 1 — ^ 
 
 -acc<4-c O-ES- 
 
 
 CO 
 
 LU 
 
 O 4-> LU 
 
 +J 
 
 CU i- LU 
 
 ■ — 1 — fO O •<— LU 
 
 1 — T-T-3CULi_rOOO>> 
 
 
 
 " L - 
 
 CD S ^ 
 
 •< 
 
 ^ r— ^ 
 
 car CD CC CC CO ^ 
 
 <cqcqcqoodq:i/h/i 
 
A5-17 
 
 Table A5-10 (continued) 
 
 o 
 
 K 
 
 t— 1 LO "^j- LO <d" «vl" 
 
 LO CO CM <3" 
 
 cr. 
 
 ■=* r-H CM CM 
 
 t-H CM CM CT 
 
 O CM 
 
 h- 
 
 =D 
 
 en cr cr> cr cr cr 
 
 CT CT CT CT 
 
 CO 
 
 CD CT) CTi CTl 
 
 CT CT CT CO 
 
 
 
 t-H r-H 
 
 en u_ 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •r— O 
 
 +- 
 
 ro CO "^t ud ro <?i- 
 
 «3" CO CM t— 4 
 
 J — 1 
 
 CO CM CM O 
 
 r— 1 "vl" t— 1 t-H 
 
 t-H CM 
 
 00 
 
 2: 
 
 .—1 t-H 1— 1 r-H C\J r— 1 
 
 CM CM CM CM 
 
 
 
 
 r-H t-H 
 
 CD 
 
 ►— t 
 
 
 1 1 1 1 
 
 
 
 
 
 Q 
 
 3: 
 
 
 
 
 
 
 
 
 _l 
 
 cm oorHinro Nin 
 
 1 — 1 1 — 1 UD CO 
 
 r\ 
 
 LO t-H O CM 
 
 CO LO^t N 
 
 LO O 
 
 
 cC 
 
 «^- M (Ti O CT> <d" cr> 
 
 LO O CM «3" 
 
 00 
 
 O LO LO CM 
 
 O CT CT t-H 
 
 CM LO 
 
 
 
 
 OJ rHconroLT) 
 
 CO CTl CM CM 
 
 O 
 
 CO CO LO LO 
 
 ^t- r-~- <3- «=j- 
 
 1-^ CO 
 
 
 < 
 
 <=j- CM CO CO CO CM CO 
 
 CO CT CT CT 
 
 LO 
 
 ^J- LO LO LO 
 
 LO LO LO LO 
 
 CO CO 
 
 
 UJ 
 
 0000000 
 
 NCOCflH 
 
 CTi 
 
 CTl LO r^ O 
 
 CD LO O O 
 
 
 
 
 zz. 
 
 
 1— 1 co en "=3- 
 
 CO 
 
 LO CM CO 
 
 LO CO LO LO 
 
 
 
 
 
 
 t — 1 1 — 1 r-H 
 
 
 
 
 
 
 ■"3 
 
 
 
 
 
 
 
 
 MnWN<tON 
 
 CTiH(MIN 
 
 CM 
 
 CO O r— 1 r^ 
 
 LO CO CM CO 
 
 ■3- r^. 
 
 
 >- 
 
 CO CXI C\J «=*■ CO CO 
 
 CM CO CO LO 
 
 O 
 
 HUJiskO 
 
 <3" CT ^ >^J- 
 
 co «3- 
 
 
 2: 
 
 
 CO CO CO CO 
 
 CM 
 
 HCMHH 
 
 CM t-H CM CM 
 
 
 . 
 
 CO N ID 'vj- O UD N 
 
 LO CO O t— 1 
 
 CT) 
 
 LO CM LO en 
 
 CO LO CO O 
 
 CT CO 
 
 
 0; 
 
 n rvtn ncocrio 
 
 •3" LO CT CO 
 
 CO 
 
 CO LO CM CM 
 
 >^J- CT <3" >^- 
 
 CO <— 1 
 
 
 
 CM iHHMrH CXI 
 
 LO r~~ LO LO 
 
 ■53- 
 
 CO LO "vf >=d- 
 
 LO <^1- LO LO 
 
 r-H CM 
 
 . 
 
 (M OrHCMNN^ 
 
 CO LO CM CO 
 
 r-H 
 
 >— 1 CO CTl CTl 
 
 ^t- 00 -=3- t-H 
 
 r^ cr 
 
 
 
 C£ 
 
 CD «3" CO LO CO LO CXI 
 
 O -=3" LO LO 
 
 r^ 
 
 O r-H O O 
 
 CM LO CM CM 
 
 CM CO 
 
 LO 
 
 ■=C 
 
 LO "^" <>{■ LO ^J- CO LO 
 
 CM CO CM CM 
 
 co 
 
 r^. en 00 co 
 
 CT CO CT CT 
 
 LO LO 
 
 LO 
 CD 
 
 21 
 
 
 t — 1 1 — It — 1 1 — 1 
 
 
 
 
 
 . 
 
 CO 00 CXI CXI CO CM CXI 
 
 CM CTl O CO 
 
 LO 
 
 NrvOlLT) 
 
 CMHU)N 
 
 *d- co 
 
 CO 
 
 CQ 
 
 CO rHC0NHU)Ln 
 
 -* NCM N 
 
 t— 1 
 
 CO <3- «3" LO 
 
 «^J- CT LO >^- 
 
 LO CO 
 
 CO 
 
 UJ 
 
 LO LO LO LO LO <3" LO 
 
 ^J- LO LO «=1- 
 
 O 
 
 CO O CT CTl 
 
 CD CT O CD 
 
 LO LO 
 
 CO 
 
 U_ 
 
 
 t— 1 r-H r-H i-H 
 
 i — 1 
 
 ^H 
 
 t-H t-H t-H 
 
 
 . 
 
 «3" O 1— 1 <^" LO LO CO 
 
 co cm cr co 
 
 co 
 
 OOICON 
 
 CT r^. O CT 
 
 CO CO 
 
 co 
 
 ^ 
 
 co co en co cxi >=3- lo 
 
 ONCOU) 
 
 CO 
 
 r^ LO 00 CTi 
 
 LO O O LO 
 
 LO CT 
 
 >- 
 
 <C 
 
 N LD IX) N N LO N 
 
 NCONN 
 
 1 — 1 
 
 CT t-H CD O 
 
 r-H t-H CM t-H 
 
 CO CO 
 
 
 ra 
 
 
 r-H t-H r-H r-H 
 
 <— 1 
 
 t-H t-H i-H 
 
 r-H t-H t-H 1 — 1 
 
 
 . 
 
 LO HHCOU3HN 
 
 co <3- cr co 
 
 
 
 t-H CO CT LO 
 
 O CM CO ^f 
 
 lo r>» 
 
 UJ 
 
 C_) 
 
 N CM Ch r^ >-< CM «* 
 
 LO CO LO 1— t 
 
 r^- 
 
 CMCOCO^ 
 
 t— 1 CO CO 
 
 <o CO 
 
 UJ 
 
 UJ 
 
 N LniONNlflN 
 
 ^t" LO LO LO 
 
 
 
 cnooo 
 
 t-H O t-H t-H 
 
 t^ r--. 
 
 en 
 
 CD 
 UJ 
 
 Q 
 
 
 1 — 1 i — 1 1 — 1 1 — 1 
 
 i — 1 
 
 t-H t-H t-H 
 
 r-H r-H t-H t-H 
 
 
 . 
 
 LO CO CO CO O i-5 CO 
 
 COHNCM 
 
 LO 
 
 CM CO "^f" LO 
 
 CO ^ CM t-H 
 
 CO CM 
 
 Q 
 
 > 
 
 LONnHLnmco 
 
 00 cn <xi 
 
 04 
 
 t-H CO t-H CT 
 
 LDCOCTiN 
 
 CT CM 
 
 
 O 
 
 lo cm ^r lo ^1- cm -^- 
 
 O r-H t-H r—t 
 
 1^- 
 
 LO NN LO 
 
 NLONN 
 
 <H/ LO 
 
 O 
 
 ^ 
 
 
 t 1 T— 1 1 It 1 
 
 
 
 
 
 ;y 
 
 
 
 
 
 
 
 
 I-H 
 
 . 
 
 LO 00 <3- CM «3" -=d- t-H 
 
 !*-» CM «=3" r-H 
 
 «— < 
 
 00 «=j- r^ 
 
 r-^ CO LO CM 
 
 "^- CO 
 
 1— 
 
 h- 
 
 tt NCM Cn^O Nhs 
 
 r^ «3- f^ 
 
 co 
 
 ■=3- CO «3" »-h 
 
 CT t-H O t-H 
 
 LO LO 
 
 <c 
 
 c_) 
 
 CXI 1— 1 1— 1 t— 1 1— 1 
 
 LO LO LO ^O 
 
 co 
 
 CM CO CO CO 
 
 ooro^-tt 
 
 t-H t-H 
 
 UJ 
 
 O 
 
 
 
 
 
 
 
 re 
 
 
 
 
 
 
 
 
 1— 
 
 CO O LO CO <— 1 O t-H 
 
 cm co cr <— > 
 
 LO 
 
 'H/Lo«^i-cO'^-Lor-.o 
 
 LO CO 
 
 1 
 
 Q_ 
 
 «=d" CO CM CXI 
 
 CMISi-HO 
 
 o^> 
 
 lo 00 r^ 
 
 t-H IO t-H CM 
 
 t-H t-H 
 
 <t 
 
 UJ 
 
 
 CM CM CM CM 
 
 
 t-H 
 
 t-H r-H t-H 
 
 
 1— 
 
 00 
 
 
 
 
 
 
 
 o 
 
 1— 
 
 
 
 
 
 
 
 
 . 
 
 0000000 
 
 co co r^. co 
 
 cr. 
 
 O LO LO LO 
 
 CM LO LO CT 
 
 
 
 
 CD 
 
 
 CM LO CO «3" 
 
 
 CM 
 
 CM t-H r-H 
 
 
 _1 
 
 
 
 
 
 
 
 
 
 < 
 
 «=£ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 0000000 
 
 <3- CD CO H 
 
 
 
 O CT O O 
 
 CT CD O LO 
 
 
 
 o 
 
 _J 
 
 
 CO <3- CM CO 
 
 
 
 
 
 2: 
 
 ZD 
 
 
 
 
 
 
 
 
 ■21 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 — 1 
 
 
 
 
 
 
 
 
 h- 
 
 
 
 
 
 
 
 
 <C 
 
 < 
 
 
 
 
 
 
 
 
 r— 
 
 z 
 
 00 £ 
 
 
 
 
 
 >, 
 
 
 CO 
 
 1 — 1 
 
 03 CD «=t 
 S- r- 1— 
 
 o> 
 
 
 
 
 •I — 
 
 
 O 
 
 
 
 cu c a 
 
 -i^ 
 
 
 •r— 
 
 C 
 
 
 
 
 ^ 
 
 C£ 
 
 CD +-> CD &- O CO ^ 
 
 fO c 
 
 
 4-> -a 
 
 "O 3 
 
 
 
 <c 
 
 <c 
 
 1 — +->-!-> -«-> «=c 
 
 -^ _J 
 
 
 as c: 00 
 
 •— >> O <C 
 
 fO 
 
 
 
 C_) 
 
 r— f0+JXI j: QIC 
 
 O 4-> 
 
 
 C (O 3 
 
 a> jx. +-> 2; 
 
 E 
 
 
 UJ 
 
 
 t X' O W Dl c 
 
 S- 00 00 
 
 
 c 1— _a c 
 
 •1— 00 00 
 
 
 
 
 J— 
 
 zc 
 
 > 1— c -r- .1- +j n: 
 
 03 1 O T- 
 
 c 
 
 •1- (U E O 
 
 >r- 3T3 D1 ZH 
 
 -c: (tj 
 
 
 <: 
 
 Y— 
 
 OJ dJ S- (U <U E w 1— 
 
 E •<- CDr— O 
 
 
 
 u > 3 -P 
 
 L0 X) CD C <C 
 
 to 00 
 
 
 1— 
 
 oc 
 
 -CQ-rOCUi — 1 — C CC 
 
 00 > S- 1 — 1— 1 
 
 <- 
 
 c: aj 1— >, 
 
 c e r— zs _i 
 
 1 — I— 
 
 
 CO 
 
 
 
 1/1 in r t. t t 
 
 •r- (U (d -r- zc 
 
 ^ 
 
 •r- 1 — id 
 
 <T3 (O O O ^ 
 
 ^- rs 
 
 
 
 **" 
 
 <C cd c£ 3 3: s: 
 
 CO Q U_ 3: O 
 
 <C 
 
 UUUQ 
 
 s: co 1— >- 
 
 l— 
 
A5-18 
 
 Table A5-10 (continued) 
 
 o 
 
 e 
 
 CT> 
 
 i — 1 
 
 OONrH 
 
 CO CM 
 
 CM CO CM CO CD 
 
 cm cn i-h 
 
 CD 
 
 LO CO CO 
 
 LO LO 
 
 t— 
 
 ZD 
 
 to 
 
 r^. 
 
 CT) 
 
 CT> CTi CTi 
 
 en cn 
 
 cn co cn cn o~> 
 
 cn 00 cn 
 
 00 
 
 cn cn cn 
 
 ct> cn 
 
 sz 
 cou_ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •i— O 
 
 +- 
 
 r^ 
 
 C\J 
 
 r-H CO CO 
 
 LO 1— 1 
 
 CON OlHN 
 
 CO CM i-H 
 
 CO 
 
 CO O r-H 
 
 cn co 
 
 V) 
 
 ^ 
 
 CM 
 
 CM 
 
 CM CM 
 
 CM CM 
 
 i-H 
 
 
 
 CM CM CM 
 
 r-H r-H 
 
 CD 
 
 t — 1 
 
 
 
 
 
 
 
 
 
 
 Q 
 
 3: 
 
 
 
 
 
 
 
 
 
 
 
 _i 
 
 co r~- 
 
 CO >=H- 
 
 co r^ 10 
 
 1— t <3- «* 
 
 1— \ i— 1 1— 1 r^. 
 
 LO «sj" «H- 
 
 <d- -^J- 
 
 co "^- r-~- 
 
 «* «^" 
 
 
 <C 
 
 co tn 
 
 cm r~» 
 
 O CM CO 
 
 Cn LO CM 
 
 I-H LO LO O CO 
 
 ■vj- LO CO 
 
 O LO 
 
 CO 00 00 
 
 00 r^ 
 
 
 ID 
 
 1— 1 CTi 
 
 NCOOHU) 
 
 ■=3- r^ lo 
 
 co «3- cm r— 1 cn 
 
 cn cm cn 
 
 00 cn 
 
 O "3- CO 
 
 CO 
 
 
 2T 
 Z^ 
 
 LO <sO 
 
 *d- r~-» 
 
 LO LO CO 
 
 ^" >* LO 
 
 LO CO LO LO LO 
 
 "^f CO LO 
 
 LO LO 
 
 CM CM CM 
 
 CM CO 
 
 
 LU 
 
 r—t r*-. 
 
 LO CTi 
 
 CO CO LO 
 
 co >* cn 
 
 ^j- CM cm cn 
 
 O CO i^- 
 
 CT> r-H 
 
 000 
 
 
 
 
 2: 
 
 co r*» 
 
 CO CO 
 
 NcOOCM^ls 
 
 CM CO r-H i-H CO 
 
 CO CM 
 
 cn lo 
 
 
 
 
 ZD 
 
 C\J r-H 
 
 1— 1 CO 
 
 r-H 
 
 r-H i-H CM 
 
 
 
 
 
 
 
 CO CO 
 
 cn r->. 
 
 CM LO LO 
 
 r^ co lo 
 
 r^~ 00 "^ lo lo 
 
 LO LO 1-^. 
 
 ^J- CO 
 
 000 
 
 CM LO 
 
 
 >- 
 
 co co 
 
 1^ CM 
 
 ■3" O <3- 
 
 co r^ co 
 
 co 00 cm i-h cn 
 
 cn r~- 
 
 ^3- CO 
 
 
 r-H CM 
 
 
 < 
 
 21 
 
 CO CO 
 
 CM LO 
 
 CM CM CM 
 
 CM CM "3" 
 
 
 
 CO CM 
 
 
 
 . 
 
 
 
 CO CO 
 
 CM CO CO 
 
 LONOl 
 
 i-H LO CO CD O 
 
 CM CO CO 
 
 CM «!}• 
 
 «3" rH «* 
 
 O "vf 
 
 
 d; 
 
 co r^. 
 
 CXI CM 
 
 CO CT> en 
 
 O i— 1 CD 
 
 r^- 00 cn cn 00 
 
 r-. cn co 
 
 r-H CO 
 
 LO CO CO 
 
 CM *H- 
 
 
 <c 
 
 •=H- LO 
 
 *3- r-» 
 
 ■=3- CO CO «vl- <3" CO 
 
 ■^- LO CO CO "=3" 
 
 co <=h- <=d- 
 
 CO LO 
 
 
 r— 1 r-H 
 
 • 
 
 VO CO 
 
 cr> co 
 
 cm r^. co 
 
 OHCO 
 
 CX> CO co «^- <^- 
 
 LO CO CO 
 
 r^ co 
 
 iHNN 
 
 «H^ CO 
 
 o 
 
 err 
 
 CO LO 
 
 CO CO 
 
 *HC0 
 
 r-~. 1— 1 1— 1 
 
 ■^l- r^ co -^- r^ 
 
 co cn lo 
 
 !->. CO 
 
 cn lo «3- 
 
 CO LO 
 
 LO 
 CO 
 
 CD 
 
 SI 
 
 VO CO 
 
 LO Cn 
 
 CO CO LO 
 
 LO CO 00 
 
 00 OM^rsco 
 
 r^ co co 
 
 CO CO 
 
 CM CO CO <3" "^1- 
 
 . 
 
 c\j co 
 
 r-^ lo 
 
 r- co «=3- 
 
 00 r^» cn 
 
 NHNOM 
 
 LO CO CM 
 
 lo 00 
 
 cn cz> cn 
 
 LO O 
 
 in 
 
 CO 
 
 CM CO 
 
 CM CD 
 
 ct> r~-. ^h- 
 
 <h- 
 
 co cn 
 
 CO CM O 
 
 LO 00 
 
 CO f^ LO 
 
 CO CO 
 
 rO 
 
 LU 
 
 co en 
 
 CO O 
 
 co r--. co 
 
 CO CO CO 
 
 cn co 
 
 00 
 
 cn en 
 
 CO «3- ^j- 
 
 LO LO 
 
 CQ 
 
 U_ 
 
 
 1—1 
 
 
 
 1— 1 1— 1 i-H 
 
 I-H r-H 
 
 
 
 
 . 
 
 CO co 
 
 CO CT> 
 
 co r*- lo 
 
 CO CM CO 
 
 co cn lo <3- cn 
 
 i-H CO CM 
 
 
 
 NOCM 
 
 CO CO 
 
 IS) 
 
 2: 
 
 LO <3- 
 
 
 
 1— 1 r-H CM 
 
 CO CM LO 
 
 HUJ^-HH 
 
 O LO CM 
 
 CM i-H 
 
 co r^ co «=j- co 
 
 >■ 
 
 <C 
 
 r-» cm 
 
 CO CM 
 
 CTlOCO 
 
 r^ CO CTi 
 
 i-H i-H CD O ^H 
 
 O r-H l-H 
 
 O i-H 
 
 r^" LO LO 
 
 CO CO 
 
 
 "ZD 
 
 r-H 
 
 I — 1 
 
 i—l 
 
 
 1 — 1 1 — 1 r-H i-H t — 1 
 
 1— 1 1— 1 i-H 
 
 r-H r-H 
 
 
 
 . 
 
 CXi CO 
 
 Cn t— 1 
 
 1— « «^- LO 
 
 co cn rj- 
 
 LO CO CM *H- CO 
 
 cn ^ct- co 
 
 CM CO 
 
 rHN W 
 
 co r^ 
 
 Ul 
 
 <_> 
 
 r~~ •—• 
 
 1— 1 cr> r^ co co 
 
 HCVJN 
 
 >=h- co cn co co 
 
 nos 
 
 O CM 
 
 r-» r~. lo 
 
 CO CO 
 
 LU 
 
 LU 
 
 CO 1 — 1 
 
 NOCOCON 
 
 r^ 1^ co 
 
 cn cn 
 
 cn T—t 
 
 cn 
 
 «H- LO LO 
 
 CO CO 
 
 o 
 
 LU 
 
 Q 
 
 1 — 1 
 
 1 — 1 
 
 
 
 1— 1 1— 1 i-H 
 
 i-H i-H 
 
 r-H 
 
 
 
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 1—1 l"»« 
 
 lo co 
 
 co >— < r^ 
 
 r-» «^- co 
 
 co ^- CO i-H CO 
 
 NCMN 
 
 >* 
 
 CM LO LO 
 
 r-^ r^ 
 
 Q 
 
 > 
 
 IO CO 
 
 CO x-i 
 
 r~^ r- 1 Cn 
 
 CO CT> CO 
 
 Cn r-H "SJ- CM CM 
 
 a~> co 1— • 
 
 cn co 
 
 00 ^ r-H 
 
 CO r-H 
 
 
 O 
 
 lo co 
 
 LO cn 
 
 co r^ lo 
 
 LO LO CO 
 
 co r^ co co r^. 
 
 LONN 
 
 LO CO 
 
 CM CO CO C i- 
 
 i — i 
 
 :s 
 
 
 
 
 
 
 
 
 
 
 . 
 
 LO LO 
 
 CO 
 
 CM O LO 
 
 cn 00 co 
 
 CO i-H 00 «— • LO 
 
 r^ «3- lo 
 
 r^ cm 
 
 cn ^d- co cm 
 
 h- 
 
 I— 
 
 r~» i—) 
 
 CO CO 
 
 r-^ lo co 
 
 CM CO <^- 
 
 lo cn cn cn r>. 
 
 lo con 
 
 r^. 
 
 LOCON 
 
 r-H CO 
 
 <C 
 
 O 
 
 CO LO 
 
 CO LO 
 
 CO CO CO 
 
 co co -=3- 
 
 CO CO CM CM CO 
 
 CM <3" CO 
 
 00 CO 
 
 
 r-H r-H 
 
 Ul 
 
 
 
 
 
 
 
 
 
 
 
 
 zc 
 
 h- 
 
 CD O 
 
 cn 00 
 
 CO «-< «tf- 
 
 LO r-H r— 1 
 
 CD CM CO O LO 
 
 ^t(MH 
 
 00 CO 
 
 OOO 
 
 O LO 
 
 _i 
 
 a. 
 
 1 — 1 I— 1 
 
 CM CO 
 
 r-~ 1— 1 1— 1 
 
 O rHN 
 
 cn co co 
 
 LO CO 1— 1 
 
 r^ cn 
 
 
 r-H 
 
 <c 
 
 LU 
 
 C\J C\i 
 
 r-H CM 
 
 r-H i—l 
 
 i—l i-H i-H 
 
 i-H 1— 1 
 
 i-H i-H 
 
 
 
 
 r— 
 o 
 1— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 . 
 
 r- «* «* 
 
 CO 
 
 CO 1— 1 T— 1 
 
 lo cn 
 
 cn cn 
 
 CO CO 
 
 OOO 
 
 O O 
 
 
 CD 
 
 CO CO 
 
 CO CM 
 
 CM 
 
 .-I CO CO 
 
 CM 
 
 i-H 
 
 t— • r-H 
 
 
 
 _J 
 
 ZD 
 
 I— 1 
 
 I—l 
 
 
 
 
 
 
 
 
 s: 
 c£ 
 
 ■=£ 
 
 
 
 
 
 
 
 
 
 
 2- 
 
 CO CsJ 
 
 «=r -=*■ 
 
 O O LO 
 
 WNH 
 
 00000 
 
 000 
 
 
 
 OOO 
 
 O O 
 
 o 
 
 _I 
 
 ■^" .-H 
 
 CO CO 
 
 CM 
 
 CM CO CO 
 
 
 
 
 
 
 iz. 
 
 ZD 
 r "3 
 
 i—l 
 
 
 
 
 
 
 
 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 
 
 1—1 
 
 l— 
 
 
 
 
 
 
 
 
 
 
 
 <=C 
 
 
 
 
 
 
 
 <C 
 
 
 
 
 h- 
 
 
 
 
 +■> 
 
 
 
 ^ 
 
 
 
 
 00 
 
 
 
 
 ■r- < 
 
 E — 
 
 fO 
 
 
 TD t-H 
 
 C _l 
 
 
 cn 
 
 
 O 
 
 
 
 
 E zz 
 
 enjz -c 
 
 O < 
 
 rO CU O 
 
 sz 
 
 CU s- 
 
 
 Z^ 
 
 
 
 SZ 
 
 ZJ < 
 
 C S- q. co 
 
 Q. _J 
 
 1 — cm 
 
 
 
 1 — ZJ 
 
 
 <C 
 
 
 
 -a 
 
 cn 00 > 
 
 2 ZJr- S_ 
 
 c in 00 
 
 CO E <C 
 
 +-> 03 CU 
 
 1— _a 
 
 
 
 (O 
 
 E 
 
 TD +J C 
 
 S- _J 
 
 O -Q CU ZS 
 
 Dio 10 •— 1 
 
 H O <_) 
 
 CO T- O 
 
 ■1- sz 
 
 
 LU 
 
 2: 
 
 •1 — 
 
 CU ra 
 
 S- CU ra 
 
 Z5 E >- 
 
 +-> (/> TD JZl 
 
 e 4-> E 
 
 -0 
 
 (1)13 C 
 
 > ra 
 
 
 1— 
 
 
 
 S_ CO 
 
 SZ -£Z 
 
 O r— r— 
 
 -Q E O to 
 
 C -r- fO CO 
 
 •r- C T- LU 
 
 -*£ -p- ZC 
 
 r— E CU 
 
 sz +-> 
 
 
 <x. 
 
 
 
 sz 
 
 QJ U 
 
 4- -a +-> 
 
 CU CU 4-> 2: 
 
 CU CU S- 1— +-> 
 
 "O (0 r— O 
 
 O > 1— 
 
 i- ZJ s- 
 
 CU S- 
 
 
 1 — 
 
 UJ 
 
 +-> S- 
 
 CD rO 
 
 HCL 
 
 CO 1— X ^Z 
 
 . 1- S- .,- +j 
 
 fO S- 1— 
 
 OO ZD 
 
 fO ■ — 
 
 <U re 
 
 
 CO 
 
 cc 
 
 O ZJ 
 
 ZJ CU 
 
 cu cu 
 
 O US dJ LU 
 
 1 — i- fO ^z •■- 
 
 CU CD -i- ZC 
 
 r— J_ O 
 
 -£Z O 1— 
 
 i_ CL 
 
 
 
 
 
 ■< CQ 
 
 lu s; 
 
 21 o_ o_ 
 
 CC O0 O0 O- 
 
 <3T LU ZC O- Q_ 
 
 aw3 cc 
 
 CQ Q_ CO 
 
 OOU. 
 
 O CO 
 
A5-19 
 
 Table A5-10 (continued) 
 
 o 
 
 t=; 
 
 r^ co lo 
 
 CM 
 
 rsLncON 
 
 r-H CO 
 
 < — 1 
 
 <3~ LO r-H CD 
 
 CM r-H 
 
 KO 
 
 co 
 
 cn 
 
 O 
 
 «* r-H 
 
 CTl 00 
 
 1 — 1 
 
 CO 
 
 I— 
 
 2: 
 
 cn cn cn 
 
 cn 
 
 cn cn cn cn 
 
 cn 
 
 
 
 cn cn 
 
 CD cn 
 
 cn 
 
 CD 
 
 en 
 
 CD 
 
 cn 
 
 en en 
 
 
 
 
 :o 
 
 
 
 
 r— t 
 
 r-H 
 
 r-H r-H 
 
 r-H 
 
 
 r-H 
 
 
 r-H 
 
 r-H 
 
 
 . — 1 
 
 1 — 1 
 
 CDU_ 
 •1— o 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4- 
 
 U3 cn^ 
 
 . — 1 
 
 LO CO 1^ CM 
 
 r-. co 
 
 LO 
 
 CO CM CT> r-H 
 
 O CM 
 
 cn 
 
 CM 
 
 r-H 
 
 CTl 
 
 CTl O 
 
 LO CO 
 
 1 — 1 
 
 LO 
 
 co 
 
 2: 
 
 1—1 1 1— 1 
 
 . — 1 
 
 1 — 1 1 — 1 1 — 1 1 — 1 
 
 r-H 
 
 CM 
 
 CO CO r-H CM 
 
 CM CO 
 
 CXI 
 
 CO 
 
 r-H 
 
 .-H 
 
 CM CM 
 
 CM CM 
 
 CM 
 
 r-H 
 
 CD 
 Q 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _J 
 
 CO LO CTl 
 
 CO 
 
 <H-«t(MC0I^ 
 
 «H- LO 
 
 < — 1 
 
 O <3" CO CD 
 
 LO LO 
 
 CO 
 
 r~- 
 
 co 
 
 1 1 
 
 r^. lo 
 
 cn co 
 
 O CM 
 
 
 <C 
 
 C\J «h- 00 
 
 "St 
 
 lo cn r--. r-n 
 
 CM CO 
 
 1 — 1 
 
 O t-H CO O 
 
 CD CO 
 
 CTi 
 
 cn 
 
 r>. 
 
 CM 
 
 «H- LO 
 
 «5f r-- 
 
 CO 
 
 CO 
 
 
 ZD 
 
 cm n co 
 
 1 — 1 
 
 CM "53- CM LO CO 
 
 co cn 
 
 r^ 
 
 co cn co r-^ 
 
 <H- CM 
 
 co 
 
 r-> 
 
 LO 
 
 LO 
 
 'H- CM 
 
 LO r-H 
 
 O CO 
 
 
 
 co i^r^ 
 
 ■=3- 
 
 CO CO CO CO CO 
 
 CM CO 
 
 t-H 
 
 CM CM 
 
 CM r-H 
 
 r-H 
 
 
 CO 
 
 CM 
 
 r-H CM 
 
 r-H 1 — 1 
 
 CM 
 
 CM 
 
 
 U) 
 
 r-~ co 00 
 
 
 
 CD O O O O 
 
 
 
 
 
 CD O O O 
 
 
 
 O 
 
 
 
 
 
 O 
 
 O O 
 
 O O 
 
 O 
 
 O 
 
 
 :s 
 
 co cm r-. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ZD 
 
 1 — 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C0U3O 
 
 CO 
 
 LO CO CM CD CO 
 
 CD CO 
 
 
 
 O O CO O 
 
 
 
 O 
 
 
 
 . — 1 
 
 O 
 
 O O 
 
 O O 
 
 O 
 
 CO 
 
 
 >- 
 
 00 cnj r~^ 
 
 CO 
 
 CM «H- CM «H- LO 
 
 LO 
 
 
 
 
 
 
 CO 
 
 
 
 
 
 
 
 2: 
 
 CM CO CM 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 old n 
 
 1— 1 
 
 OCONCTlCO 
 
 ■vt- CM 
 
 r-H 
 
 O O O LO 
 
 CT> O 
 
 CO 
 
 
 
 I — 1 
 
 CD 
 
 en co 
 
 CTl r-H 
 
 CO 
 
 CD 
 
 
 a: 
 
 1— 1 r-- 
 
 CO 
 
 LO cn «vf 00 cm 
 
 r-H LO 
 
 LO 
 
 cn CD 
 
 CTi CO 
 
 CO 
 
 
 
 
 CTl 
 
 CO CO 
 
 CO CM 
 
 CO 
 
 CM 
 
 
 < 
 
 CO CO LO 
 
 CsJ 
 
 i — 1 r— i 1 — 1 r-H CM 
 
 r-H CM 
 
 
 r-H 
 
 
 
 
 CM 
 
 
 
 
 
 r-H 
 
 . 
 
 LO r-H CM 
 
 co 
 
 CO CO CO CM CM 
 
 l^» CO 
 
 co 
 
 <3- en cn cn 
 
 CT> CTi 
 
 CM ^ «h- CM 
 
 CM CO 
 
 LO CM 
 
 
 
 CO 
 
 o 
 
 CrT 
 
 CM LO CO 
 
 CD 
 
 LO CTl LO r— 1 LO 
 
 <3- <3" 
 
 CM 
 
 1-^- O r-H r-H 
 
 r-H CO 
 
 cn 
 
 r-« 
 
 CO 
 
 CM 
 
 CTi CO 
 
 en lo 
 
 [-X- 
 
 r~x 
 
 lo 
 
 <C 
 
 r-H O O 
 
 LO 
 
 ■5}- *H- «3- LO LO 
 
 CO LO 
 
 CU 
 
 r-H CO CO 
 
 CO r-H 
 
 1 — 1 
 
 
 <* 
 
 CO 
 
 r-H CM 
 
 r-H r-H 
 
 CM 
 
 CO 
 
 CO 
 
 CD 
 
 S 
 
 1 — 1 i — 1 1 — 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 LO LO LO 
 
 
 
 r~^ co lo >^- cn 
 
 «=J- 
 
 LO 
 
 CD <h- CD LO 
 
 CO CO 
 
 CO 
 
 ^j- 
 
 CO 
 
 CO 
 
 *H- CM 
 
 CO O 
 
 CTi 
 
 CO 
 
 to 
 
 CQ 
 
 LO «sj- 00 
 
 
 
 INHCO*^ 
 
 r-~ co 
 
 CM 
 
 r^ ^j- •^^ 
 
 «H- LO 
 
 CO 
 
 co 
 
 1 — 1 
 
 CO 
 
 r~-~ i-h 
 
 CO CO 
 
 CO 
 
 r-H 
 
 re 
 
 Ul 
 
 CO r-H CM 
 
 r% 
 
 LO CO LO UD CO 
 
 «5j* CO 
 
 co 
 
 r-H 1— 1 -^J" ^ 
 
 <3" CM 
 
 CM 
 
 r-H 
 
 co 
 
 <=r 
 
 CM ^t- 
 
 CM CM 
 
 CO 
 
 LO 
 
 CQ 
 
 U_ 
 
 1— 1 r-H <— ) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO CO ^f- 
 
 CO 
 
 CM CM CTi CO CO 
 
 cm r~~ 
 
 CO 
 
 LO r-H r-H LO 
 
 <3- 
 
 ■sj- 
 
 r-. 
 
 
 
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 -^- r-s 
 
 CO ^T 
 
 CO 
 
 00 
 
 W) 
 
 ^T 
 
 CM CO <!f 
 
 CM 
 
 OJflNNN 
 
 ■^j- r^ 
 
 co 
 
 O CTi CD CO 
 
 r-H LO 
 
 CO 
 
 CO 
 
 
 
 LO 
 
 co co 
 
 CM «H- 
 
 co 
 
 CTi 
 
 >- 
 
 <C 
 
 CO CO LO 
 
 CO 
 
 r-» r-~» 1^ r~~ r-^ 
 
 CO CO 
 
 «=!- 
 
 CM CM CO CO 
 
 CO CO 
 
 CO 
 
 CM 
 
 CO 
 
 CO 
 
 CO LO 
 
 •=d- CO 
 
 LO 
 
 CO 
 
 
 •"3 
 
 t — 1 • — 1 1 — 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CM CM t— 1 
 
 CO 
 
 CO LO CO CM CM 
 
 co r^ 
 
 CO 
 
 cn ^ co 
 
 CO O 
 
 r-» 
 
 r^ «h- cm 
 
 en co 
 
 CO 
 
 CO 
 
 CM 
 
 UJ 
 
 C_) 
 
 nKUD 
 
 CM 
 
 cn cm cn co r^ 
 
 co cn 
 
 CO 
 
 <H- CM CM «H- 
 
 co r^- 
 
 
 
 r-H 
 
 «3" 
 
 CTi 
 
 CM CO 
 
 co r^. 
 
 LO 
 
 CO 
 
 LU 
 
 Ul 
 
 <d-HO 
 
 CO 
 
 IONVDNN 
 
 LO r-^ 
 
 CO 
 
 r-H CM LO CO 
 
 LO CM 
 
 co 
 
 CM 
 
 r-~ 
 
 LO 
 
 CO LO 
 
 CO CM 
 
 <^r 
 
 CO 
 
 cd 
 
 UJ 
 
 O 
 
 r— 1 r— 1 1 — 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 <h- r^ cm 
 
 co 
 
 COOlNLOtH 
 
 CO 
 
 LO 
 
 IDOHrJ- 
 
 "St CO 
 
 CO 
 
 LO 
 
 CO 
 
 r-H 
 
 r~» co 
 
 r^ CD 
 
 
 
 r-H 
 
 Q 
 
 > 
 
 HOIN 
 
 r->. 
 
 co co <3- cn co 
 
 co r^. 
 
 CM 
 
 CO CM CM r-H 
 
 CM CO 
 
 CO 
 
 O 
 
 r— 1 
 
 CO 
 
 CD r-H 
 
 O LO 
 
 r--. 
 
 CO 
 
 
 O 
 
 OCOCA 
 
 LO 
 
 «5t -St <SJ" «H- LO 
 
 CO LO 
 
 CM 
 
 r-H CO -^1- 
 
 CO r-l 
 
 . — 1 
 
 . — ! 
 
 LO 
 
 co 
 
 CM CO 
 
 CM r-H 
 
 CM 
 
 CO 
 
 CD 
 
 9 — 1 
 
 ^ 
 
 T— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 CO r-H CM 
 
 ID 
 
 CO r-H CD CO CM 
 
 cn lo 
 
 < — 1 
 
 O O CM «H- 
 
 LO O CO 
 
 O 
 
 <^~ 
 
 r-x 
 
 CM CO 
 
 .—I CO 
 
 CO 
 
 en 
 
 1— 
 
 J— 
 
 CD CO <X> 
 
 co 
 
 ^- N COLO Ol 
 
 cn 
 
 co 
 
 CO CO 
 
 CO 
 
 
 
 r^» co 
 
 CM CO 
 
 CO 
 
 «^r 
 
 CTi 
 
 <c 
 
 CD 
 
 LO -sf "=j- 
 
 CM 
 
 r-H r-H 1 — 1 r-H r-H 
 
 CM 
 
 
 
 
 
 
 r-H 
 
 
 
 
 
 
 UJ 
 
 in 
 
 CD 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 h- 
 
 LO LO CO 
 
 1— 1 
 
 co co cn 
 
 co 
 
 
 
 0000 
 
 O O 
 
 
 
 O 
 
 CO 
 
 CD 
 
 O O 
 
 
 
 
 
 
 
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 Q_ 
 
 CO CO CO 
 
 LO 
 
 r-H CO r-H CO CO 
 
 r-H 
 
 
 
 
 
 
 I — 1 
 
 
 
 
 
 
 <c 
 
 Ul 
 
 r-H 1— 1 1— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / — \ 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CD 
 
 CM CM LO 
 
 HH(M 
 
 O 
 
 O CD O O O 
 
 O O 
 
 
 
 0000 
 
 O O 
 
 
 
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 ZD 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <: 
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 < 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 cn cm en 
 
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 CD <Z) CD CD CD 
 
 O O 
 
 CD 
 
 0000 
 
 O O 
 
 
 
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 CM r-J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 ZD 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 1 — 1 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 
 
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 •1— 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 
 
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 +-> 
 
 
 
 
 
 
 
 
 
 CO 
 
 
 CO 
 
 
 CO 
 
 
 CD 
 CO 
 
 
 
 CO 
 
 CD -r- 
 
 
 
 
 
 
 s_ 
 
 
 
 
 , 
 
 
 O 
 
 O 
 
 >>•— 
 
 
 CD 
 
 
 
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 x: 
 
 
 
 
 
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 -1 — 
 
 
 ro 
 
 
 ^ 
 
 i^ 
 
 +J 1 — Ul 
 
 
 O CD CD CD 
 
 
 
 . — JZ 
 
 4-> E 
 
 
 
 
 
 x: 1 — 
 
 c 
 
 
 Li- 
 
 
 <c 
 
 <c 
 
 •r— (tJ Ul 
 
 
 Or— r— CD 
 
 O 
 
 
 •r- CD 
 
 i- O 
 
 
 
 
 
 +-> CD 
 
 ra 
 
 
 
 
 
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 CD U. CO 
 
 1 
 
 C 1 — CO 1 — "O 
 
 CU r— 
 
 
 > O 
 
 O +-> 
 
 c 
 
 
 -^ 
 
 -0 
 
 S- cn+-> t- 
 
 
 ra 
 
 
 Ul 
 
 
 CO 
 
 O 
 
 fO "r— "r" T— •! — 
 
 C l 
 
 sz 
 
 co co 00 </i 
 
 3 CO 
 
 
 
 O 
 
 
 
 sr 
 
 <t c 
 
 c: s- 
 
 
 +-> 
 
 
 h- 
 
 m 
 
 c: -a x ui 
 
 +■> 
 
 -r-> > X: > CC CO 
 
 CD -1- 
 
 •r— 
 
 C 3 ro A3 
 
 CD 
 
 +-> 
 
 "O 
 
 
 
 ra 
 
 <<o 
 
 
 •r— 
 
 
 "< 
 
 J— 
 
 -i- 3 ^ 
 
 CO 
 
 +-> X Q.XI ef 
 
 r— s- 
 
 4-> 
 
 2 o_i— o_ 
 
 +-> > 
 
 Ul 
 
 CD 
 
 -Q 
 
 1 — 
 
 4-> 
 
 +J 
 
 X 
 
 
 J— 
 
 ZD 
 
 s- a. z: 
 
 "r— 
 
 fO O E CO -^ X 
 
 •r- ro 
 
 CO 
 
 O S- r— 
 
 %- r— 
 
 =5 
 
 i- 
 
 _Q 
 
 -0 
 
 s- c 
 
 E (J 
 
 
 
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 CO 
 
 O 
 
 3 ItJ'r Ul 
 
 5_ 
 
 JC C CD ra ra Ul 
 
 -Q S 
 
 =3 
 
 t. O (dr- 
 
 O ra 
 
 
 
 n3 
 
 Z5 
 
 • 1 — 
 
 m 
 
 ra •<- 
 
 CO 
 
 • 1 — 
 
 
 
 CO 
 
 xa 00 1— 
 
 CQ 
 
 CD ^ S ^ O 1— 
 
 <c<c 
 
 < 
 
 CQ O Q Ul 
 
 U_ CD 
 
 zc 
 
 _J 
 
 _l 
 
 2: 
 
 o_ CO 
 
 CO >■ 
 
 3 
 
 3 
 
A5-20 
 
 Table A5-10 (continued) 
 
 o 
 
 K 
 
 
 r>» 
 
 
 CO 
 
 "vf *3- CO «cj- 
 
 
 LO CM LO CO CO «3" 
 
 oj r-» lo 00 
 
 I— 
 
 2: 
 
 ro 
 
 CO 
 
 
 CTl 
 
 
 CO 
 
 en cn en cn 
 
 
 CO CO CO CTl CTl CTl 
 
 CTi 00 CTi CTl 
 
 CT>Ll_ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •i— o 
 
 +- 
 
 
 LO 
 
 
 OJ 
 
 lo <=*- LO 
 
 
 r-H CO O CM CM CO 
 
 CTi i—l O 00 
 
 CO 
 
 CU 
 
 Q 
 
 2: 
 
 
 
 
 1— 1 
 
 1— 1 CM rH 1— 1 
 
 
 CM CM CM 1 *-> 
 
 t— 1 
 
 3 
 
 
 
 
 1 
 
 
 
 
 
 
 1 
 
 r-^ 
 
 CvJ 
 
 CO 
 
 en 
 
 CTl CO 1— 1 LO O 
 
 <!■ 
 
 CO'^J-COLOLOCOCTlLOi— 1 
 
 CO LO CO >^!- 
 
 
 <C 
 
 CTt 
 
 LO 
 
 h- 
 
 CO 
 
 r*. co cm co lo 
 
 CM 
 
 CMCMC0«3-L0C0'-HO 1 =d- 
 
 r--. r^ «^- lo 
 
 
 rD 
 
 «tf 
 
 O 
 
 r^ 
 
 CXI 
 
 CM 1— 1 «3" CO 1— 1 
 
 OJ 
 
 co^i-coi— icocMr^-cocn 
 
 «^- co <=n- r^. 
 
 
 2: 
 
 <0 
 
 CO 
 
 <d- 
 
 CO 
 
 co <=d- co co <?r 
 
 ^1- 
 
 LO<^-«^-LOCOCTiLO^-LO 
 
 >=i- LO «* «* 
 
 
 LU 
 
 r^. 
 
 ^r 
 
 1 — 1 
 
 
 
 00000 
 
 O 
 
 r^r^.CTiCTlLOCOCOLOCTl 
 
 CTl CO CM CO 
 
 
 2: 
 
 co 
 
 CO 
 
 LO 
 
 CTl 
 
 
 
 Kr^cnmrococo^-co 
 
 ■=3" H 
 
 
 rD 
 
 
 
 
 
 
 
 t— 1 1 — 1 Hi — 1 ^- CO 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 CTi 
 
 co 
 
 r-^ 
 
 CO 
 
 co co r»» co lo 
 
 <=f 
 
 NCMMl^CO^HNO 
 
 CO CO CTl LO 
 
 
 >■ 
 
 r^. 
 
 ro 
 
 r». 
 
 LO 
 
 lo r^ co lo co 
 
 r^ 
 
 O«3-<3-CTtC0L0C0r-~CM 
 
 cn en cn i— 1 
 
 
 < 
 
 CM 
 
 CM 
 
 1 — 1 
 
 CO 
 
 
 
 COCMCMCMCMCO«^i-i— 1 CM 
 
 l—l r— 1 
 
 . 
 
 en 
 
 cm 
 
 CO 
 
 ■3- 
 
 co r->. co CTi <—i 
 
 CO 
 
 CDCOi— 1 «5j- t— ILOLOCMLO 
 
 «3- <rj- cn 
 
 
 cc: 
 
 r— 1 
 
 lo 
 
 
 
 1— 1 
 
 rrj" CO 1— 1 1— 1 CO 
 
 CO 
 
 LOCTli— 1 NOO LOCM 'tCO 
 
 CO «^- CTl CO 
 
 
 < 
 
 LO 
 
 «tf 
 
 ■=*■ 
 
 r-- 
 
 CM CM CM CM OJ 
 
 CM 
 
 ■^■co^t-^-Lncoinco's}- 
 
 CO ^- CM CO 
 
 . 
 
 CNJ 
 
 co 
 
 CTl 
 
 r^ 
 
 CO LO CO CO "=3" 
 
 CO 
 
 LOr^COI^.'d-LOLOCTiCO 
 
 CO <— 1 CO 1— 1 
 
 o 
 
 cc: 
 
 OJ 
 
 CO 
 
 CM 
 
 00 
 
 CO O CO <3" i-H 
 
 CM 
 
 •^NOtncoco^-coH 
 
 «h- cn co en 
 
 LO 
 
 <c 
 
 CO 
 
 r^ 
 
 r-> 
 
 1— 1 
 
 LO CO LO LO CO 
 
 CO 
 
 coLOcococoocOLor^ 
 
 co r^. co co 
 
 CO 
 
 OJ 
 
 2: 
 
 
 
 
 i—i 
 
 
 
 i—i 
 
 
 . 
 
 CO 
 
 O 
 
 CXI 
 
 CO 
 
 CO 1— 1 LO CO CM 
 
 CM 
 
 LOCTiLOOOOLOCOLOCO 
 
 CD CO ^" CO 
 
 CO 
 
 CQ 
 
 CO 
 
 . — 1 
 
 
 
 CO 
 
 CO CO LO CD CM 
 
 CO 
 
 Ncnm[vcorxiH^ii3 
 
 r^ cn co cm 
 
 <n 
 
 LU 
 
 cn 
 
 CT. 
 
 CTi 
 
 00 
 
 lOI^U3 NN 
 
 r~- 
 
 cOLOcococnocor^»oo 
 
 i-« co r-» 00 
 
 CQ 
 
 U_ 
 
 
 
 
 1—1 
 
 
 
 1 — 1 
 
 
 
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 CM 
 
 CM 
 
 CO 
 
 00 
 
 «=3- CTl CO LO ^f 
 
 i—i 
 
 ^cOiHOO>-irvrocoro 
 
 O CO O CM 
 
 CO 
 
 ^ 
 
 LO 
 
 r^~ 
 
 r^ 
 
 1 — 1 
 
 ai^t-ro rHco 
 
 1^ 
 
 COCOCOCMCOCOi— ICOCO 
 
 COOCO^l- 
 
 >- 
 
 ■=£ 
 
 CNJ 
 
 1— 1 
 
 1 — 1 
 
 LO 
 
 co co r^ co co 
 
 00 
 
 oor^cooocMOjr^cTii-H 
 
 co CO cn 
 
 < 
 
 O 
 
 ■"D 
 
 r— 1 
 
 r— 1 
 
 1— 1 
 
 i—l 
 
 
 
 I—l I — 1 1 — 1 
 
 1 — 1 
 
 . 
 
 r— t 
 
 CXI 
 
 1—) 
 
 cn 
 
 LO CM CO "3" LO -v}- 
 
 COr^COOCMOOCTtCOCTi 
 
 LO CM CO LO 
 
 LU 
 
 C_> 
 
 «sj- 
 
 CO 
 
 en 
 
 ■=3- 
 
 ■^- cm cn co oj 
 
 CO 
 
 LOLOcoLocor^co>^-co 
 
 CO CTi LO O 
 
 LU 
 
 LU 
 
 . — 1 
 
 O 
 
 
 
 co 
 
 co co co r-» co 
 
 CO 
 
 MflNNOr- ICOCOO 
 
 co cn co cn 
 
 cc 
 cd 
 
 LU 
 
 Q 
 
 1 — 1 
 
 . — 1 
 
 1— 1 
 
 1— 1 
 
 
 
 r— 1 1— 1 i—l 
 
 
 . 
 
 r^» 
 
 en 
 
 OJ 
 
 1—1 
 
 CD CD CO LO CTl 
 
 CTi 
 
 <oco<vi-cocrico«^-<— 100 
 
 1— i cn lo co 
 
 Q 
 
 > 
 
 CO 
 
 ^r 
 
 OJ 
 
 cn 
 
 co -^ cn >^j- 
 
 i—l 
 
 co^j-wroNOrococM 
 
 CTi CM 00 O 
 
 
 CD 
 
 CO 
 
 co 
 
 co 
 
 co 
 
 CO LO <3" ■* LO 
 
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TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 6 
 
 SYSTEM SIZING AND APPROXIMATE METHODS 
 FOR ESTIMATING SYSTEM PERFORMANCE 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
6-i 
 TABLE OF CONTENTS 
 
 Pa£G 
 
 LIST OF FIGURES 6-ii 
 
 LIST OF TABLES 6-ii 
 
 OBJECTIVE 6-1 
 
 INTRODUCTION 6-1 
 
 SIZING THE SYSTEM 6-2 
 
 APPROXIMATE METHODS FOR COLLECTOR SIZING .... 6-2 
 
 USES OF APPROXIMATE METHODS 6-2 
 
 SYSTEMS TYPES ASSUMED 6-5 
 
 GRAPHICAL METHOD 6-5 
 
 RELATIVE AREAS METHOD 6-10 
 
6-11 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 6-1 Schematic Diagram of a Liquid-Based Solar Space 
 
 and Water Heating System ...... 6-6 
 
 6-2 Schematic Diagram of an Air-Based Solar Space 
 
 and Water Heating System ...... 6-6 
 
 6-3 Schematic Diagram of a Liquid-Based Domestic 
 
 Water Heating System ...... 6-7 
 
 6-4 Schematic Diagram of an Air-Based Domestic 
 
 Water Heating System ...... 6-7 
 
 6-5 Fraction of Annual Heating Load Supplied by Solar 
 
 Heating Systems ....... 6-8 
 
 LIST OF TABLES 
 
 Table Page 
 
 6-1 Rules of Thumb for Sizing Components of Liquid 
 
 Systems ......... 6-3 
 
 6-2 Rules of Thumb for Sizing Components of Air 
 
 Systems ......... 6-4 
 
 6-3 Constants for Relative Areas Method . . . 6-14 
 
 6-4 Table of Natural Logarithms ..... 6-17 
 
6-1 
 
 OBJECTIVE 
 
 The primary objective in this module is to present simple methods 
 for estimating the fraction of annual heating load that can be supplied 
 by a specific solar system at a given location. 
 
 INTRODUCTION 
 
 There have been various methods devised for estimating the quantity 
 of thermal energy that could be supplied by a specific solar system at a 
 particular location during a given year. The methods range from simple 
 tabular or graphical methods to very complex numerical simulation models 
 which require very large computing capability. In this module the 
 simple procedures are discussed and in Module 9 a detailed design method 
 is explained. The very complex methods are used more for research 
 purposes than for design and are not discussed in this manual. However, 
 it may be useful to know that detailed computer methods for analyzing 
 transient behavior of solar systems are available. Information on 
 procurement of the computer programs may be obtained by writing to the 
 Solar Energy Research Institute, Golden, Colorado, or to organizations 
 that developed the computer programs, such as the Solar Energy Labora- 
 tory, University of Wisconsin, Madison (TRNSYS) and Los Alamos 
 Scientific Laboratory (D0E2). 
 
6-2 
 
 SIZING THE SYSTEM 
 
 System component sizes are selected on the basis of collector area, 
 and collector area is determined by economic evaluation or is arbitrari- 
 ly selected to provide a given fraction of the annual heating load for 
 space and domestic water. Rules of thumb are generally used to select 
 component sizes once collector area is determined. Simple methods to 
 estimate system performance assume average or recommended component 
 sizes, while detailed performance estimation methods take into account 
 sizes of the components. Rules of thumb are provided for collector tilt 
 and orientation, fluid flow rate through the collector, storage size and 
 heat exchanger sizes. Standard design procedures are used to select 
 pumps and blowers, as well as pipe and duct sizes. Auxiliary furnaces 
 or boilers are sized according to design heat loss rate calculations in 
 the manner recommended by ASHRAE, SMACNA, NAHB and others; a condensed 
 version is provided in Module 5 of this manual. 
 
 The rules of thumb for sizing components of liquid- and air-type 
 solar systems for space and domestic water heating are provided in 
 Tables 6-1 and 6-2. From collector area and unit flow rates the volume 
 flow rate of pumps and blowers can be determined, but pressure drops 
 must be calculated from piping and ducting layouts. 
 
 APPROXIMATE METHODS FOR COLLECTOR SIZING 
 
 USES OF APPROXIMATE METHODS 
 
 It is important for designers of solar space and domestic water 
 heating systems to be able to estimate system performance quickly, 
 
6-3 
 
 Table 6-1 
 
 Rules of Thumb for Sizing Components of Liquid Systems 
 
 Space Heating System 
 
 Component 
 
 Recommended Value 
 
 Range of Values 
 
 Collector orientation 
 
 South 
 
 Southeast to Southwest 
 
 Collector tilt 
 
 latitude +15° 
 
 latitude -20° to vertical 
 
 Collector fluid 
 flow rate 
 
 0.02 gpm/ft 2 
 
 0.01 to 0.03 gpm/ft 2 
 
 Water storage 
 
 2 gal/ft 2 
 
 1.5 to 2.5 gal/ft 2 
 
 Collector/storage 
 Heat exchanger 
 
 F R /F R = °* 97 
 
 F R /F R >0.9 
 
 Load heat exchanger 
 
 e, C . 
 L mm 
 
 (UA) L " 2 
 
 £i C • 
 
 i , L mm ^ o 
 1 < (UA) L < 3 
 
 Domestic Water Heating 
 
 System Only 
 
 
 Component 
 
 Recommended Value 
 
 Range of Values 
 
 Collector orientation 
 
 South 
 
 Southeast to Southwest 
 
 Collector tilt 
 
 latitude 
 
 latitude -35° to 
 latitude +35° 
 
 Collector fluid 
 flow rate 
 
 0.02 gpm/ft 2 
 
 0.01 to 0.03 gpm/ft 2 
 
 Preheat storage tank 
 volume 
 
 2 times 
 DHW 
 
 auxiliary 
 tank 
 
 1.5 to 2.5 times 
 DHW auxiliary tank 
 
 Double-wall heat 
 exchanger 
 
 £ HX = °' 7 
 
 0.5 < e HX < 0.9 
 
 
 F R /F R = 0.95 
 
 F R /F R > 0.9 
 
6-4 
 
 Table 6-2 
 Rules of Thumb for Sizing Components of Air Systems 
 
 Space Heating System 
 
 Component 
 
 Recommended Value 
 
 Range of Values 
 
 Collector orientation 
 
 South 
 
 Southeast to Southwest 
 
 Collector slope 
 
 latitude +15° 
 
 latitude -20° to vertical 
 
 Collector air flow rate 
 
 2 cfm/ft 2 
 
 1.5 to 3 cfm/ft 2 
 
 Pebble-bed storage 
 
 0.75 ft 3 / ft 2 
 
 0.5 to 1 ft 3 /ft 2 
 
 Pebble size 
 
 0.75-1.5 in. 
 
 Uniform sizes 
 0.5 to 3-in. 
 
 Pebble-bed depth 
 
 6 ft 
 
 4 to 8 ft 
 
 Pressure drop in 
 pebble bed 
 
 0.15 in W.G. 
 
 0.1 to 0.3-in W.G. 
 
 Pressure drop in ducts 
 
 0.08-in W.G./100 ft 
 
 0.06 to 0.10-in. W.G./100 ft 
 
 Duct insulation 
 
 R-7 
 
 R-4 to R-13 
 
 Domestic water 
 heat exchanger 
 
 £ HX = °' 4 
 
 0.2 < e HX < 0.7 
 
 Domestic water 
 preheater tank 
 volume 
 
 2 times DHW 
 auxiliary tank 
 
 1.5 to 2.5 times 
 DHW auxiliary tank 
 
 Domestic Water Heating S 
 
 ystem Only 
 
 
 Component 
 
 Recommended Value 
 
 Range of Values 
 
 Collector orientation 
 
 South 
 
 Southeast to Southwest 
 
 Collector storage 
 
 latitude 
 
 -35° to latitude +35° 
 
 Collector air 
 flow rate 
 
 2 cfm/ft 2 
 
 1.0 to 3 cfm/ft 2 
 
 Heat exchanger 
 
 £ HX = °' 7 
 
 0.5 < e HX < 0.9 
 
 Preheater tank 
 volume 
 
 2 times DHW 
 auxiliary tank 
 
 1.5 to 2.5 times 
 DHW auxiliary tank 
 
6-5 
 
 particularly in addressing the questions of a client. If there is easy 
 access to a computer, detailed answers can be provided quickly using a 
 complex performance estimation model, but because not everyone concerned 
 has such access, rapid estimation procedures using hand-held calculators 
 will be useful. Also, during the planning stages, approximate methods 
 may be used advantageously to examine different system sizes for a 
 particular application. 
 
 There are several approximate methods for estimating system 
 performance. Two are included in the module. The accuracies of estima- 
 tion methods are dependent on location and system type. The numerical 
 values resulting from these calculations may differ from more detailed 
 performance estimation methods by as much as 20 percent. 
 
 SYSTEMS TYPES ASSUMED 
 
 The basic arrangements assumed for space and water heating systems 
 are shown in Figures 6-1 through 6-4. In general, the calculations 
 apply only to the types of systems shown. The methods are not appli- 
 cable for swimming pool heaters, solar-assisted heat pumps, nor for 
 systems using concentrating collectors. 
 
 GRAPHICAL METHOD 
 
 A simple graphical approach for estimating the fraction of annual 
 space heating load that can be supplied by a solar system is shown in 
 Figure 6-5. The curve can also be used to estimate the collector area 
 required to meet a pre-selected solar fraction. The graphical method is 
 illustrated by the examples given below: 
 
6-6 
 
 SOLAR 
 
 RELIEF 
 VALVE 
 
 HEAT EX- 
 CHANGER 
 
 MAIN 
 
 STORAGE 
 
 TANK 
 
 ^ 
 
 SERVICE 
 
 H.W. 
 
 TANK 
 
 I 
 
 lAUXIHARYl 
 
 PRE- 
 HEAT 
 TANK 
 
 WATER 
 SUPPLY 
 
 HOUSE 
 
 AUXILIARY 
 
 Figure 6-1. Schematic Diagram of a Liquid-Based Solar Space and Water 
 Heating System 
 
 HEAT 
 EXCHANGER 
 
 FAN 
 
 RETURN AIR 
 FROM HOUSE 
 
 DAMPER A 
 TO TAP 
 
 WATER 
 HEATER 
 
 DAMPER B 
 
 Figure 6-2. Schematic Diagram of an Air-Based Solar Space and Water 
 Heating System 
 
6-7 
 
 "— 0- 
 
 STORAGE 
 TANK 
 
 TO HOT 
 
 WATER 
 LOAD 
 
 Figure 6-3. Schematic Diagram of a Liquid-Based Domestic Water Heating 
 System 
 
 DOMESTIC 
 
 WATER 
 
 HEATER 
 
 WATER 
 
 PREHEAT 
 
 TANK 
 
 SUPPLY 
 MAIN 
 
 HEAT 
 EXCHANGER 
 
 Figure 6-4. Schematic Diagram of an Air-Based Domestic Water Heating 
 System 
 
6-8 
 
 
 
 
 
 
 
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6-9 
 
 Example 6-1 - Estimate the fraction of annual heating load that could be 
 supplied by a liquid-heating solar system having 300 ft of collectors 
 in a building that has an effective thermal conductance, (UA). , of 400 
 Btu/(hr*°F) and is located in Denver, Colorado. 
 
 Solution - The parameter SA/L is the ratio of available solar energy in 
 January divided by the building load for January. 
 
 From Module 3, I = 742 Btu/ft 2 -day 
 
 Therefore, S = I«n = 742 x 31 = 23002 Btu/ft 2 -mo 
 
 and SA = 23002 x 300 = 6.9 x 10 6 Btu/mo 
 
 From Module 5, L = (UA) L x 24 x DD Btu/mo 
 L = 400 x 1132 x 24 Btu/mo 
 L = 10.87 x 10 6 Btu/mo 
 SA/L = 6.9/10.87 = 0.63 
 
 From Figure 6-5, F = 0.72 
 Example 6-2 - Determine the area of collectors required to supply 50 
 percent of the annual heating load for the building of Example 6-1. 
 Solution ~ From Figure 6-5, for F = 0.5, 
 
 SA/L ~ 0.37 
 
 . _ 0.37xL _ 0. 37x10. 87xl0 6 . 17 , f 2 
 rt S 23000 
 
 The graphical method illustrated above for estimating system 
 performance (in terms of F) is very rapidly completed but a single curve 
 cannot reflect different types of systems, different collectors, nor 
 effects of geographical location, unless individualized curves are 
 developed for every different circumstance. 
 
 Other graphical procedures use a more refined approach by calculat- 
 ing monthly solar fractions based on monthly solar-to-load ratios, but 
 
6-10 
 
 the reliability of the results is only slightly improved. A universal 
 curve of the type shown in Figure 6-5 is not possible with the variety 
 of systems available. 
 
 RELATIVE AREAS METHOD 
 
 If the parameter of the horizontal axis in Figure 6-5 is expressed 
 as a relative collector area, where the basis is collector area to 
 supply approximately 50 percent of the load, the parameter AS/L could be 
 re-expressed as 
 
 SA/L _ A 
 
 SA~7E A ' 
 
 (6-1) 
 
 where A is the collector area which will supply approximately 
 50 percent of the load. 
 A curve similar to Figure 6-5 could be drawn and the curve could be 
 described by a general equation: 
 
 F _ C1 + C 2 £n (A/A Q ), (6-2) 
 
 where C-. and C ? are constants for a given system type and 
 
 location 
 
 A is a selected collector area. 
 
 The value of A is dependent upon the heating load, and the 
 
 collector and system characteristics as expressed below: 
 A s (UA) L 
 A o = F^U L (Z) (6 " 3) 
 
 whe 
 
 re Fnta is a collector characteristic (dimensionless) 
 
 2 
 FpU. is a collector loss characteristic Btu/(hr*ft *°F) 
 
6-11 
 
 (UA). is the effective thermal conductance of the 
 
 building Btu/(hr-°F) 
 A is a location -dependent value which reflects the 
 
 thermal building load (hr-ft 2 -°F)/Btu 
 Z is a location- and system-dependent value which 
 
 affects collection losses (hr*ft *°F)/Btu. 
 
 For any given location and system type, with knowledge of 4 values, 
 C-. , C~, A and Z, and the collector characteristics, F R ia and F R U. , the 
 annual solar fraction for the system may be determined. Values of 
 C-. , C ? , A and Z for a number of locations are listed in Table 6-3 
 on pages 6-14 to 6-16. The relative areas method is illustrated in 
 Example 6-3. 
 
 Example 6-3 - Estimate the fraction of annual space and DHW heating 
 load that could be supplied by a liquid-heating solar system having 300 
 ft of Miromit collectors, for a building that has an effective 
 thermal conductance (UA), of 400 Btu/(hr*°F) and is located in Denver, 
 Colorado. 
 Solution - 
 
 Collector characteristics (from Module 4) 
 
 F R ta = 0.724 F R U L = 0.947 Btu/(hr-ft 2 -°F) 
 
 From Table 6-3 
 
 A s = 0.175 Z = 0.197 C 1 = .538 C 2 = .316 
 
 Assume a heat exchanger factor, F R /F R = 0.97 
 
 Using Equation (6-3) 
 
 A = 0.175(400) „ -,. . f ,2 
 
 (0.97)(0.724) - (0.97X0. 947)(0.197) "' L ^' 6 TL 
 
 F = 0.538 + 0.312 £n (300/134.3) = 0.79 
 
6-12 
 
 Comparing the result with Example (6-1) it is noted that the 
 difference is about 10 percent in this particular example, with the 
 relative areas method considered to be more reliable than the single- 
 graph method. 
 
 For a domestic water heating system of the type illustrated in 
 
 Figure 6-3, the calculation of A changes slightly to 
 
 A D DATxlO" 3 
 A o = F'xa-F'U L (Z) ^ 
 
 where 
 
 2 
 Arv is a location-dependent variable (ft •day)/(°F«kgal) 
 
 D is daily hot water use (gal /day) 
 
 AT is average yearly temperature rise from mains temperature 
 
 to delivery temperature (°F) 
 
 Example 6-4 - Determine the number of collector modules required to 
 
 provide hot water for a family of four in a residential building in 
 
 Kansas City, Mo. , if the solar system is to supply 60 percent of the 
 
 yearly hot water requirement. Collector characteristics in F R xa = 0.724, 
 
 F R U L = 0.947 Btu/(hr-ft 2 -°F), and module size is 3 ft by 8 ft. 
 
 Solution - Assume an average family of four requires 80 gallons of hot 
 
 water per day, and average AT = (140°-50°) = 90°F. 
 
 From Table 6-3 
 
 A Q = 3.357 Z = 0.234 (^ = 0.541 C 2 = 0.332 
 
 Assume F R /F R = 0.95 
 
 Using Equation (6-4) 
 
 a - 3.357 x 80 x 90 x 10" 3 „ , n fi f .2 
 
 " (0.95)(0.724)-().95)(0. 947)(0.234) DU - bTL 
 
6-13 
 
 From Equation (6-2) 
 
 F = C ± + C 2 £n (A/A Q ) 
 
 0.6 = 0.341 + 0.332 In (A/A Q ) 
 
 £n(A/A Q ) = 0.178 
 
 = e °- 178 = 1 194 
 A/Ao e i,iy4 
 
 A = 50.6 x 1.194 = 60.4 ft 2 
 
 2 
 Since 1 module = 24 ft , 2.52 modules are required, but fractional 
 
 modules are not obtainable. Hence 3 collector modules are re- 
 quired, and more than 60 percent of the hot water needs will be met 
 by solar in average years. 
 
 In using the relative areas method, it is necessary to calculate 
 the natural logarithm, or the anti logarithm of a number. Most hand-held 
 calculators designed for scientific work include the Jin function and its 
 inverse, so no difficulty is encountered in the calculations. However, 
 for the benefit of trainees without such calculators, an abbreviated 
 table of natural logarithms of numbers is provided in this module. 
 
6-14 
 
 Table 6-3 
 Constants for Relative Areas Method 
 
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6-15 
 
 Table 6-3 (continued) 
 
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6-16 
 
 Table 6-3 (continued). 
 
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6-17 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.30 
 
 -1.204 
 
 -1.201 
 
 -1.197 
 
 -1.194 
 
 -1.191 
 
 -1.187 
 
 -1.184 
 
 -1.181 
 
 -1.178 
 
 -1.174 
 
 0.31 
 
 -1.171 
 
 -1.168 
 
 -1.165 
 
 -1.162 
 
 -1.158 
 
 -1.155 
 
 -1.152 
 
 -1.149 
 
 -1.146 
 
 -1.143 
 
 0.32 
 
 -1.139 
 
 -1.136 
 
 -1.133 
 
 -1.130 
 
 -1.127 
 
 -1.124 
 
 -1.121 
 
 -1.118 
 
 -1.115 
 
 -1.112 
 
 0.33 
 
 -1.109 
 
 -1.106 
 
 -1.103 
 
 -1.100 
 
 -1.097 
 
 -1.094 
 
 -1.091 
 
 -1.088 
 
 -1.085 
 
 -1.082 
 
 0.34 
 
 -1.079 
 
 -1.076 
 
 -1.073 
 
 -1.070 
 
 -1.067 
 
 -1.064 
 
 -1.061 
 
 -1.058 
 
 -1.056 
 
 -1.053 
 
 0.35 
 
 -1.050 
 
 -1.047 
 
 -1.044 
 
 -1.041 
 
 -1 .038 
 
 -1.036 
 
 -1.033 
 
 -1.030 
 
 -1.027 
 
 -1.024 
 
 0.36 
 
 -1.022 
 
 -1.019 
 
 -1.016 
 
 -1.013 
 
 -1.011 
 
 -1.008 
 
 -1.005 
 
 -1.002 
 
 -1.000 
 
 -0.997 
 
 0.37 
 
 -0.994 
 
 -0.992 
 
 -0.989 
 
 -0.986 
 
 -0.983 
 
 -0.981 
 
 -0.978 
 
 -0.976 
 
 -0.973 
 
 -0.970 
 
 0.38 
 
 -0.968 
 
 -0.965 
 
 -0.962 
 
 -0.960 
 
 -0.957 
 
 -0.955 
 
 -0.952 
 
 -0.949 
 
 -0.947 
 
 -0.944 
 
 0.39 
 
 -0.942 
 
 -0.939 
 
 -0.936 
 
 -0.934 
 
 -0.931 
 
 -0.929 
 
 -0.926 
 
 -0.924 
 
 -0.921 
 
 -0.919 
 
 0.40 
 
 -0.916 
 
 -0.914 
 
 -0.911 
 
 -0.909 
 
 -0.906 
 
 -0.904 
 
 -0.901 
 
 -0.899 
 
 -0.896 
 
 -0.894 
 
 0.41 
 
 -0.892 
 
 -0.889 
 
 -0.887 
 
 -0.884 
 
 -0.882 
 
 -0.879 
 
 -0.877 
 
 -0.87 5 
 
 -0.872 
 
 -0.870 
 
 0.42 
 
 -0.868 
 
 -0.865 
 
 -0.863 
 
 -0.860 
 
 -0.858 
 
 -0.856 
 
 -0.853 
 
 -0.851 
 
 -0.849 
 
 -0.846 
 
 0.43 
 
 -0.844 
 
 -0.842 
 
 -0.839 
 
 -0.837 
 
 -0.835 
 
 -0.832 
 
 -0.830 
 
 -0.828 
 
 -0.826 
 
 -0.823 
 
 0.44 
 
 -0.821 
 
 -0.819 
 
 -0.816 
 
 -0.814 
 
 -0.812 
 
 -0.810 
 
 -0.807 
 
 -0.805 
 
 -0.803 
 
 -0.801 
 
 0.45 
 
 -0.799 
 
 -0.796 
 
 -0.794 
 
 -0.792 
 
 -0.790 
 
 -0.787 
 
 -0.785 
 
 -0.783 
 
 -0.781 
 
 -0.779 
 
 0.46 
 
 -0.777 
 
 -0.774 
 
 -0.772 
 
 -0.770 
 
 -0.768 
 
 -0.766 
 
 -0.764 
 
 -0.761 
 
 -0.759 
 
 -0.757 
 
 0.47 
 
 -0.755 
 
 -0.753 
 
 -0.751 
 
 -0.749 
 
 -0.747 
 
 -0.744 
 
 -0.742 
 
 -0.740 
 
 -0.738 
 
 -0.736 
 
 0.48 
 
 -0.734 
 
 -0.732 
 
 -0.730 
 
 -0.728 
 
 -0.7 26 
 
 -0.7 24 
 
 -0.722 
 
 -0.719 
 
 -0.717 
 
 -0.715 
 
 0.49 
 
 -0.713 
 
 -0.711 
 
 -0.709 
 
 -0.707 
 
 -0.705 
 
 -0.703 
 
 -0.701 
 
 -0.699 
 
 -0.697 
 
 -0.695 
 
 0.50 
 
 -0.693 
 
 -0.691 
 
 -0.689 
 
 -0.687 
 
 -0.685 
 
 -0.683 
 
 -0.681 
 
 -0.679 
 
 -0.677 
 
 -0.675 
 
 0.51 
 
 -0.673 
 
 -0.671 
 
 -0.669 
 
 -0.667 
 
 -0.666 
 
 -0.664 
 
 -0.662 
 
 -0.660 
 
 -0.658 
 
 -0.656 
 
 0.52 
 
 -0.654 
 
 -0.652 
 
 -0.650 
 
 -0.648 
 
 -0.646 
 
 -0.644 
 
 -0.642 
 
 -0.641 
 
 -0.639 
 
 -0.637 
 
 0.53 
 
 -0.635 
 
 -0.633 
 
 -0.631 
 
 -0.629 
 
 -0.627 
 
 -0.625 
 
 -0.624 
 
 -0.622 
 
 -0.620 
 
 -0.618 
 
 0.54 
 
 -0.616 
 
 -0.614 
 
 -0.612 
 
 -0.611 
 
 -0.609 
 
 -0.607 
 
 -0.605 
 
 -0.603 
 
 -0.601 
 
 -0.600 
 
 0.55 
 
 -0.598 
 
 -0.596 
 
 -0.594 
 
 -0.592 
 
 -0.591 
 
 -0.589 
 
 -0.587 
 
 -0.585 
 
 -0.583 
 
 -0.582 
 
 0.56 
 
 -0.580 
 
 -0.578 
 
 -0.576 
 
 -0.574 
 
 -0.573 
 
 -0.571 
 
 -0.569 
 
 -0.567 
 
 -0.566 
 
 -0.564 
 
 0.57 
 
 -0.562 
 
 -0.560 
 
 -0.559 
 
 -0.557 
 
 -0.555 
 
 -0.553 
 
 -0.552 
 
 -0.550 
 
 -0.548 
 
 -0.546 
 
 0.58 
 
 -0.545 
 
 -0.543 
 
 -0.541 
 
 -0.540 
 
 -0.538 
 
 -0.536 
 
 -0.534 
 
 -0.533 
 
 -0.531 
 
 -0.529 
 
 0.59 
 
 -0 . 5 28 
 
 -0.526 
 
 -0.524 
 
 -0.523 
 
 -0.521 
 
 -0.519 
 
 -0.518 
 
 -0.516 
 
 -0.514 
 
 -0.512 
 
 0.60 
 
 -0.511 
 
 -0.509 
 
 -0.507 
 
 -0.506 
 
 -0.504 
 
 -0.503 
 
 -0.501 
 
 -0.499 
 
 -0.498 
 
 -0.496 
 
 0.61 
 
 -0.494 
 
 -0.493 
 
 -0.491 
 
 -0.489 
 
 -0.488 
 
 -0.486 
 
 -0.485 
 
 -0.483 
 
 -0.481 
 
 -0.480 
 
 .0.62 
 
 -0.478 
 
 -0.476 
 
 -0.475 
 
 -0.473 
 
 -0.472 
 
 -0.470 
 
 -0.468 
 
 -0.467 
 
 -0.465 
 
 -0.464 
 
 0.63 
 
 -0.462 
 
 -0.460 
 
 -0.4 59 
 
 -0.4 57 
 
 -0.4 56 
 
 -0.454 
 
 -0.453 
 
 -0.4 51 
 
 -0.449 
 
 -0.448 
 
 0.64 
 
 -0.446 
 
 -0.445 
 
 -0.443 
 
 -0.442 
 
 -0.4^0 
 
 -0.439 
 
 -0.437 
 
 -0.435 
 
 -0.434 
 
 -0.432 
 
 0.65 
 
 -0.431 
 
 -0.4 29 
 
 -0.428 
 
 -0.4 26 
 
 -0.425 
 
 -0.423 
 
 -0.422 
 
 -0.4 20 
 
 -0.419 
 
 -0.417 
 
 0.66 
 
 -0.416 
 
 -0.414 
 
 -0.412 
 
 -0.411 
 
 -0.409 
 
 -0.408 
 
 -0.406 
 
 -0.405 
 
 -0.403 
 
 -0.402 
 
 0.67 
 
 -0.400 
 
 -0.399 
 
 -0.397 
 
 -0.396 
 
 -0.395 
 
 -0.393 
 
 -0.392 
 
 -0.390 
 
 -0.389 
 
 -0.387 
 
 0.68 
 
 -0.386 
 
 -0.384 
 
 -0.3 83 
 
 -0.381 
 
 -0.380 
 
 -0.378 
 
 -0.377 
 
 -0.375 
 
 -0.374 
 
 -0.373 
 
 0.69 
 
 -0.371 
 
 -0.370 
 
 -0.368 
 
 -0.367 
 
 -0.365 
 
 -0.364 
 
 -0.362 
 
 -0.3 61 
 
 -0.360 
 
 -0.3 58 
 
6-18 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 0.70 
 
 -0.357 
 
 -0.355 
 
 -0.354 
 
 -0.352 
 
 -0.351 
 
 -0.350 
 
 -0.348 
 
 -0.347 
 
 -0.345 
 
 -0.344 
 
 0.71 
 
 -0.342 
 
 -0.341 
 
 -0.340 
 
 -0.338 
 
 -0.337 
 
 -0.335 
 
 -0.334 
 
 -0.333 
 
 -0.331 
 
 -0.330 
 
 0.72 
 
 -0.329 
 
 -0.327 
 
 -0.326 
 
 -0.324 
 
 -0.323 
 
 -0.322 
 
 -0.320 
 
 -0.319 
 
 -0.317 
 
 -0.316 
 
 0.73 
 
 -0.315 
 
 -0.313 
 
 -0.312 
 
 -0.311 
 
 -0.309 
 
 -0.308 
 
 -0.307 
 
 -0.305 
 
 -0.304 
 
 -0.302 
 
 0.74 
 
 -0.301 
 
 -0.300 
 
 -0.298 
 
 -0.297 
 
 -0.296 
 
 -0.294 
 
 -0.293 
 
 -0.292 
 
 -0.290 
 
 -0.289 
 
 0.75 
 
 -0.288 
 
 -0.286 
 
 -0.285 
 
 -0.284 
 
 -0.282 
 
 -0.281 
 
 -0.280 
 
 -0.278 
 
 -0.277 
 
 -0.276 
 
 |0.76 
 
 -0.274 
 
 -0.273 
 
 -0.272 
 
 -0.270 
 
 -0.269 
 
 -0.268 
 
 -0.267 
 
 -0.265 
 
 -0.264 
 
 -0.263 
 
 0.77 
 
 -0.261 
 
 -0.260 
 
 -0.259 
 
 -0.257 
 
 -0.256 
 
 -0.255 
 
 -0.254 
 
 -0.252 
 
 -0.251 
 
 -0.250 
 
 0.78 
 
 -0.248 
 
 -0.247 
 
 -0.246 
 
 -0.245 
 
 -0.243 
 
 -0.242 
 
 -0.241 
 
 -0.240 
 
 -0.238 
 
 -0.237 
 
 0.79 
 
 -0.236 
 
 -0.234 
 
 -0.233 
 
 -0.232 
 
 -0.231 
 
 -0.229 
 
 -0.228 
 
 -0.227 
 
 -0.2 26 
 
 -0.224 
 
 0.80 
 
 -0.223 
 
 -0.22 2 
 
 -0.221 
 
 -0.219 
 
 -0.218 
 
 -0.217 
 
 -0.216 
 
 -0.214 
 
 -0.213 
 
 -0.212 
 
 0.81 
 
 -0.211 
 
 -0.209 
 
 -0.208 
 
 -0.207 
 
 -0.206 
 
 -0.205 
 
 -0.203 
 
 -0.202 
 
 -0.201 
 
 -0.200 
 
 0.82 
 
 -0.198 
 
 -0.197 
 
 -0.196 
 
 -0.195 
 
 -0.194 
 
 -0.192 
 
 -0.191 
 
 -0.190 
 
 -0.189 
 
 -0.188 
 
 0.83 
 
 -0.186 
 
 -0.185 
 
 -0.184 
 
 -0.183 
 
 -0.182 
 
 -0.180 
 
 -0.179 
 
 -0.178 
 
 -0.177 
 
 -0.176 
 
 0.84 
 
 -0.174 
 
 -0.173 
 
 -0.17 2 
 
 -0.171 
 
 -0.170 
 
 -0.168 
 
 -0.167 
 
 -0.166 
 
 -0.165 
 
 -0.164 
 
 0.85 
 
 -0.163 
 
 -0.161 
 
 -0.160 
 
 -0.159 
 
 -0.158 
 
 -0.157 
 
 -0.155 
 
 -0.154 
 
 -0.153 
 
 -0.152 
 
 0.86 
 
 -0.151 
 
 -0.150 
 
 -0.149 
 
 -0.147 
 
 -0.146 
 
 -0.145 
 
 -0.144 
 
 -0.143 
 
 -0.142 
 
 -0.140 
 
 0.87 
 
 -0.139 
 
 -0.138 
 
 -0.137 
 
 -0.136 
 
 -0.135 
 
 -0.134 
 
 -0.132 
 
 -0.131 
 
 -0.130 
 
 -0.129 
 
 0.88 
 
 -0.128 
 
 -0.127 
 
 -0.126 
 
 -0.124 
 
 -0.123 
 
 -0.122 
 
 -0.121 
 
 -0.120 
 
 -0.119 
 
 -0.118 
 
 0.89 
 
 -0.117 
 
 -0.115 
 
 -0.114 
 
 -0.113 
 
 -0.112 
 
 -0.111 
 
 -0.110 
 
 -0.109 
 
 -0.108 
 
 -0.106 
 
 0.90 
 
 -0.10 5 
 
 -0.104 
 
 -0.103 
 
 -0.10 2 
 
 -0.101 
 
 -0.100 
 
 -0.099 
 
 -0.098 
 
 -0.097 
 
 -0.095 
 
 0.91 
 
 -0.094 
 
 -0.093 
 
 -0.092 
 
 -0.091 
 
 -0.090 
 
 -0.089 
 
 -0.088 
 
 -0.087 
 
 -0.086 
 
 -0.084 
 
 0.92 
 
 -0.083 
 
 -0.082 
 
 -0.081 
 
 -0.080 
 
 -0.079 
 
 -0.078 
 
 -0.077 
 
 -0.076 
 
 -0.075 
 
 -0.074 
 
 0.93 
 
 -0.073 
 
 -0.071 
 
 -0.070 
 
 -0.069 
 
 -0.068 
 
 -0.067 
 
 -0r066 
 
 -0.065 
 
 -0.064 
 
 -0.063 
 
 0.94 
 
 -0.062 
 
 -0.061 
 
 -0.060 
 
 -0.059 
 
 -0.058 
 
 -0.057 
 
 -0.056 
 
 -0.054 
 
 -0.053 
 
 -0.052 
 
 0.95 
 
 -0.051 
 
 -0.050 
 
 -0.049 
 
 -0.048 
 
 -0.047 
 
 -0.046 
 
 -0.045 
 
 -0.044 
 
 -0.043 
 
 -0.042 
 
 0.96 
 
 -0.041 
 
 -0.040 
 
 -0.03 9 
 
 -0.038 
 
 -0.037 
 
 -0.036 
 
 -0.035 
 
 -0.034 
 
 -0.033 
 
 -0.031 
 
 0.97 
 
 -0.030 
 
 -0.029 
 
 -0.028 
 
 -0.027 
 
 -0.026 
 
 -0.025 
 
 -0.024 
 
 -0.023 
 
 -0.022 
 
 -0.021 
 
 0.98 
 
 -0.020 
 
 -0.019 
 
 -0.018 
 
 -0.017 
 
 -0.016 
 
 -0.015 
 
 -0.014 
 
 -0.013 
 
 -0.012 
 
 -0.011 
 
 0.99 
 
 -0.010 
 
 -0.009 
 
 -0.008 
 
 -0.007 
 
 -0.006 
 
 -0.005 
 
 -0.004 
 
 -0.003 
 
 -0.002 
 
 -0.001 
 
 1.00 
 
 0.000 
 
 0.001 
 
 0.002 
 
 0.003 
 
 0.004 
 
 0.005 
 
 0.006 
 
 0.007 
 
 0.008 
 
 0.009 
 
 1.01 
 
 0.010 
 
 0.011 
 
 0.012 
 
 0.013 
 
 0.014 
 
 0.015 
 
 0.016 
 
 0.017 
 
 0.018 
 
 0.019 
 
 1.02 
 
 0.020 
 
 0.021 
 
 0.022 
 
 0.023 
 
 0.024 
 
 0.025 
 
 0.026 
 
 0.027 
 
 0.028 
 
 0.029 
 
 1.03 
 
 0.030 
 
 0.031 
 
 0.031 
 
 0.032 
 
 0.033 
 
 0.034 
 
 0.035 
 
 0.036 
 
 0.037 
 
 0.038 
 
 1.04 
 
 0.039 
 
 0.040 
 
 0.041 
 
 0.04 2 
 
 0.043 
 
 0.044 
 
 0.045 
 
 0.046 
 
 0.047 
 
 0.048 
 
 1.05 
 
 0.049 
 
 0.050 
 
 0.051 
 
 0.052 
 
 0.053 
 
 0.054 
 
 0.054 
 
 0.055 
 
 0.056 
 
 0.057 
 
 1.06 
 
 0.058 
 
 0.059 
 
 0.060 
 
 0.061 
 
 0.062 
 
 0.063 
 
 0.064 
 
 0.065 
 
 0.066 
 
 0.067 
 
 1.07 
 
 0.068 
 
 0.069 
 
 0.070 
 
 0.070 
 
 0.071 
 
 0.072 
 
 0.073 
 
 0.074 
 
 0.075 
 
 0.076 
 
 1.08 
 
 0.077 
 
 0.078 
 
 0.079 
 
 0.080 
 
 0.081 
 
 0.082 
 
 0.083 
 
 0.083 
 
 0.084 
 
 0.085 
 
 1.09 
 
 0.086 
 
 0.087 
 
 0.088 
 
 0.089 
 
 0.090 
 
 0.091 
 
 0.092 
 
 0.093 
 
 0.093 
 
 0.094 
 
6-19 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 • 
 9 
 
 1.10 
 
 0.095 
 
 0.096 
 
 0.097 
 
 0,098 
 
 0.099 
 
 0.100 
 
 0.101 
 
 0.102 
 
 0.103 
 
 0.103 
 
 1.11 
 
 0.104 
 
 0.105 
 
 0.106 
 
 0.107 
 
 0.108 
 
 0.109 
 
 0.110 
 
 0.111 
 
 0.112 
 
 0.112 
 
 1.12 
 
 0.113 
 
 0.114 
 
 0.115 
 
 0.116 
 
 0.117 
 
 0.118 
 
 0.119 
 
 0.120 
 
 0.120 
 
 0.121 
 
 1.13 
 
 0.122 
 
 0.123 
 
 0.124 
 
 0.125 
 
 0.126 
 
 0.127 
 
 0.128 
 
 0.128 
 
 0.129 
 
 0.130 
 
 1.14 
 
 0.131 
 
 0.132 
 
 0.133 
 
 0.134 
 
 0.135 
 
 0.135 
 
 0.136 
 
 0.137 
 
 0.138 
 
 0.139 
 
 1.15 
 
 0.140 
 
 0.141 
 
 0.141 
 
 0.142 
 
 0.143 
 
 0.144 
 
 0.145 
 
 0.146 
 
 0.147 
 
 0.148 
 
 1.16 
 
 0.148 
 
 0.149 
 
 0.150 
 
 0.151 
 
 0.152 
 
 0.153 
 
 0.154 
 
 0.154 
 
 0.155 
 
 0.156 
 
 1.17 
 
 0.157 
 
 0.158 
 
 0.159 
 
 0.160 
 
 0.160 
 
 0.161 
 
 0.162 
 
 0.163 
 
 0.164 
 
 0.165 
 
 1.18 
 
 0.166 
 
 0.166 
 
 0.167 
 
 0.168 
 
 0.169 
 
 0.170 
 
 0.171 
 
 0.171 
 
 0.172 
 
 0.173 
 
 [1.19 
 
 0.174 
 
 0.175 
 
 0.176 
 
 0.176 
 
 0.177 
 
 0.178 
 
 0.179 
 
 0.180 
 
 0.181 
 
 0.181 
 
 1.20 
 
 0.182 
 
 0.183 
 
 0.184 
 
 0.185 
 
 0.186 
 
 0.186 
 
 0.187 
 
 0.188 
 
 0.189 
 
 0.190 
 
 1.21 
 
 0.191 
 
 0.191 
 
 0.192 
 
 0.193 
 
 0.194 
 
 0.195 
 
 0.196 
 
 0.196 
 
 0.197 
 
 0.198 
 
 1.22 
 
 0.199 
 
 0.200 
 
 0.200 
 
 0.201 
 
 0.202 
 
 0.203 
 
 0.204 
 
 0.205 
 
 0.205 
 
 0.206 
 
 1.23 
 
 0.207 
 
 0.208 
 
 0.209 
 
 0.209 
 
 0.210 
 
 0.211 
 
 0.212 
 
 0.213 
 
 0.213 
 
 0.214 
 
 1.24 
 
 0.215 
 
 0.216 
 
 0.217 
 
 0.218 
 
 0.218 
 
 0.219 
 
 0.220 
 
 0.221 
 
 0.222 
 
 0.222 
 
 1.25 
 
 0.223 
 
 0.224 
 
 0.225 
 
 0.226 
 
 0.226 
 
 0.227 
 
 0.228 
 
 0.229 
 
 0.230 
 
 0.230 
 
 1.26 
 
 0.231 
 
 0.232 
 
 0.233 
 
 0.233 
 
 0.234 
 
 0.235 
 
 0.236 
 
 0.237 
 
 0.237 
 
 0.238 
 
 1.27 
 
 0.239 
 
 0.240 
 
 0.241 
 
 0.241 
 
 0.242 
 
 0.243 
 
 0.244 
 
 0.245 
 
 0.245 
 
 0.246 
 
 1.28 
 
 0.247 
 
 0.248 
 
 0.248 
 
 0.249 
 
 0.250 
 
 0.251 
 
 0.252 
 
 0.252 
 
 0.253 
 
 0.254 
 
 1.29 
 
 0.255 
 
 0.255 
 
 0.256 
 
 0.257 
 
 0.258 
 
 0.259 
 
 0.259 
 
 0.260 
 
 0.261 
 
 0.262 j 
 
 1 
 
 1.30 
 
 0.262 
 
 0.263 
 
 0.264 
 
 0.265 
 
 0.265 
 
 0.266 
 
 0.267 
 
 0.268 
 
 0.268 
 
 1 
 0.269 ; 
 
 1.31 
 
 0.270 
 
 0.271 
 
 0.272 
 
 0.272 
 
 0.273 
 
 0.274 
 
 0.275 
 
 0.275 
 
 0.276 
 
 0.277 
 
 1.32 
 
 0.278 
 
 0.278 
 
 0.279 
 
 0.280 
 
 0.281 
 
 0.281 
 
 0.282 
 
 0.283 
 
 0.284 
 
 0.284 
 
 1.33 
 
 0.285 
 
 0.286 
 
 0.287 
 
 0.287 
 
 0.288 
 
 0.289 
 
 0.290 
 
 0.290 
 
 0.291 
 
 0.292 
 
 1.34 
 
 0.293 
 
 0.293 
 
 0.294 
 
 0.295 
 
 0.296 
 
 0.296 
 
 0.297 
 
 0.298 
 
 0.299 
 
 0.299 
 
 1.35 
 
 0.300 
 
 0.301 
 
 0.302 
 
 0.302 
 
 0.303 
 
 0.304 
 
 0.305 
 
 0.305 
 
 0.306 
 
 0.307 
 
 1.36 
 
 0.307 
 
 0.308 
 
 0.309 
 
 0.310 
 
 0.310 
 
 0.311 
 
 0.312 
 
 0.313 
 
 0.313 
 
 0.314 
 
 1.37 
 
 0.315 
 
 0.316 
 
 0.316 
 
 0.317 
 
 0.318 
 
 0.318 
 
 0.319 
 
 0.320 
 
 0.321 
 
 0.321 
 
 1.38 
 
 0.322 
 
 0.323 
 
 0.324 
 
 0.3 24 
 
 0.325 
 
 0.326 
 
 0.326 
 
 0.327 
 
 0.328 
 
 0.329 
 
 1.39 
 
 0.329 
 
 0.330 
 
 0.331 
 
 0.331 
 
 0.332 
 
 0.333 
 
 0.334 
 
 0.334 
 
 0.335 
 
 0.336 
 
 1.40 
 
 0.336 
 
 0.337 
 
 0.338 
 
 0.339 
 
 0.339 
 
 0.340 
 
 0.341 
 
 0.341 
 
 0.342 
 
 0.343 
 
 1.41 
 
 0.344 
 
 0.344 
 
 0.345 
 
 0.346 
 
 0.346 
 
 0.347 
 
 0.348 
 
 0.349 
 
 0.349 
 
 0.350 
 
 .1.42 
 
 0.351 
 
 0.351 
 
 0.352 
 
 0.353 
 
 0.353 
 
 0.354 
 
 0.355 
 
 0.356 
 
 0.356 
 
 0.357 
 
 1.43 
 
 0.358 
 
 0.358 
 
 0.359 
 
 0.360 
 
 0.360 
 
 0.361 
 
 0.362 
 
 0.363 
 
 0.363 
 
 0.364 
 
 1.44 
 
 0.365 
 
 0.365 
 
 0.366 
 
 0.367 
 
 0.367 
 
 0.368 
 
 0.369 
 
 0.369 
 
 0.370 
 
 0.371 
 
 1.45 
 
 0.372 
 
 0.372 
 
 0.373 
 
 0.374 
 
 0.374 
 
 0.375 
 
 0.376 
 
 0.376 
 
 0.377 
 
 0.378 
 
 1.46 
 
 0.378 
 
 0.379 
 
 0.380 
 
 0.380 
 
 0.381 
 
 0.382 
 
 0.383 
 
 0.383 
 
 0.384 
 
 0.385 
 
 1.47 
 
 0.385 
 
 0.386 
 
 0.387 
 
 0.387 
 
 0.388 
 
 0.389 
 
 0.389 
 
 0.390 
 
 0.391 
 
 0.391 
 
 1.48 
 
 0.392 
 
 0.393 
 
 0.393 
 
 0.394 
 
 0.395 
 
 0.395 
 
 0.396 
 
 0.397 
 
 0.397 
 
 0.398 
 
 1.49 
 
 0.399 
 
 0.399 
 
 0.400 
 
 0.401 
 
 0.401 
 
 0.402 
 
 0.403 
 
 0.403 
 
 0.404 
 
 0.405 
 
6-20 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1.50 
 
 0.405 
 
 0.406 
 
 0.407 
 
 0.407 
 
 0.408 
 
 0.409 
 
 0.409 
 
 0.410 
 
 0.411 
 
 0.411 
 
 1.51 
 
 0.412 
 
 0.413 
 
 0.413 
 
 0.414 
 
 0.415 
 
 0.415 
 
 0.416 
 
 0.417 
 
 0.417 
 
 0.418 
 
 1.52 
 
 0.419 
 
 0.419 
 
 0.420 
 
 0.421 
 
 0.421 
 
 0.422 
 
 0.423 
 
 0.423 
 
 0.424 
 
 0.425 
 
 1.53 
 
 0.425 
 
 0.426 
 
 0.427 
 
 0.427 
 
 0.428 
 
 0.429 
 
 0.429 
 
 0.430 
 
 0.430 
 
 0.431 
 
 1.54 
 
 0.432 
 
 0.432 
 
 0.433 
 
 0.434 
 
 0.434 
 
 0.435 
 
 0.436 
 
 0.436 
 
 0.437 
 
 0.438 
 
 1.55 
 
 0.438 
 
 0.439 
 
 0.440 
 
 0.440 
 
 0.441 
 
 0.441 
 
 0.442 
 
 0.443 
 
 0.443 
 
 0.444 
 
 1.56 
 
 0.445 
 
 0.445 
 
 0.446 
 
 0.447 
 
 0.447 
 
 0.448 
 
 0.449 
 
 0.449 
 
 0.450 
 
 0.450 
 
 1.57 
 
 0.451 
 
 0.452 
 
 0.452 
 
 0.453 
 
 0.A54 
 
 0.454 
 
 0.^55 
 
 0.456 
 
 0.456 
 
 0.457 
 
 1.58 
 
 0.457 
 
 0.458 
 
 0.459 
 
 0.459 
 
 0.460 
 
 0.461 
 
 0.461 
 
 0.462 
 
 0.462 
 
 0.463 
 
 1.59 
 
 0.464 
 
 0.464 
 
 0.465 
 
 0.466 
 
 0.466 
 
 0.467 
 
 0.468 
 
 0.468 
 
 0.469 
 
 0.469 
 
 1.60 
 
 0.470 
 
 0.471 
 
 0.471 
 
 0.472 
 
 0.473 
 
 0.473 
 
 0.474 
 
 0.474 
 
 0.475 
 
 0.476 
 
 1.61 
 
 0.476 
 
 0.477 
 
 0.477 
 
 0.478 
 
 0.479 
 
 0.479 
 
 0.480 
 
 0.481 
 
 0.481 
 
 0.482 
 
 1.62 
 
 0.482 
 
 0.483 
 
 0.484 
 
 0.484 
 
 0.485 
 
 0.486 
 
 0.486 
 
 0.487 
 
 0.487 
 
 0.488 
 
 1.63 
 
 0.489 
 
 0.489 
 
 0.490 
 
 0.490 
 
 0.491 
 
 0.492 
 
 0.492 
 
 0.493 
 
 0.493 
 
 0.494 
 
 1.64 
 
 0.495 
 
 0.495 
 
 0.496 
 
 0.497 
 
 0.497 
 
 0.498 
 
 0.498 
 
 0.499 
 
 0.500 
 
 0.500 
 
 1.65 
 
 0.501 
 
 0.501 
 
 0.502 
 
 0.503 
 
 0.503 
 
 0.504 
 
 0.504 
 
 0.505 
 
 0.506 
 
 0.506 
 
 1.66 
 
 0.507 
 
 0.507 
 
 0.508 
 
 0.509 
 
 0.509 
 
 0.510 
 
 0.510 
 
 0.511 
 
 0.512 
 
 0.512 
 
 1.67 
 
 0.513 
 
 0.513 
 
 0.514 
 
 0.515 
 
 0.515 
 
 0.516 
 
 0.516 
 
 0.517 
 
 0.518 
 
 0.518 
 
 1.68 
 
 0.519 
 
 0.519 
 
 0.520 
 
 0.521 
 
 0.521 
 
 0.522 
 
 0.522 
 
 0.523 
 
 0.524 
 
 0.524 
 
 1.69 
 
 0.525 
 
 0.525 
 
 0.526 
 
 0.527 
 
 0.527 
 
 0.528 
 
 0.528 
 
 0.529 
 
 0.529 
 
 0.530 
 
 1.70 
 
 0.531 
 
 0.531 
 
 0.532 
 
 0.532 
 
 0.533 
 
 0.534 
 
 0.534 
 
 0.535 
 
 0.535 
 
 0.536 
 
 1.71 
 
 0.536 
 
 0.537 
 
 0.538 
 
 0.538 
 
 0.539 
 
 0.539 
 
 0.540 
 
 0.541 
 
 0.541 
 
 0.542 
 
 1.72 
 
 0.542 
 
 0.543 
 
 0.543 
 
 0.544 
 
 0.545 
 
 0.545 
 
 0.546 
 
 0.546 
 
 0.547 
 
 0.548 
 
 1.73 
 
 0.548 
 
 0.549 
 
 0.549 
 
 0.550 
 
 0.550 
 
 0.551 
 
 0r552 
 
 0.552 
 
 0.553 
 
 0.553 
 
 1.74 
 
 0.554 
 
 0.554 
 
 0.555 
 
 0.556 
 
 0.556 
 
 0.557 
 
 0.557 
 
 0.558 
 
 0.558 
 
 0.559 
 
 1.75 
 
 0.560 
 
 0.560 
 
 0.561 
 
 0.561 
 
 0.562 
 
 0.562 
 
 0.563 
 
 0.564 
 
 0.564 
 
 0.565 
 
 1.76 
 
 0.565 
 
 0.566 
 
 0.566 
 
 0.567 
 
 0.568 
 
 0.568 
 
 0.569 
 
 0.569 
 
 0.570 
 
 0.570 
 
 1.77 
 
 0.571 
 
 0.57 2 
 
 0.572 
 
 0.573 
 
 0.573 
 
 0.574 
 
 0.574 
 
 0.575 
 
 0.575 
 
 0.576 
 
 1.78 
 
 0.577 
 
 0.577 
 
 0.578 
 
 0.578 
 
 0.579 
 
 0.579 
 
 0.580 
 
 0.581 
 
 0.581 
 
 0.582 
 
 1.79 
 
 0.582 
 
 0.583 
 
 0.583 
 
 0.584 
 
 0.584 
 
 0.585 
 
 0.586 
 
 0.586 
 
 0.587 
 
 0.587 
 
 1.80 
 
 0.588 
 
 0.588 
 
 0.589 
 
 0.589 
 
 0.590 
 
 0.591 
 
 0.591 
 
 0.592 
 
 0.592 
 
 0.593 
 
 1.81 
 
 0.593 
 
 0.594 
 
 0.594 
 
 0.595 
 
 0.596 
 
 0.596 
 
 0.597 
 
 0.597 
 
 0.598 
 
 0.598 
 
 1.82 
 
 0.599 
 
 0.599 
 
 0.600 
 
 0.600 
 
 0.601 
 
 0.602 
 
 0.602 
 
 0.603 
 
 0.603 
 
 0.604 
 
 1.83 
 
 0.604 
 
 0.60 5 
 
 0.605 
 
 0.606 
 
 0.606 
 
 0.607 
 
 0.608 
 
 0.608 
 
 0.609 
 
 0.609 
 
 1.84 
 
 0.610 
 
 0.610 
 
 0.611 
 
 0.611 
 
 0.612 
 
 0.612 
 
 0.613 
 
 0.614 
 
 0.614 
 
 0.615 
 
 1.85 
 
 0.615 
 
 0.616 
 
 0.616 
 
 0.617 
 
 0.617 
 
 0.618 
 
 0.618 
 
 0.619 
 
 0.620 
 
 0.620 
 
 1.86 
 
 0.621 
 
 0.621 
 
 0.622 
 
 0.622 
 
 0.623 
 
 0.623 
 
 0.624 
 
 0.624 
 
 0.625 
 
 0.625 
 
 1.87 
 
 0.626 
 
 0.626 
 
 0.627 
 
 0.628 
 
 0.628 
 
 0.629 
 
 0.629 
 
 0.630 
 
 0.630 
 
 0.631 
 
 1.88 
 
 0.631 
 
 0.63 2 
 
 0.632 
 
 0.633 
 
 0.633 
 
 0.634 
 
 0.634 
 
 0.635 
 
 0.636 
 
 0.636 
 
 1.89 
 
 0.637 
 
 0.637 
 
 0.638 
 
 0.638 
 
 0.639 
 
 0.639 
 
 0.640 
 
 0.640 
 
 0.641 
 
 0.641 
 
6-21 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1.90 
 
 0.642 
 
 0.642 
 
 0.643 
 
 0.643 
 
 0.644 
 
 0.644 
 
 0.645 
 
 0.646 
 
 0.646 
 
 0.647 
 
 1.91 
 
 0.647 
 
 0.648 
 
 0.648 
 
 0.649 
 
 0.649 
 
 0.650 
 
 0.650 
 
 0.651 
 
 0.651 
 
 0.652 
 
 1.92 
 
 0.652 
 
 0.653 
 
 0.653 
 
 0.654 
 
 0.654 
 
 0.655 
 
 0.655 
 
 0.656 
 
 0.656 
 
 0.657 
 
 1.93 
 
 0.658 
 
 0.658 
 
 0.659 
 
 0.659 
 
 0.660 
 
 0.660 
 
 0.661 
 
 0.661 
 
 0.662 
 
 0.662 
 
 1.94 
 
 0.663 
 
 0.663 
 
 0.664 
 
 0.664 
 
 0.665 
 
 0.665 
 
 0.666 
 
 0.666 
 
 0.667 
 
 0.667 
 
 1.95 j 
 
 0.668 
 
 0.668 
 
 0.669 
 
 0.669 
 
 0.670 
 
 0.670 
 
 0.671 
 
 0.671 
 
 0.672 
 
 0.672 
 
 1.96 I 
 
 0.673 
 
 0.673 
 
 0.674 
 
 0.674 
 
 0.675 
 
 0.675 
 
 0.676 
 
 0.677 
 
 0.677 
 
 0.678 
 
 1.97 
 
 0.678 
 
 0.679 
 
 0.679 
 
 0.680 
 
 0.680 
 
 0.681 
 
 0.681 
 
 0.682 
 
 0.682 
 
 0.683 
 
 1.98 
 
 0.683 
 
 0.684 
 
 0.684 
 
 0.685 
 
 0.685 
 
 0.686 
 
 0.686 
 
 0.687 
 
 0.687 
 
 0.688 
 
 1.99 
 
 0.688 
 
 0.689 
 
 0.689 
 
 0.690 
 
 0.690 
 
 0.691 
 
 0.691 
 
 0.692 
 
 0.692 
 
 0.693 
 
 2.00 
 
 0.693 
 
 0.694 
 
 0.694 
 
 0.695 
 
 0.695 
 
 0.696 
 
 0.696 
 
 0.697 
 
 0.697 
 
 0.698 
 
 2.01 
 
 0.698 
 
 0.699 
 
 0.699 
 
 0.700 
 
 0.700 
 
 0.701 
 
 0.701 
 
 0.702 
 
 0.702 
 
 0.703 
 
 2.02 
 
 0.703 
 
 0.704 
 
 0.704 
 
 0.705 
 
 0.705 
 
 0.706 
 
 0.706 
 
 0.707 
 
 0.707 
 
 0.708 
 
 2.03 
 
 0.708 
 
 0.709 
 
 0.709 
 
 0.710 
 
 0.710 
 
 0.710 
 
 0.711 
 
 0.711 
 
 0.712 
 
 0.712 
 
 2.04 
 
 0.713 
 
 0.713 
 
 0.714 
 
 0.714 
 
 0.715 
 
 0.715 
 
 0.716 
 
 0.716 
 
 0.717 
 
 0.717 
 
 2.05 
 
 0.718 
 
 0.718 
 
 0.719 
 
 0.719 
 
 0.720 
 
 0.720 
 
 0.721 
 
 0.721 
 
 0.722 
 
 0.722 
 
 2.06 
 
 0.723 
 
 0.723 
 
 0.724 
 
 0.724 
 
 0.725 
 
 0.725 
 
 0.726 
 
 0.726 
 
 0.727 
 
 0.727 
 
 2.07 
 
 0.7 28 
 
 0.728 
 
 0.729 
 
 0.729 
 
 0.729 
 
 0.730 
 
 0.730 
 
 0.731 
 
 0.731 
 
 0.732 
 
 2.08 
 
 0.732 
 
 0.733 
 
 0.733 
 
 0.734 
 
 0.734 
 
 0.735 
 
 0.735 
 
 0.736 
 
 0.736 
 
 0.737 
 
 2.09 
 
 0.737 
 
 0.738 
 
 0.738 
 
 0.739 
 
 0.739 
 
 0.740 
 
 0.740 
 
 0.741 
 
 0.741 
 
 0.741 
 
 2.10 
 
 0.742 
 
 0.742 
 
 0.743 
 
 0.743 
 
 0.744 
 
 0.744 
 
 0.745 
 
 0.745 
 
 0.746 
 
 0.746 
 
 2.11 
 
 0.747 
 
 0.747 
 
 0.748 
 
 0.748 
 
 0.749 
 
 0.7A9 
 
 0.750 
 
 0.750 
 
 0.750 
 
 0.751 
 
 2.12 
 
 0.751 
 
 0.752 
 
 0.752 
 
 0.753 
 
 0.753 
 
 0.754 
 
 0.754 
 
 0.755 
 
 0.755 
 
 0.756 1 
 
 2.13 
 
 0.756 
 
 0.757 
 
 0.757 
 
 0.758 
 
 0.758 
 
 0.758 
 
 0.759 
 
 0.759 
 
 0.760 
 
 0.760 
 
 2.14 
 
 0.761 
 
 0.761 
 
 0.762 
 
 0.762 
 
 0.763 
 
 0.763 
 
 0.764 
 
 0.764 
 
 0.765 
 
 0.765 
 
 2.15 
 
 0.765 
 
 0.766 
 
 0.766 
 
 0.767 
 
 0.767 
 
 0.768 
 
 0.768 
 
 0.769 
 
 0.769 
 
 0.770 
 
 2.16 
 
 0.770 
 
 0.771 
 
 0.771 
 
 0.771 
 
 0.772 
 
 0.772 
 
 0.773 
 
 0.773 
 
 0.774 
 
 0.774 
 
 2.17 
 
 0.775 
 
 0.775 
 
 0.776 
 
 0.776 
 
 0.777 
 
 0.777 
 
 0.777 
 
 0.778 
 
 0.778 
 
 0.779 
 
 2.18 
 
 0.779 
 
 0.780 
 
 0.780 
 
 0.781 
 
 0.781 
 
 0.782 
 
 0.782 
 
 0.783 
 
 0.783 
 
 0.783 
 
 2.19 
 
 0.784 
 
 0.784 
 
 0.785 
 
 0.785 
 
 0.786 
 
 0.786 
 
 0.787 
 
 0.787 
 
 0.788 
 
 0.788 
 
 2.20 
 
 0.788 
 
 0.789 
 
 0.789 
 
 0.790 
 
 0.790 
 
 0.791 
 
 0.791 
 
 0.792 
 
 0.792 
 
 0.793 
 
 2.21 
 
 0.793 
 
 0.793 
 
 0.794 
 
 0.794 
 
 0.795 
 
 0.795 
 
 0.796 
 
 0.796 
 
 0.797 
 
 0.797 
 
 2.22 
 
 0.798 
 
 0.798 
 
 0.798 
 
 0.799 
 
 0.799 
 
 0.800 
 
 0.800 
 
 0.801 
 
 0.801 
 
 0.802 
 
 2.23 
 
 0.802 
 
 0.802 
 
 0.803 
 
 0.803 
 
 0.804 
 
 0.804 
 
 0.805 
 
 0.805 
 
 0.806 
 
 0.806 
 
 2.24 
 
 0.806 
 
 0.807 
 
 0.807 
 
 0.808 
 
 0.808 
 
 0.809 
 
 0.809 
 
 0.810 
 
 0.810 
 
 0.810 
 
 2.25 
 
 0.811 
 
 0.811 
 
 0.812 
 
 0.812 
 
 0.813 
 
 0.813 
 
 0.814 
 
 0.814 
 
 0.814 
 
 0.815 
 
 2.26 
 
 0.815 
 
 0.816 
 
 0.816 
 
 0.817 
 
 0.817 
 
 0.818 
 
 0.818 
 
 0.818 
 
 0.819 
 
 0.819 
 
 2.27 
 
 0.820 
 
 0.820 
 
 0.821 
 
 0.821 
 
 0.822 
 
 0.822 
 
 0.822 
 
 0.823 
 
 0.823 
 
 0.824 
 
 2.28 
 
 0.824 
 
 0.825 
 
 0.825 
 
 0.825 
 
 0.826 
 
 0.826 
 
 0.827 
 
 0.827 
 
 0.828 
 
 0.828 
 
 2.29 
 
 0.829 
 
 0.829 
 
 0.829 
 
 0.830 
 
 0.830 
 
 0.831 
 
 0.831 
 
 0.832 
 
 0.832 
 
 0.83 2 
 
6-22 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2.30 
 
 0.833 
 
 0.833 
 
 0.834 
 
 0.834 
 
 0.835 
 
 0.83 5 
 
 0.836 
 
 0.836 
 
 0.836 
 
 0.837 
 
 2.31 
 
 0.837 
 
 0.838 
 
 0.838 
 
 0.839 
 
 0.839 
 
 0.839 
 
 0.840 
 
 0.840 
 
 0.841 
 
 0.841 
 
 2.32 
 
 0.842 
 
 0.842 
 
 0.842 
 
 0.843 
 
 0.843 
 
 0.844 
 
 0.844 
 
 0.845 
 
 0.845 
 
 0.845 
 
 2.33 
 
 0.846 
 
 0.846 
 
 0.847 
 
 0.847 
 
 0.848 
 
 0.848 
 
 0.848 
 
 0.849 
 
 0.849 
 
 0.850 
 
 2.34 
 
 0.850 
 
 0.851 
 
 0.851 
 
 0.851 
 
 0.852 
 
 0.852 
 
 0.853 
 
 0.853 
 
 0.854 
 
 0.854 
 
 2.35 
 
 0.854 
 
 0.855 
 
 0.855 
 
 0.856 
 
 0.856 
 
 0.857 
 
 0.857 
 
 0.857 
 
 0.858 
 
 0.858 
 
 2.36 
 
 0.859 
 
 0.859 
 
 0.860 
 
 0.860 
 
 0.860 
 
 0.861 
 
 0.861 
 
 0.862 
 
 0.862 
 
 0.862 
 
 2.37 
 
 0.863 
 
 0.863 
 
 0.864 
 
 0.864 
 
 0.865 
 
 0.865 
 
 0.865 
 
 0.866 
 
 0.866 
 
 0.867 
 
 2.38 
 
 0.867 
 
 0.868 
 
 0.868 
 
 0.868 
 
 0.869 
 
 0.869 
 
 0.870 
 
 0.870 
 
 0.870 
 
 0.871 
 
 2.39 
 
 0.871 
 
 0.872 
 
 0.872 
 
 0.873 
 
 0.873 
 
 0.873 
 
 0.874 
 
 0.874 
 
 0.875 
 
 0.875 
 
 2.40 
 
 0.875 
 
 0.876 
 
 0.876 
 
 0.877 
 
 0.877 
 
 0.878 
 
 0.878 
 
 0.878 
 
 0.879 
 
 0.879 
 
 2.41 
 
 0.880 
 
 0.880 
 
 0.880 
 
 0.881 
 
 0.881 
 
 0.882 
 
 0.882 
 
 0.883 
 
 0.883 
 
 0.883 
 
 2.42 
 
 0.884 
 
 0.884 
 
 0.885 
 
 0.885 
 
 0.885 
 
 0.886 
 
 0.886 
 
 0.887 
 
 0.887 
 
 0.887 
 
 2.43 
 
 0.888 
 
 0.888 
 
 0.889 
 
 0.889 
 
 0.890 
 
 0.890 
 
 0.890 
 
 0.891 
 
 0.891 
 
 0.892 
 
 2.44 
 
 0.892 
 
 0.892 
 
 0.893 
 
 0.893 
 
 0.894 
 
 0.894 
 
 0.894 
 
 0.895 
 
 0.895 
 
 0.896 
 
 2.45 
 
 0.896 
 
 0.896 
 
 0.897 
 
 0.897 
 
 0.898 
 
 0.898 
 
 0.899 
 
 0.899 
 
 0.899 
 
 0.900 
 
 2.46 
 
 0.900 
 
 0.901 
 
 0.901 
 
 0.901 
 
 0.902 
 
 0.902 
 
 0.903 
 
 0.903 
 
 0.903 
 
 0.904 j 
 
 2.47 
 
 0.904 
 
 0.905 
 
 0.905 
 
 0.905 
 
 0.906 
 
 0.906 
 
 0.907 
 
 0.907 
 
 0.907 
 
 0.908 
 
 2.48 
 
 0.908 
 
 0.909 
 
 0.909 
 
 0.909 
 
 0.910 
 
 0.910 
 
 0.911 
 
 0.911 
 
 0.911 
 
 0.912 
 
 2.49 
 
 0.912 
 
 0.913 
 
 0.913 
 
 0.913 
 
 0.914 
 
 0.914 
 
 0.915 
 
 0.915 
 
 0.915 
 
 0.916 
 
 2.50 
 
 0.916 
 
 0.917 
 
 0.917 
 
 0.917 
 
 0.918 
 
 0.918 
 
 0.919 
 
 0.919 
 
 0.919 
 
 0.920 
 
 2.51 
 
 0.920 
 
 0.921 
 
 0.921 
 
 0.921 
 
 0.922 
 
 0.922 
 
 0.923 
 
 0.923 
 
 0.923 
 
 0.924 
 
 2.52 
 
 0.924 
 
 0.925 
 
 0.925 
 
 0.925 
 
 0.926 
 
 0.926 
 
 0.927 
 
 0.927 
 
 0.927 
 
 0.928 
 
 2.53 
 
 0.928 
 
 0.929 
 
 0.929 
 
 0.929 
 
 0.930 
 
 0.930 
 
 0.-931 
 
 0.931 
 
 0.931 
 
 0.932 
 
 2.54 
 
 0.932 
 
 0.933 
 
 0.933 
 
 0.933 
 
 0.934 
 
 0.934 
 
 0.935 
 
 0.935 
 
 0.935 
 
 0.936 
 
 2.55 
 
 0.936 
 
 0.936 
 
 0.937 
 
 0.937 
 
 0.938 
 
 0.938 
 
 0.938 
 
 0.939 
 
 0.939 
 
 0.940 
 
 2.56 
 
 0.940 
 
 0.940 
 
 0.941 
 
 0.941 
 
 0.942 
 
 0.942 
 
 0.942 
 
 0.943 
 
 0.943 
 
 0.944 
 
 2.57 
 
 0.944 
 
 0.944 
 
 0.945 
 
 0.945 
 
 0.945 
 
 0.946 
 
 0.946 
 
 0.947 
 
 0.947 
 
 0.947 
 
 2.58 
 
 0.948 
 
 0.948 
 
 0.949 
 
 0.949 
 
 0.949 
 
 0.950 
 
 0.950 
 
 0.950 
 
 0.951 
 
 0.951 
 
 2.59 
 
 0.952 
 
 0.952 
 
 0.952 
 
 0.953 
 
 0.953 
 
 0.954 
 
 0.954 
 
 0.954 
 
 0.955 
 
 0.955 
 
 2.60 
 
 0.956 
 
 0.956 
 
 0.956 
 
 0.957 
 
 0.957 
 
 0.957 
 
 0.958 
 
 0.958 
 
 0.959 
 
 0.959 
 
 2.61 
 
 0.959 
 
 0.960 
 
 0.960 
 
 0.960 
 
 0.961 
 
 0.961 
 
 0.962 
 
 0.962 
 
 0.962 
 
 0.963 
 
 2.62 
 
 0.963 
 
 0.964 
 
 0.964 
 
 0.964 
 
 0.965 
 
 0.965 
 
 0.965 
 
 0.966 
 
 0.966 
 
 0.967 
 
 2.63 
 
 0.967 
 
 0.967 
 
 0.968 
 
 0.968 
 
 0.969 
 
 0.969 
 
 0.969 
 
 0.970 
 
 0.970 
 
 0.970 
 
 2.64 
 
 0.971 
 
 0.971 
 
 0.972 
 
 0.972 
 
 0.972 
 
 0.973 
 
 0.973 
 
 0.973 
 
 0.974 
 
 0.974 
 
 2.65 
 
 0.975 
 
 0.975 
 
 0.975 
 
 0.976 
 
 0.976 
 
 0.976 
 
 0.977 
 
 0.977 
 
 0.978 
 
 0.978 
 
 2.66 
 
 0.978 
 
 0.979 
 
 0.979 
 
 0.979 
 
 0.980 
 
 0.980 
 
 0.981 
 
 0.981 
 
 0.981 
 
 0.982 
 
 2.67 
 
 0.982 
 
 0.98 2 
 
 0.983 
 
 0.983 
 
 0.984 
 
 0.984 
 
 0.984 
 
 0.985 
 
 0.985 
 
 0.985 
 
 2.68 
 
 0.986 
 
 0.986 
 
 0.987 
 
 0.987 
 
 0.987 
 
 0.988 
 
 0.988 
 
 0.988 
 
 0.989 
 
 0.989 
 
 2.69 
 
 0.990 
 
 0.990 
 
 0.990 
 
 0.991 
 
 0.991 
 
 0.991 
 
 0.992 
 
 0.992 
 
 0.993 
 
 0.993 
 
6-23 
 
 TABLE OF NATURAL LOGARITHMS 
 
 N 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2.70 
 
 0.993 
 
 0.994 
 
 0.994 
 
 0.994 
 
 0.995 
 
 0.995 
 
 0.995 
 
 0.996 
 
 0.996 
 
 0.997 
 
 2.71 
 
 0.997 
 
 0.997 
 
 0.998 
 
 0.998 
 
 0.998 
 
 0.999 
 
 0.999 
 
 1.000 
 
 1.000 
 
 1.000 ! 
 
 2.72 
 
 1.001 
 
 1.001 
 
 1.001 
 
 1.002 
 
 1.002 
 
 1.002 
 
 1.003 
 
 1.003 
 
 1.004 
 
 1.004 | 
 
 2.73 
 
 1.004 
 
 1.005 
 
 1.005 
 
 1.005 
 
 1.006 
 
 1.006 
 
 1.006 
 
 1.007 
 
 1.007 
 
 1.008 ! 
 
 2.74 
 
 1.008 
 
 1.008 
 
 1.009 
 
 1.009 
 
 1.009 
 
 1.010 
 
 1.010 
 
 1.011 
 
 1.011 
 
 1.011 j 
 
 2.75 
 
 1.012 
 
 1.012 
 
 1.012 
 
 1.013 
 
 1.013 
 
 1.013 
 
 1.014 
 
 1.014 
 
 1.015 
 
 1.015 
 
 2.76 
 
 1.015 
 
 1.016 
 
 1.016 
 
 1.016 
 
 1.017 
 
 1.017 
 
 1.017 
 
 1.018 
 
 1.018 
 
 1.018 
 
 2.77 
 
 1.019 
 
 1.019 
 
 1.020 
 
 1.020 
 
 1.020 
 
 1.021 
 
 1.021 
 
 1.021 
 
 1.022 
 
 1.022 j 
 
 2.78 
 
 1.022 
 
 1.023 
 
 1.023 
 
 1.024 
 
 1.024 
 
 1.024 
 
 1.025 
 
 1.025 
 
 1.025 
 
 1.026 
 
 2.79 
 
 1.026 
 
 1.026 
 
 1.027 
 
 1.027 
 
 1.027 
 
 1.028 
 
 1.028 
 
 1.029 
 
 1.029 
 
 1.029 
 
 2.80 
 
 1.030 
 
 1.030 
 
 1.030 
 
 1.031 
 
 1.031 
 
 1.031 
 
 1.032 
 
 1.032 
 
 1.03 2 
 
 1.033 
 
 2.81 
 
 1.033 
 
 1.034 
 
 1.034 
 
 1.034 
 
 1.035 
 
 1.035 
 
 1.035 
 
 1.036 
 
 1.036 
 
 1.036 
 
 2.82 
 
 1.037 
 
 1.037 
 
 1.037 
 
 1.038 
 
 1.038 
 
 1.039 
 
 1.039 
 
 1.039 
 
 1.040 
 
 1.040 
 
 ! 2.83 
 
 1.040 
 
 1.041 
 
 1.041 
 
 1.041 
 
 1.042 
 
 1.04 2 
 
 1.042 
 
 1.043 
 
 1.043 
 
 1.043 
 
 2.84 
 
 1.044 
 
 1.044 
 
 1.045 
 
 1.045 
 
 1.045 
 
 1.046 
 
 1.046 
 
 1.046 
 
 1.047 
 
 1.047 
 
 2.85 
 
 1.047 
 
 1.048 
 
 1.048 
 
 1.048 
 
 1.049 
 
 1.049 
 
 1.049 
 
 1.050 
 
 1.050 
 
 1.050 
 
 2.86 
 
 1.051 
 
 1.051 
 
 1.052 
 
 1.052 
 
 1.052 
 
 1.053 
 
 1.053 
 
 1.053 
 
 1.054 
 
 1.054 | 
 
 2.87 
 
 1.054 
 
 1.055 
 
 1.055 
 
 1.055 
 
 1.056 
 
 1.056 
 
 1.056 
 
 1.057 
 
 1.057 
 
 1.057 i 
 
 2.88 
 
 1.058 
 
 1.058 
 
 1.058 
 
 1.059 
 
 1.059 
 
 1.060 
 
 1.060 
 
 1.060 
 
 1.061 
 
 1.061 1 
 
 2.89 
 
 1.061 
 
 1.062 
 
 1.062 
 
 1.062 
 
 1.063 
 
 1.063 
 
 1.063 
 
 1.064 
 
 1.064 
 
 1.064 | 
 i 
 
 2.90 
 
 1.065 
 
 1.065 
 
 1.065 
 
 1.066 
 
 1.066 
 
 1.066 
 
 1.067 
 
 1.067 
 
 1.067 
 
 1.068 | 
 
 2.91 
 
 1.068 
 
 1.068 
 
 1.069 
 
 1.069 
 
 1.070 
 
 1.070 
 
 1.070 
 
 1.071 
 
 1.071 
 
 1.071 I 
 
 2.92 
 
 1.07 2 
 
 1.072 
 
 1.072 
 
 1.073 
 
 1.073 
 
 1.073 
 
 1.074 
 
 1.074 
 
 1.074 
 
 1.075 | 
 
 2.93 
 
 1.075 
 
 1.075 
 
 1.076 
 
 1.076 
 
 1.07 6 
 
 1.077 
 
 1.-077 
 
 1.077 
 
 1.078 
 
 1.078 
 
 2.94 
 
 1.078 
 
 1.079 
 
 1.079 
 
 1.079 
 
 1.080 
 
 1.080 
 
 1.080 
 
 1.081 
 
 1.081 
 
 1.081 ! 
 
 2.95 
 
 1.082 
 
 1.082 
 
 1.082 
 
 1.083 
 
 1.083 
 
 1.083 
 
 1.084 
 
 1.084 
 
 1.085 
 
 1.085 
 
 2.96 
 
 1.085 
 
 1.086 
 
 1.086 
 
 1.086 
 
 1.087 
 
 1.087 
 
 1.087 
 
 1.088 
 
 1.088 
 
 1.088 
 
 2.97 
 
 1.089 
 
 1.089 
 
 1.089 
 
 1.090 
 
 1.090 
 
 1.090 
 
 1.091 
 
 1.091 
 
 1.091 
 
 1.092 
 
 2.98 
 
 1.092 
 
 1.092 
 
 1.093 
 
 1.093 
 
 1.093 
 
 1.094 
 
 1.094 
 
 1.094 
 
 1.095 
 
 1.095 
 
 2.99 
 
 1.095 
 
 1.096 
 
 1.096 
 
 1.096 
 
 1.097 
 
 1.097 
 
 1.097 
 
 1.098 
 
 1.098 
 
 1.098 
 
 3.00 
 
 1.099 
 
 1.099 
 
 1.099 
 
 1.100 
 
 1.100 
 
 1.100 
 
 1.101 
 
 1.101 
 
 1.101 
 
 1.102 
 
 3.01 
 
 1.102 
 
 1.102 
 
 1.103 
 
 1.103 
 
 1.103 
 
 1.104 
 
 1.104 
 
 1.104 
 
 1.105 
 
 1.105 
 
 3.02 
 
 1.105 
 
 1.106 
 
 1.106 
 
 1.106 
 
 1.107 
 
 1.107 
 
 1.107 
 
 1.108 
 
 1.108 
 
 1.108 
 
 3.03 
 
 1.109 
 
 1.109 
 
 1.109 
 
 1.110 
 
 1.110 
 
 1.110 
 
 1.1.11 
 
 1.111 
 
 1.111 
 
 1.112 
 
 3.04 
 
 1.112 
 
 1.112 
 
 1.113 
 
 1.113 
 
 1.113 
 
 1.114 
 
 1.114 
 
 1.114 
 
 1.114 
 
 1.115 
 
 3.05 
 
 1.115 
 
 1.115 
 
 1.116 
 
 1.116 
 
 1.116 
 
 1.117 
 
 1.117 
 
 1.117 
 
 1.118 
 
 1.1181 
 
 3.06 
 
 1.118 
 
 1.119 
 
 1.119 
 
 1.119 
 
 1.120 
 
 1.120 
 
 1.120 
 
 1.121 
 
 1.121 
 
 1.121 
 
 3.07 
 
 1.122 
 
 1.122 
 
 1.122 
 
 1.123 
 
 1.123 
 
 1.123 
 
 1.124 
 
 1.124 
 
 1.124 
 
 1.125. 
 
 3.08 
 
 1.125 
 
 1.125 
 
 1.126 
 
 1.126 
 
 1.126 
 
 1.127 
 
 1.127 
 
 1.127 
 
 1.128 
 
 1.128) 
 
 3.09 
 
 1.128 
 
 1.128 
 
 1.129 
 
 1.129 
 
 1.129 
 
 1.130 
 
 1.130 
 
 1.130 
 
 1.131 
 
 1.131 1 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 7 
 COMPONENTS OF LIQUID SYSTEMS 
 
 HEAT STORAGE 
 CONTROLS 
 HEAT EXCHANGERS 
 PUMPS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
7-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 Page 
 7-i i i 
 
 OBJECTIVE 
 
 INTRODUCTION 
 
 HEAT STORAGE 
 
 WATER STORAGE .... 
 
 Recommended Water Volume . 
 
 Water Tanks 
 
 Storage Location 
 
 Installation 
 
 Special Provisions . 
 PHASE-CHANGE STORAGE 
 SYSTEM CONTROLS .... 
 BASIC COMPONENTS 
 PRINCIPLES OF OPERATION . 
 
 Collecting Solar Heat 
 
 Control of Space Heating . 
 
 Control of Domestic Water Heat 
 COMPONENTS .... 
 
 Differential Thermostat . 
 
 Room Thermostat 
 
 Temperature Sensors . 
 
 ng 
 
 7-1 
 
 7-1 
 
 7-1 
 
 7-2 
 
 7-2 
 
 7-4 
 
 7-6 
 
 7-7 
 
 7-8 
 
 7-10 
 
 7-12 
 
 7-12 
 
 7-13 
 
 7-13 
 
 7-17 
 
 7-18 
 
 7-19 
 
 7-19 
 
 7-20 
 
 7-21 
 
7~ii 
 
 
 Page 
 
 INSTALLATION OF CONTROL HARDWARE . 
 
 7-21 
 
 Control Panels ...... 
 
 7-21 
 
 Locations of Temperature Sensors 
 
 7-22 
 
 AUXILIARY HEAT CONTROL 
 
 7-22 
 
 CONTROL SYSTEM CHECK-OUT 
 
 7-22 
 
 HEAT EXCHANGERS 
 
 7-23 
 
 COLLECTOR TO STORAGE HEAT EXCHANGER 
 
 7-23 
 
 Shell -and-Tube Type ..... 
 
 7-23 
 
 Selection ....... 
 
 7-25 
 
 Installation ...... 
 
 7-31 
 
 LOAD HEAT EXCHANGER 
 
 7-31 
 
 DOUBLE-WALLED HEAT EXCHANGER .... 
 
 7-36 
 
 PUMPS 
 
 7-37 
 
 REFERENCES 
 
 7-41 
 
7-iii 
 LIST OF FIGURES 
 
 Figure Page 
 
 7-1 Effect of Storage Size on Solar Heat Contribution 
 
 to Total Load ........ 7-3 
 
 7-2 Cylindrical Tanks ....... 7-5 
 
 7-3 Reinforced Concrete Block Tank .... 7-5 
 
 7-4 A Prefabricated Water Tank for Thermal Energy 
 
 Storage ......... 7-6 
 
 7-5 Bottom Insulation and Support Scheme for Flat- 
 Bottom Water Storage Tanks ..... 7-8 
 
 7-6 Heat Storage in Phase-Change Materials . . . 7-11 
 
 7-7 Basic Components of Controls ..... 7-12 
 
 7-8 Sensor Locations in a Typical Liquid-Heating 
 
 System 7-14 
 
 7-9 Typical Temperature Profiles of Collector and 
 
 Storage Liquids in a Liquid-Heating System . . 7-15 
 
 7-10 Typical Circuitry for a Differential Thermostat . 7-19 
 
 7-11 Pictorial Representation of Hysteresis in the 
 
 Differential Thermostat ...... 7-20 
 
 7-12 Single-Pass Counterflow Shell-and-Tube Heat 
 
 Exchanger ......... 7-23 
 
 7-13 Multiple-Tube Heat Exchanger ..... 7-24 
 
 7-14 Effectiveness for a Counterflow Single-Pass Shell- 
 and-Tube Heat Exchanger ...... 7-28 
 
 7-15 Effectiveness of Cross-Flow Water-to-Air Heat 
 
 Exchanger ......... 7-34 
 
 7-16 Typical Performance Curves for a Centrifugal Pump . 7-37 
 
 7-17 Friction Loss in Copper Tubing .... 7-39 
 
 7-18 Pressure Loss in Various Elements .... 7-40 
 
7-1 
 
 OBJECTIVE 
 
 The objective in this module is to present information on 
 components of liquid systems so that participants will be able to: 
 
 1. Select the appropriate size storage unit. 
 
 2. Properly size pumps. 
 
 3. Select heat exchangers. 
 
 4. Install a control unit for the system. 
 
 INTRODUCTION 
 
 The principal components of liquid- type solar systems are the 
 collectors, heat storage units, pumps, and heat exchangers which are 
 interconnected with pipes and regulated by automatic controls. Collec- 
 tors were described in a previous module and specific attention is 
 devoted here to other components of the solar system. 
 
 HEAT STORAGE 
 
 Storage of solar thermal energy is required in solar heating and 
 cooling systems so that solar heat can be delivered to the building 
 during non-sunny periods. The volume of storage needed is principally 
 dependent on collector area. In liquid-based systems where solar heat 
 is generally first collected in storage before delivery to the load, the 
 storage unit should be large enough for all-day solar heat collection 
 without penalizing collector efficiency, and small enough to raise the 
 temperature in storage to meet load requirements. 
 
7-2 
 
 Heat may be stored by raising the temperature of the storage medium 
 (sensible heat storage), changing the state of the medium from solid to 
 liquid (latent heat storage), or by chemical reaction of a suitable 
 medium. Heat may be recovered by lowering the temperature of the stor- 
 age medium, changing the phase from liquid to solid or by reversing the 
 chemical reaction. For solar heating and cooling systems, sensible heat 
 storage in water is commonly used. Some phase-change materials (PCM) 
 are commercially available, but as yet there has been little practical 
 experience using PCM storage units in solar heating and cooling systems. 
 Chemical heat storage is appropriate for high temperature systems and is 
 not being actively considered for space heating and cooling systems. 
 
 WATER STORAGE 
 
 The specific heat of water is 1 Btu/(lb*°F) which means that one 
 Btu of heat energy can be stored in one pound of water when the tempera- 
 ture of the water is raised one degree Fahrenheit. One gallon (U.S.) of 
 water can store about 8.25 Btu for each degree of temperature rise 
 (between 100°F to 160°F) or 495 Btu can be stored when the temperature 
 is raised from 100°F to 160°F. A water tank with 1000 gallons of water 
 will thus store 495,000 Btu of heat energy when the temperature is 
 raised from 100°F to 160°F, which is a typical operating temperature 
 range for water storage tanks in liquid- type solar heating systems. 
 
 Recommended Water Volume 
 
 Precise determination of water storage volume is not required for 
 effective system operation, but there is a practical range of 1.5 to 
 
7-3 
 
 2.5 gallons of water storage for each square foot of collector area. 
 Thus, for a system with a collector area of 400 ft 2 , storage volume 
 should be in the range of 600 to 1000 gallons. The effect of storage 
 volume on the annual fraction of the total heating load supplied by the 
 solar system is illustrated in Figure 7-1. 
 
 c 
 o 
 
 o 
 o 
 
 o 
 
 C 
 C 
 
 < 
 
 No 
 Storage 
 
 of Storage Volumes 
 
 Large 
 Volumes of 
 Storage 
 
 Figure 7-1. Effect of Storage Size on Solar Heat Contribution to 
 Total Load 
 
 With no storage the amount of solar heat provided is limited 
 because solar heat could be delivered and used only during the day when 
 the thermostat calls for heat. The contribution of solar heat to the 
 load increases rapidly with storage size, and the lower limit of the 
 practical range is the knee in the curve. Theoretically, as the storage 
 volume continues to increase, the solar fraction should also increase. 
 
7-4 
 
 However, the maximum temperature achieved in storage reduces with 
 increases in size, and with lower temperatures less useful heat is 
 delivered to the load. Storage volume should not be oversized for solar 
 heating and cooling systems. 
 
 Water Tanks 
 
 There are several types of water tanks that can be used in solar 
 systems. Steel and fiber-reinforced plastic (FRP) tanks of the type 
 shown in Figure 7-2 are commonly used, with steel tanks being more 
 appropriate for higher water temperatures. With FRP tanks, even those 
 that are especially designed for high temperature liquids, there should 
 be controls to limit the water temperature in the tank. 
 
 Tanks made of concrete or masonry blocks and lined with waterproof 
 liners may also be used, as illustrated in Figure 7-3. It may be con- 
 venient to utilize part of the building foundation walls to form one or 
 more sides of the tank. The foundation for concrete tanks is of special 
 concern because settlement can cause cracks to develop and the water- 
 proof liner can be damaged if the cracks are large. Hypalon or butyl 
 rubber liners are especially suitable for such installations. 
 
 A prefabricated modular tank of rectangular shape, as shown in 
 Figure 7-4, is commercially available and is suitable for storage of 
 water. The tank is made of flat sections with foam insulation sand- 
 wiched between two thin galvanized steel plates. Special connectors, 
 corner sections, and steel channel whalers are used to form a struc- 
 turally sound box, the time required for assembly of which is only a few 
 hours. The preinsulated tank is especially well suited for retrofit 
 systems because pieces can be easily carried through doorways. A water- 
 proof liner is required. 
 
7-5 
 
 UNDERGROUND STORAGE TANK 
 
 © 
 
 1 
 
 \ / 
 
 ABOVE-GROUND STORAGE TANK 
 Figure 7-2. Cylindrical Tanks 
 
 HYPALON LINING 
 ALTERNATIVES: 
 
 1 BUTYL RUBBER 
 
 2 MORTAR & COAL 
 TAR MEMBRANE 
 
 REINFORCED 
 CONCRETE BASE 
 
 TOP a BOTTOM 
 COURSE OF BOND 
 BEAM BLOCK 
 
 VERTICAL a HORIZONTAL 
 REINFORCING 
 
 Figure 7-3. Reinforced Concrete Block Tank 
 
7-6 
 
 URETHANE FOAM 
 
 STEEL STRAPS 
 
 GALVANIZED STEEL 
 PLASTIC LINER 
 
 REINFORCEMENT KIT 
 
 SPEED-LOK OPERATOR 
 TONGUE & GROOVE 
 CAM ACTION SPEED-LOK 
 
 Figure 7-4. A Prefabricated Water Tank For Thermal Energy Storage 
 
 Storage Location 
 
 Water tanks may be located below or above ground level, and may be 
 inside or outside the building. It is strongly recommended that heat 
 storage tanks be placed within the building enclosure for ease of in- 
 stallation and maintenance. An indoor storage location also protects 
 the vessel and insulation from weathering. When storage tanks are 
 located indoors, heat losses from the tank can meet part of the heat 
 requirements of the building. To avoid overheating in summer, heat 
 
7-7 
 
 storage should normally not be in use. Another arrangement is to locate 
 the storage tank in a room where heat can be vented outdoors during the 
 summer and communicated to the interior space during the winter. 
 
 Installation 
 
 Storage tanks are normally the first component of a solar system to 
 be installed. Because of their size, it is advantageous to install the 
 tank before the building is enclosed (for new construction), but the 
 tank should also be placed where removal and replacement are possible. 
 Sectional tanks discussed in the previous section are particularly 
 suitable for installation in existing buildings. 
 
 Storage tanks should be well insulated on all surfaces with 
 insulation that rates to about R-30. For cylindrical tanks the bottom 
 and saddle, or leg supports, are the most difficult to insulate. If a 
 flat-bottom tank is installed, rigid insulation may be used below it as 
 shown in Figure 7-5. However, the insulation should be supported above 
 the floor so that it will not become wet when there is standing water on 
 the floor. The prefabricated and preinsulated tank shown in Figure 7-4 
 can be supported on a base placed on the floor so that the bottom of the 
 tank will be dry. 
 
 When storage tanks are placed underground, the insulation around 
 the tank must be of a type which will not absorb moisture. Materials 
 such as neoprene foam could be used. The tank should be placed below 
 the frost line unless a concrete- lined pit is provided. Underground 
 installations have not been very successful in practice and should 
 
7-8 
 
 HEAT STORAGE 
 WATER TANK 
 
 FOUNDATION 
 
 Figure 7-5. Bottom Insulation and Support Scheme for Flat-Bottom Water 
 Storage Tanks 
 
 be avoided if possible. Whether storage tanks are placed underground or 
 in the building, the tank and piping should be leak- tested after 
 assembly. 
 
 Special Provisions 
 
 There should be provisions for draining water tanks. Steel tanks 
 are generally provided with fittings for gravity drainage, but com- 
 mercial FRP tanks may not have suitable openings. Special connections 
 are available for installation on FRP tanks. Piping connections for 
 tanks with liners are usually made through the lid because penetrations 
 through the liner are sources for leakage. To drain such tanks, the 
 water must be pumped out. 
 
7-9 
 
 Connections of dissimilar metals to steel tanks should be avoided 
 to prevent galvanic corrosion. When copper pipes are to be attached to 
 steel tanks, it is advisable to use neoprene or silicone rubber hose 
 between steel pipe stubs and copper piping. Special nylon or teflon- 
 lined pipe connections are available. 
 
 Water will expand and contract with temperature changes, so an open 
 vent should be provided to prevent storage tanks from becoming pressur- 
 ized. For most residential-sized tanks, a 2-in diameter pipe vent 
 should be adequate. There will be vapor loss through the vent and there 
 should be provisions for adding make-up water. Water can be added from 
 a supply pipe with manual valve control, using a sight-glass to observe 
 the water level in the tank, or a float control valve may be installed 
 in the supply line to maintain a minimum water level. 
 
 Boiling can occur in the storage tank and a vent will prevent 
 damage to the system, the tank, and the contents of the building. While 
 it is an uncommon occurrence during the heating season, boiling may be 
 expected during the summer while the system is used only for domestic 
 water heating. Frequent boiling will also cause build-up of mineral 
 deposits with consequent corrosion, so water softeners are recommended 
 for removal of minerals from the storage water. Make-up water should 
 also be treated. 
 
 In some systems, unvented pressurized tanks are used, particularly 
 in conjunction with hydronic distribution piping and hot water boilers 
 for auxiliary heat supply. Pressurized expansion tanks then must also 
 be used to accommodate the changing liquid volumes. If boiling occurs, 
 a pressure relief valve permits steam to escape through a vent. 
 
7-10 
 
 A high temperature shut-off control switch for the collector pump 
 may be used with some collectors to avoid boiling in storage. In such 
 designs, boiling must be permitted in the collectors, or they must be 
 drained, and the collectors must be able to sustain the high stagnation 
 temperatures that will be reached with no fluid flowing through the 
 col lectors. 
 
 Corrosion is a potential problem whenever water is contained in a 
 steel tank, and the probability of corrosion greatly increases as the 
 temperature rises. Various types of lining will increase the life of 
 the steel tank but will add substantially to the cost. Removal of 
 minerals with a water softener and corrosion inhibitors in storage water 
 are recommended whenever steel tanks are used. 
 
 Water leakage is to be avoided, but some leakage from pipe fittings 
 is inevitable. Floor drains should therefore be provided near the tank. 
 
 PHASE-CHANGE STORAGE 
 
 Large amounts of solar heat can be stored in special materials such 
 as salt hydrates with a change in phase from a solid to a liquid state. 
 When the solid material is heated and melting temperature is reached, a 
 large quantity of heat is absorbed during the melting process. Further 
 heating raises the temperature of the liquid phase and more heat is 
 stored. The process is illustrated in Figure 7-6. 
 
 During the reverse cycle, when the temperature of the storage 
 medium drops, heat is recovered from the liquid, and when the freezing 
 point is reached, a large quantity of heat is released as the liquid 
 changes to a solid. A very small temperature difference is sufficient 
 to change the phase of the material from solid to liquid or liquid to 
 solid state. 
 
7-11 
 
 SENSIBLE HEAT 
 IN LIQUID 
 
 SOLID PHASE 
 
 PHASE CHANGE 
 
 £ TEMPERATURE 
 DIFFERENCE 
 
 TEMPERATURE 
 
 Figure 7-6. Heat Storage in Phase-Change Materials 
 
 There are two principal advantages to use of latent heat storage 
 materials. The first is that it takes less volume to store a given 
 quantity of heat compared to water storage, and the second is that the 
 temperature remains nearly constant during phase change. A constant 
 storage temperature, if relatively low, is conducive to good collector 
 efficiency. There are, however, some disadvantages with latent heat 
 storage units. The useful service life is generally limited, although 
 significant improvements are being made. The melting temperatures of 
 suitable materials, like Glaubers salt, are too low for effective use in 
 space heating. (Glaubers salt melts at about 90°F.) Currently PCM 
 materials are expensive when compared to water storage units, and con- 
 tainerizing is costly also. Lastly, a current handicap is limited 
 practical experience with PCM materials in solar heating systems. 
 
7-12 
 
 SYSTEM CONTROLS 
 
 Controls in solar systems must: (1) regulate the automatic 
 collection and distribution of solar heat, and (2) operate the con- 
 ventional heating system in conjunction with the solar system. Properly 
 installed controls will maximize solar energy collection and distribu- 
 tion and minimize electrical energy consumption to operate the system. 
 Designing controls is a specialized field and is beyond the scope of 
 this manual and training course, but it is important that basic func- 
 tions of controls and principles of proper installation be understood. 
 
 BASIC COMPONENTS 
 
 A block diagram of the three basic components of a control system 
 is shown in Figure 7-7. The sensors are generally temperature-measuring 
 
 SENSORS 
 
 COMPARATORS 
 
 OUTPUT 
 DEVICES 
 
 Figure 7-7. Basic Components of Controls 
 
 devices although optical sensors may be involved in certain systems. 
 Comparators are differential thermostats which determine the difference 
 in temperatures of two sensors. When the difference in temperatures is 
 greater or less than preset values, output devices respond according to 
 a prearranged plan. The output devices are the mechanical components of 
 
7-13 
 
 the system, which in liquid systems are pumps, motorized valves, 
 circulating fans or fan-coil units and auxiliary heaters. 
 
 Although there are several types of controllers, the most common 
 type is an "on-or-off" system where the mechanical device, such as a 
 pump, is activated or stopped depending upon open or closed electrical 
 circuits. Another type of control system regulates the speed of the 
 pump (or selects an appropriate stage of a multiple-speed pump motor) 
 according to the temperature difference of two sensors. This type of 
 controller is yet uncommon, and experiments are being conducted to 
 determine if the benefits of sophistication in controls are sufficient 
 to overcome the disadvantages of greater cost and complexity. 
 
 PRINCIPLES OF OPERATION 
 Collecting Solar Heat 
 
 A schematic diagram of a liquid- type solar heating system is 
 illustrated in Figure 7-8. The system consists of flat-plate liquid- 
 heating collectors with an antifreeze solution in the "collector loop" 
 which is circulated by pump No. 1. A shell -and- tube type liquid- to- 
 liquid heat exchanger is used to transfer heat to water in the storage 
 tank, circulated by pump No. 2. Hot water from storage is circulated to 
 a load heat exchanger by pump No. 3 to heat the building space. Two 
 solenoid-operated valves are required; valve No. 1, which is normally 
 open, controls water flow from the solar storage tank, and valve No. 2, 
 which is normally closed, controls circulation through the auxiliary 
 heater loop. 
 
7-U 
 
 u 
 > 
 
 _l 
 < 
 > 
 
 ■p 
 
 I/) 
 
 >> 
 
 to 
 
 O) 
 
 c 
 
 -p 
 rd 
 
 CD 
 
 I 
 
 T3 
 •r— 
 
 ZS 
 O" 
 
 03 
 U 
 
 •r— 
 
 Q- 
 
 rrj 
 
 c 
 
 -p 
 
 ro 
 O 
 
 s- 
 o 
 
 c 
 
 <D 
 
 00 
 
 s- 
 
 D5 
 
7-15 
 
 Domestic hot water is preheated with solar heated water from the 
 storage tank. To separate the non-potable water in storage from the 
 potable water in the preheat tank, a double-wall heat exchanger is used. 
 Pumps No. 4 and No. 5 circulate the storage and domestic water through 
 separate pipe loops. 
 
 There are three temperature sensors identified in Figure 7-8. 
 Sensor SI is located near the top of one collector in the array, S2 is 
 located near the bottom of the storage tank and S4 is located near the 
 bottom of tne pre-heat tank. Sensor S3 is a two-stage thermostat 
 located in the heated space. 
 
 Typical variations in temperature of the liquids at collector exit 
 and in storage are shown on Figure 7-9. The solid curve shows the 
 storage temperature as sensed by S2 and the dashed line is the collector 
 temperature at SI. The collector fluid temperature is low in the 
 
 o 
 
 O. 
 
 E 
 
 Col lector 
 
 Temperature 
 at SI / 
 
 / 
 
 ' \'\A 
 
 y 
 
 Storage \ 
 
 Temperature \ 
 
 at S2 
 
 J L 
 
 12 
 Time (hours) 
 
 8 
 
 24 
 
 Figure 7-9. Typical Temperature Profiles of Collector and Storage 
 Liquids in a Liquid-Heating System 
 
7-16 
 
 morning but starts to rise as soon as solar radiation is absorbed in the 
 collector. At about 0830 hrs the collector temperature exceeds the 
 storage temperature, and because there is no flow through the collector, 
 the temperature rises rapidly. When the collector temperature exceeds 
 the storage temperature by a preset amount, typically 20°F (at point 
 ), pumps 1 and 2 are activated simultaneously by the controller. 
 When liquid circulation begins, a surge of cold liquid in the pipes 
 moves through the collectors. Because the intensity of solar radiation 
 on the collectors is low in the morning, the cold liquid does not heat 
 up rapidly and the temperature at SI drops to point (2) . If the tem- 
 perature difference between SI and S2 drops to another preset value, 
 typically 3°F, pumps 1 and 2 deactivate. With no circulation, the 
 liquid in the collector is heated rapidly, the temperature at SI rises 
 to point Q) , and pumps 1 and 2 are again activated. As the liquid in 
 the pipe loop is still cool, the temperature at SI drops again as circu- 
 lation commences. The number of on-off cycles at system start-up in the 
 morning depends on solar intensity, setting of the differential thermo- 
 stats, fluid flow rate, and volume of water in the collector loop. Gen- 
 erally, on-off cycling should be minimized to reduce wear of pump motor 
 and starter relay contacts. After two or three cycles at the beginning, 
 the fluid temperature at SI will continue to increase as illustrated in 
 the figure and the pumps will remain on. 
 
 After mid-day the temperature at SI decreases but storage 
 temperature continues to rise until mid-afternoon. When the temperature 
 difference between SI and S2 decreases to shut-off point © , pumps 1 
 and 2 deactivate. After circulation stops, SI will rise again because 
 solar energy is still being received. The difference in temperature 
 
7-17 
 
 between SI and S2 again reaches 20°F and the pumps are activated at 
 point (§) . However, the intensity of solar energy is not sufficient to 
 maintain high temperature at SI and the pumps shut off at point © . 
 The number of cycles which may occur at the end of the day depends on 
 control settings and fluid flow rates, just as it does at the beginning 
 of the day. 
 
 Control of Space Heating 
 
 Fluid circulation through the load heat exchanger is controlled by 
 thermostat, S3. When the room cools and the first stage contact is 
 made, pump 3 is activated. Valve 1 is normally open and valve 2 is 
 normally closed, so that water from the storage tank is circulated and 
 solar-heated water is first used to heat the rooms. If the solar-heated 
 water in storage is not sufficiently warm to meet the heating demand, 
 the room air continues to cool down and the second stage is contacted. 
 Valve 1 closes, valve 2 opens and simultaneously the auxiliary boiler is 
 activated. Since the auxiliary boiler size is adequate to supply the 
 heating load for the coldest night during the winter, the room air will 
 be heated. When the room air temperature rises beyond the thermostat 
 set point by about 1°F, the auxiliary heater and pump 3 shut off. 
 
 In the control scheme described above, the room air temperature 
 will drop 2°F to 3°F to activate the first stage and another 2°F to 3°F 
 to reach second stage. Hysteresis adds another 1°F to 2°F above the set 
 point so that when solar heat in storage has been depleted, a tempera- 
 ture "swing" as large as 8°F can occur (64°F to 72°F) in the rooms. 
 
7-18 
 
 To minimize the temperature swing the thermostat can be adjusted so 
 that the temperature differences between stages and set point are re- 
 duced to 1°F to 2°F. However, when the temperature differences are too 
 small, frequent cycling may occur in the load loop. An alternative 
 strategy to reduce temperature swing in the rooms is to limit use of 
 storage water above a set temperature, say 100°F. When the first stage 
 is contacted and the storage temperature is above 100°F, solar-heated 
 water is circulated to the load heat exchanger, but if storage water 
 temperature is below 100°F, the auxiliary heater is activated at the 
 first stage contact, preventing further cooling of the rooms. 
 
 The advantage of the latter control strategy is reduction in 
 temperature variations in the rooms. A disadvantage is limitation in 
 use of the solar heat in storage since there may be many occasions when 
 water temperature less than 100°F is adequate to supply heat to the 
 rooms. 
 
 Control of Domestic Water Heating 
 
 A differential thermostat is normally used to control the 
 pre-heating of domestic water. When the temperature difference between 
 S2 and S4 is greater than a set point, say 20°F, pumps 4 and 5 are 
 activated and water is circulated through the respective loops. Heat is 
 exchanged from the solar-heated water in the storage tank to water in 
 the pre-heat tank. As water in the pre-heat tank is warmed, the tem- 
 perature difference decreases and the pumps shut off when a lower set 
 point is reached, say at 3°F. 
 
 With selection of proper pump sizes and heat exchangers, a 
 significant portion of the DHW load can be supplied by solar energy 
 
7-19 
 
 because solar heat in the main storage tank can be used to pre-heat 
 domestic water even when the main tank temperature is less than 100°F. 
 During the evening hours and at night when use of hot water increases, 
 the main thermal storage tank will be significantly warmer than the cold 
 water temperature entering the pre-heat tank from the city mains. 
 
 COMPONENTS 
 Differential Thermostat 
 
 Sensors used in liquid systems are typically thermistors, and 
 matching sensors are usually provided with the controller. A typical 
 circuitry for a single-function differential thermostat (controller) is 
 shown in Figure 7-10. Temperature sensors are connected to a 
 
 Collector 
 Sensor s ( 
 
 Storage 
 Sensor s 2 
 
 Vref 
 
 X 
 
 Hysteresis 
 
 Output 
 Device 
 
 Figure 7-10. Typical Circuitry for a Differential Thermostat 
 
 comparator and to an output device. Hysteresis is the range in tempera- 
 ture between the start and stop set points. A pictorial representation 
 of hysteresis is shown in Figure 7-11, which is achieved electrically by 
 the feedback loop shown in Figure 7-10. As the temperature difference 
 increases and eventually reaches an upper set point, AT~ N , the electri- 
 cal circuit to the output device is completed and the device is turned 
 
7-20 
 
 a 
 
 
 
 
 
 Hysteresis 
 
 
 On 
 
 
 
 
 
 
 
 Off 
 
 " a 
 ' » 1 
 
 
 
 ' 
 
 i ^ 
 
 AX 
 
 Off 
 
 AT 
 
 On 
 
 Temperature 
 Difference 
 
 Figure 7-11. Pictorial Representation of Hysteresis in 
 the Differential Thermostat 
 
 on. When the temperature difference decreases to the point where it is 
 equal to AT Q rr, the electrical circuit is broken and shuts off the 
 output device. To minimize on-off cycling, the ratio of on to off 
 temperature differences should be 5 to 7. In the preceding example, the 
 starting temperature difference was 20°F and the stopping temperature 
 difference was 3°F. The ratio is slightly less than seven and is satis- 
 factory. A larger ratio will delay starting time and a smaller ratio 
 will cause cycling. 
 
 Room Thermostat 
 
 A thermostat with two-stage heating control is recommended for 
 residential solar heating systems (with one-stage control for the cool- 
 ing system if necessary). Various thermostat designs feature, "on", 
 "off", or "automatic" fan control to circulate the room air, with 
 "heat", "cool", or "automatic" switches for heating and cooling func- 
 tions. Usually the thermostat is the only control with which the occu- 
 pant needs to be concerned. Once set to winter or summer comfort levels 
 
7-21 
 
 no further manual intervention is necessary unless the occupant wishes 
 to change room temperature. 
 
 Thermostats should be installed at locations where average room 
 temperatures are sensed. Instructions are normally supplied by the 
 manufacturer. 
 
 Temperature Sensors 
 
 There are many types of temperature sensors that can be used in the 
 control subsystem, such as thermocouples, thermistors, silicon tran- 
 sistors, bimetallic elements, and liquid or vapor expansion units. 
 Liquid or vapor expansion units are seldom used because other tempera- 
 ture sensors are cheaper and dependable. Thermocouples are frequently 
 used for temperature measurement but are not often used in controls 
 because the voltage output is low, in the millivolt range, and without 
 amplification the voltage is insufficient for reliable use in controls. 
 Thermistors and silicon transistors are commonly used because the 
 voltage outputs from these sensors are high (3-10 volts). 
 
 INSTALLATION OF CONTROL HARDWARE 
 Control Panels 
 
 Except for temperature sensors, components of controls are 
 generally packaged in a compact control box or panel. Prewired units 
 are provided with lugs for attaching wires leading to temperature sen- 
 sors, motors, and valves. Power for the control panel will usually be 
 household, 115-volt, single-phase AC power, which is stepped down to 24 
 volts for room thermostats, and control relays which activate motors and 
 valves. An instruction manual should be provided with the controller. 
 
7-22 
 
 Locations of Temperature Sensors 
 
 Locations of temperature sensors are important, and there are some 
 preferred locations. The sensor which measures fluid temperature at the 
 collector exit should be located in the outlet pipe from a collector in 
 an upper row of an array. It is preferred that the sensor be in a wet 
 well, but it is acceptable for the sensor to be in a dry well provided 
 there is good thermal contact of the sensor with the wall of the dry 
 well. Both wet and dry wells should be well insulated. The collector 
 sensor should be placed as near to the outlet as possible so that it can 
 register the temperature of the collector fluid when it is not 
 circulating. 
 
 The sensor in the storage tank should be located near the bottom 
 because the coldest water will be at the lower levels. The sensor in 
 the hot water pre-heat tank should also be located near the bottom. If 
 a temperature limiter is used, the sensor should be located near the top 
 of the tank. 
 
 AUXILIARY HEAT CONTROL 
 
 Conventional boilers and furnaces are activated in conjunction with 
 the pumps and blowers in the solar system. The second stage thermostat 
 is generally the main control for activating an auxiliary heater. 
 
 CONTROL SYSTEM CHECK-OUT 
 
 The control system should be checked after installation with a 
 "dry" run through the full sequence of modes. The room thermostat can 
 usually be manipulated to require heating or cooling, and temperature 
 sensor terminals can be "shorted" to represent high temperature to start 
 
7-23 
 
 a heat collection mode or domestic water pre-heating mode. A 
 pre-operational check-out will assure that the system will "work" when 
 it is put into operation. Adjustments to the control system may some- 
 times be necessary to achieve high performance of the system. A common 
 adjustment is resetting of "on" and "off" set points to start and stop 
 solar heat collection at proper times of the day. 
 
 HEAT EXCHANGERS 
 
 COLLECTOR TO STORAGE HEAT EXCHANGER 
 Shell-and-Tube Type 
 
 A heat exchanger is used to transfer heat from collector fluid to 
 storage fluid. Among several designs for heat exchangers a shell-and- 
 tube type, shown schematically in Figure 7-12, is the simplest. 
 
 HOT COLLECTOR FLUID 
 
 COOL 
 
 STORAGE 
 
 FLUID 
 
 Figure 7-12. Single-Pass Counterflow Shell-and-Tube Heat Exchanger 
 
7-24 
 
 A tube which passes either the cold or hot fluid, shown as cold fluid in 
 Figure 7-12, is placed concentrically inside a larger tube which forms 
 the shell. The hot and cold fluids may flow in the same direction 
 (parallel flow) or in opposite directions (counterflow) as shown. It 
 has been assumed in this case that the cold fluid is being circulated at 
 twice the flow rate of the hot fluid, so its temperature changes only 
 half as many degrees. A counterflow type is appropriate for solar 
 systems to minimize the temperature difference between storage and 
 collector exit fluid temperatures. In parallel flow heat exchangers, 
 the cold fluid can never be warmer than the hot fluid, while with coun- 
 terflow types the exit temperature of the cold fluid can be higher than 
 the exit temperature of the hot fluid (shown equal in the figure). A 
 counterflow design also requires less surface area to transfer heat at a 
 given rate than a parallel type. 
 
 A more practical design for a shell -and-tube heat exchanger 
 involves multiple tubes within a shell as shown in Figure 7-13. There 
 are baffles within the shell which force the shell side flow to move in 
 a serpentine path across the baffles as shown by the arrows. With 
 multiple tubes, there is a larger surface area for heat exchange within 
 a given shell diameter, enabling a shorter length of heat exchanger to 
 
 Figure 7-13. Multiple-Tube Heat Exchanger 
 
7-25 
 
 be used as compared to single- tube design. There are also multiple-pass 
 heat exchanger designs which cause flow in the tubes to reverse direc- 
 tions within the shell. 
 
 Selection 
 
 The rate of heat transfer from the hot fluid to the cold fluid, 
 Quy, in a shell -and-tube heat exchanger may be written as 
 
 Q HX = (mc p ) c (T 1 -T 2 ), (Btu/hr) (7-1) 
 
 where 
 
 (mc ) is the heat-capacity flow rate of the collector 
 p c liquid, Btu/(hr-°F), 
 
 m is the mass flow rate of the collector liquid, 
 lb/hr, 
 
 c is the heat capacity of the collector liquid 
 " at constant pressure, Btu/(lb*°F), 
 
 T-, and 1 9 are the entrance and exit temperatures of the 
 1 L hot fluid, °F. 
 
 The rate of heat absorbed by the storage liquid is written as 
 
 Q HX = (mc p ) s (t 2 -t 1 ), (Btu/hr) (7-2) 
 
 where 
 
 (mc ) is the heat capacity flow rate of the storage 
 
 p s fluid, Btu/(hr-°F) 
 
 t-, and t 9 are the entrance and exit temperatures of the 
 
 1 d cold fluid, °F. 
 
 If an average temperature difference between the two temperature 
 profiles, shown in Figure 7-12, could be determined, the heat flow rate 
 from the collector fluid to the storage fluid could also be written 
 
 Q HX = (UA) HX (AT) (7-3) 
 
7-26 
 
 where 
 
 (UA)nw is the heat conductance rate through the walls of 
 the heat exchanger tubes and is a function of 
 fluid flow rates and the tube material and surface 
 area of the interior tubes, Btu/(hr*°F) 
 
 AT is an average temperature difference which is most 
 frequently expressed as a log-mean temperature 
 difference, (LMTD), °F. 
 
 In Equation (7-3), if AT (LMTD) can be determined, the size of the 
 
 heat exchanger can be selected because the heat transfer surface area, 
 
 A, can be calculated for given tube material and heat flow rate, Quw. 
 
 The difficulty is that LMTD is not readily determinable because the 
 
 temperature profiles along the heat exchanger are not fully known, and 
 
 the exit temperatures of the hot and cold fluids are dependent upon the 
 
 (UA)nu of the heat exchanger. The log-mean temperature difference is 
 
 written as 
 
 (T 1 -t ? )-(T ? -t 1 ) 
 LMTD = (T x -t 2 ) «-V 
 
 l09 e TTft? 
 
 where the temperatures are indicated in Figure 7-12. 
 
 A method convenient for sizing heat exchangers, which is not 
 dependent upon knowledge of T ? and t ? and only on T-, and t-., utilizes 
 a factor called heat exchanger effectiveness , £,,„. Heat exchanger 
 effectiveness is the ratio of actual rate of heat transfer to a 
 theoretical maximum rate that would occur if the heat exchanger 
 surface area were very large (infinite). Expressed in symbols, 
 
 (mc P ) c ( v T 2 ) ovscyy . q H x n ,, 
 
 hv • ~ ~ n \' 3) 
 
 nA (mc ) . (Vt-.) (mc ) . (T,-t n ) W TH 
 v p y min v 1 V v p y min v 1 V 
 
7-27 
 
 where 
 
 (mc ) . is the smaller value of the heat-capacity flow rate 
 " min for the collector or storage liquids. To simplify 
 the symbolism, hereafter we will use C for the 
 heat-capacity flow rate. 
 
 Q T| , is the theoretical maximum heat transfer rate. 
 
 Once e H y is known, the heat transfer rate is determined directly 
 
 from Equation (7-5) rewritten as Equation (7-6) 
 
 «HX = «HX C rtn« T i-V (7 " 6) 
 
 The heat exchanger effectiveness can also be expressed in terms of the 
 material used in the heat exchanger and fluid capacitance rates as 
 
 r 
 t r UA / n min. n 
 l-exp[- p (1 - p )] 
 
 mi_n max a-i\ 
 
 £iiy p p \ ' ~ I ) 
 
 -, min r UA ,-, min xl 
 1 - p exp [- ■* (1 - p )] 
 
 max min max 
 
 in which UA/C . is designated the number of transfer units, abbreviated 
 min 3 
 
 NTU. The equation is presented graphically in Figure 7-14 and is valid 
 
 in general for a counterflow heat exchanger. A parallel flow heat 
 
 exchanger would have a different expression for e,,w. The number of 
 
 transfer units, NTU, is related to heat exchanger surface area and heat 
 
 transfer coefficient, U, as 
 
 NTU = M- . (7-8) 
 
 min 
 
 Typical values of the overall heat transfer coefficient, U, for shell- 
 and-tube exchangers made of metal vary from 80 to 105 Btu/(hr-ft 2 *°F), 
 depending upon fluid temperature and types of fluid used. Low values 
 are appropriate for low flow rates, and high values of U for high flow 
 rates. For different fluids, flow rates and heat exchanger sizes, £ H w 
 for counterflow heat exchangers can be determined from Figure 7-14. 
 
7-28 
 
 .0 
 
 0.9 
 
 CO 
 
 o 
 
 o 
 
 0.8 
 
 X 
 
 V 
 
 CO 
 CO 
 
 w 0.7 
 
 UJ 
 
 > 
 
 I- 
 o 
 
 UJ 
 
 u_ 
 
 u_ 
 
 UJ 
 
 cc 
 
 UJ 
 
 < 
 
 X 
 
 o 
 
 X 
 
 UJ 
 
 < 
 
 UJ 
 
 X 
 
 0.6 
 
 0.5 
 
 0.4 
 
 0.3 
 
 
 
 o/ y 
 
 
 
 
 <4 
 
 
 
 
 
 
 / S < 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 2 3 
 
 NTU = UA/C, 
 
 mm 
 
 Figure 7-14. Effectiveness for a Counterflow Single-Pass 
 Shell-and-Tube Heat Exchanger 
 
7-29 
 
 Example 7-1 - Select a heat exchanger for a liquid system with a 
 collector area of 500 ft 2 . The collector has the following 
 characteristic parameters: 
 
 F R (ta) n =0.7 
 
 F R U L = 0.93 Btu/(hr-ft 2 -°F) 
 
 Assume a particular time of day when the intensity of solar radiation on 
 the tilted collector, I T , is at a near-maximum level of 300 Btu/ 
 (hr*ft 2 ), inlet fluid temperature, to the collector, T., is 130°F, 
 storage water temperature is 128°F, and ambient temperature, T is 
 30°F. The collector fluid is a 50 percent mixture of ethylene glycol. 
 
 Solution - The heat delivery rate from the collector is 
 
 Q c = A c [I T F R (ta) n - F R U L ( Ti -T a )] 
 
 Q c = 500[300(0.7) - 0.93(130-30)] 
 
 Q = 58,500 Btu/hr 
 ^c 
 
 To size the heat exchanger in the collector loop, flow rates for the 
 collector and storage liquids are needed. The desired flow rate through 
 the collector is 0.02 gpm/ft 2 of collector, so the total flow is 500 x 
 0.02 = 10 gpm. The rate of storage water flow through the heat ex- 
 changer is typically twice the rate through the collector, or 20 gpm. 
 The heat capacitance flow rate for the collector fluid is calcu- 
 lated from C = (mc ) . The temperature rise through the collector is 
 
 determined as T = T. + Q /C . From Figure 4-9, c =0.8 Btu/(lb-°F) 
 1 c c p 
 
7-30 
 
 and from Figure 4-10, the density is 1.048 g/ml which is equal to 8.34 x 
 1.048 = 8.74 lb/gal. Thus 
 
 C c = 10 ( afl)x S.TA x 60(^X0.8^ 
 
 and 
 
 C = 4195 Btu/hr-°F 
 c 
 
 T Q = 130 + 58,500/4195 = 144°F. 
 
 The heat capacitance rate of the storage water at a temperature of about 
 130° F is, 
 
 C S = 20( mTFf ) x 8 - 34( iiT ) x °' 985t x 60 (KF) x 1( TEtV = 9858 Btu/hr-°F 
 
 Clearly, C < C c , and C . /C = 4195/9858 = 0.43. To choose a heat 
 J ' c S mm max 
 
 exchanger, calculate 8 H w, 
 
 _ 58,500 _ fl ft7 
 e HX ~ 4195(144-125) u ' 0/ ' 
 
 From Figure 7-14, select NTU for £ = 0.87, C . /C v = 0.43, NTU = 
 3 cs mm max 
 
 2.8. The area of heat exchanger tube surface required, for an estimated 
 U = 120 Btu/(hr-ft 2 -°F), is 
 
 AU - NUT =2.8 
 
 min 
 
 A= 2.8(4195) =9?9ft2 
 
 With this information a heat exchanger can be selected from a 
 manufacturer's catalog. 
 
 ^0.985 is the specific gravity of water at 130°F (See Figure 4-10) 
 
7-31 
 
 Installation 
 
 Heat exchangers should be installed as close to the storage tank as 
 possible. Pressure drops in heat exchangers are relatively large, and 
 short pipe lengths in the fluid loops will minimize overall pressure 
 drops and requirements for pumping power, and also will reduce heat 
 losses. 
 
 Supports for heat exchangers are generally necessary because of 
 size and weight. The entire outside surface of the heat exchanger 
 should be well insulated, including the shell and the support frame. 
 Before insulating, however, the pipe connections should be tested for 
 leaks. 
 
 LOAD HEAT EXCHANGER 
 
 There are several types of heat exchangers that may be used to 
 transfer heat from storage to the rooms. Solar heated water may be 
 circulated through radiant panels, through fan-coil units, through 
 baseboard heating strips, or through duct coils of central air heating 
 systems. If water temperature to a radiant wall, floor, or ceiling 
 panel is 100°F to 120°F and a large panel area is used, room heating 
 will be adequate. For fan-coil units and duct heating coils, water 
 temperatures of 120° to 150° are needed. Baseboard heating strips 
 require higher temperatures for effective operation, generally in the 
 160° to 190° range. 
 
 Load heat exchangers discussed in this module are water- to-air 
 cross-flow types. As with liquid-to-liquid heat exchangers, water- to- 
 air heat exchangers can be sized to deliver any desirable rate of heat 
 delivery to the room. From practical considerations, the load heat 
 
7-32 
 
 exchanger should be limited to a size such that water at about 145°F can 
 
 meet the design heating load. The heat delivery rate from a water-toair 
 
 heat exchanger is determined by Equation (7-6) with 8. substituted for 
 
 8 H w. If the heat delivery rate is equal to the heat loss rate from the 
 
 building enclosure, 
 
 £. C . T n -T 
 L mm _ R a (7-q^ 
 
 «r y t r 
 
 where 
 
 T R is room temperature, °F 
 
 T is design outdoor temperature, °F, 
 a 
 
 lc is storage water temperature, °F. 
 For a location where T a = 0°F, T R = 70°F and T $ = 140°F, 
 
 T R" T a 70-0 - 
 T $ -T R " 140-70 "' L > 
 
 and when extremely cold temperatures are experienced outdoors, T D -T 
 
 k a 
 
 would be larger than 70°F and correspondingly the water supply tempera- 
 ture must be higher than 140°F to be able to provide adequate heat to 
 the rooms. 
 
 If a large heat exchanger is used (large s.C . ), water at lower 
 temperature can supply the heating rate to meet the load. Let us assume 
 
 that £,C . /(UA), = 3. In the example used above, 
 L mm L 
 
 3 <YV = Y T a 
 3(T $ -70) =70-0 
 
 T $ = 93°F 
 
 Storage water temperature at 93°F through the heat exchanger would 
 deliver heat at a rate sufficient to heat the room air. The load heat 
 exchanger effectiveness, and the size (UA) of the heat exchanger, can be 
 
7-33 
 
 determined with use of Figure 7-15. The example below illustrates the 
 method. 
 
 Example 7-2 - Select a load heat exchanger such that when storage 
 
 water temperature is 100°F, there will be sufficient heat transfer 
 
 to meet a design building load. A heat loss calculation has been made 
 
 for the building and (UA). is 715 Btu/(hr«°F) with a design outdoor 
 
 temperature of 0°F. Determine the design air flow and water flow rates 
 
 through the heat exchanger. 
 
 Solution- To determine £, C . /(UA). , use Equation (7-9). 
 L mm L 
 
 £, C • 
 L mln (j -t \ i t - T 
 (UA). U S V 'R a 
 
 -^^ (100-70) = 70-0 
 
 L min 70 9 „ 
 (UA). " 30 "' *"" 
 
 Select a heat exchanger effectiveness of 0.85. Then 
 
 c = 2.33 x (715) _ ig60 Btu 
 
 'min 0.85 hr-°F 
 
 n , , ,. . . , n .is usually the heat 
 
 Generally, for a water-to-air heat exchanger, Cmin J 
 
 capacitance rate for air. The required air flow rate is calculated as 
 
 follows: 
 
 C . = 60V p (c ) (7-10) 
 
 air a K a v p'a v J 
 
 where 
 
 V is the volumetric air flow rate, ft 3 /min 
 a 
 
7-34 
 
 1.0 
 
 0.9 
 
 0.8 
 
 
 co" 0.7 
 
 CO 
 UJ 
 
 z 
 
 Ul 
 
 > 
 
 a o.6 
 
 u_ 
 u. 
 
 UJ 
 
 QC 
 Id 
 O 
 
 < 
 
 X 
 
 o 
 
 X 
 
 UJ 
 
 < 
 
 UJ 
 
 X 
 
 0.5 
 
 0.4 
 
 0.3 
 
 0.2 
 
 
 
 .4./ 
 
 
 
 
 \ 
 
 •A 
 
 / ys 
 
 / ° 
 
 f^^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Figure 7-15. 
 
 NTU = (UA) /C . 
 HX mm 
 
 Effectiveness of Cross-Flow Water-to-Air 
 Heat Exchanger 
 
7-35 
 
 p is air density, lb/ft 3 
 
 a 
 
 (c ) is specific heat of air. 
 At 70°F, p = 0.075 lb/ft 3 , (c ) = 0.24 Btu/(lb-°F) 
 
 Thus, 
 
 1960 
 V a " (0.75)(0.24)(60) " 1815 cfm 
 
 From Figure 7-15 select a heat exchanger with minimum surface area. 
 
 Usinq the curve C . /C = 0.25, NTU = 2.6, the overall heat transfer 
 3 mm max 
 
 coefficient, U, can vary from 10 to 30 Btu/(hr*ft 2 *°F) for water-to-air 
 heat exchangers. In this example use U = 25. Thus a heat exchanger 
 with a surface area, A, equal to 
 
 A = (2^X1160) = 2 04 ft* 
 25 
 
 is required. 
 
 The water flow rate through the heat exchanger is calculated below: 
 C ,1260=7840 Btu 
 
 water 0.25 hr-°F ' 
 
 and because C . = 60G p *(c ) *S 
 water w"w p w w 
 
 where 
 
 G is flow rate, gal /mi n, 
 
 p is water density, (8.34) lb/gal 
 
 (c ) is specific heat of water, (0.993) Btu/(lb-°F) 
 
 S is specific gravity of water at a given 
 temperature (1). 
 
 r 7840 1t; o 
 
 w " (8. 34)(l)x(0. 993)(60) " lb - a gpm - 
 
 It should be noted that the required air flow rate is large for a 
 building with a heat loss rate of 715 Btu/(hr-°F), and the heat 
 
7-36 
 
 exchanger size is large. If the design condition is selected for 
 storage water temperature at 140°F, a smaller air flow rate and heat 
 exchanger size would result, but with the storage temperature below 
 140°F, the heat flow rate from solar storage would be unable to meet the 
 design load, so auxiliary heating would be required. 
 
 DOUBLE-WALLED HEAT EXCHANGER 
 
 To prevent contamination of household water and water mains, 
 double-walled heat exchangers should be used for transfer of heat from 
 solar storage to domestic water. Double-walled heat exchangers are not 
 as commonly available as single-walled shell-and-tube heat exchangers. 
 Liquid leaks through either wall must be readily detectable so that the 
 unit may be repaired or replaced. One type utilizes a tube wrapped 
 around the outside of the preheat tank. A Roll-Bond w sheet is par- 
 ticularly suitable for this purpose. Other designs involve concentric 
 serpentine tubes with water inside the inner tube and outside the outer 
 tube. The annul us between the tubes is vented so that leaks can be 
 detected. Another design involves parallel tubes cross-connected with 
 many heat transfer fins to conduct heat from the hot tube to the cold 
 tube, similar to baseboard heating strips. 
 
 A design procedure for double-walled heat exchangers is not well 
 established but fortunately, sizing is not critical for domestic water 
 pre-heating. Typical flow rates for both sides of the heat exchanger 
 are 2 to 3 gpm. Temperature drops of 5°F to 10°F across the heat ex- 
 changer are satisfactory and temperature difference of about 20°F be- 
 tween the hot and cold fluids is tolerable. Since the water circulation 
 rate is small, pressure drop is low and only fractional horsepower 
 circulation pumps (1/10 to 1/30) are needed. 
 
7-37 
 
 PUMPS 
 
 Centrifugal pumps are best suited for liquid-heating solar systems. 
 Typical performance curves for a centrifugal pump are shown in Figure 
 7-16. 
 
 Desirable Operating 
 Region 
 
 Discharge 
 Figure 7-16. Typical Performance Curves for a Centrifugal Pump 
 
 The "head" is the pressure generated by the pump expressed in feet 
 of water and is the difference in pressure between the suction and 
 discharge sides. The head generated by the pump is equal to the sum of 
 the pressure drops across the components of the circulation loop. The 
 efficiency of the pump is the ratio of fluid (or brake) power generated 
 by the pump, to the electrical power delivered to the motor. From the 
 curves in Figure 7-16 it is readily seen that pumps should be chosen to 
 circulate the desired flow rate at required head to operate near peak 
 efficiency. The size of motor needed for the pump is determined by the 
 brake horsepower and pump efficiency. 
 
7-38 
 
 Since the head produced by a pump is exactly balanced by the head 
 losses in the system, it is necessary to estimate the head losses in the 
 piping loops, across collectors, and through heat exchangers before 
 selecting pumps. A chart for estimating friction losses in copper 
 tubing is shown in Figure 7-17. Similar charts are available for other 
 types of piping from suppliers. A nomograph for estimating head losses 
 across valves and fittings is shown in Figure 7-18. Head losses for 
 collectors and heat exchangers are given in manufacturers' catalogs and 
 brochures. 
 
 To estimate head losses in a particular loop, a piping layout 
 (schematic) should be made with valves, fittings, filters, and other 
 components shown in the loop. Pipe sizes should be selected so that 
 flow velocities will not exceed about 7 ft/sec. With discharges 
 selected and pressure losses calculated for each circulation loop, pump 
 selections can be made from manufacturers' catalogs. 
 
7-39 
 
 10 
 
 10 10 
 
 FRICTION LOSS ( feet of water per 100 ft ) 
 
 Figure 7-17. Friction Loss in Copper Tubing 
 
7-40 
 
 (TWWT) 
 
 For Sudden Enlorgemenls ond Sudden 
 Contractions the Equivalent Length is in 
 feet of Pipe of the Smaller Diometer.d. 
 
 The Dashed Line Shows the Determin- 
 ation of the Equivalent Length of a 6 in. 
 Standard Elbow. 
 
 3000 
 -2000 
 
 ;I000 
 
 •500 
 
 -300 
 200 
 
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 -50 J- 
 
 o 
 
 -30 < 
 
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 -20 w 
 
 SUDDEN ENLARGEMENT. ..^^^ 
 d/D-l/4 
 
 d/D-l/2 10 
 
 d/D-3/4 
 
 STANDARD ELBOW OR RUN OF 
 TEE REDUCED 1/2 
 
 MEDIUM SWEEP ELBOW OR RUN 
 OF TEE REDUCED 1/4 
 
 LONG SWEEP ELBOW OR RUN 
 OF STANDARD TEE 
 
 ORDINARY ENTRANCE 
 
 D -=^0— 
 _| 
 
 SUDDEN CONTRACTION 
 
 d/D-l/4 
 
 d/D-l/2 • 
 
 d/D-3/4 
 
 45° ELBOW 
 
 48- 
 
 42- 
 
 36 — 
 
 30- 
 
 24 — 
 
 O 
 O 
 
 22- 
 
 20- 
 
 18- 
 
 14- 
 
 12- 
 
 10- 
 
 7- 
 
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 3 
 
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 Figure 7-18. Pressure Loss in Various Elements 
 
7-41 
 
 REFERENCES 
 
 1. Dickinson, W.S. , Neifert, R.D., Lof, G.O.G., and Winn, C.B., 
 (1975). " Performance Handbook for Solar Heating Systems". Pre- 
 sented at the 1975 International Solar Energy Society Congress, 
 University of California at Los Angeles, California. 
 
 2. Klein, S.A. , Beckman, W.A. , and Duffie, J. A., (1975). "A Design 
 Procedure for Solar Heating Systems". Presented at the 1975 Inter- 
 national Solar Energy Society Congress, University of California at 
 Los Angeles, California. 
 
 3. Duffie, J. A. and Beckman, W.A. , (1974). Solar Energy Thermal 
 Processes , John Wiley and Sons, New York. 
 
 4. Pickering, Ellis E. , (1975). "Residential Hot Water Solar Energy 
 Storage", Proceedings of the Workshop on Solar Energy Storage 
 Subsystems for the Heating and Cooling of Buildings, Charlottes- 
 ville, Virginia, April 1975. 
 
 5. Peltzman, E.C., "Differential Thermostats for Solar Energy 
 Systems", Rho Sigma, Inc., 15150 Raymer Street, Van Nuys, CA 
 91405. 
 
 6. Krieth, F. , (1966). Principles of Heat Transfer , International 
 Textbook Co. , Scranton, PA. 
 
 7. ASHRAE (1972) Handbook of Fundamentals, ASHRAE, New York. 
 
 8. ASHRAE (1972) Guide and Data Book, ASHRAE, New York. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 8 
 COMPONENTS OF AIR SYSTEMS 
 
 HEAT STORAGE 
 CONTROLS 
 HEAT EXCHANGERS 
 BLOWERS, AIR HANDLERS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
8-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 8-iii 
 
 OBJECTIVE 8-1 
 
 INTRODUCTION 8-1 
 
 HEAT STORAGE 8-1 
 
 PEBBLE BEDS 8-1 
 
 Pebble-Bed Containers ...... 8-2 
 
 Sizing the Pebble Bed 8-5 
 
 Horizontal Pebble Beds 8-7 
 
 Rocks for the Pebble Bed 8-7 
 
 PHASE CHANGE STORAGE 8-8 
 
 SYSTEM CONTROLS 8-8 
 
 PRINCIPLES OF OPERATION .8-9 
 
 Collecting Solar Heat ...... 8-9 
 
 Delivering Heat to Storage . . . . 8- 11 
 
 Delivering Beat to Rooms . . . . . 8- 13 
 
 Heating from Storage ...... 8-13 
 
 Domestic Water Preheating ..... 8-14 
 
 TEMPERATURE SENSORS 8-14 
 
 INSTALLATION OF CONTROL HARDWARE 8-15 
 
 Control Panels 8-15 
 
 Location of Temperature Sensors .... 8-15 
 
 Auxiliary Furnace Control ..... 8-16 
 
 Control System Check-Out 8-16 
 
8-ii 
 
 HEAT EXCHANGER FOR SERVICE HOT WATER 
 BLOWERS, AIR HANDLERS 
 
 PERFORMANCE CURVES . 
 
 BLOWER SELECTION 
 REFERENCES 
 
 Page 
 8-17 
 8-18 
 8-18 
 8-19 
 8-22 
 
8-111 
 
 LIST OF FIGURES 
 
 Page 
 
 Typical Temperature Stratification in a 
 
 Pebble Bed 8-3 
 
 Pebble-Bed Heat Storage Unit 8-4 
 
 Pressure Drop Through a Pebble Bed 
 
 with 3/4- to 1-1/2-Inch Rocks 8-5 
 
 Horizontal-Flow Pebble Bed 8-7 
 
 Sensor Locations in Typical Air-Heating System . 8-10 
 
 Typical Temperature Variations at SI and S2 . . 8-12 
 
 Typical Efficiency Curves for Blowers . . . 8-18 
 
 Friction Loss in a Straight Duct .... 8-20 
 
 LIST OF TABLES 
 
 Table Page 
 
 8-1 Pressure Loss in Pebble Beds ..... 8-6 
 
 F- 
 
 igure 
 
 8- 
 
 ■1 
 
 8- 
 
 ■2 
 
 8- 
 
 ■3 
 
 8- 
 
 ■4 
 
 8- 
 
 ■5 
 
 8- 
 
 ■6 
 
 8- 
 
 ■7 
 
 8- 
 
 •8 
 
8-1 
 
 OBJECTIVE 
 
 The objective is to present information on components of air 
 systems so that participants will be able to: 
 
 1. Select an appropriate-size heat storage unit. 
 
 2. Select blowers. 
 
 3. Install components properly to operate air systems. 
 
 INTRODUCTION 
 
 Air systems contain the same types of components as liquid systems, 
 namely collectors, thermal energy storage units, heat exchangers for 
 domestic water heating, prime movers to circulate heated fluid streams, 
 and automatic controls. Module 7 contains general discussion of system 
 components as well as comments on specific items applicable for liquid 
 systems. This module is limited to discussion of specific components of 
 air systems. 
 
 HEAT STORAGE 
 
 PEBBLE BEDS 
 
 Rock pebbles are commonly used in air-heating solar systems to 
 store sensible heat. Hot air from the collectors flows through a bed of 
 pebbles and heat is rapidly transferred from the air to the rocks. The 
 air cools as it passes through the pebble bed and leaves at a tempera- 
 ture nearly equal to the temperature of the rocks at the exit end of 
 
8-2 
 
 storage. The resulting temperature stratification in the bed is an 
 advantage to collector operation and also to the supply of heat from 
 storage to the rooms. For collection, cool air is returned to the 
 collectors and operation is always at highest efficiency. When stored 
 heat is delivered to the rooms, air flow direction through storage is 
 reversed so that cool room air enters the cool end of the pebble bed, is 
 heated as it flows through warm layers of rocks, and leaves at the 
 opposite (hot) end of storage. Typical variations of temperatures 
 during a full cycle of charging and discharging of heat in a pebble bed 
 are shown in Figure 8-1. 
 
 Although it is not essential, heated air from collectors should 
 enter at the top of the pebble bed in vertical-flow storage beds and 
 cool room air should be circulated from the bottom toward the top. In 
 this arrangement the bottom of storage, which is coolest, is adjacent to 
 the floor, so heat loss to the ground is minimized. 
 
 Pebble-Bed Containers 
 
 Pebble-bed containers can be wood frame boxes, poured concrete 
 bins, masonry (concrete block) structures, or steel bins. Wood frame 
 boxes are easily constructed even in places where access is limited. 
 All containers must be structurally adequate and joints must be pre- 
 vented from cracking either from the force of pebbles inside the con- 
 tainer or by settlement of the foundation. 
 
 Air leaks from containers should be minimized. A wooden box 
 container is illustrated in Figure 8-2, with plenums at the top and 
 bottom. The bottom plenum is created by supporting the pebbles on a 
 screen resting on steel frames or on spaced concrete blocks. 
 
8-3 
 
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8-4 
 
 COLD AIR 
 CONNECTION 
 
 I in. CONCRETE 
 AGGREGATE 
 
 RIGID INSULATION 
 
 Figure 8-2. Pebble-Bed Heat Storage Unit 
 
 Concrete blocks or other types of masonry may be used for the walls 
 of pebble beds. They should be reinforced and insulated, and the in- 
 terior should be lined or sealed to prevent air leakage. Insulating the 
 walls to achieve R-10 to R-13 rating is generally satisfactory. 
 
 A container made from poured concrete walls is relatively 
 economical when constructed at the same time as basement walls. Only 
 two additional walls in one corner of the basement are needed to form 
 
8-5 
 
 the rock bin. Insulation should be placed against the inside walls, and 
 the construction should be essentially air-tight. 
 
 Sizing the Pebble Bed 
 
 A maximum depth of about 8 feet of pebbles is recommended to limit 
 pressure drops through the bed. The cross-sectional area of the con- 
 tainer (perpendicular to flow direction) should be sized to achieve a 
 superficial flow velocity of about 20 ft per minute. In 5 to 8 ft of 
 path length, the pressure drop will be about 0.10- to 0.16-inch water 
 gauge through a pebble bed containing 3/4- to 1.5- in diameter pebbles. 
 A curve of pressure drop through a pebble bed as a function of super- 
 ficial air velocity through the bed is shown in Figure 8-3. 
 
 
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 0.002 
 
 0.00 1 
 0.0008 
 0.0005 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6 8 10 12 14 
 AIR VELOCITY , fpm 
 
 18 
 
 20 
 
 Figure 8-3. Pressure Drop Through a Pebble Bed with 3/4- to 
 1-1/2-Inch Rocks 
 
8-6 
 
 The effect of pebble size and air velocity on the pressure loss 
 through the bed is indicated in Table 8-1. At a typical face velocity 
 of 20 ft/mi n, the pressure loss in a pebble bed 6 feet deep is 0.17 inch 
 water gauge if uniform 3/4-inch rock is used, and 0.09 inch water gauge 
 if 1^-inch rock is used. If the rock is a mixture of sizes between 
 these limits, the pressure loss is approximately the same as that pre- 
 vailing with the smallest size, i.e., the 3/4-inch material. 
 
 Table 8-1 
 Pressure Loss in Pebble Beds 
 
 Air Face Velocity 
 Feet Per Minute 
 
 Pressure Loss 
 Inches Water Gauge/foot of length 
 
 3/4-Inch Pebbles 
 
 lVlnch Pebbles 
 
 10 
 15 
 20 
 25 
 
 0.008 
 0.017 
 0.028 
 0.046 
 
 0.0025 
 0.008 
 0.015 
 0.023 
 
 The volume of pebble bed recommended for air systems is one-half to 
 one cubic foot for each square foot of collector area. Thus, for 400 
 
 ft 2 of collectors, 200 to 400 ft 3 of rocks are desired. With 200 ft 3 
 
 2 
 
 the container should have a cross-sectional area of about 40 ft , and 
 
 3 
 the depth will be about 5 ft. For 400 ft , the cross-sectional area 
 
 2 
 should be about 50 ft , and the depth will be about 8 ft. 
 
8-7 
 
 Horizontal Pebble Beds 
 
 Pebble beds with horizontal flow can be constructed if vertical 
 space is limited. Channeling of airflow across the top of the bed is 
 the principal concern because of settlement of the rocks in the con- 
 tainer. Barriers along the top placed perpendicular to the flow will 
 reduce channelling, but air flow along the top could still persist if 
 there is a gap. To maintain uniform flow and temperature stratifica- 
 tion, horizontal separators, such as plastic films or sheets, placed 
 about 12 inches apart as shown in Figure 8-4 can be helpful. It is more 
 difficult, because of space restrictions, to maintain large cross- 
 sectional areas and short path lengths in horizontal pebble beds. 
 Superficial flow velocities greater than 20 ft/min and path lengths 
 longer than 10 ft, both of which may be necessary, will add substan- 
 tially to electrical power requirements for air circulation. 
 
 Screen 
 
 Figure 8-4. Horizontal-Flow Pebble Bed 
 
 Rocks for the Pebble Bed 
 
 Rocks suitable for use as concrete aggregate are suitable for 
 pebble-bed storage. Uniformity in size of pebbles is important to 
 create uniform airflow through the pebble bed. Crushed rock or river 
 
8-8 
 
 gravel should be screened for sizes usually from 0.75 to 1.5 inch and 
 washed before placement if not reasonably clean and free of debris. 
 When filling, the rock should be placed in a manner which minimizes 
 fracturing. Small particles which fill the spaces between the pebbles 
 will restrict air passage and cause non- uniformity of air flow and heat 
 storage within the pebble bed. 
 
 PHASE-CHANGE STORAGE 
 
 Some phase-change storage materials (PCM's) for use with air 
 heating systems are commercially available. Salt hydrates are packaged 
 in tubular or capsule form, and heat is transferred to and from them by 
 blowing air across the encapsulated materials. A large amount of heat 
 can theoretically be stored in a small volume of material, but presently 
 available compounds have freezing and melting temperatures that are too 
 low (80°F to 95°F) for conventional warm-air heating systems. To store 
 heat at higher temperatures, the temperature of the melted material must 
 be increased, but because volume is limited, large quantities of sen- 
 sible heat cannot be stored at higher temperatures. PCM costs are high, 
 and temperatures are not suitable for forced air heating systems. 
 Through continued research, appropriate PCM devices for space heating 
 systems may become practical in the future. 
 
 SYSTEM CONTROLS 
 
 Components of a basic control subsystem for an air-heating solar 
 system consist of sensors, differential thermostats, and relays or 
 switches to activate the mechanical devices. The components are 
 
8-9 
 
 substantially the same as for liquid-heating solar systems explained in 
 Module 7. 
 
 PRINCIPLES OF OPERATION 
 Collecting Solar Heat 
 
 A schematic diagram of a one-blower air-heating solar system is 
 shown in Figure 8-5. The system consists of flat-plate collectors, 
 pebble-bed storage, air handler, auxiliary furnace, and a domestic 
 water-heating subsystem. Depending on the mode of operation, the 
 dampers in the air handler open and close to circulate air through 
 appropriate ducts. 
 
 There are three temperature sensors: SI located near the top of 
 the collector, S2 located at the bottom of storage or in the air duct 
 supplying the collector, and S4 near the bottom of the domestic water 
 pre-heat tank. The room thermostat is designated S3 and consists of 
 two-stage contacts for heating. Sensor SI may be placed either in the 
 air stream near the top of the collector or attached to the back side of 
 the absorber plate. Temperature difference settings will be different 
 for the two placements, with a larger difference setting required if the 
 sensor is attached to the absorber plate. Normally SI is placed in the 
 air stream within the collector. 
 
 To initiate collection of solar heat, the temperature difference 
 between SI and S2 is considered. If the difference is greater than a 
 preset amount, say 15°F to 20°F, the blower in the air handler is 
 activated and heat is delivered from the collectors. Unlike a liquid 
 system, the air system can be controlled to deliver heat directly to the 
 rooms as well as to storage. 
 
8-10 
 
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8-11 
 
 Delivering Heat to Storage - Simultaneously with blower activation, 
 dampers in the air handler are automatically positioned to circulate air 
 through the blower and to the top of storage. The motorized damper at 
 the bottom of storage is closed and air is directed to the collectors. 
 Since all of the useful thermal energy collected (above room tempera- 
 ture) is stored in the rock bed, the air temperature at the bottom of 
 storage is cool. The pebbles at the bottom of storage will be at room 
 temperature at the start of a collection day and S2 will remain constant 
 until the thermal front advances all the way through the pebble bed. 
 With proper sizing of storage, S2 will typically remain at room tempera- 
 ture through the entire collection day during the winter as indicated in 
 Figure 8-1. 
 
 Temperature variations at sensors SI and S2 are shown for a typical 
 winter day in Figure 8-6. The blower is activated at point (T) when the 
 temperature difference is, for example, about 15°F. As soon as the 
 blower starts, the collector is cooled and air temperature at SI drops 
 to point (2) . If the difference is less than the minimum set point, 
 the blower stops and restarts a few minutes later. A minimum tempera- 
 ture difference setting for shutting off the blower may be as low as 2°F 
 or 3°F. As the intensity of solar energy increases during the day, air 
 temperature at SI increases and reaches a maximum at midday. In the 
 afternoon, air temperature at SI continually decreases because of de- 
 clining solar intensity, and the blower stops at point (3) when the 
 temperature difference reaches the minimum set point. The collector 
 temperature then rises slightly (to point ), after the blower stops 
 because of additional solar radiation on the absorber and heat retention 
 in the collector. If point @ is high enough, the blower may restart 
 and run for a few minutes before again shutting down. 
 
8-12 
 
 i 
 
 Li. 
 
 o 
 
 Q. 
 
 E 
 o> 
 
 Collector Air 
 Temperature S 
 
 Air Temperature 
 at Bottom of 
 ® Storages 
 
 -^- 
 
 12 18 
 
 Time (hours) 
 
 24 
 
 Figure 8-6. Typical Temperature Variations at SI and S2 
 
 Normally, with a start set point of 15°F difference between SI and 
 S2 and a stop set point of 2°F to 3°F, collection will begin on sunny 
 winter days between 0800 and 0830 hrs, and stop between 1630 and 1700 
 hrs in the afternoon. With a start-to-stop temperature set point ratio 
 as high as 5 to 7, on-and-off cycling of the blower will not usually 
 occur either at the start of collection or at termination of collection. 
 
 The foregoing temperature difference settings are small enough to 
 provide virtually the maximum collectable solar heat to storage and to 
 direct use. When air is supplied to the collector at about 70°F, these 
 settings permit heat delivery to storage and directly to the rooms at 
 temperatures as low as 85° (start-up) and even at 72° (shut-down). 
 Because these temperatures may be too low for comfortable supply to the 
 rooms, differential settings may, in common practice, be considerably 
 higher. In a widely used air system, for example, the manufacturer 
 
 
8-13 
 
 recommends (and provides factory settings) a start-up temperature 
 difference of 40°F and a shut-down difference of 25°F. These settings 
 assure air deliveries to the heated space at temperatures no less than 
 95°F. 
 
 Delivering Heat to Rooms- When solar heat is being collected and 
 thermostat S3 calls for room heating, dampers in the air handler and at 
 the bottom of storage open and close appropriately to direct the air 
 stream to the rooms. If the temperature of the air stream from the 
 collector is not sufficiently warm to heat the room adequately, the 
 second stage contact of the thermostat is completed and the auxiliary 
 furnace is activated. Since the auxiliary furnace is sized to heat the 
 rooms adequately by itself, room temperature will soon rise above the 
 thermostat setting, the auxiliary furnace will be deactivated, dampers 
 in the air handler will be repositioned, and solar heated air will then 
 be directed to storage. 
 
 Heating from Storage 
 
 Only the thermostat S3 is required to control room heating from 
 storage. The first stage calls for solar heat from storage. When heat 
 delivery is inadequate to meet the room requirements, the second stage 
 of the thermostat activates the auxiliary furnace. Room air is always 
 circulated through storage whether auxiliary heating is required or not; 
 thus all stored heat, regardless of its temperature, is utilized for 
 space heating. 
 
8-14 
 
 Domestic Water Pre-heating 
 
 The control for pre-heating domestic water is a differential 
 thermostat for sensors SI and S4. The temperature difference setting to 
 start pre-heating may be about 15°F, and to stop pre-heating, the set 
 point may be as low as 3°F. There is considerable variation in prac- 
 tice, however, settings as high as 40° "on" and 25° "off" being 
 observed. 
 
 For water heating during the summer a by-pass duct may be used with 
 a summer-winter damper that permits air circulation only through collec- 
 tor and water coil. A temperature limit switch may be advisable to 
 prevent boiling. With the system shown in Figure 8-5, where attic air 
 is drawn through the collector and hot air is discharged outdoors, it is' 
 not necessary to include a temperature limiter. However, if hot air is 
 recirculated through the collector during the summer, air temperatures 
 may become high enough for water to boil in the pre-heater tank. This 
 condition is usually avoided by using S4 to turn off the blower and 
 water pump when a preset temperature limit is reached. 
 
 TEMPERATURE SENSORS 
 
 Thermistors are usually employed as temperature sensors in air 
 systems because they deliver ample voltage (2 to 6 volts) to the con- 
 troller, and the signal is nearly linear. Sensors with output voltage 
 that is linear with temperature provide more consistent control for 
 solar energy collection and water heating because the temperature dif- 
 ference setting is independent of absolute temperatures. That is, with 
 "linear output" sensors, temperature difference settings are more 
 rel iable. 
 
8-15 
 
 INSTALLATION OF CONTROL HARDWARE 
 
 Control Panels 
 
 Control panels are usually compactly packaged for easy mounting. 
 Connections to sensors and output devices are usually labeled and easy 
 to attach. Some manufacturers include the control assembly with the air 
 handler, and connections to dampers and the motor are wired at the 
 factory. Only the sensor and thermostat connections are required for 
 such units. For systems with damper motors outside the air handler, 
 control wires will have to be attached separately. Instructions for 
 installation should be provided with the system. 
 
 Location of Temperature Sensors 
 
 The sensor in the collector should be located near the exit of the 
 top collector in an array with air flow from bottom to the top of the 
 array. With or without forced air movement, the temperature is highest 
 at the exit. The sensor at the bottom of storage should be in contact 
 with the pebbles at the bottom. An alternative location for the sensor 
 is in the bottom plenum or in the duct leading to the collector. 
 
 Locating a sensor S2 (see Figure 8-5) in the return duct to the 
 collectors rather than at the bottom of storage can cause difficulty if 
 positioned too close to the collector. Even with a damper between the 
 sensor and the collector, cold air from the idle collector may settle 
 downward in the duct and cool S2. Air circulation may thus be initiated 
 even when storage is warmer than the air at the collector outlet. The 
 system will operate until warm air from storage heats sensor S2 and 
 periodic cycling can result. Convenience in installation may be served, 
 however, by a duct-mounted sensor S2, so a location near the bottom of 
 
8-16 
 
 the pebble bed, just beyond the junction with the duct returning cold 
 air from the rooms, should then be used. 
 
 The sensor in the domestic water pre-heat tank should be located 
 near the bottom where the coldest water is present. 
 
 Auxiliary Furnace Control 
 
 The auxiliary furnace is activated by the second stage of the room 
 thermostat and shuts off when the thermostat set point is reached. To 
 reduce room temperature fluctuation, the furnace is usually immediately 
 activated if the temperature at the top of storage, determined by 
 another sensor at that point, is below a preset level, such as 90°F. 
 Use of such a control scheme will decrease slightly the solar contri- 
 bution to the seasonal heating load but will increase comfort. 
 
 Control System Check-Qut 
 
 To assure reliable performance, all operating modes of the system 
 should be checked out after installation. To initiate heat collection, 
 in the absence of sunshine, the terminals of sensor SI at the controller 
 can be short-circuited to simulate a high collector temperature. The 
 blower should start, and if the room thermostat is at a low setting 
 (below actual room temperature), air should flow through storage. The 
 domestic water circulation pump should also start. While in this col- 
 lection mode, increasing the room thermostat setting to the first stage 
 contact should result in air circulation through the rooms. A further 
 increase in thermostat setting, until the second stage is contacted, 
 should activate the auxiliary furnace. With the short circuit removed 
 (and little or no solar radiation), a thermostat setting slightly above 
 
8-17 
 
 room temperature should start air circulation through storage to the 
 rooms, and finally the second stage of the thermostat should activate 
 the furnace. If the sun is at an intensity sufficient for collection, 
 room heating from storage can be forced by disconnecting one of the 
 leads from sensor SI. 
 
 HEAT EXCHANGER FOR SERVICE HOT WATER 
 
 Only one heat exchanger, a cross-flow air-to-water type such as 
 described in Module 7, is required in an air-heating solar system in 
 which service hot water is provided. Water circulation rates of 2 to 3 
 gpm are usually satisfactory for most domestic systems. Temperature 
 rise in the heat exchanger will depend upon air temperature from the 
 collectors, but a maximum rise of 15°F at midday with air temperature 
 near 140°F will be satisfactory. Air flow rate through the heat ex- 
 changer is established by the area of collectors. With this infor- 
 mation, manufacturers or their representatives should be able to 
 recommend a heat exchanger size. 
 
 The heat exchanger should be in a location where it cannot freeze. 
 By placing it in the heated space inside the building, there is reason- 
 able protection from freezing. But if the exchanger is in the hot air 
 duct between collector and blower (air handler), and if the collector 
 damper in the air handler does not close tightly during the night heat- 
 ing mode from storage, cold air from the collector could flow through 
 the duct and freeze the water in the heat exchanger. A better location 
 for the heat exchanger is between the air handler and storage as shown 
 
8-18 
 
 in Figure 8-5. Even if the collector damper is not tightly closed, cold 
 air cannot come in contact with the heat exchanger in this location. 
 
 BLOWERS, AIR HANDLERS 
 
 PERFORMANCE CURVES 
 
 Representative performance curves for a centrifugal blower are 
 illustrated in Figure 8-7. The pressure-discharge curve has a dip at 20 
 to 30 percent of peak capacity and a maximum at mid range. The brake 
 horsepower (BHP) curve increases monotonically. Peak efficiency occurs 
 to the right of peak pressure. For a blower that is belt-coupled to the 
 motor, the speed of the impeller is variable. The effect of impeller 
 speed on performance is illustrated by dashed curves, the rotational 
 speed Np being less than N-. . 
 
 o 
 
 c 
 
 o 
 
 UJ 
 
 a. 
 
 x 
 
 CD 
 
 <D 
 
 l— 
 
 (/) 
 
 to 
 
 CD 
 
 Pressure - Discharge 
 
 Volume Flow Rate 
 
 Figure 8-7. Typical Efficiency Curves for Blowers 
 
8-19 
 
 BLOWER SELECTION 
 
 To select a blower, the pressure drop in the system and air flow 
 rate are needed. The air flow rate is established by collector area, 
 and the pressure drop in the system must be estimated. A rough layout 
 of the ducts must be made and approximate sizes selected so that air 
 flow velocity does not exceed about 600 feet per minute in the main 
 circulation ducts. 
 
 Pressure drop through the collector for various flow rates will be 
 provided by the manufacturer, but duct losses must be estimated. A 
 graph for friction losses in ducts, shown in Figure 8-8, will assist in 
 estimating the losses. Each mitered elbow or tee with turning vanes 
 will cause an additional 0.005 in. water gauge pressure drop with air 
 velocities of 600 ft per minute. Pressure drop through storage must be 
 included. 
 
 With a single blower, the circulation rate through the distribution 
 system must be adequate for heating the rooms, and the blower size 
 selected for collecting solar heat must match room heating requirements. 
 When the two circulation requirements are significantly different, a 
 two-speed blower may be selected, one speed for collecting heat and 
 another for distribution. As an approximate rule, if a system is sized 
 to provide about 50 percent of the annual heating load, the air flow 
 rate for the solar system will match the requirements for air circula- 
 tion through the rooms. 
 
 Many residential and commercial air-heating solar systems have been 
 provided with a blower and motorized dampers preassembled in a cabinet 
 to which ducts are simply connected by the installer. These air 
 handlers are commercially available in a one-blower configuration for 
 
8-20 
 
 
 i/% 
 
 I0 : 
 
 a> 
 
 3 
 
 0> 
 Q. 
 
 ro 
 
 i- 10 
 
 o 
 
 -J 
 
 2 . 
 
 0' 
 
 o ~o' ( &oooo* 1&o¥ > 
 
 _]» t-jj ni i hi i i/i i V i i i nil 
 
 I0" 2 10"' 40° 10' 
 
 FRICTION LOSS ( inches of water perlOOft) 
 
 Figure 8-8. Friction Loss in a Straight Duct 
 
8-21 
 
 systems such as described above, or in a design suitable for use with a 
 second blower, usually part of a commercial warm air furnace. The 
 latter system is more fully described in Module 10. 
 
8-22 
 
 REFERENCES 
 
 1. Dickinson, W.S., Neifert, R.D., Lof, G.O.G., and Winn, C.B., 
 (1975). "Performance Handbook for Solar Heating Systems". Pre- 
 sented at the 1975 International Solar Energy Society Congress, 
 University of California at Los Angeles, California. 
 
 2. Klein, S.A. , Beckman, W.A., and Duffie, J. A., (1975). "A Design 
 Procedure for Solar Heating Systems". Presented at the 1975 Inter- 
 national Solar Energy Society Congress, University of California 
 at Los Angeles, California. 
 
 3. Duffie, J. A. and Beckman, W.A. , (1974). Solar Energy Thermal 
 Processes , John Wiley and Sons, New York. 
 
 4. Close, D.J., (1965). "Rock Pile Thermal Storage for Comfort Air 
 Conditioning", Mechanical and Chemical Engineering Transactions of 
 the Institution of Engineers, Australia, Vol. MCI, No. 1, May 1965. 
 
 5. Peltzman, E.C., "Differential Thermostats for Solar Energy 
 Systems", Rho Sigma, Inc., 15150 Raymer Street, Van Nuys, CA 
 91405. 
 
 6. Kreith, F. , (1966). Principles of Heat Transfer , International 
 Textbook Co. , Scranton, PA. 
 
 7. ASHRAE (1972) Handbook of Fundamentals, ASHRAE, New York. 
 
 8. ASHRAE (1972) Guide and Data Book, ASHRAE, New York. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 9 
 
 DOMESTIC HOT WATER SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
9-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 9-i i i 
 
 LIST OF TABLES 9-iii 
 
 OBJECTIVES 9-1 
 
 INTRODUCTION 9-1 
 
 TYPES AND CHARACTERISTICS OF SOLAR HOT WATER HEATERS . . 9-2 
 
 NON-CIRCULATING TYPE 9-2 
 
 DIRECT HEATING, THERMOSIPHON CIRCULATING TYPE . . 9-3 
 
 DIRECT HEATING, PUMP CIRCULATION TYPES .... 9-5 
 
 DIRECT HEATING, PUMP CIRCULATION, DRAINABLE TYPES . . 9-7 
 
 CIRCULATING TYPE, INDIRECT HEATING 9-9 
 
 Liquid Transfer Media ...... 9-9 
 
 Air Transfer Media ....... 9-11 
 
 AUXILIARY HEAT 9-13 
 
 TEMPERATURE STRATIFICATION IN SOLAR HOT WATER TANK . . 9-14 
 
 TEMPERATURE CONTROL LIMIT 9-15 
 
 LOCATION OF COLLECTORS 9-18 
 
 ORIENTATION AND TILT OF COLLECTORS 9-18 
 
 PERFORMANCE OF TYPICAL SYSTEMS 9-19 
 
 GENERAL REQUIREMENTS 9-19 
 
 QUANTITATIVE PERFORMANCE 9-21 
 
 SIZING THE COLLECTORS 9-25 
 
 SIZING EXAMPLES 9-28 
 
9-ii 
 
 Page 
 
 Example 9-1 9-28 
 
 Example 9-2 9-29 
 
 REFERENCES 9-29 
 
9-1 ii 
 
 LIST OF FIGURES 
 
 Figure ^2£ 
 
 9-1 Direct Heating, Thermosiphon Circulating Solar 
 
 Water Heater . • 9-4 
 
 9-2 Direct Heating, Pump Circulation Solar Water Heater 
 with Automatic Drain-Down (Applicable also to a Two- 
 Tank System) 9 " 6 
 
 9-3 Indirect Heating, Pump Circulation Solar Water Heater 
 
 with Liquid Heat Transfer Media .... 9-10 
 
 9-4 Solar Water Heater with Air Collectors . . . 9-12 
 
 9-5 Absorber and Tank Temperatures for Thermosiphon Flow 
 
 During a Typical Day 9-25 
 
 9-6 Fraction of Annual Load Supplied by Solar as a Function 
 
 of January Conditions for Hot Water Heaters . . 9-26 
 
 2 
 9-7 Average Daily Solar Radiation (Btu/ft ), Month of 
 
 January .....••••• 9-27 
 
 LIST OF TABLES 
 
 Table £*££ 
 
 9-1 Daily Means for Twelve Consecutive Months of 
 Operation of Solar Water Heaters at Various 
 Localities 9 ~ 23 
 
 9-2 Solar Water Heater Performance in Melbourne, 
 
 Australia 9 ~ 24 
 
9-1 
 
 OBJECTIVES 
 
 From the contents of this module the trainee should be able to: 
 
 1. Identify the types of domestic hot water systems available. 
 
 2. Select a type of solar domestic hot water system that is 
 appropriate for a particular location. 
 
 3. Select a suitable collector area and storage tank size for a 
 specific application. 
 
 4. Design a solar domestic hot water system and specify the 
 installation requirements. 
 
 INTRODUCTION 
 
 The oldest and simplest domestic use of solar energy is for heating 
 water. Solar hot water heaters were used in the United States at least 
 75 years ago, first in southern California and later in southern 
 Florida. Although the use of solar water heaters in the United States 
 declined during the last 40 years, use in Australia, Israel, and Japan 
 has risen rapidly, particularly in the last 15 years. Since 1974, solar 
 water heating is again increasing in the United States as a direct 
 result of the general public interest in solar energy applications, the 
 demonstration programs of public utility companies, and the Solar Demon- 
 stration Program and the research and development activities supported 
 by the U. S. Department of Energy. 
 
9-2 
 
 TYPES AND CHARACTERISTICS OF SOLAR HOT WATER HEATERS 
 
 Most of the solar hot water heaters that have been experimentally 
 and commercially used can be placed in two main groups: 
 
 1. Non-circulating types, involving the use of water containers 
 that serve both as solar collectors and storage. 
 
 2. Circulating types, involving the supply of solar heat to a 
 fluid circulating through a collector and storage of hot water 
 in a separate tank. 
 
 The circulating group may be divided into the following types and 
 sub-types: 
 
 1. Direct heating, single-fluid types in which domestic water is 
 heated directly in the collector, by: 
 
 (a) Thermosiphon circulation between collector and storage. 
 
 (b) Pumped circulation between collector and storage. 
 
 2. Indirect heating, dual-fluid types in which a non-freezing 
 medium is circulated through the collector for subsequent heat 
 exchange with water, when: 
 
 (a) Heat transfer medium is a non-freezing liquid. 
 
 (b) Heat transfer medium is air. 
 
 NON-CIRCULATING TYPE 
 
 Although of little potential interest in the United States, a type 
 of solar water heater extensively used in Japan involves heat collection 
 and water storage in the same unit. The most common type comprises a 
 set of four to eight black plastic tubes about six inches in diameter 
 and several feet long placed side-by-side in a box covered with glass 
 
9-3 
 
 or clear plastic. Usually mounted in a tilted position, the tubes are 
 filled each morning with water and heated by solar energy throughout the 
 day. The filling can be accomplished by use of a float-controlled valve 
 and a small supply tank. Late in the day, heated water can be drained 
 from the tubes for bathing and other household uses not requiring pres- 
 surized hot water service. 
 
 Another type that can be used in non-freezing climates consists of 
 a storage tank located inside a glazed and insulated box or cabinet 
 placed at ground level outside the building. An insulated door on the 
 south side of the box can be closed at night to reduce heat losses from 
 the tank. The system operates with mains pressure so no pump is re- 
 quired. Tanks can be supported at a tilted angle to maximize exposure 
 of the blackened sides to sunshine, or the tank may be placed horizon- 
 tally and an insulated lid added to expose more of the tank wall to 
 direct sunlight. 
 
 DIRECT HEATING, THERMQSIPHON CIRCULATING TYPE 
 
 The most common type of solar water heater in non-freezing climates 
 is shown in Figure 9-1. The collector, usually single glazed, may vary 
 in size from about 30 square feet to 80 square feet, and the insulated 
 storage tank is commonly in the range of 40 to 80 gallons capacity. The 
 hot water requirements of a family of four persons can usually be met by 
 a system in the middle of this size range, in a sunny climate. 
 
 The thermosiphon system may be designed to operate at supply line 
 pressure, or as an unpressurized system by installing a float valve in 
 the storage tank. Alternatively a float-controlled elevated head tank 
 can be utilized. For unpressurized systems, gravity flow from the hot 
 water tank to hot water faucets would have to be accepted, although an 
 automatic pump could be installed to provide pressure in the hot water 
 
9-4 
 
 Collector Area 
 Varies from 
 30 ro 60 t " 
 
 40 to &6 gallon Capacity 
 Insulated Storage Tank 
 
 vr, 
 
 Figure 9-1. Direct Heating, Thermosiphon Circulating 
 Solar Water Heater 
 
 supply line. Plumbing systems and fixtures in the United States 
 normally require a pressurized system. 
 
 Locating the tank higher than the top of the collector permits 
 circulation of water from the bottom of the tank through the collector 
 and back to a point near the top of the tank. The density difference 
 between cold and hot water produces the circulating flow. Temperature 
 stratification in the storage tank permits operation of the collector 
 under most favorable conditions, water at the lowest available tempera- 
 ture being supplied to the collector and the highest available tempera- 
 ture being provided to service. Circulation occurs only when solar 
 energy is being received, so the system is self-controlling. The higher 
 the radiation level, the greater the heating and the more rapid the cir- 
 culating rate will be. In a typical collector under full sun, a 
 
9-5 
 
 temperature rise of 15°F to 20°F is commonly realized in a single pass 
 through the collector. 
 
 To prevent reverse circulation and cooling of stored water when no 
 solar energy is being received, the bottom of the tank should be located 
 above the top header of the collector. If the collector is on a sloping 
 house roof, the tank may also be on the roof or in the attic space above 
 the collector level . 
 
 Although seldom used in cold climates, the thermosiphon type of 
 solar water heater can be protected from freezing by draining the col- 
 lector. To avoid draining the storage tank also, thermostatically 
 actuated valves in the lines between collector and storage tank must 
 close when freezing threatens; a collector drain valve must open, and a 
 collector vent valve must also be open. The collector will then drain 
 and air will enter the collector tubes. Water in the storage tank, 
 either inside the heated space or sufficiently well insulated to avoid 
 freezing, does not enter the collector during the period when sub- 
 freezing temperatures prevail. Resumption of operation requires auto- 
 matic closure of the drain and vent valves and opening of the valves in 
 the circulating line. The possibility of control failure or valve 
 malfunction makes this complex system unattractive in freezing climates. 
 
 DIRECT HEATING, PUMP CIRCULATION TYPES 
 
 If placement of the storage tank above the collector is 
 inconvenient or impossible, the tank may be located below the collector 
 and a small pump used for circulating water between the collector and 
 storage tank. This arrangement is usually more practical than the ther- 
 mosiphon type in most residential buildings, because the collector would 
 
9-6 
 
 often be located on the roof with a storage tank in the basement. 
 Instead of thermosiphon circulation when the sun shines, a temperature 
 sensor actuates a small pump which circulates water through the 
 collector-storage loop. A schematic arrangement is shown in Figure 9-2. 
 
 Air Vent 
 
 Normally Open 
 Solenoid Valve 
 
 Temp. S Pres. 
 Valve 
 
 _/" Relief 
 
 Sensor 
 
 Collectors 
 
 ^H, 
 
 Mixing Valve 
 
 :z ~\ Auxiliary 
 "J Elements 
 
 Cold Water 
 Hot Water 
 
 Drain 
 
 Gate Valve 
 
 Gate Valve Normally Closed 
 Strainer ^ aTe valve Solenoid Valve 
 
 Drain 
 
 Figure 9-2. Direct Heating, Pump Circulation Solar Water Heater with 
 Automatic Drain-Down (Applicable also to a Two-Tank System) 
 
 To obtain maximum utilization of solar energy, control is based on 
 the difference in water temperature at collector outlet and bottom of 
 storage tank. Whenever this difference exceeds a preset number of 
 degrees, say 10°F, the pump motor is actuated. The sensor at the col- 
 lector outlet must be located close enough to the collector so that it 
 is affected by collector temperature even when the pump is not running. 
 Similarly, the sensor in the storage tank should be located in or near 
 
9-7 
 
 the bottom outlet from which the collector is supplied. When the 
 temperature difference is less than a somewhat lower preset value, say 
 2°F to 5°F, the pump is shut off and circulation ceases. To prevent 
 reverse thermosiphon circulation and consequent water cooling when no 
 solar energy is being received, a check valve should be located in the 
 circulation line. 
 
 If hot water use is not sufficient to maintain storage tank 
 temperature at normal levels (as during several days of non-use), boil- 
 ing may occur in the collector. If a check valve or pressure-reducing 
 valve prohibits back flow from the storage tank into the main, a relief 
 valve must be provided in the collector-storage loop. The relief valve 
 will permit the escape of steam and prevent damage to the system. 
 
 DIRECT HEATING, PUMP CIRCULATION, DRAINABLE TYPES 
 
 If the solar water heater described above is used in a cold 
 climate, it may be protected from freeze damage by draining the collec- 
 tor when sub-freezing temperatures are encountered. Several methods can 
 be used, all of which must provide dependable drainage, even when elec- 
 tric power may not be available. One arrangement is shown in Figure 
 9-2. 
 
 Drainage of the collector in freezing weather can be accomplished 
 by automatic valves which provide water outflow to a drain (sewer) and 
 air inflow to the collector. Although not the most common control 
 system, one arrangement operates so that whenever the circulating pump 
 is not running, these two valves are open. To assure maximum reliabil- 
 ity, the valves should be mechanically driven to the drain position (by 
 springs or other means), rather than electrically, so that in the event 
 of a power failure, the collector can automatically drain. A 
 
9-8 
 
 disadvantage of this design is the daily exposure of collector tubing to 
 air and its corrosive action. 
 
 The drainage system shown in Figure 9-2 is actuated by the 
 temperature sensor ("Freeze Sensor") at the bottom of the collector. 
 When it indicates a possibility of freezing, it causes the drainage and 
 vent valves to open, thereby providing protection. Simultaneously with 
 the opening of these valves, a motorized valve between the storage tank 
 and pump inlet closes and a check valve in the line between collector 
 and storage tank is forced shut, so that water pressure is retained in 
 the tank. The temperature sensor can be of the vapor pressure type, 
 with capillary tube connections to mechanical valve actuators, or of the 
 electrical type where the valves are held open by electrical means, 
 automatically closing at low temperatures and/or when electrical failure 
 occurs. 
 
 Start-up of a vented collector system must permit the displacement 
 of air from the collector. In either the line-pressure system or the 
 unpressurized system, the entry of water into the collector (from the 
 shut-off valve or pump) forces air from the collector to the atmosphere 
 through a simple air bleed valve of a type which automatically passes 
 air but shuts off when water reaches it. The vent valve which admits 
 air to the collector may be electrically operated (such as a normally 
 open solenoid type), or it may be a "vacuum breaker" valve which is 
 forced open by the decrease in pressure resulting from opening the drain 
 valve. 
 
 Reduction in the number of automatic valves required in this 
 system, with at least two activators, is being attempted through design 
 of one automatic valve unit, with multiple ports, stems, and seats, 
 which can perform all the functions of the several valves now commonly 
 
9-9 
 
 used. Considerable simplification, cost reduction, and reliability 
 improvement may then be achieved. 
 
 CIRCULATING TYPE, INDIRECT HEATING 
 
 The needs and means for collector drainage of direct heating 
 systems in freezing climates involve added costs, and there is still a 
 risk of freezing. The drainage requirement can be eliminated by the use 
 of a non-freezing heat transfer medium in the solar collector and a heat 
 exchanger for transfer of heat from the solar-heated collecting medium 
 to the service water. The collector never needs to be drained, and 
 there is little risk of freezing. Corrosion rate in the wet collector 
 tubes is also decreased because they are always liquid-filled and there 
 is no free oxygen in the heat transfer medium. 
 
 Liquid Transfer Media 
 
 A method for solar water heating with a liquid heat transfer medium 
 in the solar collector is illustrated in Figure 9-3. The most commonly 
 used liquid is a solution of ethylene glycol (automobile radiator anti- 
 freeze) in water. A pump circulates this unpressurized solution, as in 
 the direct water heating system, and delivers the liquid to and through 
 a liquid-to-liquid double-wall heat exchanger. Simultaneously, another 
 pump circulates domestic water from the storage tank through the ex- 
 changer, back to storage. The control system is essentially the same as 
 that in Figure 9-2. If the heat exchanger is located below the bottom 
 of the storage tank, and if the pipe sizes and heat exchanger design are 
 adequate, thermosiphon circulation of water through the heat exchanger 
 can be used and the pump can be eliminated from the water loop. A small 
 expansion tank needs to be provided in the collector loop, preferably 
 near the high point of the system if in an unpressurized collector 
 circuit. This tank must have a vent to the atmosphere. If the 
 
9-10 
 
 -CM 
 
 S- 
 
 
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 -p 
 
 
 03 
 
 
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 s- 
 
 
 0) 
 
 
 ■»-> 
 
 
 03 
 
 
 3: 
 
 
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 ^— 
 
 
 o 
 
 
 oo 
 
 
 c 
 
 
 o 
 
 
 •r- 
 
 
 -f-> 
 
 
 oj 
 
 
 1—" 
 
 
 Z3 
 
 
 u 
 
 
 S- 
 
 03 
 
 • ^ 
 
 *l 
 
 C_) 
 
 "O 
 
 
 a> 
 
 cxs: 
 
 E 
 
 
 Z5 
 
 S- 
 
 Q_ 
 
 <D 
 
 
 <4- 
 
 #> 
 
 l/> 
 
 CJ) 
 
 c 
 
 C 
 
 03 
 
 •r~ 
 
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 03 
 
 
 0) 
 
 H-J 
 
 re 
 
 03 
 
 
 O) 
 
 +-> 
 
 :r 
 
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 <D 
 
 ■a 
 
 S- 
 
 •r— 
 
 •r— 
 
 =5 
 
 ■a 
 
 CT 
 
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 03 
 
9-11 
 
 collector loop is operated under positive pressure, an expansion tank 
 containing a diaphragm balanced by air pressure may be located at a 
 convenient point, usually in the line near the solution pump. 
 
 To meet most code requirements, the heat exchanger must be of a 
 design such that rupture or corrosion failure will not permit flow from 
 the collector loop into the domestic water, even if pressure on the 
 water side of the exchanger drops below that on the antifreeze side. A 
 conventional tube-and-shell exchanger would therefore not usually be 
 acceptable. Similarly, a single pipe coil inside the storage tank, 
 through which the collector fluid is circulated, would not be satis- 
 factory. Parallel tubes with metal bonds between them, so that per- 
 foration of one tube could not result in liquid entry into the other 
 tube, would be satisfactory. A finned tube air-to-liquid heat exchanger 
 can also be used by circulating the two liquids through alternate rows 
 of tubes, heat transfer being by conduction through the fins. Tubes 
 within tubes, with slight clearance between them for outflow of leaked 
 fluid, may be used as immersed coils. 
 
 Although aqueous solutions of ethylene glycol and propylene glycol 
 
 appear to be most practical for solar energy collection, organic liquids 
 
 (R) (R) 
 
 such as silicone oil, Dowtherm J and Therminol 55 w may be employed. 
 
 Price and viscosity are drawbacks, but chemical stability and assurance 
 
 against boiling are advantages over the antifreeze mixtures. 
 
 Air Transfer Media 
 
 An air-heating collector can be used to heat domestic water with an 
 air-to-water heat exchanger, as illustrated in Figure 9-4. A solar air 
 heater is supplied with air from a blower, the air is heated by passage 
 
■Afl/V 
 
 Sensor 
 
 Col lectors 
 
 Motor 
 Damper 
 
 iH 
 
 Duct 
 
 Motor 
 Damper 
 
 •jam 
 'DID:'! 
 
 '"Hni"'i 
 : oJDl 
 
 9-12 
 
 Differential 
 /Thermostat 
 
 1 l5volt AC 
 
 Air-To-Water 
 Heat Exchanger 
 
 Sensor 
 
 XJ£ 
 
 Drain 
 
 ^M 
 
 Cold 
 Water 
 
 -/ 
 
 Mixing Valve 
 
 Hot Water 
 
 =----=] 
 
 [Auxiliary 
 Element 
 
 BAux i Mai 
 Elemen 
 
 Drain 
 
 Storage Tank 
 
 Auxiliary Heater 
 
 Blower 
 
 Figure 9-4. Solar Water Heater with Air Collectors 
 
 through the collector, and the hot air is then cooled in the heat 
 exchanger through which domestic water from a storage tank is either 
 pumped or circulated by thermosiphon action. Air from the heat ex- 
 changer is recirculated to the collector. Differential temperature 
 control (between collector and storage) is employed as in the other 
 systems described. Advantages of the air heat transfer medium are the 
 absence of corrosion in the collector loop, freedom from liquid leakage, 
 and freedom from freezing, boiling, and evaporation of collector fluid. 
 Disadvantages are the larger conduit between collector and heat ex- 
 changer, higher power consumption for circulation, and larger collector 
 surface requirements compared to liquid-heating collectors. 
 
9-13 
 
 AUXILIARY HEAT 
 
 A dependable supply of hot water requires the availability of 
 auxiliary heat for supplementing the solar source. The numerous methods 
 of providing auxiliary heat vary in cost and effectiveness. A general 
 principle for maximizing solar supply and minimizing auxiliary use is to 
 avoid direct or indirect auxiliary heat input to the fluid entering the 
 solar collector. If auxiliary heat input is added to the solar hot 
 water storage tank, so that the temperature of the liquid supplied to 
 the collector is increased above that which only the solar system would 
 provide, efficiency is reduced because of higher heat losses from the 
 collector. Thus, auxiliary heat should be added at a point beyond 
 (downstream from) the solar collector-storage system. A conventional 
 electric hot water heater is shown in Figures 9-3 and 9-4 supplied with 
 hot water from the solar tank (whenever a hot water tap is opened). Any 
 deficiency in temperature is made up by electricity in the thermostatted 
 conventional heater. To avoid confusion in terminology, the first, or 
 solar heated, tank is commonly referred to as the "pre-heat" tank or 
 "solar pre-heat" tank, and the second one as the "auxiliary hot water 
 heater". It is evident that auxiliary heat supply in these designs 
 cannot adversely affect the operation of the solar system. 
 
 A one-tank system with the electric resistance heaters in the upper 
 portion of the solar storage tank, as shown in Figure 9-2, is cheaper 
 than the two-tank type, and should have nearly the same solar collection 
 efficiency. Temperature stratification in the tank, accomplished by 
 bringing cold water from the main into the bottom and by circulating 
 through the collector from the bottom of the tank to the upper portion 
 
9-14 
 
 of the tank, prevents auxiliary heat from increasing the temperature of 
 the water supplied to the collector. Water returning from the collector 
 may be brought into the tank below the level of the resistance heater so 
 that a supply of hot water is always available at the thermostatted 
 temperature. In effect, the two tanks shown in Figures 9-3 and 9-4 are 
 combined into one, with temperature stratification providing a separa- 
 tion. The total amount of storage is reduced unless the one tank is 
 increased in size, but heat losses are also reduced. If relatively 
 high-temperature water is desired, there may be an undesirable influence 
 of auxiliary supply on collector efficiency because of some mixing in 
 the tank. 
 
 If auxiliary heating is by gas or oil, a two-tank system must be 
 used because burners are located at the bottom of the heater tank. 
 Auxiliary heat can thus raise the temperature of water near the bottom 
 of the tank and adversely affect collector efficiency if the fuel-fired 
 water heater is also used as the solar supply tank. 
 
 Although the description of the above system refers to direct 
 circulation of water through the collector, the same factors apply to 
 the systems involving heat exchange with antifreeze solutions or air 
 circulating through the collector. In all cases, auxiliary heat should 
 be supplied downstream from the solar heat supply, regardless of whether 
 the water itself is circulated through the collector or whether heat is 
 exchanged between the domestic water and a solar heat transfer fluid. 
 
 TEMPERATURE STRATIFICATION IN SOLAR HOT WATER TANK 
 
 As in a conventional hot water heater, the temperature in the upper 
 part of a solar hot water tank will normally be considerably higher 
 
9-15 
 
 than at the bottom. The lower density of hot water permits this 
 stratification, provided that turbulence at inlet and outlet connections 
 is not excessive. The supply of relatively cold water from the bottom 
 of the tank to the collector permits the collector to operate at its 
 highest possible efficiency under the prevailing ambient conditions. 
 With a circulation rate such that a temperature rise through the col- 
 lector of 15°F to 20°F occurs, water from the lower part of the storage 
 tank is furnished to the collector for maximum effectiveness. If little 
 hot water is withdrawn from the tank during a sunny day, the late after- 
 noon temperature at the bottom of an 80-gallon tank connected to a 40- 
 to 50-square-foot collector may be well above 100°F — even approaching 
 the temperature at the top of the tank. Collection efficiency thus 
 varies throughout the day, depending not only on solar availability but 
 also on the temperature of water supplied to the collector from the tank 
 bottom. Data presented at the end of this module illustrate the range 
 of temperatures achievable in solar water heaters. 
 
 TEMPERATURE CONTROL LIMIT 
 
 In addition to the differential temperature control desirable in 
 most solar water heating systems (which sense temperature differences 
 between collectors and storage), protection against excessive water 
 temperature may be necessary. Several possible methods can be used. In 
 nearly all types of systems, whether direct heating of the potable water 
 or indirect heating through a heat exchanger, a thermostatically con- 
 trolled mixing valve (tempering valve) can be used to provide hot water 
 at constant temperature for household use as shown in Figures 9-3 and 
 
9-16 
 
 9-4. Cold water is admitted to the hot water line immediately 
 downstream from the auxiliary heater in sufficient proportion to secure 
 the desired preset temperature. The solar hot water tank is allowed to 
 reach any temperature attainable, and the auxiliary heater furnishes 
 additional energy only when the auxiliary tank temperature drops below 
 the thermostat set point. Maximum solar heat delivery is thus achieved, 
 and no solar heat needs to be discarded except that which might some- 
 times be delivered when the solar preheat tank is at the boiling point. 
 Any additional solar heat collected under that condition would be dumped 
 through a relief valve with steam escaping to the surroundings. 
 
 Venting of steam from a solar hot water system involving a dual- 
 liquid design, with heat exchanger, should normally be through a tem- 
 perature-actuated valve in the hot water loop. Loss of collector fluid 
 by boiling and vaporization is thereby avoided. It is necessary, how- 
 ever, in this design, that the boiling temperature of the collector 
 fluid be at least 20°F higher than the temperature at which the steam 
 vent valve in the storage loop is actuated. If, for example, the relief 
 valve at the top of the storage tank opens at 210°F, so that hot water 
 and steam are discharged, the glycol solution should not boil at 230°F. 
 Maintenance of a 50-percent mixture will prevent boiling as long as the 
 liquid is circulated, even if not pressurized. A pressure of 15 psi on 
 the glycol solution, commonly provided, further protects it from boiling 
 and loss through the safety vent on the collector loop. If an organic 
 liquid such as silicone oil or Dowtherm J ^ is used as the collector 
 fluid, there is no risk of boiling in the collector even in an unpres- 
 surized collection circuit. The temperature in the storage tank must be 
 limited as in the case above. 
 
9-17 
 
 Another option for high-temperature protection is available if an 
 organic liquid or air is used as the heat collection medium. To prevent 
 the storage tank from reaching a temperature higher than desired, a 
 limiting thermostat in that tank can be used simply to discontinue 
 circulation of the heat transfer fluid (organic liquid or air) through 
 the collector and heat exchanger. No additional heat is therefore 
 supplied to the hot water, and the intercepted solar energy is dissi- 
 pated in the form of collector heat loss. The collector temperature 
 rises substantially, frequently above 300°F, but with proper design, 
 there should be no damage. With a reliable limit switch in the storage 
 tank, there can be no dangerous pressure developing anywhere in the 
 system. In addition, there is no loss of water (in the form of steam) 
 even when there is no use of hot water for long periods. 
 
 If a hot water/cold water mixing valve downstream from the 
 auxiliary heater is not provided, a temperature limit control in the 
 solar storage tank can be set at the maximum desired temperature of 
 service hot water. Water cannot then be delivered at a temperature 
 higher than the set point in the solar storage tank or the set point in 
 the auxiliary heater, whichever is higher. Less solar storage capabil- 
 ity would be involved in this design because the solar storage tank is 
 prevented from achieving higher temperatures, even when solar energy is 
 available. 
 
 In a drain-down type of solar water heater operating at line 
 pressure, with potable water circulating through the collector, the air 
 bleed valve at the top of the collector may be able to vent sufficient 
 steam to avoid overheating service water when usage is small. A tem- 
 perature-actuated relief valve, set at a temperature or 210°F of less, 
 
9-18 
 
 should also be provided in the top of the solar preheat tank to allow 
 additional discharge of steam and hot water, if necessary. 
 
 LOCATION OF COLLECTORS 
 
 If the slope and orientation of a roof are suitable, the most 
 economical location for a solar collector in a residential water heating 
 system is on the south-facing portion of the roof. The cost of a struc- 
 ture to support the collector is thereby eliminated, and pipe or duct 
 connections to the conventional hot water system are usually convenient. 
 In new dwellings, most installations can be expected on the house roof. 
 Even in retrofitting existing dwellings with solar water heaters, a 
 suitable roof location can usually be provided. 
 
 If the mounting of collectors on the roof is impractical, for any 
 of several reasons, a separate structure adjacent to the house may be 
 used. A sloping platform supported on a suitable foundation can be the 
 base for the collector. Pumps, storage tank, and heat exchanger, if 
 used, can be located inside the dwelling. Effective insulation on ducts 
 and piping must be provided, however, so that cold-weather operation 
 will not be handicapped by excessive heat losses. In cold climates, 
 collectors in which water is directly heated must be located so that 
 drainage of the collector and exterior piping can be dependably and 
 effectively accomplished. 
 
 ORIENTATION AND TILT OF COLLECTORS 
 
 When roof orientation and slope are not ideally suited for 
 collector mounting, i.e., roof does not face due south and is not tilted 
 
9-19 
 
 at the latitude angle, roof mounting may still be satisfactory. While 
 collectors should be oriented to face due south whenever possible, 
 variations as much as 15 degrees east or west of due south will have 
 only slight effect on system performance. If the collectors are subject 
 to shading in the late afternoon (say after 2:30 pm), orienting the 
 collectors 15 degrees to the east will be beneficial to total heat 
 collection during the day. Similarly, if morning cloudiness usually 
 prevails because of local climatic conditions, it may be beneficial to 
 face the collectors a few degrees to the west of south. 
 
 For maximum annual heat collection, a south-facing collector should 
 be tilted at about latitude angle. However, variations of 10 degrees 
 greater or less than latitude angle will generally not decrease the 
 amount of heat collected by more than 5 percent. 
 
 PERFORMANCE OF TYPICAL SYSTEMS 
 
 GENERAL REQUIREMENTS 
 
 A typical family of four persons, in the United States, requires 
 about 80 gallons of hot water per day. At a customary supply tempera- 
 ture of about 140°F and a cold water inlet temperature of 60°F, this is 
 about 55,000 Btu per day. 
 
 There is a wide variation in the solar availability from region to 
 region and from season to season in a particular location. There are 
 also the short-term radiation fluctuations due to cloudiness and the 
 day-night cycle. 
 
 Seasonal variations in solar availability result in a 200 to 400 
 percent difference in the solar heat supply to a hot water system. In 
 
9-20 
 
 the winter, for example, an average recovery of 40 percent of 1200 
 Btu/ft 2 of solar energy on a sloping surface would require approximate- 
 ly 100 ft 2 of collector for an average daily requirement of 50,000 Btu. 
 Such a design would provide essentially all of the hot water needs on an 
 average winter day, but would fall short on days of less than average 
 sunshine. By contrast, a 50-percent recovery of an average summer 
 radiant supply of 2000 Btu/ft 2 would involve the need for only 50 ft 2 of 
 
 collector for satisfying the average hot water requirements. 
 
 2 
 It is evident that if 50 ft of collectors were installed, it could 
 
 supply the major part, perhaps nearly all, of the summer hot water 
 requirements, but it could supply less than half the winter needs. If 
 100 ft 2 of collectors were used to meet more of the winter demand, the 
 system would be oversized for summer operation and excess solar heat 
 would have to be wasted. In such circumstances, if an aqueous collec- 
 tion medium were used, boiling of the system would frequently occur and 
 collector or storage venting of steam would have to be provided. 
 
 The more important disadvantage of the oversized collector (for 
 summer operation) is the economic penalty associated with investment 
 which is not fully utilized. Although the cost of a 100 ft 2 collector 
 system would be approximately double that of a 50 ft 2 unit, the annual 
 useful heat delivered would be considerably less than double. The 
 larger system would, of course, deliver about twice as much heat in the 
 winter season, when nearly all of it could be used, but in the other 
 seasons, particularly in summer, heat overflow would occur. The net 
 effect of these factors is a lower economic return per unit of invest- 
 ment for the larger system. Stated another way, more Btu per dollar of 
 investment (hence cheaper solar heat) can be delivered by the smaller 
 system. 
 
9-21 
 
 As a conclusion to the above example, practical design of solar 
 water heaters should be based on desired hot water output in the sunni- 
 est months rather than at some other time of year. If based on average 
 daily radiation in the sunniest months, the unit will be slightly over- 
 sized and a small amount of heat will be wasted on days of maximum solar 
 input. And quite naturally, on partly cloudy days during the season, 
 some auxiliary heat must be provided. In the month of lowest average 
 solar energy delivery, typically one-half to one-third as much solar- 
 heated water can be supplied, or equivalently the same quantity of water 
 is supplied but with a temperature increase above inlet only one-half to 
 one-third as high. Thus, fuel requirements for increasing the tempera- 
 ture of solar-heated water to the desired (thermostatted) level could 
 involve one-half to two-thirds of the total energy needed for hot water 
 heating in a mid-winter month. 
 
 QUANTITATIVE PERFORMANCE 
 
 Although hundreds of thousands of solar water heaters have been 
 used in the United States and abroad, quantitative performance data on 
 systems in practical use have seldom been obtained. In households where 
 no auxiliary heat was used, the solar system probably supplied hot water 
 most of the time, but failed during bad weather. If booster heat was 
 used, hot water was always available, but the relative contributions of 
 solar and auxiliary were not known. 
 
 In a few research laboratories, particularly in Australia, some 
 analytical studies of solar water heater performance, confirmed in part 
 by experimental measurements, have been performed. More recently, 
 analytical studies at the University of Wisconsin have been carried out, 
 
9-22 
 
 and performance data on typical heaters have been obtained at the 
 National Bureau of Standards. Table 9-1, based on an Australian study, 
 shows the performance of a double-glazed, 45 ft 2 solar water heater at 
 several locations in that country where climatic conditions are similar 
 to those in parts of the U.S. Variable solar energy and ambient tem- 
 perature throughout the year result in 1.4 to 2.5 times as much solar 
 heat supply to water in summer as in winter. Climatic differences 
 produced a solar heat percentage ranging from 60 percent to 81 percent 
 of the annual total hot water requirements. Table 9-2 shows monthly 
 performance of the same system in Melbourne, Australia, with average 
 collection efficiency varying between 29 and 40 percent of incident 
 radiation. Variation in inlet, outlet, and ambient temperature in a 
 typical thermosiphon type of solar water heater is shown in Figure 9-5. 
 
 In a simulation study at the University of Wisconsin, hot water 
 usage was programmed for a hypothetical residential user. The results 
 show only slight variation in solar heat utilization at several use 
 schedules and indicate only minor influence of storage temperature 
 stratification on collector efficiency. 
 
 In summary, the normal output of well-designed solar water heating 
 systems can be roughly estimated by assuming approximately 40 percent 
 solar collection efficiency. Average monthly solar radiation multiplied 
 by collector area and 40 percent delivery efficiency can provide a rough 
 measure of daily or monthly Btu delivery. The total Btu requirements 
 for the hot water supply, based on the volume used and the temperature 
 increase set, then serves as the basis for computing the percentage 
 contribution from solar and the portion required to be supplied by fuel 
 or electricity. 
 
9-23 
 
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9-24 
 
 Table 9-2 
 Solar Water Heater Performance in Melbourne, Australia 
 
 Month 
 
 Mean 
 Insolation 
 on Absorber 
 
 Mean Daily 
 Supplemen- 
 tary Energy 
 
 Mean Daily 
 Solar Energy 
 Contribution 
 
 
 
 System 
 Efficiency 
 
 Btu/ft z -day 
 
 kWh 
 
 Percent 
 
 kWh 
 
 Percent 
 
 January 
 
 1630 
 
 2.9 
 
 75 
 
 8.9 
 
 40 
 
 February 
 
 2220 
 
 0.5 
 
 95 
 
 9.5 
 
 32 
 
 March 
 
 1690 
 
 2.6 
 
 74 
 
 7.4 
 
 33 
 
 April 
 
 1240 
 
 5.2 
 
 52 
 
 5.6 
 
 34 
 
 May 
 
 1290 
 
 6.2 
 
 47 
 
 5.5 
 
 32 
 
 June 
 
 1220 
 
 7.7 
 
 39 
 
 4.9 
 
 30 
 
 July 
 
 1290 
 
 8.1 
 
 38 
 
 5.0 
 
 29 
 
 August 
 
 1530 
 
 6.1 
 
 50 
 
 6.1 
 
 30 
 
 September 
 
 1600 
 
 4.9 
 
 59 
 
 7.1 
 
 33 
 
 October 
 
 1860 
 
 3.9 
 
 67 
 
 7.9 
 
 32 
 
 November 
 
 1880 
 
 3.7 
 
 68 
 
 7.9 
 
 32 
 
 December 
 
 1790 
 
 3.5 
 
 72 
 
 9.0 
 
 38 
 
 Year 
 
 1610 
 
 4.6 
 
 61 
 
 7.2 
 
 35 
 
9-25 
 
 MELBOURNE 21 "4-55 
 BRIGHT SUNSHINE 
 
 140 
 
 120 
 
 ABSORBER 45 sq ft. 
 TANK 70 IMP gal. 
 
 UJ 
 
 § 100 
 
 \- 
 < 
 
 K 80 
 
 UJ 
 
 60 
 
 40 
 
 
 ABSORBEI 
 
 * OUTLEJ/^ 
 
 
 
 
 
 
 
 
 7 /k&$ 
 
 ORBER 
 
 INLET 
 
 
 
 AT 
 
 max/' 
 
 
 
 
 
 25.4° F 
 
 
 Ambient 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 Figure 9-5. 
 
 10 II 12 13 
 
 TIME OF DAY (hours) 
 
 14 
 
 15 
 
 16 
 
 Absorber and Tank Temperatures for Thermosiphon Flow 
 During a Typical Day 
 
 SIZING THE COLLECTORS 
 
 The curves shown in Figure 9-6 may be used to estimate the solar 
 collector size required for hot water service in residential buildings 
 having typical hot water systems. The system is assumed to be a pumped 
 liquid type, with a liquid- to-liquid heat exchanger, delivering hot 
 water to scheduled residential uses from 6:00 a.m. until midnight. A 
 collector, of good quality (but not with the highest efficiency avail- 
 able), is mounted at a tilt angle equal to the latitude; water is heated 
 by collector and auxiliary from 50°F to 140°F. The shaded band repre- 
 sents results of computer calculations for eleven different locations in 
 the United States. The cities included in the study are Boulder, 
 Colorado; Albuquerque, New Mexico; Madison, Wisconsin; Boston, 
 Massachusetts; Oak Ridge, Tennessee; Albany, New York; Manhattan, 
 
9-26 
 
 Q 
 LU 
 
 a. 0.8 
 
 en 
 
 8 
 
 0.6 
 
 O 
 
 O 
 
 I- 
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 0.4 
 
 < 
 
 z> 
 
 0.2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^MEDIAN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 TILT = i 
 
 .ATITUDE 
 
 
 
 
 
 
 
 S = MEAN JANUARY SOLAR 
 
 RADIATION ON A HORIZONTAL 
 
 
 
 
 
 SURFACE, Btu/(ft 2 )(day) 
 = AVERAGE nAIIY HOT 
 
 
 
 
 
 WATER 
 
 LOAD, Bt 
 
 u/day 
 
 
 
 
 
 
 
 
 
 
 
 
 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 
 
 SA/L 
 
 Figure 9-6. Fraction of Annual Load Supplied by Solar as a Function 
 of January Conditions for Hot Water Heaters 
 
 Kansas; Gainesville, Florida; Santa Maria, California; St. Cloud, 
 Minnesota; and Washington, D.C. 
 
 The hot water loads used in the computations range from 50 gallons 
 per day (gpd) to 2000 gpd. The sizing curves are approximate and should 
 not be expected to yield results closer than 10 percent of actual value. 
 
 The vertical axis shows the fraction of the annual water heating 
 load supplied by solar. The horizontal axis shows values of the para- 
 meter, Sj A/L, which involves the average daily January radiation on a 
 horizontal surface, Sjj the required collector area, A, to supply a 
 certain percentage of the daily hot water load, L. The January average 
 daily total radiation at locations in the United States can be estimated 
 from the radiation map in Figure 9-7. Values on the map are given in 
 Btu/(ft 2 *day). The curves are not applicable for values of solar 
 fraction, f, greater than 0.9. 
 
9-28 
 
 It should be remembered that the service hot water load will be 
 nearly constant throughout the year while the solar energy collected 
 will vary from season to season. A system sized for January, with 
 collectors tilted at the latitude angle, will deliver high temperature 
 water and may even cause boiling in the summer. A system sized to meet 
 the load in July will not provide all of the load in the winter months. 
 Tilting of the collector partially overcomes the effect of month-to- 
 month differences in radiation and temperature. 
 
 SIZING EXAMPLES 
 Example 9-1 
 
 Determine the approximate size of collector needed to provide hot 
 water for a family of four in a residential building in Kansas City, 
 Missouri. 
 
 SOLUTION: The average daily service hot water load in January is: 
 L=80 gallons/day x 8.34 pounds/gallon 
 
 x 1 Btu/(lb)(°F) x (140°F-50°F) = 60,048 Btu/day 
 The desired service water temperature is 140°F and the temperature of 
 the cold water from the main is 50°F. The monthly average daily solar 
 radiation, S,, available in January, from Figure 9-7, is about 680 
 Btu/(ft 2 «day). For a water system to provide 60 percent of the annual 
 load, from Figure 9-6, S, A/L is about 0.8. Therefore: 
 
 A = 0.8 x L/Sj = (0.8 x 60048)7680 = 70.6 ft 2 . 
 
 If 3-by-8-foot collector modules are available, 2.9 units would be 
 required. Three collector units should therefore be used. 
 
9-29 
 
 Example 9-2 
 
 Determine the size of collector needed to provide hot water for a 
 family of four in Albuquerque, New Mexico. 
 
 SOLUTION: The monthly load will be approximately the same as in 
 Example 9-1: 
 L=60,048 Btu/day 
 From Figure 9-7, S, = 1115 Btu/(ft 2 *day). For a system to provide 60 
 percent of the annual load, Figure 9-6 shows that S,A/L is approximately 
 0.8. The collector area required is: 
 
 A = (0.8 x 60048)71115 = 43.1 ft 2 
 
 Using 3-by-6-foot collector modules, 2.4 units would be required for 
 this system; either two or three modules should be used. If two modules 
 are used, the system would be expected to provide less than 60 percent 
 of the annual load. 
 
 REFERENCES 
 
 Hollander, P., M. 0'Neil and W. Fisher (1978) Installation 
 Guidelines for Solar DHW Systems In One and Two Family Dwellings . 
 Franklin Research Center. 
 
 U. S. Department of Energy (1978) "Solar Heating and Cooling 
 Project Experiences Handbook" (preliminary issue). Prepared 
 jointly by U. S. Department of Energy Project Management Centers, 
 ASHRAE and the University of Alabama, July. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 10 
 
 SOLAR SYSTEMS FOR SPACE HEATING 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
10-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES .... 
 LIST OF TABLES 
 
 OBJECTIVE 
 
 INTRODUCTION 
 
 SYSTEM TYPES 
 
 LIQUID SYSTEMS 
 
 SINGLE-LIQUID (DRAIN-BACK) SYSTEMS 
 
 DUAL-LIQUID COLLECTION SYSTEM . 
 LIQUID SUBSYSTEMS AND COMPONENTS . 
 
 COLLECTORS AND STORAGE . 
 
 COLLECTOR-STORAGE HEAT EXCHANGERS 
 
 SUBSYSTEMS FOR SUPPLY OF SOLAR HEAT TO USE 
 
 AUXILIARY HEAT .... 
 
 AUXILIARY HEAT PUMP . 
 
 SERVICE HOT WATER . 
 
 PUMPS, PIPING AND ACCESSORIES . 
 SYSTEM INTEGRATION AND CONTROL 
 
 SYSTEM CONTROL .... 
 
 PROTECTION AGAINST FREEZING AND BOILING 
 AIR SYSTEMS 
 
 DOUBLE-BLOWER DESIGN 
 
 Storing Solar Heat and Heating Hot Water 
 Daytime Space Heating 
 Space Heating from Storage 
 Summer Water Heating 
 
 • 
 
 10-i ii 
 
 • 
 
 10-i v 
 
 . 
 
 10-1 
 
 • 
 
 10-1 
 
 • 
 
 10-2 
 
 • 
 
 10-3 
 
 • 
 
 10-4 
 
 • 
 
 10-8 
 
 ♦ 
 
 10-11 
 
 • 
 
 10-11 
 
 • 
 
 10-12 
 
 • 
 
 10-14 
 
 • 
 
 10-16 
 
 • 
 
 10-17 
 
 • 
 
 10-22 
 
 • 
 
 10-24 
 
 • 
 
 10-26 
 
 
 10-28 
 
 
 10-33 
 
 
 10-35 
 
 
 10-36 
 
 
 10-36 
 
 
 10-42 
 
 
 10-43 
 
 
 10-44 
 
10-ii 
 
 SINGLE-BLOWER DESIGN .... 
 
 10-45 
 
 STORAGE SYSTEM 
 
 10-45 
 
 AIR FLOW RATES 
 
 10-48 
 
 AUXILIARY HEAT 
 
 10-49 
 
 BLOWERS, DUCTS AND DAMPERS 
 
 10-51 
 
10- iii 
 
 LIST OF FIGURES 
 
 Figure 
 10-1 
 
 10-2 
 
 10-3 
 10-4 
 
 10-10 
 
 10-11 
 10-12 
 10-13 
 10-14 
 10-15 
 10-16 
 
 10-17 
 10-18 
 10-19 
 
 10-20 
 
 Page 
 
 Schematic Diagram of a Single-Liquid (Drain-Back) Space 
 
 Heating and Water Heating System (Gravity Return) . . 10-5 
 
 Schematic Diagram of a Single-Liquid (Drain-Back) Space 
 Heating and Water Heating System (Siphon Return with 
 
 Motorized Air Inlet Valve) 10-5 
 
 Schematic Diagram of Dual -Li quid Space Heating and Hot 
 
 Water System ' 10-10 
 
 Typical Temperature Profiles in a Single-Pass Counterflow 
 
 Heat Exchanger ......... 10-13 
 
 ng with Auxiliary Furnace .... 10-15 
 
 n Heating Mode 10-18 
 
 n Cooling Mode ...... 10-18 
 
 ng with Auxiliary Air- to- Air Heat Pump . . 10-19 
 
 ng System with Auxiliary Heat from Air-to-Water 
 
 10-21 
 
 Solar-Assisted Heat Pump (Liquid-to-Liquid) Heat Pump in 
 
 Series with Solar Storage ...... 10-21 
 
 Collector Loop Fittings and Details, Dual-Liquid System. 10-25 
 
 Typical Controls for Dual-Liquid Solar Heating System . 10-29 
 
 Two-Blower Air-Heating Solar System .... 10-37 
 
 Storing Heat from Collectors ...... 10-39 
 
 Heating Building from Collectors ..... 10-39 
 
 Heating Building from Storage Unit (Also heating from 
 
 auxiliary) 10-40 
 
 Service Hot Water Heating (Summer Operation) . . . 10-40 
 
 Single-Blower System ....... 10-46 
 
 Solar Heating System with Air- to-Air Heat Pump 
 
 Auxiliary 10-50 
 
 General Layout of Typical Air-Heating Solar System . 10-52 
 
 10-5 
 
 Solar Heati 
 
 10-6 
 
 Heat Pump i 
 
 10-7 
 
 Heat Pump i 
 
 10-8 
 
 Solar Heati 
 
 10-9 
 
 Solar Heati 
 
 
 Heat Pump . 
 
10-iy 
 
 LIST OF TABLES 
 
 Table Page 
 
 10-1 Recommended Pipe Diameters for Various Flow Rates . . 10-26 
 
 10-2 Control Truth Table for Dual-Liquid Solar Heating 
 
 System 10-30 
 
 10-3 Control Truth Table for a Two-Blower, Air-Heating Solar 
 
 System Operation ........ 10-38 
 
10-1 
 
 OBJECTIVE 
 
 The objective of this module is to detail the design, operation, 
 and performance of the principal types of solar heating systems. The 
 trainee should be able to: 
 
 1. Determine the heating requirements of buildings and select 
 solar heating systems best suited to those requirements. 
 
 2. Develop schematic and working plans of solar heating systems. 
 
 3. Specify compatible system components. 
 
 4. Determine the proper size of system components. 
 
 5. Provide design guidance and advice to installers of solar 
 heating systems. 
 
 INTRODUCTION 
 
 In Module 2, the general principles of solar heating are presented. 
 Subsequent modules contain design and operating details on solar collec- 
 tors and other system components; solar systems for service hot water 
 are covered in Module 9. The purpose of this module is the integration 
 of the preceding information on components and sub-systems. 
 
 Successful application of solar heating requires careful selection 
 of components, their proper sizing, and their skillful assembly into 
 well -functioning systems. Collectors, heat storage units, pumps and 
 fans, controls, heat exchangers, and auxiliary heaters must be effec- 
 tively integrated. A practical solar system must function automatical- 
 ly, provide the desired comfort level in the building at all times. 
 
10-2 
 
 require little maintenance, and operate reliably over a long period of 
 time. 
 
 After selecting a system type and specific components, the designer 
 must determine the collector area requirements and storage volumes 
 needed for providing the desired portion of the annual heat demands. 
 Air and liquid flow rates, and blower and pump sizes can then be estab- 
 lished. Heat exchangers are selected in accordance with the required 
 heat transfer rates and the exchanger characteristics. The auxiliary 
 furnace is sized by conventional methods to meet the design heating load 
 of the building. 
 
 SYSTEM TYPES 
 
 General descriptions of solar heating systems employing flat-plate 
 liquid and air collectors are presented in Module 2. Although there is 
 a great deal of variety in system design among these two main types, 
 most of the practical installations can be classified into similar 
 groups and sub-groups. 
 
 Liquid collectors are used in drain-back systems, with and without 
 siphon return of water to storage, and in dual-liquid designs with a 
 heat exchanger for transfer of heat from a non-freezing collector liquid 
 to water storage. If heat is distributed in a hydronic system, auxili- 
 ary heat is usually supplied by use of a water boiler, but sometimes a 
 liquid-to-liquid or air-to-liquid heat pump is used. If heat is dis- 
 tributed in warm air, a water-to-air exchanger is used for the solar 
 supply, and a warm-air furnace is usually employed as auxiliary. An 
 air-to-air heat pump may be used instead of the auxiliary furnace. 
 
10-3 
 
 Most practical air solar systems involve some type of air-heating 
 solar collector, a vertical-flow pebble bed for heat storage, and an 
 air-to-water heat exchanger for service hot water supply. Variations in 
 system design are usually limited to the air moving equipment (blowers 
 and dampers) and auxiliary heat supply. A single blower and four 
 motorized dampers are used in an air handler in numerous residential air 
 solar systems, whereas two blowers and two motorized dampers are used in 
 many others. A warm air furnace or air-to-air heat pump nearly always 
 provides auxiliary heat. 
 
 LIQUID SYSTEMS 
 
 There are two main types of liquid solar heating systems in common 
 use: one in which water is the heat collecting fluid, and the other 
 which involves use of two liquids, one for collection and the second for 
 storage. They differ in the principle applied to protect the collectors 
 from freezing during cold sunless periods. There are also several 
 arrangements for distributing heat from storage to the living space. 
 The use of forced warm air from central heat exchangers, and hydronic 
 loops with various types of exchangers in each room, are the most common 
 methods. Additional variations involve the type of auxiliary heater, 
 its energy supply, and its position in the heating system. The way in 
 which service hot water supply is integrated with the solar heating 
 system, and the methods for system control in winter and summer are 
 further design and operating options. 
 
10-4 
 
 SINGLE-LIQUID (DRAIN-BACK) SYSTEMS 
 
 Two designs for solar heat collection and storage involving water 
 as the heat collection and storage medium are shown in Figures 10-1 and 
 10-2. Heat is collected and stored in water, and freezing is avoided by 
 draining the collector when it is not in use (Figure 10-1), or when 
 freezing might occur (Figure 10-2). 
 
 A primary requirement of all types of drain-back liquid systems is 
 the design and positioning of collectors and piping on at least a slight 
 slope. Any incidental upturns or lengthy horizontal piping sections 
 result in incomplete drainage. Freezing can then cause rupture of pipes 
 and collector tubing. 
 
 Probably the most reliable type, shown in Figure 10-1, requires no 
 specific controls for collector drainage. When pump operation is inter- 
 rupted by the proper control signal, water drains from the collector 
 back through the idle pump into the tank, while air rises into the 
 collector from the top of the storage tank through the large (one-to 
 two-inch) pipe between collector outlet and storage. If there are no 
 water traps in the collector and piping, and if the down-flow pipe is of 
 adequate size, this system is virtually fail-safe. But the lack of a 
 water-filled, down-flow pipe requires the pump to deliver water against 
 the full static head between collector top and tank water level, and the 
 nightly exposure of the collector tubing and system piping to humid air 
 increases normal liquid corrosion rates. 
 
 Pumping power can be minimized by use of the siphon return design 
 shown in Figure 10-2. Static head between storage and the top of the 
 collector is recovered in the water-filled, down-flow return line (typi- 
 cally one-half- to three-fourths-inch diameter). An automated air inlet 
 
10-5 
 
 PARTIALLY FILLED 
 RETURN PIPE 
 
 VENT 
 
 A 
 
 DOMESTIC 
 
 HOT 
 
 WATER 
 
 TANK 
 
 TO BUILDING 
 " HOT WATER 
 SYSTEM 
 
 THERMAL 
 STORAGE 
 (WATER 
 TANK) 
 
 PRE- 
 HEAT 
 TANK 
 
 HEAT TO 
 ROOMS 
 
 FROM 
 
 COLD 
 
 WATER 
 
 SUPPLY 
 
 Figure 10-1. Schematic Diagram of a Single-Liquid (Drain-Back) Space 
 Heating and Water Heating System (Gravity Return) 
 
 AUTOMATIC AIR 
 VENT VALVEi 
 
 AUTOMATIC AIR 
 VALVE 
 
 MOTORIZED r- 
 
 DRAIN VALVE tJ-V' 
 (OPTION) 
 
 VENT 
 
 A 
 
 DOMESTIC 
 
 HOT 
 
 WATER 
 
 TANK 
 
 TO BUILDING 
 " HOT WATER 
 SYSTEM 
 
 THERMAL 
 
 STORAGE 
 
 (WATER 
 
 TANK) 
 
 - c o- 
 
 HEAT TO 
 ROOMS 
 
 FROM 
 
 COLD 
 
 WATER 
 
 SUPPLY 
 
 Figure 10-2. 
 
 Schematic Diagram of a Single-Liquid (Drain-Back) Space 
 Heating and Water Heating System (Siphon Return with 
 Motorized Air Inlet Valve) 
 
10-6 
 
 valve ("siphon breaker") at the collector top opens when the collector 
 temperature approaches the freezing point (or if there is a power 
 outage). The open air inlet permits drainage of the collector and 
 piping into the storage tank through the two connecting pipes while the 
 collector fills with air from the atmosphere. When collector tempera- 
 ture again rises, pumping resumes and air is forced out of the collector 
 circuit through the automatic air vent valve, which closes when air is 
 no longer being vented. Although this system requires less pumping 
 power than the non-siphoning type shown in Figure 10-1, dependence on a 
 control sensor and automatic valve, even though opening without power, 
 increases the risk of freeze-damage. 
 
 Three additional design variations in single-liquid (water) systems 
 are used with sufficient frequency to merit description. The first is a 
 modification of the drain-back design shown in Figure 10-2. Instead of 
 using an electrically actuated air inlet valve, a motorized water drain 
 valve on a branch of the return pipe (shown in dotted outline) may be 
 used. When a sensor in the collector shows a temperature near the 
 freezing point, (or if there is a loss of electric power), this valve 
 opens. Because of the pipe opening into the air space in the tank, the 
 weight of water in the return line causes a negative pressure at the top 
 of the collector. This negative pressure causes the automatic air inlet 
 valve to open and the collector to drain. When pumping is again 
 started, both valves close, air is eliminated through the vent near the 
 top of the collector, and water circulation is reestablished. 
 
10-7 
 
 Another procedure for draining the collector is used when a 
 pressurized hydronic system is required. Most conventional hot water 
 heating systems operate at a hydraulic pressure of at least 15 psi. 
 When a single-liquid solar system is incorporated, all components are 
 under pressure. The storage tank is completely water-filled and a small 
 expansion tank (sometimes called a compression tank) is used as in 
 conventional hydronic systems. Freeze protection is provided by use of 
 a motorized valve in the collector-storage circuit which opens to a 
 drain (sewer). The pressure decrease causes the automatic air inlet 
 valve to admit air to the collector while a motorized valve on the line 
 from the tank outlet to the pump and a check valve on the line from the 
 collector to the storage tank both close. Pressure is thus maintained 
 in the storage tank as a small volume of water in the collectors and 
 piping is drained away. Make-up water must be automatically supplied to 
 replace the volume discharged. Start-up of the system involves reversal 
 of the operations, air being purged through the automatic vent. 
 
 A third alternative design involves circulation of water from 
 storage through the collector when freezing would otherwise occur. In 
 areas where freezing is very infrequent, a low- temperature sensor in the 
 collector causes the pump to supply sufficient flow from storage to 
 prevent freezing. The loss of heat which this procedure entails need 
 not be excessive in regions suitable for this design. This is not a 
 fail-safe design because a power outage or pump failure might occur 
 during freezing weather. This risk can be avoided by supply of service 
 water (from pressurized mains) to the collector through another auto- 
 matic valve to the drain. Both valves can be actuated (opened) by 
 low- temperature signal or by loss of power. 
 
10-8 
 
 DUAL-LIQUID COLLECTION SYSTEM 
 
 A widely used solar liquid heating design is shown in Figure 10-3. 
 The system is arranged to collect solar heat in a non-freezing liquid, 
 deliver the heat to water storage via a liquid- to- liquid heat exchanger, 
 and supply heat from storage to the space heating and service hot water 
 equipment. When solar heat cannot meet the demand of either domestic 
 water or space heating, auxiliary heat is supplied from one or both of 
 the conventional units shown. Although a solar domestic hot water 
 heater can be completely separate from a solar space heating system, it 
 is more convenient and economical to combine them. During the warm 
 months of the year the collectors in an integrated system, which would 
 otherwise be unused, can supply practically all of the required domestic 
 water heating. 
 
 The most commonly used liquid in the collector loop is a mixture of 
 water and ethylene glycol (ordinary automobile radiator antifreeze), 
 although propylene glycol and water may also be used. The advisable 
 glycol concentration depends on the minimum temperature expected in the 
 region where used. A 50-50 mixture provides maximum protection to 
 -34°F. A centrifugal pump, usually at the lowest position in the loop, 
 circulates the liquid solution through collectors and heat exchanger, 
 typically at a rate of about 0.02 gallon per minute per square foot of 
 collector. An expansion tank with open vent or pressure relief valve is 
 installed preferably at the highest point in the loop. This tank should 
 have a sight-glass or other liquid level indicator, and it should have a 
 volume equal at least to half the volume in the collector loop. This 
 tank is also a convenient point for charging the system with liquid. 
 
10-9 
 
 In many dual -liquid systems, the collector loop is pressurized to a 
 moderate (15 psi) pressure. The likelihood of boiling is thereby re- 
 duced, positive pressure at pump inlet is assured, and fluid loss is 
 minimized. Instead of a vented expansion tank near the top of the 
 collector, a pressurized expansion tank of a few gallons capacity (such 
 as in conventional hydronic heating systems) is usually mounted in the 
 line near the circulating pump. This tank contains a flexible bladder 
 which separates the liquid from pressurized air in the upper part of the 
 tank. An automatic air vent and a pressure relief (safety) valve are 
 also provided. After filling the collector loop through a suitable pipe 
 connection on the suction side of the pump, compressed air is supplied 
 to the expansion tank (usually by a hand pump) up to the desired 
 pressure. 
 
 In a more limited number of systems, some type of oil is used as 
 the heat collection fluid. Silicones, diphenyl, Dowtherm w , 
 Therminol ^ are examples. In addition to providing complete protection 
 from freezing, these liquids will not boil at temperatures attainable in 
 flat-plate collectors and they are non-corrosive. They are more expen- 
 sive than antifreeze solutions, however, and their heat transfer proper- 
 ties are not as favorable. 
 
 A heat exchanger and water heat storage are always used in systems 
 with non-freezing liquids because of the excessive cost of filling a 
 thermal storage tank with such expensive liquids. The heat exchanger is 
 usually a commercial tube-and-shell type through which water is circu- 
 lated from storage by a centrifugal pump at a volumetric rate one to two 
 times that in the collection loop. The pump is supplied from the bottom 
 of the tank, and after being heated in the exchanger, the water is 
 
10-10 
 
 Lc O^ 
 
 EXPANSION TANK AND 
 PRESSURE 
 RELIEF 
 
 VALVE 
 
 NON-FREEZING 
 LIQUID 
 
 THERMAL 
 
 STORAGE 
 
 (WATER 
 
 TANK) 
 
 DOMESTIC 
 
 HOT 
 
 WATER 
 
 TANK 
 
 TO BUILDING 
 ' HOT WATER 
 SYSTEM 
 
 PRE- 
 HEAT 
 TANK 
 
 FROM 
 
 COLD 
 
 WATER 
 
 SUPPLY 
 
 HEAT TO 
 ROOMS 
 
 Figure 10-3. Schematic Diagram of Dual -Liquid Space Heating and 
 Hot Water System 
 
 returned to the tank near its top. In some systems, storage is heated 
 more directly by circulating the collector fluid through long coils of 
 tubing submerged in the tank. The water pump is thus eliminated, but 
 pressure loss through the coil is higher than through an external heat 
 exchanger, so power requirements in the collector pump are higher and 
 access to the heat exchange surface and its connections is more 
 difficult. 
 
10-11 
 
 LIQUID SUBSYSTEMS AND COMPONENTS 
 
 The individual components of heating systems in which solar heat is 
 collected and stored in liquids are discussed in Module 7. The discus- 
 sion is continued here, but with emphasis on equipment characteristics 
 which affect, and are affected by, system design and performance. 
 
 COLLECTORS AND STORAGE 
 
 The efficiency of collectors in a solar system is influenced by all 
 other components in the system. So that heat loss from the collector 
 can be minimized, it should be supplied with liquid at the lowest avail- 
 able temperature. With proper design and operation, moderate tempera- 
 ture stratification in a water tank can be obtained; warm, lower density 
 liquid lies near the surface, and colder, heavier liquid near the bottom 
 of the tank. Water from the bottom of the storage tank should therefore 
 be circulated directly or indirectly to the collector. If a heat ex- 
 changer is used, as in Figure 10-3, water is circulated from the bottom 
 of the storage tank, through the heat exchanger, back to the top of the 
 tank. In a drain-down design, as in Figures 10-1 and 10-2, water from 
 the bottom of storage is pumped through the collector. Heated water 
 returns to the top of the tank. Typical rise in temperature of water 
 flowing through the collector or through the heat exchanger is 10°F to 
 20°F during sunny mid-day periods. 
 
 In addition to dependence on heat input from the collector, storage 
 temperatures are affected by the rate of heat delivery to the load, 
 dependent, in turn, on the characteristics of the load heat exchangers. 
 
10-12 
 
 Selection and sizing of heat exchangers are therefore important in 
 system design. While oversizing the heat exchangers has minor influence 
 on system performance, undersizing can reduce the quantity and effici- 
 ency of solar heat collection. 
 
 COLLECTOR-STORAGE HEAT EXCHANGERS 
 
 If a non-freezing liquid is circulated through the collector, a 
 heat exchanger must be provided to transfer heat from the collector 
 fluid to water storage. Because of temperature limitations in flat- 
 plate solar collectors, the temperature difference across heat ex- 
 changers should be small. This temperature difference is minimized in 
 two ways: (1) by providing a large surface area for heat transfer in the 
 exchanger and (2) by maintaining high flow rates through the exchanger. 
 Tube-in-shel 1 heat exchangers are simple, efficient, and readily avail- 
 able. They usually consist of multiple tubes enclosed within an outer 
 shell. One fluid passes through the tubes while the other fluid passes 
 outside the tubes. Large heat transfer surface can be provided in 
 compact arrangements. 
 
 The performance characteristics of a single-pass, counterflow heat 
 exchanger are illustrated in Figure 10-4. A single tube is shown for 
 simplicity but multiple tubes are usually involved. It can be seen from 
 the temperature profiles that the temperature difference between fluids 
 is reasonably small along the length of the heat exchanger. 
 
 The manufacturer's guide should be followed in selecting a heat 
 exchanger. If appropriate information is lacking, the manufacturer's 
 representative should be consulted for assistance and/or advice. Data 
 necessary for heat exchanger sizing and fluid flow rate determination 
 
10-13 
 
 are the temperatures of the two fluids entering the exchanger and the 
 Btu-per-hour heat transfer rate desired. 
 
 At high fluid velocities and flow rates, good heat exchanger 
 effectiveness can be achieved, but at the expense of pumping power. A 
 practical compromise in these two opposing objectives is sought in 
 system design. 
 
 HOT COLLECTOR FLUID 
 
 COOL 
 STORAGE 
 FLUID ~* 
 
 Fiqure 10-4. Typical Temperature Profiles in a Single-Pass 
 Counterflow Heat Exchanger 
 
10-14 
 
 SUBSYSTEMS FOR SUPPLY OF SOLAR HEAT TO USE 
 
 Heat from a solar hot water storage tank may be distributed to 
 living spaces either in hot water or in warm air. For water distribu- 
 tion, methods and equipment commonly used in conventional hydronic 
 heating systems are employed. When activated by a room thermostat, a 
 pump supplies solar-heated water from the top of the storage tank to one 
 of several types of heating coils in each heated space in the building 
 and returns the water to the lower part of the tank. Figures 10-1, 10-2 
 and 10-3 illustrate this application, the schematic heating coil in the 
 building representing any type of liquid- to-air exchanger. 
 
 Conventional baseboard strip heaters widely used with fuel-fired 
 and electric hot water boilers* normally operate at water supply temper- 
 atures of 160°F to 180°F. The limited heat transfer surfaces formed by 
 a single water tube through closely spaced metal fins necessitate the 
 use of these comparatively high temperatures. Temperatures in storage 
 tanks supplied from typical flat-plate collectors seldom exceed 150°F in 
 winter, so either additional baseboard heating surface is needed in 
 solar systems or solar heat usage in cold weather must be heavily sup- 
 plemented. A doubling of the usual baseboard heat transfer surface 
 permits reduction in design (maximum) temperature to 130°F to 140°F and 
 a substantial increase in solar heat usage at these temperatures where 
 collection efficiency is materially improved. 
 
 Solar-heated water can be distributed in conventional hydronic 
 systems involving multiple fan-coil exchangers, pipe coils imbedded in 
 floors and ceilings, and cast iron hot water "radiators". Temperatures 
 
 * So-called boilers for residential space heating may in fact produce 
 steam, but more commonly they serve as water heaters for hydronic 
 (liquid water) heat distribution systems. 
 
10-15 
 
 and flow rates are compatible with the requirements of most fuel- 
 operated systems. 
 
 In ducted warm air heating systems, hot water is supplied from 
 solar storage to a finned coil heat exchanger in the main air duct and 
 returned by a centrifugal pump to the tank (Figure 10-5). Air is circu- 
 lated through the exchanger by a conventional fan or blower, and is 
 usually heated from about 70°F to a temperature within 10°F to 15°F of 
 the hot water supplied from storage. As explained below, a conventional 
 warm air furnace is usually employed in this system so that the tempera- 
 ture of air supplied from the solar coil can be increased when needed. 
 
 FROM 
 COLLECTOR 
 
 OR HEAT iVENT 
 EXCHANGER 
 
 TO 
 
 COLLECTOR 
 
 OR HEAT 
 
 EXCHANGER 
 
 THERMAL 
 STORAGE 
 
 ( WATER 
 TANK) 
 
 COLD 
 
 AIR 
 
 RETURN 
 
 FINNED 
 
 WARM 
 
 AIR 
 SUPPLY 
 
 ft 
 
 AUXILIARY 
 WARM AIR 
 
 EXCHANGER FURNACE 
 AND 
 BLOWER 
 
 Figure 10-5. Solar Heating with Auxiliary Furnace 
 
10-16 
 
 AUXILIARY HEAT 
 
 There are several methods for supplying auxiliary heat in a liquid 
 solar system for space heating. In virtually all practical solar heat- 
 ing designs, auxiliary heat is supplied to the fluid stream in which 
 heat is distributed to the various zones in the building. With hydronic 
 distribution (baseboard strips, individual fan coils, imbedded tubing, 
 cast radiators), a fuel-fired or electrically heated hot water boiler is 
 used as in Figures 10-1, 10-2, and 10-3. If a central heat exchanger 
 and ducted warm air are employed, as in Figure 10-5, auxiliary heat is 
 most economically and practically supplied in a furnace or electric 
 heater through which the solar-heated air passes to the rooms. 
 
 In hydronic distribution systems, the hot water boiler is best used 
 in parallel with the solar supply from storage rather than in series 
 with it, so that only one source is used at a time. The series design 
 is seldom used because some of the heat supplied to the water passing 
 through a thermostatted auxiliary boiler would flow on through the load 
 exchangers and be accumulated in the solar heat storage tank. The 
 resulting temperature rise in solar storage would reduce collector 
 efficiency and capacity for solar heat storage. Figures 10-1, 10-2, and 
 10-3 show a single pump and automatic valve for hot water supply either 
 from solar storage or from the auxiliary boiler. Suitable control 
 equipment, explained below, regulates the system so that when the demand 
 cannot be met by solar, auxiliary is used. 
 
 If heat is distributed in warm air heated by exchange with 
 solar-heated water, auxiliary heat is usually supplied to the air in a 
 warm-air furnace located downstream from the solar coil as shown in 
 Figure 10-5. There is no possibility that auxiliary heat can affect 
 
10-17 
 
 solar storage in this design, so the series arrangement is advantageous. 
 Use of stored solar heat even at comparatively low temperature (e.g. 
 80°F to 90°F) is thus made possible by further heating of the tepid air 
 to useful temperatures of 130°F to 160°F. 
 
 AUXILIARY HEAT PUMP 
 
 A special type of auxiliary heater for solar systems is an 
 electrically driven heat pump. A heat pump uses electrical energy to 
 extract heat from a low temperature source and deliver the heat at a 
 higher temperature. By this process, heat delivery at useful tempera- 
 ture may be several times the electric energy input. In practice, 
 annual performance factors (heat delivery per unit electric input) of 
 about 2 are commonly achieved, although in colder climates, a somewhat 
 lower factor generally prevails. The process is identical to a refrig- 
 eration cycle, and the same machine that is used as a heat pump in 
 winter may be used as a refrigeration air-conditioner in summer. 
 Switching between heating and cooling is usually done inside the machine 
 by reversing the evaporator and condenser units, as shown in Figures 
 10-6 and 10-7. 
 
 One method of heat pump use in a warm air distribution system, il- 
 lustrated in Figure 10-8, involves the condenser coil (heating coil) of 
 an air-to-air heat pump in the air circuit downstream from the solar- to- 
 air exchanger. Because of pressure limitations in the heat pump, the 
 flow of water through the solar exchanger is usually interrupted when 
 auxiliary heat is required so that air is not supplied to the heat pump 
 evaporator coil at excessive temperatures (e.g., not above 100°F). As 
 in conventional heat pump installations, electric resistance coils are 
 provided for use during severe cold weather. 
 
10-18 
 
 r 
 
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 -0- 
 
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 Exchanger 
 
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 Condenser 
 (Heat to 
 Load) 
 
 ■©■ 
 
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 Expansion 
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 i-O- J — & 
 
 Heat 
 Exchanger 
 
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 ^— I Evaporator 
 ( Heat from Aux, 
 Solar, Amb. Air, 
 ^ or Ground H 2 0) 
 
 --T Compressor 
 
 -<D- Closed Valve 
 -0- Open Valve 
 
 Figure 10-6. Heat Pump in Heating Mode 
 
 -c 
 
 V. 
 
 -©- 
 
 Heat 
 Exchanger 
 
 ■e 
 
 Evaporator 
 (Space Cooling) 
 
 ■e- 
 
 Receiver 
 
 Expansion 
 Valve 
 
 -CD-i 
 
 Condenser 
 
 (Heat Rejection 
 
 to Ambient) 
 
 O Closed Valve 
 Open Valve 
 
 Figure 10-7. Heat Pump in Cooling Mode 
 
10-19 
 
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10-20 
 
 Another design (Figure 10-9) involves an air-to-water heat pump 
 rather than a hot water boiler for auxiliary heat supply. Replacement 
 of the boiler in Figure 10-1, 10-2, or 10-3 with the heat pump condenser 
 coil and back-up electric resistance heater permits a reduction in 
 energy consumption by virtue of a COP greater than unity. Heat dis- 
 tribution may be in water or air as with fuel auxiliary. 
 
 A third method for combining a heat pump with a solar heat supply 
 is shown in Figure 10-10. In this application the water-to-water type 
 is often referred to as a solar-assisted heat pump. The concept of a 
 solar-assisted heat pump is the supply of stored solar heat to the 
 evaporator of the machine at a temperature higher than outdoor ambient 
 air. Higher COP and lower collector supply temperatures (with higher 
 efficiency) could then result. If water in solar storage is not hot 
 enough to meet demands directly, it is used as a source of heat to the 
 heat pump evaporator coil. Heat is then supplied to the building by 
 heating water in the condenser coil, with circulation to the living 
 space or by exchange with air. In multizone distribution systems where 
 individual water- to-air heat pumps in each zone are supplied with low- 
 temperature water, the use of solar preheated water as the heat pump 
 supply may reduce electricity use, provide heated air where and when 
 needed, and minimize heat distribution cost. Because the fluid tempera- 
 ture delivered from the collectors may be as low as 80°F to 100°F, 
 collection efficiency can be higher than that obtained in a solar system 
 supplying heat directly to use at water temperatures of 120°F to 180°F. 
 It might also be possible to use cheaper collectors designed specifical- 
 ly for operation at lower temperatures. When solar storage may approach 
 the freezing point in midwinter, as a result of large withdrawals of 
 
10-21 
 
 VENT 
 A 
 
 FROM 
 COLLECTOR 
 
 OR »» 
 
 HEAT 
 EXCHANGER 
 
 TO 
 COLLECTOR 
 
 OR -* 
 
 HEAT 
 EXCHANGER 
 
 g 
 
 THERMAL 
 STORAGE 
 
 ( WATER TANK) 
 
 OUTDOOR 
 AIR COIL 
 
 THREE-WAY VALVE 
 D 
 
 — tjw 
 
 INDOOR 
 WATER 
 COIL WITH 
 RESISTANCE 
 HEATER 
 
 HEAT PUMP 
 
 -q> 
 
 HEAT TO 
 ROOMS 
 
 Figure 10-9. 
 
 Solar Heating System with Auxiliary Heat from 
 Air-to-Water Heat Pump 
 
 FROM 
 
 COLLECTOR 
 OR HEAT 
 EXCHANGER 
 
 VENT 
 A 
 
 TO COLLECTOR 
 
 OR HEAT «« 
 
 EXCHANGER 
 
 THREE-WAY VALVE 
 
 THERMAL 
 
 STORAGE 
 
 (WATER TANK) 
 
 D 
 
 EVAPORATOR CONDENSER 
 COIL COIL 
 
 HEAT TO 
 ROOMS 
 
 ^ — &o 
 
 ^THREE-WAY 
 
 VALVE 
 
 HEAT PUMP 
 
 Figure 10-10. 
 
 Solar-Assisted Heat Pump (Liquid-to-Liquid) 
 Heat Pump in Series with Solar Storage 
 
10-22 
 
 heat for heat pump supply, electric resistance elements are called upon 
 to meet the demand. 
 
 This series arrangement of collector to storage to heat pump to 
 load is handicapped, however, by excessive draw-down of storage in 
 midwinter so that storage temperature is rarely sufficient for direct 
 heating of the building. Nearly all of the heating demand during the 
 cold months must therefore be met by electric energy either as heat pump 
 supply or as resistance heating. The annual electricity requirement has 
 usually been found greater than that for operating the parallel systems 
 in which ambient air is the heat pump source. 
 
 SERVICE HOT WATER 
 
 Solar heat for service hot water is usually obtained by circulating 
 water from the top of the main storage tank through a double-walled heat 
 exchanger as shown in Figures 10-1 to 10-3. Simultaneously, potable 
 water from the solar pre-heat tank is circulated through the heat ex- 
 changer and back to the top of the pre-heat tank. These pumps operate 
 whenever the temperature in the storage tank is greater than the water 
 temperature in the pre-heat tank by a preset amount. When useful heat 
 cannot be delivered from storage to the pre-heat tank or when the pre- 
 heat tank has reached a limiting high temperature, say 175°F, the pumps 
 do not operate. 
 
 During the heating season, water temperature will frequently be 
 less than 140°F, so dependable delivery of hot service water requires an 
 auxiliary heater. Solar heat is therefore used to pre-heat cold water 
 from the water main before it enters the hot water heater. During the 
 summer, the water temperature in the pre-heat tank will usually be 
 greater than 150°F, so auxiliary heating is only occasionally required. 
 
10-23 
 
 Suppose that average use of service hot water in a household is 75 
 gallons per day. Also assume that the water temperature from the main 
 is about 60°F and that the desired water delivery temperature is 140°F. 
 The daily quantity of heat necessary to raise the temperature of the 
 service water from 60°F to 140°F is therefore about 50,000 Btu. Deliv- 
 ery of 50,000 Btu from 1000 gallons of storage to the service water 
 heating system will cause a drop in storage water temperature of 6°F 
 (assuming no heat is delivered from the collectors to storage in this 
 period). If the storage tank temperature is less than 140°F, useful 
 heat delivery to the service water heating system will be less than that 
 indicated above, and the auxiliary heating unit will be required to 
 maintain the desired water temperature in the hot water heater. In the 
 summer months, there is usually enough heat in the solar heated tank to 
 supply all of the service hot water requirements. 
 
 To comply with most plumbing codes, the heat exchanger between main 
 solar storage and the potable water supply must be double-walled. By 
 this design, a perforation in a tube wall will not permit mixing of the 
 two fluids, regardless of pressure difference. The resulting water leak 
 will, instead, run out of the exchanger and prevent cross-contamination. 
 Several designs for accomplishing this purpose are available. 
 
 Another option for auxiliary use is an electric resistance heating 
 element near the top of the solar pre-heat tank rather than a separate 
 conventional water heater. Solar heated water is brought into the tank 
 at a level below the electric heating element so that temperature strat- 
 ification can be maintained. This design accomplishes the same purpose 
 at somewhat lower cost than incurred with a separate electric water 
 heater as auxiliary. 
 
10-24 
 
 PUMPS, PIPING AND ACCESSORIES 
 
 Centrifugal pumps are normally used for circulating liquids in the 
 several loops of a solar heating system. For the design flow rates and 
 system head losses, pumps may be selected from stock items in catalogs, 
 or made to specifications by pump manufacturers. Centrifugal pumps 
 should be located so that priming is not necessary, five feet of head on 
 the suction side normally being sufficient. 
 
 A check valve, strainer or filter, and an expansion tank should be 
 installed in the collector loop. Figure 10-11 shows a portion of a 
 vented, dual-liquid system. The check valve prevents thermosiphon flow 
 and heat loss from the collector when the pump is not running and the 
 collector is colder than the storage tank. A filter or strainer pre- 
 vents entry into the collector of any particulate matter in the piping 
 and collector fluid. 
 
 An expansion tank must be provided in the collector loop to 
 accommodate the increase in volume of the collector fluid as it is 
 heated. The volume of the tank should be at least half the volume of 
 the fluid in the collectors and headers. If positioned near the top of 
 the collector array, it may be vented to the atmosphere or provided with 
 a pressure relief valve to prevent dangerous pressure increase in the 
 collector loop if boiling occurs. Alternatively, an expansion tank 
 containing a flexible diaphragm or bladder may be used anywhere in the 
 collector loop, and a pressurized system may then be operated. 
 
 In single-liquid, drain-back systems, pump and piping 
 considerations have been outlined in an earlier section of this module. 
 
 The amount of electric energy used for circulating liquids through 
 collectors, heat exchangers, storage tanks, and distribution systems 
 
10-25 
 
 CONNECTIONS TO ALLOW 
 FOR THERMAL 
 EXPANSION AND CONTRACTI 
 
 UPPER HEADER 
 
 SOLAR 
 COLLECTORS 
 
 \r 
 
 AVENT 
 
 EXPANSION 
 TANK 
 
 CONNECTIONS 
 TO ALLOW FOR 
 THERMAL EXPANSION 
 AND CONTRACTION 
 
 SOLAR 
 COLLECTORS 
 
 TOR FILLING 
 
 'TO HEAT EXCHANGER 
 
 LTER 
 
 ^CHECK VALVE 
 
 <J 
 
 * 
 
 J -MANUAL VALVES 
 
 (NORMALLY CLOSED) n 
 
 FROM COLLECTOR 
 PUMP 
 
 Figure 10-11. Collector Loop Fittings and Details, Dual-Liquid System 
 
10-26 
 
 depends heavily on system design and collector type. In systems 
 designed to require minimum pumping power, electricity use can be as low 
 as five percent of solar heat delivery, but ten to fifteen percent is 
 commonly employed. 
 
 Piping may consist of either copper or high temperature (CPVC) 
 plastic pipe, and all pipes should be insulated with appropriate 
 material such as fiberglass pipe insulation at least one inch in thick- 
 ness. Care should be taken to allow thermal expansion of the pipes, and 
 long pipe lengths should provide more freedom for expansion than short 
 lengths. Pipes should be sized so that water velocity does not exceed 
 five feet per second. In Table 10-1, recommended pipe diameters are 
 indicated for various flow rates. 
 
 Table 10-1 
 Recommended Pipe Diameters for Various Flow Rates 
 
 Select 
 Pipe Size 
 
 Gallons per 
 Minute 
 
 Velocity 
 FPS 
 
 Pressure Drop per 
 100 feet, PSI 
 
 3/8 
 
 2 
 
 3.36 
 
 6.58 
 
 1/2 
 
 4 
 
 4.22 
 
 7.42 
 
 3/4 
 
 8 
 
 4.81 
 
 6.60 
 
 1 
 
 15 
 
 5.57 
 
 6.36 
 
 1-1/4 
 
 25 
 
 5.37 
 
 4.22 
 
 SYSTEM INTEGRATION AND CONTROL 
 
 Assembly of the several solar components into a well-functioning 
 system, and control, are requirements of exceptional importance. Col- 
 lector, storage, heat exchangers, auxiliary heater, pumps and piping, 
 
10-27 
 
 and control system must be mutually compatible in size, function, 
 materials, reliability, and cost. Although a great variety of compo- 
 nents may be assembled into functional systems, experience shows that 
 certain equipment combinations and control methods provide superior 
 performance. 
 
 Previous subsections of this module in which solar collectors and 
 heat storage were discussed show the principal methods for combining 
 these two major components. Design studies and practical experience 
 show that the storage capacity for the most economical heat supply is 
 sufficient for accumulating a full day's solar collector output, and 
 that the cost of larger storage is greater than the value of the small 
 added increment of solar heating capability. Approximately 1.5 to 2.5 
 gal/ft 2 of collector are therefore usually employed, with 1.5a practi- 
 cal average. Even though the storage tank is usually inside the build- 
 ing, it should be well insulated with fiberglass or plastic foam having 
 an insulating value of at least R-10. 
 
 The relative merits of drain-back and dual-liquid collector/storage 
 systems have been explained. Pumps, valves and piping in either system 
 should be sized in accordance with flow requirements, manufacturers' 
 specifications, and accepted practice. All components should be placed 
 in locations where there is convenient access for maintenance. Suitably 
 oriented roofs usually provide the most economical base for supporting 
 the collector, and the mass of the storage unit nearly always dictates 
 its support on a basement floor or a ground floor. The tank can be 
 installed in the ground near the building, but limited access, moisture 
 problems, and heat loss in buried installations make storage in the 
 heated space a definite advantage. The other system components can be 
 advantageously located near the tank. 
 
10-28 
 
 Selection of collector size (which also results in storage size 
 determination) is a matter of balancing numerous design factors. Cli- 
 mate (annual heating degree-days), the heat loss rate and hot water 
 demands of the building, solar energy availability, the fraction of 
 total heat requirements to be met by solar, the solar collector charac- 
 teristics, and the control and configuration of the complete solar 
 system, all affect the required collector/storage size. Several proce- 
 dures of various complexity and accuracy for collector sizing are ex- 
 plained in Modules 6 and 11. 
 
 SYSTEM CONTROL 
 
 The fundamental operating modes of solar heating systems are 
 collecting and storing solar heat and delivering heat from storage to 
 load. The auxiliary unit must be controlled to provide heating when 
 there is insufficient solar heat in storage to meet the demand. A 
 typical control system is shown schematically in Figure 10-12, and the 
 functioning of its principal elements is shown in Table 10-2. 
 
 A practical method for controlling the solar collection process 
 involves use of temperature sensors which actuate the collector pump 
 (and also the storage circulation pump if a heat exchanger is used) 
 whenever the temperature of the liquid leaving the collector exceeds the 
 lowest temperature in storage by a preset amount, say 15°F* (first line 
 in Table 10-2). Sensor SI, placed in the flow passage as close as pos- 
 sible to the collector exit, and sensor S2, near the bottom of the stor- 
 age tank where storage water is likely to be coldest, provide the signal 
 which is compared electronically with a signal produced by a preset 
 
 * This different must include a 5° to 10° difference in the heat 
 exchanger, if a dual-liquid system is used. 
 
10-29 
 
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10-31 
 
 temperature difference to start and stop circulation pumps No. 1 and No. 
 2. The temperature difference which shuts off the pumps, say 3°F, is 
 less than the temperature difference which turns them on, so that exces- 
 sive on-and-off cycling at the beginning and end of the day is avoided. 
 
 When liquid first circulates through the collectors in the morning, 
 the temperature rise from inlet to exit is only a few degrees (typically 
 3° to 5°F) because of low solar intensity. As solar intensity in- 
 creases, the temperature rise in the circulating liquid increases to 
 15°F to 20°F by mid-day. During the circulation period, the storage 
 water temperature increases gradually until late afternoon. When the 
 solar intensity decreases to a level such that the collector can no 
 longer provide useful heat to storage, circulation stops. 
 
 The best control strategy for heat delivery to the building is by 
 use of a room thermostat, S3, with dual set points. When heat is re- 
 quired, the first stage contact of the thermostat is completed and water 
 from the storage tank is circulated to the load heat exchanger (third 
 line in table). If the storage water is warm enough, room temperature 
 rises, and circulation stops. 
 
 If the storage water is not warm enough to deliver heat at a rate 
 greater than the rate of heat loss from the building, room temperature 
 continues to fall until the second thermostat contact is made (fourth 
 line in table). The auxiliary water boiler or auxiliary warm air fur- 
 nace is then activated to restore the rooms to the comfort temperature 
 set at the thermostat. If an auxiliary water boiler is used, an auto- 
 matic valve is also positioned to terminate water flow from the storage 
 tank and to supply hot water from the auxiliary unit to the load heat 
 exchanger. When room temperature rises to the preset temperature, the 
 
10-32 
 
 entire heat supply system then shuts off. In most designs, a low 
 temperature sensor in storage, S2, can override the above sequence so 
 that if storage is colder than a preset temperature, say 90°, the first 
 contact in the room thermostat causes immediate use of auxiliary rather 
 than the inadequate solar storage (last line in table). 
 
 The control of a warm air furnace auxiliary is also by a second 
 (lower temperature) contact in the room thermostat. When it is actu- 
 ated, energy (fuel or electricity) is supplied to the furnace, all other 
 operations continuing. Thus, the solar supply via the load-exchanger is 
 augmented by auxiliary heat. If, however, storage is below a preset 
 temperature, its usefulness is not usually enough to justify operation 
 of the load pump and sensor S2 turns it off. And as in the system 
 involving a hot water boiler, the furnace is switched on immediately by 
 the first contact in the room thermostat if storage is colder than the 
 low- limit setting. 
 
 Solar pre-heating of domestic water is best regulated by a tempera- 
 ture difference comparator similar to the control of the collection 
 loop. The temperature sensor S2 at the bottom of the solar storage tank 
 may also be used for the DHW pre-heater loop control, and a typical 
 difference in temperature between the bottom and top of the main solar 
 storage tank may be included in the temperature difference setting. 
 Alternatively, a sensor may be installed at the top of the solar storage 
 tank to control the pre-heater circulation pumps. The difference in 
 temperature between sensors S2 and S4 controls pumps 4 and 5, as shown 
 in Figure 10-12 and Table 10-2. 
 
10-33 
 
 PROTECTION AGAINST FREEZING AND BOILING 
 
 Protection of liquid collector/storage systems against damage 
 caused by freezing or boiling of the collector fluid is a matter both of 
 design and control. Freeze protection in dual-liquid systems requires 
 maintenance of adequate concentration of ethylene glycol in the circu- 
 lating solution. Periodic checking of the solution both for glycol 
 concentration (by simple hydrometer similar to a tester for automobile 
 radiator protection) and for pH (acidity) by litmus paper or other color 
 indicator is essential to safe long-term operation. Antifreeze tables 
 are commonly available for making up solutions that can provide freeze 
 protection to temperatures ten degrees colder than recorded minimums. A 
 50-50 solution has the lowest freezing point, approximately -34°F. 
 Because of deterioration and dilution by vapor loss and subsequent 
 make-up with water, glycol concentrations should be maintained well 
 above the lowest requirements. 
 
 Decomposition of glycols by heat, with resulting acid formation, 
 poses substantial corrosion hazards unless properly dealt with. 
 Periodic replacement of collector fluid, at one- to two-year intervals, 
 is highly desirable. An occasional pH check can show whether more or 
 less frequent replacement is necessary. The use of neutralizing addi- 
 tives, as needed, can reduce the frequency of solution replacement, but 
 careful monitoring is necessary. 
 
 In drain-back systems controlled by sensing dangerously low 
 collector temperature, thereby actuating suitable valves, inspection and 
 checking at the start of each heating season is essential. Piping and 
 manual valves must be free to drain completely. 
 
 A design and operating technique for avoiding collector freezing in 
 mild winter climates involves use of water (without additives) in the 
 
10-34 
 
 collector, but without drainage even when freezing weather occurs. The 
 infrequency of such occasions justifies circulation, preferably at low 
 rate, of water from storage through the collector during such cold, 
 sunless periods. Moderate heat loss occurs, but freezing is avoided at 
 modest cost. Such systems are vulnerable, of course, to equipment 
 failure and power outages and could logically be used only where sub- 
 freezing temperatures are rarely encountered. Another option in such 
 climates is the use of a low temperature sensor to open valves (requir- 
 ing power to close) that allow a slow flow of water from the main, 
 through the collector, to a drain. 
 
 There are several designs and operating procedures for control of 
 boiling in the collector when heat demand is so low that high storage 
 temperatures result. In drain-down and drain-back systems, boiling can 
 be permitted, the vented steam being made up by automatic or manual 
 addition of water to the storage tank. The collector may, alternative- 
 ly, be allowed to drain when the collector temperature exceeds a limit 
 setting, but prolonged exposure of the collector to the resulting high 
 temperature can reduce its useful life. 
 
 Closed loop collector systems (dual-liquid types) may also dis- 
 charge excess heat by venting steam from the storage tank. The higher 
 boiling point of the antifreeze solution protects it from boiling as 
 long as there is circulation to the collector/storage heat exchanger. 
 Water make-up to storage must then be provided. If circulation is 
 interrupted by pump failure or power outage, boiling of the collector 
 liquid can occur, even to the point of insufficient liquid in the system 
 for subsequent start-up and operation. Water and anti-freeze solution 
 must then be promptly added to the collector loop. 
 
10-35 
 
 Another method for excess heat disposal in single- and dual-liquid 
 systems involves the use of an air-cooled fan-coil exchanger (similar to 
 an automobile radiator) through which overheated storage water is pumped 
 and cooled. A tank sensor actuates the load pump, the exchanger fan, 
 and a diverter valve when the tank temperature exceeds a preset limit 
 such as 200°F. 
 
 In all of the designs for freeze and boiling protection, the most 
 important consideration is high reliability, because even one failure 
 can result in serious equipment damage and high repair cost. 
 
 AIR SYSTEMS 
 
 In addition to the obvious differences between heat collection in 
 liquids and in air, the following technical and operational factors may 
 be noted. 
 
 1. Solar air systems involve the same medium for solar collection 
 and space heating; solar-heated air can be delivered directly 
 to the building without heat exchange or storage. 
 
 2. Heat storage can be accomplished in a bed of loose solids, 
 typically 1- to 2-in gravel, which also serves as the heat 
 exchanger. 
 
 3. Temperature stratification in a pebble bed and the return of 
 air to the collector directly from the living space both 
 provide low temperature (70°F) air to the collector with 
 resulting favorable efficiency. 
 
 4. The combination of air density, specific heat, and practical 
 flow rates provides a considerably higher temperature rise 
 through the collector, typically a 60° to 90° increase, than 
 in a liquid type. 
 
10-36 
 
 DOUBLE-BLOWER DESIGN 
 
 As with liquid-heating solar systems, there are numerous options 
 for integrating a solar air collector and a pebble-bed heat storage unit 
 into a complete building heating assembly. A widely used solar air 
 system requires two blowers, one for circulating air through the collec- 
 tor and the other for supplying warm air to the rooms. A schematic 
 design of a two-blower, air-heating solar system for both space and 
 domestic water heating is shown in Figure 10-13. There are six princi- 
 pal components: solar collector, heat storage unit, air handler, auxili- 
 ary heater and fan, a water heating coil, and a controller (not shown). 
 The water heating coil is coupled to a storage tank and circulating 
 pump, and piped to a conventional hot water heater. By combining the 
 blower, dampers, and hot water coil in an "air handler", the installa- 
 tion and operation of the system are simplified. The control sequences 
 to operate the system in all modes are detailed in a "truth table" 
 (Table 10-3). The operating modes are shown in Figures 10-14 through 
 10-17. In the table and figures, the abbreviation MD denotes a motor- 
 ized damper and BD a back-draft damper which swings shut except when air 
 is being forced against one of its faces. 
 
 Storing Solar Heat and Heating Hot Water 
 
 Solar collection and delivery of heat to storage are achieved by 
 circulating air between collector and storage whenever a sufficient 
 temperature rise can be achieved in the collector. The collector blower 
 in the air handler is actuated by a differential thermostat, with the 
 hot sensor in the air passage at the collector exit and the cold sensor 
 near the cold end of the storage bed or in the air passage leading to 
 
10-37 
 
 SOLAR COLLECTORS 
 
 MOTORIZED DAMPER 
 
 MOTORIZED DAMPER 
 
 VA 
 
 BACK -DRAFT 
 DAMPERS 
 
 WARM 
 
 AIR 
 
 TO 
 ROOMS 
 
 RETURN AIR 
 FROM ROOMS 
 
 Figure 10-13. Two-Blower Air-Heating Solar System 
 
10-38 
 
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10-39 
 
 ROOMS 
 
 Figure 10-14. Storing Heat from Collectors 
 
 FILTER 
 
 IMDI 
 COLLECTOR BLOWER 
 
 |MD2 
 
 AUXILIARY 
 FURNACE 
 
 DISTRIBUTION 
 BLOWER 
 
 ILTER 
 
 ROOMS 
 
 Figure 10-15. Heating Building from Collectors 
 
10-40 
 
 ti "^BD2 1 [FILTER 
 
 DISTRIBUTION- 
 BLOWER 
 
 - L 
 
 Figure 10-16. Heating Building from Storage Unit 
 (Also heating from auxiliary) 
 
 ROOMS 
 
 STORAGE 
 
 (PEBBLE 
 
 BED) 
 
 SUMMER 
 BY- PASS r 
 
 BD 
 
 AIR 
 HANDLER 
 
 HOT 
 
 WATER 
 
 COIL 
 
 ZU FILTER 
 
 1 1 Hh-QMDi 
 
 COLLECTOR BLOWER 
 
 I 0MD2 
 
 AUXILIARY 
 FURNACE 
 
 i } BD2 1 [FILTER 
 
 -*— lj— 
 
 DISTRIBUTION 
 BLOWER 
 
 ROOMS 
 
 Figure 10-17. Service Hot Water Heating (Summer Operation) 
 
10-41 
 
 the collector. When the hot sensor reaches a temperature about 45°F 
 higher than the cold sensor, blower operation commences.* The signal 
 from the controller that actuates the blower also positions dampers so 
 that air passes from the collector to the hot end of the storage bed, 
 through the pebbles, and from the cold end back to the collector. 
 Figure 10-14 illustrates this mode of operation. 
 
 At a flow rate of about 2 cfm/ft 2 of collector, midday air 
 temperatures from the collector usually range from 130°F to 170°F when 
 air is being admitted to the collector at 70°F. As sundown approaches, 
 the temperature declines, and when the preset turn-off difference is 
 reached, usually about 20°F, the controller turns off the blower and 
 repositions directional dampers.* 
 
 The pebble bed operates both as heat exchanger and heat-storage 
 medium. The large heat exchange surface provided by the pebbles and the 
 very low thermal conductivity from one pebble to another result in rapid 
 transfer of heat from air to rock and a steep temperature gradient 
 through the bed in the direction of air flow. 
 
 In most residential air-heating solar systems, solar heated water 
 is also provided. A common finned coil is usually mounted at the air 
 handler outlet leading to the pebble bed. During typical operation on 
 sunny days, a small pump circulates water from the bottom of an insulat- 
 ed 50 to 100 gallon "pre-heat" tank, through the coil, and back to the 
 top of the tank. If the temperature at collector outlet is higher than 
 the tank bottom temperature by a preset amount, the pump is actuated. 
 
 *These control temperatures are the actual factory settings on a 
 controller in a widely used air-heating solar system. As explained 
 in Module 8, an "on" setting as low as 15° difference and an "off" 
 setting of 2° to 3° will permit additional solar heat collection, but 
 air delivery temperatures at these control points are lower than 
 usually needed for space heating without auxiliary boosting. 
 
10-42 
 
 The coil is sized so that a relatively small fraction of the collected 
 solar heat is transferred to the water, usually enough to decrease the 
 air temperature two or three degrees. The rise in water temperature per 
 pass depends on the temperature in the tank as well as on the air tem- 
 perature. Normally when heat is being stored in the pebble bed, water 
 is also being heated. 
 
 Experience has shown that the coil location in Figures 10-13 to 
 10-17 is more satisfactory than in the duct between the collector and 
 air handler, primarily because the possibility of freezing caused by 
 nocturnal leakage of air through damper MD 1 is eliminated. 
 
 As shown in Figures 10-1, 10-2 and 10-3, solar heated water for 
 domestic use is usually supplemented with auxiliary heat in a conven- 
 tional water heater. The same arrangement is used with air- type collec- 
 tion systems. The two-tank design is nearly always employed if a fuel 
 auxiliary is involved, but a single tank may be used if electric boost- 
 ing is provided. In that case, solar heated water from the heat ex- 
 changer enters the tank at a point about one-third of the distance down 
 from the top of the tank, and the electric element is positioned immedi- 
 ately above that point. Electrically heated water is therefore only in 
 the upper third of the tank, and because of temperature stratification, 
 the auxiliary heat does not adversely affect solar heat exchange. A 
 tempering (mixing) valve should be installed in the service hot water 
 supply line to prevent delivery of overheated water to the taps. 
 
 Daytime Space Heating 
 
 When heat is needed in the building at the same time solar energy 
 is being collected, a room thermostat signals the control unit to move 
 dampers and direct the flow of heated air from the collector directly to 
 
10-43 
 
 the zones requiring heat, bypassing storage, as shown in Figure 10-15. 
 In this mode, hot air passes from the collector through the collector 
 blower, through the furnace with only its blower also in operation, and 
 into the warm-air distribution system. Air circulates back from the 
 rooms to the collector through conventional cold air return ducts. 
 Either a motorized damper or a check damper (BD 2) (operated by slight 
 pressure difference) is in this return duct. When room temperature 
 requirements are satisfied, the thermostat breaks contact, and the 
 storing mode is resumed. 
 
 When there is a high heat demand and when the temperature of the 
 air being delivered from the collector is insufficient to meet the 
 demand, room temperature will continue to decline. A lower thermostat 
 set point then turns on the fuel in the auxiliary heater, thereby in- 
 creasing the temperature of air supplied to the rooms. The full design 
 capacity of the furnace will always provide sufficient heat to meet any 
 demand, so the building temperature will be restored to the preset 
 value. 
 
 Most commercially available warm-air furnaces for residential use 
 contain a blower for circulation of warm air through the building via 
 distribution ducts. In a typical all-air solar installation, the fur- 
 nace blower is used in the normal manner for distributing warm air, 
 supplied either from the collectors or from storage. The solar system 
 blower operates when air is circulated through the collector either to 
 storage or to distribution. 
 
 Space Heating from Storage 
 
 The third mode of operation, illustrated in Figure 10-16, is called 
 for when heat is required in the building and solar collection is not 
 taking place. Under these conditions, a room thermostat signals the 
 
10-44 
 
 distribution blower in the furnace to operate and dampers to move so 
 that room air will flow to the cold end of the storage bed, then from 
 the hot end of the bed through the distribution blower and the furnace 
 to the rooms via the air distribution system. Air leaving the hot end 
 of the bed is only a few degrees below the rock temperature at that 
 level. Heat is thus supplied to the room air by transfer from the 
 heated pebbles. 
 
 If the pebble-bed discharge temperature is sufficient, air entering 
 the rooms will provide enough heat to satisfy the thermostat, and after 
 a sufficient period, the blower will cease operation. If, however, room 
 temperature continues to drop, the auxiliary heat supply will be actu- 
 ated by the lower thermostat set point, and auxiliary heat will also be 
 supplied. This operation continues until room temperature rises to the 
 upper thermostat set point and fuel and blower are shut off. 
 
 It can be seen from the above description that the use of solar 
 heat is maximized by (1) collecting solar heat whenever moderate temper- 
 ature delivery of 90°F to 100°F is possible; (2) utilizing even such low 
 temperature heat, supplemented if necessary with auxiliary; (3) provid- 
 ing, by means of temperature stratification, high temperature storage 
 even when the storage unit is only partially heated; (4) bypassing 
 storage when heat is needed during sunny hours; (5) using auxiliary 
 energy only as a supplement, not as a replacement for solar. 
 
 Summer Water Heating 
 
 So that the domestic hot water supply can be solar heated in the 
 summer when no space heating is needed, the heat storage unit and heated 
 space can be by-passed as shown in Figure 10-17. A manual or automatic 
 damper is opened in a by-pass duct so that air is circulated in a closed 
 
10-45 
 
 loop between collector, water heating coil, and the collector blower. 
 Dampers MD 2, BD 1, and BD 2 in closed positions and a manual shut-off 
 prevent flow of hot air to storage or to the rooms. The blower and 
 water pump are actuated by the difference in temperature between collec- 
 tor outlet and hot water storage. 
 
 SINGLE-BLOWER DESIGN 
 
 Another damper arrangement does not require a furnace blower, so 
 only the solar system blower is needed. Four motorized dampers are 
 required (rather than two), but only two actuators are used. This 
 system type is shown in Figure 10-18, with the blower and motorized 
 dampers in an air handler cabinet. Although the cost of one blower and 
 motor can be saved by this design, two additional dampers are required, 
 the controls are more complicated, and airflow rates in the several 
 modes are less adjustable. This arrangement is applicable when the air 
 flow rate through the collectors is nearly equal to the air flow rate 
 required in the heat delivery system to the rooms. 
 
 Additional details on the single-blower system and on the air 
 handler utilized with it are presented in Module 8. 
 
 STORAGE SYSTEM 
 
 A pebble bed as a heat storage component has been discussed in 
 Module 8. There are, however, some additional features that affect the 
 use of a pebble bed in a complete solar heating system. 
 
 Heat flow in a pebble bed in the absence of air circulation is 
 almost negligible, even in designs involving an air flow direction such 
 that the hot end is at the bottom, the cold end at the top. Convective 
 
10-46 
 
 heat transfer is minimized by the limited space for air movement between 
 pebbles, and conduction is of little concern because of minimal pebble- 
 to-pebble contact. Temperature profiles in a well-designed pebble bed 
 do not change significantly overnight unless heat is being withdrawn by 
 circulating air. At the bed center, for example, the temperature 
 changes less than 1°F in 8 hours. 
 
 ROOMS 
 
 FROM 
 ROOMS 
 
 BACK- 
 DRAFT 
 DAMPERS 
 
 BDI /BD2 ^-FILTER 
 
 Figure 10-18. Single-Blower System 
 
 For similar reasons, heat loss from the pebble bed through the 
 container walls can be easily controlled. Thick insulation is not re- 
 quired, both because of low conduction between the pebbles and the wall 
 and also because the bed is usually in the building so that heat trans- 
 ferred through the container wall is not actually lost. Insulation with 
 an R factor of 10 is more than satisfactory. Ordinary concrete block, 
 reinforced concrete, and wood plank or plywood with gypsum board liner 
 
10-47 
 
 may be used. A box formed of conventional insulated stud walls 3-1/2 
 in. thick with fiberglass between studs, and a similar top, is another 
 option. In all of these arrangements, an overnight loss of heat through 
 the walls from a completely charged storage unit should not exceed 1% of 
 the thermal content. 
 
 The direction of air flow in the pebble bed is usually dictated by 
 the position of heating system components rather than by thermal per- 
 formance considerations. With storage depths of 6 ft or more, tests 
 show that the performance of units having the hot end at the bottom is 
 virtually the same as those heated from the top. The location of the 
 blower, auxiliary furnace, and other system components, usually in the 
 basement, may minimize duct lengths if the hot end is at the bottom of 
 the pebble bed. But unless there is some practical reason to do other- 
 wise, heated air should be supplied to the top of the bed so that there 
 is minimum loss of temperature stratification and minimum heat loss from 
 the bottom of the bed into the concrete base and underlying ground. 
 
 Horizontal-flow pebble beds have also been used, but the top cover 
 of the bed must be in close contact with the pebbles so that air does 
 not channel through an open space above the packing. There is some 
 evidence that channeling of warm air through the pebbles in the upper 
 part of the bed and of cool air through the lower part may occur. If a 
 horizontal position cannot be avoided, vertical baffles or horizontal 
 separators should be provided to prevent channeling, as shown in Module 
 8. 
 
 A pebble bed containing about one-half to three-fourths cubic foot 
 of rock (weighing 50 to 75 pounds) per square foot of collector can 
 store all of the heat deliverable from the collector on a completely 
 sunny day. If all the heat collected during the day is delivered to 
 
10-48 
 
 storage, maximum mid-winter collection of 800 Btu per square foot of 
 collector would result in heating the pebbles from a starting tempera- 
 ture of 70 degrees to a final average temperature of 125°F to 150°F. 
 During the winter months, in most practical systems, half to two- thirds 
 of this heat would be placed in storage, the balance being used directly 
 in the daytime. Essentially all of the stored heat would then usually 
 be delivered to the heated space during the following night. 
 
 Studies have shown that the performance of a pebble-bed heat 
 storage unit is dependent primarily on the mass of material and is 
 comparatively insensitive to type of rock, dimensions of the bed, pebble 
 size, and air flow rate. As a heat exchanger, effectiveness tends to 
 increase with length of bed and with decreases in air flow rate and 
 pebble size. But pressure loss and blower power requirements also 
 increase with bed length and pebble fineness. Optimum design is thus an 
 economic combination of these factors. Most commercially built pebble 
 beds in single family houses are of nearly cubic shape, 5 to 7 feet 
 dimension, containing 5 to 15 tons of locally sold screened gravel or 
 crushed rock commonly used in concrete mixes. Rock size is usually 3/4 
 to 1-1/2 inch, with very little undersize material. Size uniformity is 
 important for maintaining good heat transfer characteristics and low 
 pressure loss and fan power consumption. Air velocity in typical pebble 
 beds is usually not more than one-half foot per second, and pressure 
 drop is generally less than 0.2 inch water gauge. 
 
 AIR FLOW RATES 
 
 An important design consideration is the flow rate through a solar 
 air collector. Air delivery temperature decreases and solar collection 
 efficiency increases with increased circulation rate. Fan power 
 
10-49 
 
 requirement also rises with air flow, and there are practical limits to 
 air circulation rates in the occupied space of a building. The effici- 
 ency of a solar air collector depends not only on volumetric flow, but 
 also on air velocity. The type of manifolding, the length of travel of 
 air in the collector, and the width of the air passages affect velocity. 
 In a typical commercial type of air collector, efficiency and 
 pressure drop are at satisfactory levels with a flow of about 2 cfm/ft 2 
 of collector and a linear velocity of approximately 10 ft/sec. At an 
 air flow rate of 2 cfm with a 13-ft air path through a solar collector 
 having a 1/2- in. air passage, a pressure drop of approximately 0.25 in. 
 of water is typical. Power requirements at this point of operation are 
 moderate, less than 1 hp for circulating 1000 cfm of air through the 
 collector and pebble bed. Total electric energy usage for solar energy 
 collection, storage, and distribution in well-designed systems is less 
 than ten percent of the solar energy supplied to use. 
 
 AUXILIARY HEAT 
 
 Auxiliary heat is usually supplied in solar air systems by use of a 
 warm air furnace in series with the collector and storage units (Figures 
 10-15 and 10-16). This design permits maximum supply of solar energy by 
 utilizing the solar system as a pre-heater of the air when heat require- 
 ments are greater than solar heat availability. Essentially all of the 
 collected and stored solar heat can thus be used, even if at low 
 temperature. 
 
 Warm air furnaces can be fueled with gas, oil, or propane, or they 
 can be supplied with electricity. Control of auxiliary fuel or electri- 
 city is usually provided through a dual-stage house thermostat, the 
 lower temperature contact actuating the fuel valve or electric switch. 
 
10-50 
 
 Electric motors for blowers in warm air furnaces are frequently 
 mounted in the cabinet through which air passes, and are thereby air- 
 cooled. When used as an auxiliary heater in a solar air system, this 
 motor usually operates in a warm air stream, occasionally at tempera- 
 tures as high as 175°. A "type B" motor, suitable for operation at such 
 temperatures, should therefore be used rather than the "type A" usually 
 supplied in the furnace. The motor in the (solar) air handler, if also 
 in the warm air stream, should be of the same type. 
 
 An air-to-air heat pump may also be used for supplying auxiliary 
 heat, as shown in Figure 10-19. The condenser coil of the heat pump 
 provides heat to the house air as the outdoor evaporator coil utilizes 
 ambient air as the source of heat. Electric resistance back-up is also 
 necessary for meeting high heating demands. Summer cooling can be 
 supplied by reversing the evaporator and condenser functions so that 
 electrically driven vapor-compression air-conditioning is provided in a 
 conventional manner. 
 
 AIR HANDLER 
 
 HEAT PUMP 
 
 FROM 
 COLLECTOR 
 
 TO AND FROM 
 STORAGE 
 
 COLD AIR RETURN 
 TO COLLECTOR" 
 AND STORAGE 
 
 OUTDOOR UNIT 
 
 ELECTRIC 
 
 RESISTANCE 
 
 COIL 
 
 ^ T0 
 ROOMS 
 
 FROM 
 ROOMS 
 
 Figure 10-19. Solar Heating System with Air-to-Air Heat Pump Auxiliary 
 
10-51 
 
 Because of pressure limitations in commercially available heat 
 pumps, they are not usually operated as temperature boosters for solar 
 heated air. An air temperature of 100°F may not be sufficient for 
 heating the building, but supply of air at that temperature to the 
 condenser coil would cause excessive pressure in the heat pump. For 
 this reason, air is supplied to the heat pump from the house air return 
 via the by-pass shown in Figure 10-19 rather than from the solar system. 
 A motor-operated damper in the by-pass duct opens when this operating 
 mode is required. This damper and the heat pump compressor and fans are 
 controlled by the low temperature contact in the two-stage house thermo- 
 stat, which simultaneously closes the damper at the air handler outlet. 
 The electric resistance back-up coil is usually controlled by a tempera- 
 ture sensor in the heat pump system. 
 
 BLOWERS, DUCTS AND DAMPERS 
 
 An illustrative layout of a typical air-heating solar system 
 (auxiliary heater and hot water tanks not shown) is presented in Figure 
 10-20. Although the positions of the several components will differ, 
 the general arrangement in the two-blower system is usually as shown. 
 
 Important operating considerations in the air- type system are 
 blower power requirements and air leakage. A well-designed air system 
 has approximately equal pressure loss through the collectors and pebble 
 bed, typically about 1/4-inch water gauge in each unit, although pres- 
 sure differences across well-designed pebble beds are often as low as 
 0.1 inch W.G. With ducting, dampers, and filters, the total system 
 pressure drop can approach one inch of water . This pressure difference 
 is about twice that usually encountered in a conventional forced air 
 
10-52 
 
 COLLECTOR 
 ARRAY 
 
 HOT AIR FROM 
 COLLECTORS - 
 
 BACK-DRAFT 
 DAMPERS 
 
 HOT WATER COIL 
 MOTORIZED DAMPER- I 
 
 AIR HANDLER 
 MOTORIZED DAMPER -2 
 
 SUPPLY AIR TO THE BLDG. a TO THE 
 
 HEAT 
 
 STORAGE 
 
 UNIT 
 
 TOP PLENUM 
 
 -ROCK- 
 %" TO 
 
 l'/ 2 " SIZE 
 
 BOTTOM PLENUM 
 
 AUXILIARY HEATING UNIT 
 
 Figure 10-20. General Layout of Typical Air-Heating Solar System 
 
 distribution system, so additional blower power is required for its 
 operation. A typical requirement in a conventional system is one-half 
 to three- fourths horsepower for an air flow rate of 1000 to 1500 cfm. 
 In a double-blower system, the collector blower motor is usually three- 
 fourths to one horsepower, depending on collector area (300 to 700 
 square feet), and the distribution blower motor is of conventional size, 
 usually about one-half horsepower. In a one-blower system, a one- 
 horsepower motor will generally be required. The blowers also operate 
 for longer periods than in the conventional system because of their use 
 both for solar heat collection and for heat distribution. A one-inch 
 water gauge pressure loss is about the maximum acceptable from the 
 standpoint of blower power cost, although the electricity requirement 
 is usually less than 10 percent of the solar heat supply. 
 
10-53 
 
 Leakage of air in ducts, collectors, and storage is of greater 
 concern in a solar heating system than in a conventional system because 
 the pressure is higher, there is more ducting, the system operates for 
 longer periods, and there may be more ducting through unheated space. 
 Ducts should therefore be carefully inspected during installation and 
 all joints should be sealed with a silicone sealing compound if sheet 
 metal ducts are used. Ducts made of fiberglass board should be taped 
 carefully at all corners and joints, and any perforations in the foil 
 wrapper should be sealed. Insulation is needed to reduce heat loss 
 through duct walls, particularly in unheated spaces such as attics. At 
 least one inch of fiberglass with a rating of R-4 is recommended for 
 duct insulation, with two inches for ducts in unheated spaces. Insula- 
 tion may be either inside or outside sheet metal ducts. 
 
 It is especially important with a solar air system that a well- 
 scheduled installation be made. More space and access must be provided 
 in the building for ducting than for pipes in a liquid system. Ductwork 
 and component assembly can be done at the same time that the distri- 
 bution ducts and furnace are installed in a typical construction sched- 
 ule. There must be provision for construction and installation space 
 and for full access to the space for systems and components. 
 
 If fiberglass ductboard is used, it should not be in locations 
 where it can be damaged by moving objects or occupants. Joints should 
 be sealed with tapes or mastics recommended by the industry. Duct bends 
 should be provided with turning vanes to reduce pressure loss. Ducts 
 should be sized for air velocities between 600 and 800 feet per minute. 
 
 Blowers, dampers, and auxiliary heaters may be provided by a single 
 solar system supplier or they may be purchased separately. Factory 
 
10-54 
 
 mounting of motorized dampers and water heating coil in or on a blower 
 cabinet, to provide complete hot air handling capability, substantially 
 reduces site labor and increases quality and reliability of the instal- 
 lation. Blowers should be forward-curved squirrel cage type and prefer- 
 ably belt-driven to enable adjustments in air-flow rates. Direct- 
 coupled blowers with motors in the air stream may be used and have the 
 advantage of quieter operation, but disadvantages are the need for a 
 type-B (high temperature) motor and the impossibility of blower speed 
 adjustment. Flexible connections between blowers and ducts are recom- 
 mended. 
 
 Louver- type dampers with neoprene or live silicone rubber seals are 
 recommended for positive shutoff and smooth stroking. Damper drive 
 motors should be located on the outside of ducts or air handlers and 
 directly coupled to the damper shaft or through linkages. Special 
 attention should be given to the linkages during installation to assure 
 tight damper closure. In the one-blower system, damper pairs may be 
 operated by the same drive motor so that one is closed when the other is 
 open. Damper motors are available which operate on low voltage (24 
 volt) with spring returns, but greater reliability can be obtained by 
 use of positive drive in two directions. 
 
 Back-draft dampers, used in ducts to prevent reverse air flow, may 
 be of the flexible flap type or shutter type. They must be mounted to 
 provide a positive seal against reverse airflow. 
 
 To prevent fouling and increased pressure loss in the pebble bed, 
 filters should be installed in the air streams entering both ends of the 
 storage unit. The filters should be changed or cleaned every few weeks 
 during the first several months of operation to remove the initial dust 
 from the system and building. 
 
10-55 
 
 The complete solar heating installation requires carpenters or 
 masonry workers to construct and fill the pebble-bed container, plumbers 
 to connect the domestic water heating system, heating and sheet metal 
 workers to install collectors, ducts, dampers, controls, and furnace, 
 and electricians to wire blowers and dampers. Consequently, the general 
 contractor and the solar system contractor should coordinate their 
 activities so that each task is accomplished at the most appropriate and 
 convenient stage during construction. Quality installation is an impor- 
 tant requirement for obtaining good performance of an air-heating solar 
 system. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 11 
 
 DESIGN PROCEDURES 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS., COLORADO 
 
11-1 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 
 Page 
 11- i i i 
 11- i i i 
 
 OBJECTIVE 
 
 INTRODUCTION 
 
 THE f-CHART METHOD 
 
 DESCRIPTION 
 
 CORRECTION FOR COLLECTOR/STORAGE HEAT EXCHANGER 
 
 CORRECTION FOR AIR FLOW RATE THROUGH COLLECTOR 
 
 CORRECTION FOR STORAGE . 
 
 CORRECTION FOR LOAD HEAT EXCHANGER 
 
 DOMESTIC WATER HEATING ONLY . 
 
 CALCULATION PROCEDURE 
 
 Incident Angle Modifier . 
 
 Collector/Storage Heat Exchanger Correction 
 Factor 
 
 EXAMPLE 11-1 . 
 
 EXAMPLE 11-2 . 
 
 WORKSHEET A - AIR SYSTEMS 
 
 WORKSHEET B - AIR SYSTEMS 
 
 WORKSHEET C - AIR SYSTEMS 
 
 WORKSHEET D - AIR SYSTEMS 
 
 WORKSHEET E - AIR SYSTEMS 
 
 WORKSHEET F - AIR SYSTEMS 
 
 WORKSHEET G - AIR SYSTEMS 
 
 11-1 
 
 11-1 
 
 11-2 
 
 11-2 
 
 11-5 
 
 11-7 
 
 11-9 
 
 11-10 
 
 11-11 
 
 11-12 
 
 11-14 
 
 11-14 
 11-15 
 11-15 
 11-17 
 11-19 
 11-20 
 11-21 
 11-22 
 11-23 
 11-24 
 
11-ii 
 
 Page 
 
 WORKSHEET A - LIQUID SYSTEMS 
 
 WORKSHEET B - LIQUID SYSTEMS 
 
 WORKSHEET C - LIQUID SYSTEMS 
 
 WORKSHEET D - LIQUID SYSTEMS 
 
 WORKSHEET E - LIQUID SYSTEMS 
 
 WORKSHEET F - LIQUID SYSTEMS 
 
 WORKSHEET G - LIQUID SYSTEMS 
 
 
 
 
 11-25 
 
 
 
 • 
 
 11-27 
 11-28 
 
 
 
 • 
 
 11-29 
 
 
 
 • 
 
 11-31 
 11-32 
 
 • 
 
 
 • 
 
 11-33 
 
 OLLECTO 
 
 R SIZES 
 
 
 11-34 
 
11-111 
 
 LIST OF FIGURES 
 
 Figure 
 
 11-1 
 
 11-2 
 
 11-3 
 
 11-4 
 
 11-5 
 
 11-6 
 
 11-7 
 
 11-8 
 
 f-Chart for Liquid-Heating Solar Systems 
 
 f-Chart for Air-Heating Solar Systems 
 
 Heat Exchanger Factor F R /F R 
 
 Collector Capacitance Factor (Air), K-. 
 
 Storage Capacitance Factor, K« 
 
 Load Heat Exchanger Factor, K. 
 
 Hot Water Factor, K« 
 
 f-Chart for Liquid-Heating Solar Systems 
 (for Example Problem 11-2) 
 
 
 Page 
 
 • 
 
 11-3 
 
 • 
 
 11-4 
 
 ■ 
 
 11-6 
 
 • 
 
 11-8 
 
 • 
 
 11-9 
 
 ■ 
 
 11-11 
 
 
 11-12 
 
 11-35 
 
 LIST OF TABLES 
 
 Table 
 
 11-1 
 
 Monthly Temperature (T ) in °F at Source for 
 City Water in 14 Selected Cities 
 
 Page 
 
 11-37 
 
11-1 
 
 OBJECTIVE 
 
 The objective of this module is to present a detailed method for 
 
 estimating performance of solar heating systems. The trainee should be 
 
 able to complete an f-chart system sizing procedure by "hand" 
 calculation. 
 
 INTRODUCTION 
 
 Solar heating systems are sized to provide a desired fraction of 
 the total annual heating load of the building. The desired fraction can 
 be chosen arbitrarily or determined from economic analysis to minimize 
 the annual cost of space heating and water heating with a solar- 
 auxiliary system. Using approximate methods, the calculations lead to 
 determination of collector area, and other components of the system are 
 sized relative to the collectors. In detailed computations, collector 
 area, storage size, heat exchanger size, and fluid flow rates through 
 the collector are variable within practical ranges, and performance 
 calculations include their variability. 
 
 Among several detailed methods devised for estimating system 
 performance, the one described in this module is the "f-cnart" method 
 developed by Klein, Beckman and Duffie at the University of Wisconsin. 
 The f-chart method is based on hour-by-hour simulations of performance 
 of typical solar heating systems having wide ranges of system parameters 
 in several geographic locations. Generalized correlation charts 
 (f-charts) were developed for predicting the monthly fractions of the 
 heating load supplied by solar energy. One chart was developed for 
 
11-2 
 
 liquid-heating systems and another for air-heating systems. The f-chart 
 method is applicable to system types described in Module 6. 
 
 Several assumptions were made in developing the f-charts: 
 
 1. Heat losses from storage are negligible. 
 
 2. Average domestic hot water demand is distributed throughout 
 the hours of 6:00 a.m. to 1:00 a.m. in a nonuniform manner 
 peaking at hours of 9:00 to 10:00 a.m. and 7:00 to 8:00 p.m. 
 and the pattern is repeated every day. 
 
 3. Flat-plate collector performance can be characterized by two 
 parameters, F R (xa) and F R U, . 
 
 THE f-CHART METHOD 
 
 DESCRIPTION 
 
 There are separate f-charts for liquid- and air-type systems as 
 
 shown on Figures 11-1 and 11-2, respectively. The coordinate axes X and 
 
 Y characterize collector performance in relationship to the heating load 
 
 for a specific month. In particular, 
 
 x _ collector losses = A c F R U L (T ref " V At m-l) 
 monthly heating load L ^ 
 
 and 
 
 A F xa S 
 Y _ collector heat gain ... c R (n-2) 
 
 monthly heating load L 
 
 where X and Y are dimensionless, and the variables are explained below: 
 
 A„ is the total collector area, ft 
 c 
 
 F R U, is the slope of the collector efficiency curve, 
 
 Btu/(hr-ft 2 -°F) 
 Fp ia is the intercept on the collector efficiency curve, 
 
 corrected for incidence angle, dimensionless 
 
11-3 
 
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11-5 
 
 T ref is 212°F 
 
 T is the average ambient (air) temperature for a 
 a 
 
 specific month, °F 
 At is the number of hours for a specific month, hr/mo 
 L is the monthly space and water heating load, Btu/mo 
 
 S is the average monthly solar radiation on a tilted 
 
 2 
 collector per unit area, Btu/(ft -mo) 
 
 The area is chosen arbitrarily, F R U, and F R ia are determined for 
 
 a specific collector from performance curves, and T for specific cities 
 
 a 
 
 is given in Module 3. The monthly heating load, L, is the sum of the 
 DHW and space heating load, and S is determined from the monthly average 
 daily solar radiation on a tilted surface (as described in Module 3), 
 multiplied by the number of days in the month. 
 
 The f-charts of Figures 11-1 and 11-2 are solutions of bivariant 
 equations. For liquid-based systems, 
 
 f = 1.029Y - 0.065X - 0.245Y 2 + 0.0018X 2 + 0.0215Y 3 
 
 for F Y F 3 and F X F 18. (11-3) 
 
 and for air-based systems, 
 
 f = 1.040Y - 0.065X - 0.159Y 2 + 0.00187X 2 - 0.0095Y 3 
 
 for F Y F 3 and F X F 18 (11-4) 
 
 CORRECTION FOR COLLECTOR/STORAGE HEAT EXCHANGER 
 
 A heat exchanger in the collector-to-storage flow circuit results 
 in reduction of collector efficiency because the temperature of the 
 collector return liquid is higher than it would otherwise be without a 
 heat exchanger. The reduction of collector efficiency and net energy 
 
11-6 
 
 collection is expressed as a fraction, F R /F R , which is termed the heat 
 exchanger factor. 
 
 Either the graph in Figure 11-3 or Equation (11-5) may be used 
 to determine F R /F R . The coordinates for Figure 11-3 are determined 
 as follows: 
 
 in which 
 
 x = 
 
 £ C . 
 cs mm 
 
 C is the collector fluid heat capacity rate, Btu/(hr*°F) 
 
 e is the heat exchanger effectiveness, dimensionless 
 
 C • is the minimum of the collector or storage fluid 
 min a 
 
 capacitance ratio, Btu/(hr*°F) 
 
 u? 
 
 o 
 
 ti 
 
 >- 
 
 0.02- 
 
 X = 
 
 i 
 
 Figure 11-3. Heat Exchanger Factor F R /F R 
 
11-7 
 
 and, 
 
 y = 
 
 V F R U L> 
 C c 
 
 where 
 
 2 
 A„ is the collector area, ft 
 
 c ' 
 
 F R U. is the collector characteristic determined from the 
 collector performance test data, as provided by the 
 manufacturer, Btu/(hr*ft 2 *°F) 
 
 The heat exchange factor may also be calculated from Equation (11-5) 
 
 F 
 
 R 
 
 F7 ~ 1 + y(x-l) ^'^ 
 
 Corrections are made to X and Y values calculated in Equations (11-1) 
 and (11-2) as follows. 
 
 X(new value) = X • F R /F R (11-6) 
 
 Y(new value) = Y • F R /F R . (11-7) 
 
 The new values of X and Y are used to determine monthly estimates of f 
 from the chart, or Equations (11-3) and (11-4). In an air system, there 
 is no heat exchanger between the collector and storage for space heat- 
 ing, so a correction factor is not applied. 
 
 CORRECTION FOR AIR FLOW RATE THROUGH COLLECTOR 
 
 Air collector efficiencies are sensitive to air flow rates through 
 the collector, and correction factors are appropriate if the airflow 
 rate is different from the collector manufacturer's recommendation. The 
 correction factor is applied to the X value as follows: 
 
11-8 
 
 where Kl 
 
 X(new value) = X • ^ (11-8) 
 
 is determined from Figure 11-4 or from the Equation (11-9): 
 
 _ . C c .0.28 
 "l 4.13A./ 
 
 for 1 < C 7A„ < 5 
 c c 
 
 (11-9) 
 
 where 
 
 C is capacitance flow rate through the collector 
 c 
 
 A is collector area 
 c 
 
 1.3 
 
 I.I 
 
 1.0 
 
 0.9 
 
 0.8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 f 
 
 .0 2.0 3.0 4.0 5.0 
 
 — — Btu/h-°F-ft 2 
 A c 
 
 Figure 11-4. Collector Capacitance Factor (Air), K-^ 
 
11-9 
 
 CORRECTION FOR STORAGE 
 
 The normal storage capacity is assumed to be two gallons of water 
 
 2 
 per square foot of collector [16.7 Btu/(ft -°F)] for a liquid system and 
 
 0.75 ft 3 of pebbles per square foot of collector [15 Btu/(ft 2 -°F)] for 
 
 an air system. When storage sizes differ from these values, the effect 
 
 is determined by a correction to the X value in the following way: 
 
 X (corrected value) = X • K £ (11-10) 
 
 where Kp is determined from Figure 115 or Equation (11-11) for water 
 storage and Equation (11-12) for a pebble bed. 
 
 Mc 
 
 K 2 (water storage) = ( 16 ^ A ) 
 
 p x-.25 
 
 for 5 < Mc /A < 60 
 P c 
 
 (11-11) 
 
 20 30 40 50 60 
 
 (Mc p ) s 
 
 ~a7~ 
 
 Btu/ft 2 «°F 
 
 Figure 11-5. Storage Capacitance Factor, K 2 
 
11-10 
 
 where 
 
 M is mass of storage (lb) 
 
 c is specific heat of storage mass (Btu/lb*°F) 
 
 2 
 A is collector area (ft ) 
 c 
 
 Mc 
 K 2 (pebble bed) = (j$-) 3 
 
 c 
 
 for 5 < Mc /k < 60 (11-12) 
 
 p c 
 
 CORRECTION FOR LOAD HEAT EXCHANGER 
 
 One additional correction factor should be considered for a liquid- 
 based system: the size of the load heat exchanger. A small load heat 
 exchanger will affect the storage tank temperature and the temperature 
 of the fluid circulated to the collector. The correction factor is 
 expressed as a function of the load heat exchanger effectiveness in 
 comparison to the UA of the building, and is applied to Y as follows: 
 Y (corrected value) = Y • K 4 (11-13) 
 
 where K, is determined from Figure 11-6 or Equation (11-14). 
 
 -0.139(UA) 
 
 K A = 0.39 + 0.65 exp ( ? 21Ha ) 
 
 4 £ L L min 
 
 for .5 < -jj^ < 10 (11-14) 
 
 where 
 
 £. is load heat exchanger effectiveness 
 
 C • is the smaller capacitance flow rate through the heat 
 mm r 
 
 exchanger 
 (UA),,. is the thermal conductance for the building 
 
11-11 
 
 .0 
 
 0.9 
 
 0.8 
 
 *: 
 
 0.7 
 
 0.6 
 
 0.5 
 
 
 
 € L c min 
 (UA) 
 
 10.0 
 
 bldg 
 Figure 11-6. Load Heat Exchanger Factor, K. 
 
 DOMESTIC WATER HEATING ONLY 
 
 The f-charts in Figures 11-1 and 11-2 were developed for combined 
 space and water heating systems but may be used for solar domestic water 
 heating systems by applying a correction to X. The correction factor 
 depends upon temperatures of the hot water supply, cold water inlet, and 
 ambient air and is applied in the following manner: 
 
 X (for DHW) = X • K 3 (11-15) 
 
 where K 3 is determined from Figure 11-7 or Equation (11-16). 
 
 K 3 = 
 
 1.18T W + 3.86 T M 
 
 202 - T 
 
 2.32 T - 66.2 
 a 
 
 (11-16) 
 
11-12 
 
 "~ 1 -i — 
 
 HW Supply Temp.= l40°F 
 HW Supplv Temp. = 1 20°F 
 
 CW Supply 
 Temp.= 70° F 
 
 20 4 60 80 100 
 
 Average Doy-Time Temperature (X), °F 
 
 Figure 11-7. Hot Water Factor, K^ 
 
 where 
 
 T w is the hot water supply temperature, °F 
 T„ is the cold water inlet temperature, °F, 
 
 (see Table 11-1 at end of this module) 
 T is the average ambient air temperature while 
 
 collecting, °F. 
 
 CALCULATION PROCEDURE 
 
 The f-chart calculation procedure is outlined step-by-step and is 
 followed by an example calculation. Space and DHW heating loads must be 
 known or determined before beginning an f-chart performance analysis and 
 it is helpful to use worksheets to organize the necessary computations. 
 Separate worksheets are provided for air and liquid systems. 
 
11-13 
 
 Step 1 . Solar System Data. Complete Worksheet A. Use available 
 data from blueprints, specifications, inspections and 
 handbooks. A heat load analysis for the building is 
 required. For determining the UA of the building, refer 
 to Worksheet B. 
 Step 2 . Monthly and Annual Heating/DHW Loads, L. Use Worksheet 
 B. If the design heating load for the building is not 
 available, an analysis is required. (Refer to Module 5). 
 Step 3 . Total Monthly Solar Radiation, S. Use Worksheet C. 
 Step 4 . Collector Performance Characteristics, F R (xa), F R U, . Use 
 Worksheet D. Lines 1, 2, 3 and 4 are transferred from 
 Worksheet A. 
 Corrections to F R (xa) , F R U, are necessary when the horizontal 
 axis of the collector efficiency chart is based on fluid temperature 
 other than the inlet temperature to the collector, T. . Although col- 
 lector test standards suggest use of T. in expressing collector effi- 
 ciencies, manufacturers do not always show collector characteristics in a 
 
 uniform manner. The corrections to F n (xa) , and F D U, for different 
 
 R n K l 
 
 cases are explained below. 
 
 T* - T 
 Case 1 . In — ? , T* is T. . (fluid inlet temperature) 
 
 No correction is needed 
 
 T. + T 
 Case 2. If T* is — — ? ou , which is the average of the inlet 
 
 and outlet temperatures, 
 
 F R (xa) (new value) = Fn(xot) (from efficiency curve) x F-n — t- 
 
 1 + R L c 
 1 2C 
 c 
 
11-14 
 
 where C is capacitance flow rate of the fluid through 
 
 the collector, (m c ) Btu/(hr-°F) 
 
 P c 
 
 F R U. (new value) = F R U. (from efficiency curve) x f— n — j— 
 
 1 + R L c 
 1 2 C 
 
 c 
 
 r _ • „ _ ,volumetriCw~, . , j oor .n. w w heat w time . 
 C c " m c p " ( flow rate )(fluid density)( capacitance )( conversion ) 
 
 Case 3 . If T* is T . (fluid outlet temperature)Btu/hr°F 
 
 FdC™),, = FdC™),, (from efficiency curve) x f-tt — a - 
 
 k n k n 'd^i " 
 
 l + R k c 
 
 L c 
 
 F R U. = F R U. (from efficiency curve) x r-n — jr- 
 
 L c 
 Incident Angle Modifier 
 
 Corrections to transmittance, t, through the cover plates, and 
 absorptance, a, for the absorber plate are necessary because of sun 
 angle variations on the collector during the day. The F R (ta) deter- 
 mined for normal incidence during collector testing must be corrected 
 for an effective daily transmittance-absorptance product, (ia). 
 
 to" _ ,0.91 for two cover plates 
 (xa) *0.93 for one cover plate 
 
 Collector/Storage Heat Exchanger Correction Factor 
 
 For air systems there is no correction. For liquid systems, 
 correction is made to F R in accordance with Module 7 (see Worksheet D 
 Liquid Systems). 
 
 Step 5 . Correction Factors K-,, K ? and K.. Use Worksheet E. 
 
 Step 6 . System Performance parameters. Use Worksheet F. 
 
 Step 7 . System Performance Calculations, f and ^ , . Use 
 Worksheet G. 
 
11-15 
 
 EXAMPLE 11-1 
 
 Estimate the performance of an air-type solar space and water 
 
 heating system for a three bedroom house located in Denver, Colorado. A 
 
 2 
 collector area of 300 ft is planned. The house is wood framed with 
 
 R-19 wall insulation and R-30 ceiling insulation. The overall dim- 
 ensions of the house are 28 feet wide and 50 feet long and it is com- 
 pletely weatherized. 
 
 The heat loss calculations for the building have been made, and the 
 overall UA (heat conductance) is 450 Btu/(hr-°F). Using the time con- 
 version from hour to day, the heating and domestic hot water load for 
 the building is 10,800 Btu/DD. Complete Steps 1 through 7. 
 
 Step 1. Complete Worksheet A. (pp. 11-17, 11-18) 
 
 Step 2. Complete Worksheet B. (p. 11-19) 
 
 Step 3. Complete Worksheet C. (p 
 
 Step 4. Complete Worksheet D. (p 
 
 Step 6. Complete Worksheet F. (p 
 
 Step 7. Complete Worksheet G. (p 
 
 11-20) 
 11-21) 
 11-23) 
 11-24) 
 
 2 
 
 Answer . For collector area of 300 ft , the air- type heating 
 
 system will provide 76 percent of the total annual space and water 
 heating load. 
 
 EXAMPLE 11-2 
 
 Estimate the performance of a liquid-type space and water heating 
 system for a three bedroom house located in Fort Collins, Colorado. The 
 UA for the building is 714 Btu/(hr-°F) and hot water use is 80 gallons 
 per day. The owner desires to install 500 ft of RQP Company collectors 
 at a tilt of 50°. Collector characteristics are: 
 
11-16 
 
 F R (T«) n = 0.73 
 
 F R U L = 0.54 Btu/(hr-ft 2 -°F) 
 
 based on (T. - T )/I T . 
 l a I 
 
 A mixture of 30 percent ethylene glycol and water is specified for 
 
 2 
 the collector loop. Storage volume is 1.5 gal/ft of collector. 
 
 Answer . The solar system is estimated to provide 87.4 million Btu 
 
 of useful heat for space and water heating, which is 68 percent of the 
 
 total load. 
 
11-17 
 
 Worksheet A 
 Sheet 1 of 2 
 AIR SYSTEMS 
 
 SOLAR SYSTEM DATA 
 
 Building Owner 
 
 Address Y)cy\ 
 
 PW <_ ftVs3 J^Kh D^VKWcd 
 
 * 
 
 Vcv Q>tov^4o Ph. \<6l-OOGft 
 
 Contractor SoUv (p^^\x^\;<y^ Co Ph. Ar^X—QQC \ 
 
 Type of System (liquid or air, H/DHW) ttll \ H/DH W 
 
 Site and Building Data 
 
 1. Location: Nearest Cit y ftevxvcv Latitude 3^. 5° N 
 
 Building UA ^50 Btu/(hr-°F) 
 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. 
 9. 
 10. 
 
 DHW volume per day 
 
 %o 
 
 gallons/day 
 
 Collector manufacturer. 
 Collector area 
 
 A */ Z Cdtn ^M 
 
 30A 
 
 fv 
 
 Collector tilt 
 
 55 
 
 degrees 
 
 Tilt = latitude + 
 
 15 
 
 Collector orientation 
 Collector shading 
 
 degrees 
 
 o 
 
 degrees 
 from south 
 
 % in December 
 
 Collector efficiency data 
 (a) F R (xa) n 
 
 OJd 
 
 (b) F R U L 
 
 (c) Fluid temperature basis (circle one) 
 
 Case 1 IT 
 
 Case 2 T. + T . 
 
 i out 
 
 0,%0 Btu/(hr-ft 2 -°F) 
 
 Case 3 
 
 out 
 
H_18 Worksheet A 
 
 Sheet 2 of 2 
 AIR SYSTEMS 
 
 11. Collector Fluid: 
 
 (a) Composition: Q ( y~ 
 
 (b) Flow rate 6 LOO ft 3 /min 
 
 (c) Capacitance Flow rate (cfm)x(density)x(specific heat)x6Q m/hr 
 1 r col lector area 
 
 2 ,0 Btu/(hr-ft 2 -°F) 
 
 Storage Data 
 
 12. Storage medium re jg \>\<~ DeQ 
 
 13. Unit volume \,Q ft 3 /ft 
 
 14. Total volume (item 5 x 13) ZQQ ft 
 
 15. Storage Capacitance (vo1 ^^"^^^'^^ 
 
 3 r collector area 
 
 3 
 
 30 Btu/(ft 2 -°F) 
 
 Auxiliary Furnace/Boiler 
 
 Type \Aof /riV 
 
 Manufacturer Leyin<? K 
 
 Rated Capacity SO OOO Btu/hr 
 
 Auxiliary energy source Elcvry.'ci \ y 
 Auxiliary DHW Unit 
 
 Size AO gal 
 
 Auxiliary energy source f- lcc*tv|cc 4^ 
 
 Hot water set temperature 1 A-Q 9 F 
 
11-19 
 
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11-20 
 
 Worksheet C 
 AIR SYSTEMS 
 
 TOTAL MONTHLY SOLAR RADIATION AVAILABLE, S 
 
 Project 
 
 Location 
 
 Collector Tilt 
 
 Nearest Data Site 
 
 Sk^ W^ &&5jjg*C 
 
 c= 
 
 Den 
 
 v€ r 
 
 Ut t)5° 
 
 ueyvu 
 
 V\f cv* 
 
 1 
 
 Month 
 
 Monthly Avg. 
 Daily Rad. 
 on TiU Surf. 
 
 l J 
 Btu/(Dayft 2 ) 
 
 No. of Days 
 in month 
 N 
 
 Tot. Monthly 
 Radiation 
 on Tilt Surf. 
 
 S 
 Btu/(Mo-ft 2 ) 
 
 Jan. 
 
 1175" 
 
 31 
 
 LL22S 
 
 Feb. 
 
 A>57 
 
 28 
 
 57.516 
 
 March 
 
 ZOoX 
 
 31 
 
 k3.34y 
 
 April 
 
 LSli 
 
 30 
 
 £4 , A'SO 
 
 May 
 
 I4 7A 
 
 31 
 
 JS\,Uh 
 
 June 
 
 ITIO 
 
 30 
 
 fl ?OQ 
 
 July 
 
 Q3 
 
 31 
 
 f.3.04«7 
 
 Aug. 
 
 67 6 
 
 31 
 
 £&j 156 
 
 Sept. 
 
 Z0&6> 
 
 30 
 
 feL sso 
 
 Oct. 
 
 a^ 4 - 
 
 31 
 
 £3,4S4- 
 
 Nov. 
 
 Ut4- 
 
 30 
 
 55 1 120 
 
 Dec. 
 
 USr 
 
 31 
 
 S>.5(?fr 
 
11-21 
 
 Worksheet D 
 AIR SYSTEMS 
 
 COLLECTOR COMBINED PERFORMANCE CHARACTERISTICS, F R (xa), F R U L 
 
 PROJEC T ^>un \)& X <\ K^ld ^Vic- 
 
 Collector Efficiency Data from Worksheet A (lines 10(a), (b)) 
 1. Intercept, F R (xa) n = () , U^ 
 
 2. Slope, F R U L 
 s ence Temperature 
 
 3. Collector area, A, 
 
 Q-zo 
 
 Reference Temperature Basis: 1. ft. ,] 2. 
 
 t. + t . 
 in out 
 
 3 00 ft 2 
 
 3. t 
 
 out 
 
 4. Collector volumetric flow rate (Worksheet A, 11(d)) 
 
 QOQ ft 3 /min 
 
 Correction to t. basis 
 
 5. Case 1: (no correction) F D (xa) 
 
 k n 
 
 F R U L 
 
 6. Case 2: F R (xa) = F R xa x 
 
 6. 6,1 
 
 0>tO 
 
 h\ A c 
 
 1 + 
 
 2 C. 
 
 UA 
 
 ¥l =f r u l x 
 
 F R U L A c 
 
 1 + 
 
 m± 
 
 2 C 
 
 8. 
 9, 
 
 C = itl _ /volumetric 
 
 time wspecificx 
 conversion' ^heat ' 
 
 *„ = m_ _ /voiumexricw,. ... w 
 c c « (,4n^., ~,4.~ MdensityH 
 p v flow rate v J ' v i 
 
 where: for liquids, density = (8.34 lb/gal) x 
 
 ( g?avity C) for air ' densit y = °- 075 lb / ft3 
 
 at 70° and 1 atm. specific heat = 0.24 Btu/lb-°F 
 
 7. Case 3: F D (xa) n = F D (xa) n x 
 
 R VLW 'n 'R^ u/ n 
 
 L l + 
 
 F R U L A c 
 
 xlb- 
 
 F R U L 
 
 F R U L 
 
 1 
 
 1 + 
 
 F R U L A c 
 
 KiA 
 
 t . . 4. „ n M j.£. (xa) r.91, for two cover plates 
 Incident Angle Modifier, j^j- = { >93j for one covep |\, ate 
 
 xa 
 
 F R Cra) » F R (H)„ X p^- ■ ^£L x _A«_ - _&i£ 
 
11-22 
 
 Worksheet E 
 AIR SYSTEMS 
 
 CORRECTION FACTORS, K. , K 2 
 
 PROJEC T Oun WgjL \es \ \ c 
 
 HC<_ 
 
 Collector Flow Factor, K, 
 
 1. Air Flow rate (Worksheet A, line 11(b)) = 
 
 2. Capacitance Flow rate (from Worksheet A, 
 line 11(c)) 
 
 3. K, = (from Figure 11-4) = 
 
 600 
 
 3to 
 
 HAL 
 
 cfm 
 
 - 
 
 I 
 
 Btu/(h-ft 2 -°F)! 
 
 Storage Mass Capacitance Factor, K 2 
 
 4. Storage Capacitance (Worksheet A, 
 line 15 =) 
 
 5. Kp = (from Figure 11-5) = 
 
 ^ 
 
 Btu/ft 
 
 2.0| 
 
 OAl^ 
 
11-23 
 
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11-25 
 
 Worksheet A 
 Sheet 1 of 2 
 LIQUID SYSTEMS 
 
 SOLAR SYSTEM DATA 
 
 Building Owner 
 
 Address par f- 
 
 to 
 
 v t* 
 
 S Um 5 U i vi e 
 
 fJVcZ 
 
 k] on a ^^vybaJ 
 
 t- 
 
 Cole Ph. 4$3~OOQ Q 
 
 Contracto r SoUr t-oa'sKucf joa (^9 Ph. 4g"^ ? ~^ ? <^<J / 
 
 Type of System (liquid or air, H/DHW) Lifru.d , H / I) tf W 
 
 + 
 Site and Building Data 
 
 1. Location: Nearest City Foy-f Coflin^ Latitude 4£).<£°A/ 
 Building UA 7 / 4- Btu/(hr-°F) 
 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. 
 9. 
 10. 
 
 11 
 
 DHW volume per day SO 
 
 Collector manufacturer 
 
 Collector area f7oO 
 
 Collector tilt 5 O 
 
 H3- 
 
 gallons/day 
 
 ft : 
 
 Tilt = latitude + 
 
 a 
 
 Collector orientation 
 Collector shading 
 
 A 
 
 degrees 
 
 
 
 degrees 
 degrees 
 from south 
 
 % in December 
 
 Collector efficiency data 
 
 (a) 
 
 (b) 
 
 F R (Ta) n 
 F R U L 
 
 13 
 
 j£4r Btu/(hr-ft 2 -°F) 
 
 (c) Fluid temperature basis (circle one) 
 
 Case 1 
 Case 2 
 
 Case 3 
 
 Q 
 
 T i + T out 
 
 T 
 
 out 
 
 ItLL 
 
 Collector Fluid: 
 
 (a) Composition: 
 
 (b) Specific heat, c (from Mod. 4) 
 
 (c) Fluid density, p (from Mod. 4) 
 
 (d) Flow rate G 
 Storage Data 
 
 12. Storage medium W^vT £ v 
 
 13. Unit volume 
 
 14. Total volume (item 5 x 13) 
 
 W ejVl^ We. cA^co) ] V>°1 
 
 QAO Btu/(1b-°F) 
 %32z lb/gal 
 
 I Q gal/min 
 
 ,5" 
 
 150 
 
 gal/ft 2 or ft 3 /ft 2 
 gal or ft 3 
 
11-26 Worksheet A 
 
 Sheet 2 of 2 
 LIQUID SYSTEMS 
 
 15. Specific heat of storage material c | Btu/(lb«°F) 
 
 16. Density ff 34- lb/gal 
 
 17. Total mass (14 x 16) M (J55 lb. 
 
 18. Total heat capacity (17 x 15) 
 
 C s = Mc p L2S5 Btu/°F 
 
 19. Total heat capacity per unit 
 
 collector area (18 v 5) \2.S Btu/(ft 2 -°F) 
 
 Heat Exchangers 
 
 20. Collector/storage type ( ouVifay rlovy/ and 
 
 manufacturer N au^A KaAiaias 
 
 21. Storage loop flow rate J \ 5" gal/min 
 
 22. Heat exchange effectiveness e „ 0.1 S 
 
 cs — ^-x 
 
 23. Load heat exchanger type C\ios<- ^\ov) wc\.tgv - co^ and 
 manufacturer Mouw^ \<iA\<i\or 
 
 24. Load loop flow rate ^ \2 gal/min 
 
 25. Building air supply flow rate IQ-ffcQ ft 3 /min 
 
 26. Heat exchanger effectiveness e. Q t 75^ 
 
 DHW Pre-heater 
 
 27. Collector/storage heat exchanger type (^-...^-Uyfiow and 
 manufacturer Mftuwi r\*Ji <"a Yov 
 
 28. Collector loop flow rate J — gal/min 
 
 29. Heat exchanger effectiveness g„ Q* 1 
 
 30. Storage volume fiO gal 
 
 31. Storage mass, M s - (line 30 x 8.34) fa& 7 lb 
 
 Auxiliary Furnace/Boiler 
 
 32. Type Cold Den Ur 
 
 33. Manufacturer r\C\ y (T^»np<\vvW 
 
 34. Rated capacity ) DQ t OOQ Btu/hr 
 
 35. Auxiliary energy source ^ Wcfrv'io 4^ 
 
 Auxiliary DHW Unit 
 
 36. Size >VQ gal 
 
 37. Auxiliary energy source cJU^OdS^ 
 
 38. Hot water set temperature \ ^cO Q F 
 
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11-28 
 
 Worksheet C 
 LIQUID SYSTEMS 
 
 TOTAL MONTHLY SOLAR RADIATION AVAILABLE, S 
 
 Project 
 
 San \>oAh r\c^id<?Hce_ 
 
 Location 
 
 'Fort (6 ll; s < 
 
 Collector Tilt 
 
 La T 15° 
 
 Nearest Data Site 
 
 Vc**\\<Lr 
 
 1 
 
 Month 
 
 Monthly Avg. 
 Daily Rad. 
 on Ttlt Surf. 
 
 h 
 Btu/(Dayft 2 ) 
 
 No. of Days 
 in month 
 
 Tot. Monthly 
 Radiation 
 on Tilt Surf. 
 
 S 
 Btu/(Mo-ft 2 ) 
 
 Jan. 
 
 14 3 1 
 
 31 
 
 4&+&Q3 
 
 Feb. 
 
 L£33 
 
 28 
 
 43,^4- 
 
 March 
 
 log 
 
 31 
 
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 April 
 
 LL1 
 
 30 
 
 4± S^O 
 
 May 
 
 *25. 
 
 31 
 
 41 , 175' 
 
 June 
 
 July 
 Aug. 
 Sept, 
 
 Oct. 
 
 Nov 
 
 Dec. 
 
 Hi 
 
 1453 
 
 Ll£3 
 
 30 
 
 31 
 
 31 
 
 30 
 31 
 
 30 
 
 31 
 
 44-,~7 3Q 
 4 7, 5 55 
 
 AS, 310 
 4 3,^T^ 
 
11-29 
 
 Worksheet D 
 Sheet 1 of 2 
 LIQUID SYSTEMS 
 
 COLLECTOR COMBINED PERFORMANCE CHARACTERISTICS, F^(xa)-F^U L 
 
 PROJECT OUn \ar>Au K'<] a <Z\\C 
 
 Collector Efficiency Data from Worksheet A (lines 10(a), (b)) 
 
 1. Intercept, F D (xa) 
 
 k n 
 
 2. Slope, F R U L 
 
 0,13 
 
 o. s*r 
 
 Reference Temperature Basis: 1. ft. ,J 2, 
 3. Collector area, A_ 
 
 t. + t . 
 in out 
 
 3. t 
 
 out 
 
 50Q 
 
 ft : 
 
 4. Collector volumetric flow rate (Worksheet A, 11(d)) 
 
 i gal /mi n or ft 3 /min 
 
 Correction to t. basis 
 
 5. Case 1: (no correction) FrCto) = , J S 
 
 F R U L 
 
 CL ££ - 
 
 6. Case 2: F R (TO) n = F„ to x 
 
 1 + 
 
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 2 C. 
 
 tilt 
 
 F R U L 
 
 =F R U L X 
 
 1 + 
 
 F R U L fl c 
 2 C 
 
 W/fV 
 
 r - ^ - /volumetricx / ,. „ ... ,\ /time 
 C c " mc p " ( flow rate X densit yK 
 
 conversion^heat 
 
 specific 
 
 = lot &<ax&n*aio " 4^17 KhJlM t • °0 
 
 where: for liquids, density - (8.34 lb/gal) x 
 
 ( g?a$ity C) for air > densit y = °- 075 lb / ft3 
 
 at 70 Q and 1 atm. specific heat = 0.24 Btu/lb-°F 
 
 7. Case 3: F R (xa) n = F R (Ta) n x 
 
 1 
 
 1 + 
 
 F R U L A c 
 
 KUl 
 
 F R U L 
 
 = F R U L 
 
 1 + 
 
 F R U L A c 
 
 Hfc 
 
 8. Incident Angle Modifier, iM- = {'*} f ° r two cover P] ates 
 
 (xa) .93 for one cover plate 
 
11-30 
 
 Worksheet D 
 
 Sheet 2 of 2 
 
 LIQUID SYSTEMS 
 
 R 
 Collector Loop Heat Exchanger Modifier, -^ 
 
 ""R 
 
 9. For air systems and liquid systems without a collector/storage 
 
 F' 
 R 
 
 heat exchanger, p— = 1 
 
 r R 
 
 Capacitance Rate: 
 
 10. C c = (from line 6) = ^"S 11 Btu/(hr-°F) 
 
 11. C s = (calc. as for C c above) = iSOG Btu/(hr-°F) 
 
 12. C min = (lesser of C c and C g ) = 4 % \1 Btu/(hr-°F) 
 
 13. Collector Storage Heat Exchanger Effectiveness, e = Q , IS 
 
 14. x--J£— . 4gl7/4.73~f*g/7) ■ I-J3 
 
 cs min (from Worksheet A, line 22) 
 
 15 . .y.WJi. &*{.<*■) I +?ll - ,QSL 
 
 c 
 
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 16> \~ 1 + y(x-l) " '-^ 
 
 17. FfcCES) = F R (xa) n x M- x J* = ( Q.l tif.WCI*) ~ Ul 
 
 n 'R 
 
 18. F^U L = F R U L x / = CSA)(M) r .^ T3> 
 
 K 
 
 
11-31 
 
 Worksheet E 
 LIQUID SYSTEMS 
 
 CORRECTION FACTORS, Kg, K 4 
 
 PROJECT l3u,n\)JL \^\<\c *c 
 
 Storage Mass Capacitance Factor, K 2 
 
 Note: M includes hot water storage volume where it is solar 
 heated 
 
 1. gals/ft of collector 
 
 \s 
 
 2. K 2 = (from Figure 11-5) = 1 ,Q7 
 
 Load Heat Exchange Factor, K, 
 
 3. e L (from Worksheet A, line 26) = ; 75" 
 
 4 * C hot water supply loop = mc p = C H 
 
 (from Worksheet A, lines 24 x 8.25 x 60) = 
 
 (oOQ5~ Btu/(hr-ft 2 ) 
 
 5. C. , =mc=C 
 
 air loop p A 
 
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 [0 1C Btu/(hr-ft 2 ) 
 
 6. C min = smaller of C H and C A = \^ { \ b Btu/(hr-ft 2 ) 
 
 7. (UA) bldg = (from Worksheet A, or B) = 
 
 7 (j~ Btu/(hr-°F) 
 
 8. 
 
 !^Mln = \. 3G 
 
 9. K 4 = (from Figure 11-6) = 0^1 
 
11-32 
 
 
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11-34 
 
 SOLAR FRACTION FOR DIFFERENT COLLECTOR SIZES 
 
 In Example 11-2, the detailed calculations yielded the result that 
 
 2 
 solar energy, with 500 ft of RQP collectors and compatible system 
 
 components, provides 68 percent of the total annual space and domestic 
 
 hot water heating load for the building. To determine the annual solar 
 
 fraction provided by a system with different collector areas, the 
 
 2 
 f-chart used for the computations with 500 ft of collectors, and Work- 
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 2 
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 of collectors can be determined by following the procedure below: 
 
 Step 1. - For each month, locate the point (X,Y) on the f-chart 
 
 2 
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 Step 2. - Join the points with the origin, (X=0, Y=0), by a 
 
 straight 
 
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 Step 3. - The distance from the origin to the point along the line 
 
 2 
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 origin to the point and locate the point that represents 
 
 300 ft 2 . 
 
 2 
 Step 4. - Read the appropriate f-value representing 300 ft and 
 
 enter the value on Worksheet G (p. 11-36). 
 
 Step 5. - Complete Worksheet G and determine the annual fraction, 
 
 The procedure described above is followed as shown in Figure 11-8. 
 
 2 
 With 300 ft of liquid-heating collectors, the system will provide 49 
 
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Worksheet A 
 Sheet 1 of 2 
 AIR SYSTEMS 
 
 SOLAR SYSTEM DATA 
 
 Building Owner 
 
 Address Ph. 
 
 Contractor Ph. 
 
 Type of System (liquid or air, H/DHW) 
 
 Site and Building Data 
 
 1. Location: Nearest City Latitude 
 
 2. Building UA Btu/(hr-°F) 
 
 3. DHW volume per day gallons/day 
 
 4. Collector manufacturer 
 
 5. Collector area ft 2 
 
 6. Collector tilt degrees 
 
 7. Tilt = latitude + degrees 
 
 8. Collector orientation degrees from south 
 
 9. Collector shading % in December 
 
 10. Collector efficiency data 
 
 (a) F R (xa) n 
 
 (b) F R U L Btu/(hr-ft 2 -°F) 
 
 (c) Fluid temperature basis (circle one) 
 
 Case 1 T, 
 
 Case 2 T i * T out 
 
 2 
 
 Case 3 T out 
 
Worksheet A 
 Sheet 2 of 2 
 AIR SYSTEMS 
 
 11. Collector Fluid: 
 
 it 
 
 (a) Composition: 
 
 (b) Flow rate G ft 3 /min 
 
 (c) Capacitance Flow rate (cfm)x(density)x(specific heat)x60 m/hr 
 v ' r collector area 
 
 = Btu/(hr-ft 2 -°F) 
 
 Storage Data 
 
 12. Storage medium_ 
 
 13. Unit volume ft 3 /ft 2 
 
 14. Total volume (item 5 x 13) ft 3 
 
 15. Storage Capacitance ^^^±1^ 
 
 collector area 
 
 Btu/(ft 2 .°F) 
 
 Auxiliary Furnace/Boiler 
 Type 
 
 Manufacturer 
 
 Rated Capacity Btu/hr 
 
 Auxiliary energy source 
 
 Auxiliary DHW Unit 
 
 Size gal 
 
 Auxiliary energy source 
 
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 Btu/Mo. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ID 
 
 E 
 t— 
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 «3- 
 
 Temp. 
 Water 
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 op 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 Vol. of 
 
 DHW 
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 co 
 
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 co 
 
 o 
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 CO 
 
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 co 
 
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 Monthly 
 Space 
 Htg Load 
 
 Btu/Mo. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 Monthly 
 Degree 
 Days DD 
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Worksheet C 
 AIR SYSTEMS 
 
 TOTAL MONTHLY SOLAR RADIATION AVAILABLE, S 
 
 Project 
 
 Location 
 
 Collector Tilt 
 
 Nearest Data Site 
 
 
 1 
 
 2 
 
 3 
 
 Month 
 
 Monthly Avg. 
 Daily Rad. 
 on Tilt Surf. 
 
 T T 
 Btu/(Dayft 2 ) 
 
 No. of Days 
 in month 
 N 
 
 Tot. Monthly 
 Radiation 
 on Tilt Surf. 
 
 S 
 Btu/(Mo-ft 2 ) 
 . ._ _. _ _ ^ J 
 
 Jan. 
 
 
 31 j | 
 
 Feb. 
 
 
 28 
 
 j 
 
 March 
 
 
 i 
 
 31 ' i 
 
 i 
 
 April 
 
 
 • 1 
 
 30 | 
 
 May 
 
 
 3i i 
 
 1 \ 
 
 June 
 
 
 30 
 
 July 
 
 
 31 
 
 : . 
 
 Aug. 
 
 
 31 
 
 
 Sept. 
 
 
 30 
 
 
 Oct. 
 
 
 31 
 
 
 Nov. 
 
 
 30 
 
 
 Dec. 
 
 
 31 
 
 
Worksheet D 
 AIR SYSTEMS 
 
 COLLECTOR COMBINED PERFORMANCE CHARACTERISTICS, F R (xo), F R U L 
 
 PROJECT 
 
 Collector Efficiency Data from Worksheet A (lines 10(a), (b)) 
 
 1. Intercept, F R ( T a) n = 
 
 2. Slope, F D U, = _______ 
 
 R L _____ 
 
 Reference Temperature Basis: 1. t. , 2. in g — ^— » 
 
 3. Collector area, A„ = ft 2 
 
 3. t 
 
 4. Collector volumetric flow rate (Worksheet A, 11(d)) 
 
 ft 3 /min 
 
 Correction to t. basis 
 
 5. Case 1: (no correction) F R ( T a) n = 
 
 F R \ - 
 
 out 
 
 6. Case 2: F R ( TOt ) n = F R xa x 
 
 F R U L =F R U L x 
 
 1 + 
 
 F R U L A c 
 2 C_ 
 
 1 + 
 
 F R U L A c 
 2 C_ 
 
 C. = m. _ /volumetricw,. .. wW time 
 c c p " ( f low rate M denslt yM 
 
 )( 
 
 specific 
 
 conversion' v heat ' 
 where: for liquids, density = (8.34 lb/gal) x 
 
 ( gravity C) for air ' densitv = °- 075 lb / ft3 
 
 at 70° and 1 atm. specific heat = 0.24 Btu/lb»°F 
 
 1 
 
 Case 3: F R (xa) n = F R (xa) n x 
 
 1 + 
 
 F R U L A c 
 
 8. 
 9, 
 
 F R U L 
 
 = F R U L 
 
 1 + 
 
 F R U L A c 
 
 T . , . . , M ,. r . (xa) r. 91, for two cover plates 
 Incident Angle Modifier, |^j- = { >93j for one cover ^ 
 
 n 
 
 F R (xa) - F R (xa) n x -^ 
 
 l( * _. = p.M x 0. 93 = 0X<f 
 n 
 
Worksheet E 
 AIR SYSTEMS 
 
 CORRECTION FACTORS, K ] , K 2 
 
 PROJECT 
 
 Collector Flow Factor, K-, 
 
 1. Air Flow rate (Worksheet A, line 11(b)) = cfm 
 
 2. Capacitance Flow rate (from Worksheet A, 
 
 line 11(c)) Btu/(h-ft 2 -°F) 
 
 3. K-, = (from Figure 11-4) = 
 
 Storage Mass Capacitance Factor, K 2 
 
 4. Storage capacitance (Worksheet A, 
 
 line 15 =) Btu/ft 2 -°l 
 
 5. K 2 = (from Figure 11-5) = 
 
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 - 
 
 Tot. Monthly 
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 Btu/(Mo-ft 2 ) 
 
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 Actual 
 Solar 
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 Btu/mo. 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Solar 
 
 Fraction/ 
 
 mo. 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 co 
 
 System 
 Parameter 
 Y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CM 
 
 System 
 
 Parameter 
 
 X 
 
 
 
 
 
 
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SOLAR SYSTEM DATA 
 
 Worksheet A 
 Sheet 1 of 2 
 LIQUID SYSTEMS 
 
 Building 
 
 Owner 
 
 
 
 
 Address 
 
 
 Ph. 
 Ph. 
 
 
 
 Contractor 
 
 
 Type of System (liquid or air, H/DHW) 
 
 
 Site and 
 
 Building Data 
 
 
 
 
 1. 
 
 Location: Nearest City 
 
 Lati 
 
 tude 
 
 
 2. 
 
 Building UA 
 
 
 Btu/(hr-°F) 
 
 
 3. 
 
 DHW volume per day 
 
 
 gallons/day 
 
 
 4. 
 
 Collector manufacturer 
 
 
 
 
 5. 
 
 Collector area 
 
 
 ft 2 
 
 
 6. 
 
 Collector tilt 
 
 
 degrees 
 
 
 7. 
 
 Tilt = latitude + 
 
 
 degrees 
 
 
 8. 
 
 Collector orientation degrees 
 
 
 from south 
 
 
 9. 
 
 Collector shading 
 
 
 % in December 
 
 i 
 
 10. 
 
 Collector efficiency data 
 (a) F R (xa) n 
 
 
 
 
 
 (b) F R U, 
 
 
 Btu/(hr-ft 2 - 
 
 °F) 
 
 
 (c) Fluid temperature basis (circle one) 
 
 
 
 
 
 Case 1 T i 
 
 Case 2 T i + T out 
 
 2 
 
 Case 3 T . 
 
 out 
 
 
 
 
 11. 
 
 Collector Fluid: 
 (a) Composition: 
 
 
 
 
 
 (b) Specific heat, c (from Mod. 4) 
 
 
 Btu/(lb-°F) 
 
 
 
 (c) Fluid density, p (from Mod. 4) 
 
 
 lb/gal 
 
 
 
 (d) Flow rate G 
 
 
 gal /mi n 
 
 
 Storage 1 
 
 Data 
 
 
 
 
 12. 
 
 Storage medium 
 
 
 
 
 13. 
 
 Unit volume 
 
 
 gal/ft 2 or 
 
 ft 3 /ft 2 
 
 14. 
 
 Total volume (item 5 x 13) 
 
 
 gal or ft 3 
 
 
15. Specific heat of storage material c 
 
 16. Density 
 
 17. Total mass (14 x 16) M 
 
 18. Total heat capacity (17 x 15) 
 
 C c = Mc n 
 s p 
 
 19. Total heat capacity per unit 
 collector area (18 * 5) 
 
 Heat Exchangers 
 
 20. Collector/storage type 
 manufacturer 
 
 21. 
 22. 
 23. 
 
 Storage loop flow rate 
 Heat exchange effectiveness e 
 Load heat exchanger type __ 
 manufacturer 
 
 cs 
 
 24. 
 25. 
 26. 
 
 Load loop flow rate 
 
 Building air supply flow rate 
 
 Heat exchanger effectiveness e. 
 
 DHW Pre-heater 
 
 27. Collector/storage heat exchanger type 
 manufacturer 
 
 28. 
 29. 
 30. 
 31. 
 
 Collector loop flow rate 
 
 Heat exchanger effectiveness £■, 
 
 Storage volume 
 
 Storage mass, M st (line 30 x 8.34) 
 
 Auxiliary Furnace/Boiler 
 
 32. Type 
 
 33. 
 34. 
 35. 
 
 Manufacturer 
 
 Rated capacity 
 Auxiliary energy source 
 
 Auxiliary DHW Unit 
 
 36. Size 
 
 37. Auxiliary energy source 
 
 38. Hot water set temperature 
 
 Worksheet A 
 Sheet 2 of 2 
 LIQUID SYSTEMS 
 
 Btu/(lb< 
 
 lb/gal 
 
 lb. 
 
 Btu/°F 
 
 Btu/(ft 2 -' 
 
 and 
 
 F) 
 
 gal /mi n 
 
 and 
 
 gal /mi n 
 ft 3 /min 
 
 and 
 
 gal /mi n 
 
 gal 
 lb 
 
 Btu/hr 
 
 gal 
 
 T) 
 

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Worksheet C 
 LIQUID SYSTEMS 
 
 TOTAL MONTHLY SOLAR RADIATION AVAILABLE, S 
 
 Project 
 
 Location 
 
 Collector Tilt 
 
 Nearest Data Site 
 
 
 1 
 
 2 
 
 3 
 
 Month 
 
 Monthly Avg. 
 Daily Rad. 
 on Tilt Surf. 
 
 r T 
 Btu/(Dayft 2 ) 
 
 No. of Days 
 in month 
 N 
 
 Tot. Monthly 
 Radiation 
 on Tilt Surf. 
 
 S 
 Btu/(Mo-ft 2 ) 
 
 Jan. 
 
 
 31 
 
 
 Feb. 
 
 
 28 
 
 
 March 
 
 
 31 
 
 
 April 
 
 
 30 
 
 
 May 
 
 
 31 
 
 
 June 
 
 
 30 
 
 
 July 
 
 
 31 
 
 
 Aug. 
 
 
 31 
 
 
 Sept. 
 
 
 30 
 
 
 Oct. 
 
 
 31 
 
 
 Nov. 
 
 
 30 
 
 
 Dec. 
 
 
 31 
 
 
Worksheet D 
 Sheet 1 of 2 
 LIQUID SYSTEMS 
 
 COLLECTOR COMBINED PERFORMANCE CHARACTERISTICS, F r (to)-F r U,_ 
 
 PROJEC T 
 
 Collector Efficiency Data from Worksheet A (lines 10(a), (b)) 
 
 1. Intercept, F D (xa) = 
 
 k n ■ 
 
 2. Slope, F D U, = _________ 
 
 R L t. + t 
 
 Reference Temperature Basis: 1. t. , 2. in ? ou , 3. t . 
 
 3. Collector area, A, 
 
 ft : 
 
 4. Collector volumetric flow rate (Worksheet A, 11(d)) 
 
 gal/min or ft 3 /min 
 
 Correction to t. basis 
 
 5. Case 1: (no correction) F R (xa) = 
 
 F R U L 
 
 6. Case 2: F r (tcx) = F R ia x 
 
 Ll + 
 
 F R U L A c 
 2 C_ 
 
 F R U L =F R U L x 
 
 L l + 
 
 F R U L A c 
 2 C_ 
 
 r . ,- vu i Mi!!i' i,i i«,,w. , ,\ ,' >, i um \/SpecifiC\ 
 
 C„ - mc„ - U-,_ _ + „ )(density)( ^^JuL* ) 
 
 volumetric' 
 'c " ""-p " v flow rate 
 
 time 
 conversion /v heat 
 
 where: for liquids, density = (8.34 lb/gal) x 
 
 ( g?a$ity C) for air > densit y = °- 075 lb / ft3 
 
 at 70° and 1 atm. specific heat = 0.24 Btu/lb-°F 
 
 7. Case 3: F R (xa) p = F R (xa) n x 
 
 Ll + 
 
 F R U L A c 
 
 F R U L 
 
 = F R U L 
 
 L l + 
 
 F R U L A c 
 
 8. Incident Angle Modifier, i^) = {•£ f ° r two cover P^ es 
 
 (ia) .93 for one cover plate 
 
Worksheet D 
 Sheet 2 of 2 
 LIQUID SYSTEMS 
 
 F R 
 Collector Loop Heat Exchanger Modifier, -fA 
 
 9. For air systems and liquid systems without a collector/storage 
 
 F R 
 heat exchanger, *- = 1 
 
 ■R 
 Capacitance Rate: 
 
 10. C = (from line 6) = Btu/(hr-°F) 
 
 11. C = (calc. as for C_ above) = Btu/(hr«°F) 
 
 12. C . = (lesser of C and C ) = Btu/(hr-°F) 
 
 mm c s 
 
 13. Collector Storage Heat Exchanger Effectiveness, e = 
 
 14. x = 
 
 16. 
 
 15. y= , 
 
 u c 
 
 e cs min (from Worksheet A, line 22) 
 A C (F R U L ) 
 
 F R " l +y(x-l) 
 
 17. F R (xa) ■ F R (xa) n x gj- X £ 
 
 : n 'R 
 
 18 - F R U L =F R U L X ^ 
 
Worksheet E 
 LIQUID SYSTEMS 
 
 CORRECTION FACTORS, Kg, K 4 
 
 PROJECT 
 
 Storage Mass Capacitance Factor, Ko 
 
 Note: M includes hot water storage volume where it is solar 
 heated 
 
 1. gals/ft 2 of collector 
 
 2. K 2 = (from Figure 11-5) = 
 
 Load Heat Exchange Factor, K, 
 
 3. e. (from Worksheet A, line 26) = 
 
 4 * C hot water supply loop " : mc p =: C H 
 
 (from Worksheet A, lines 24 x 8.25 x 60) = 
 
 5. C . t = mc = C« 
 air loop p A 
 
 (from Worksheet A, line 25 x 0.075 x .24 x 60) = 
 
 8. 
 
 £■ C • 
 
 L mm 
 
 UA 
 9. K, = (from Figure 11-6) 
 
 Btu/(hr-ft 2 ) 
 
 Btu/(hr-ft 2 ) 
 
 6. C min = smaller of C R and C A = Btu/(hr-ft 2 ) 
 
 7. (UA) bldg = (from Worksheet A, or B) = 
 
 Btu/(hr-°F) 
 

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 Parameter 
 Y 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Parameter 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 Tot. Mo. 
 Htg. Load 
 
 Btu/mo. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4-> 
 
 C 
 O 
 
 2Z 
 
 
 
 -Q 
 OJ 
 U_ 
 
 
 
 2: 
 
 •1— 
 
 a. 
 < 
 
 >> 
 
 rO 
 
 2: 
 
 0) 
 
 c 
 ■-0 
 
 
 CJ> 
 
 Q. 
 CO 
 
 O 
 
 O 
 
 > 
 O 
 
 O 
 CU 
 Q 
 
 =3 
 
 o 
 
 CO ^J. 
 
 C Cr— 
 
 E E 
 
 3 3d) 
 r— r— S- 
 
 O O 3 
 O O O) 
 
 CQ U- U_ 
 
 
 +J +-> +-> = 
 
 
 Q) CD d) +-> 
 
 
 (D CD CD S- 
 
 
 x: -C .c re 
 
 
 CO CO CO -d 
 
 
 a;^:^ u_i 
 
 
 S- S- S- 
 
 
 O O O M- X 
 
 
 3: 3 3 = 
 
 
 4- 
 
 
 E E E E 
 
 
 O O O O II 
 
 
 S- S_ S- &- 
 
 
 U. U. U. U. UJ 
 
 -!-> 
 
 
 O 
 
 
 4-> 
 
 
 1 — cm ro -^-un 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 12 
 
 ECONOMIC CONSIDERATIONS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS., COLORADO 
 
12-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 12- i i i 
 
 LIST OF TABLES 12-iv 
 
 OBJECTIVES 12-1 
 
 INTRODUCTION 12-1 
 
 FACTORS IN ANALYSES 12-2 
 
 EXAMPLE 12-1 12-12 
 
 EXAMPLE 12-2 12-13 
 
 EXAMPLE 12-3 12-13 
 
 ENERGY COSTS 12-15 
 
 INFLATION RATES 12-19 
 
 SOLAR SYSTEM COSTS 12-21 
 
 EQUIPMENT AND INSTALLATION TIME ESTIMATES . . . 12-22 
 
 Liquid-Heating Systems ...... 12-22 
 
 Air-Heating Systems ....... 12-23 
 
 Domestic Water Heaters ...... 12-24 
 
 TYPICAL INSTALLED COSTS 12-26 
 
 Space Heating System - Liquid Collectors . . 12-26 
 
 Space Heating System - Air Collectors . . . 12-26 
 
 Domestic Water Heaters ...... 12-27 
 
 MORTGAGE PAYMENTS 12-29 
 
 TAX CREDIT 12-29 
 
 PROPERTY TAXES 12-31 
 
 INSURANCE 12-31 
 
12-ii 
 
 
 
 
 
 Page 
 
 ADDITIONAL INCOME TAX CREDITS 
 
 • 
 
 
 
 12-32 
 
 OPERATING COSTS 
 
 . 
 
 
 
 12-38 
 
 MAINTENANCE COSTS . 
 
 . 
 
 
 
 12-39 
 
 ECONOMIC ANALYSIS WORKSHEETS 
 
 
 
 
 12-40 
 
 WORKSHEET LCA-1 
 
 
 
 
 12-40 
 
 WORKSHEET LCA-2 
 
 
 
 
 12-40 
 
 WORKSHEET LCA-3 
 
 
 
 
 12-45 
 
 WORKSHEET LCA-4 
 
 
 
 
 12-48 
 
 EXAMPLE 12-4 . 
 
 . 
 
 
 
 12-50 
 
 EXAMPLE 12-5 . 
 
 . 
 
 
 
 12-55 
 
 APPENDIX - State Solar Legislai 
 
 Lion 
 
 
 
 
12-1 ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 12-1 Energy Cost per Million Btu for Natural Gas, 
 
 Propane, and No. 2 Fuel Oil 12-17 
 
 12-2 Energy Cost per Million Btu for Electricity . . 12-18 
 
 12-3 Inflation Factors 12-20 
 
 12-4 Repayment on Loan 12-30 
 
12-iv 
 LIST OF TABLES 
 
 Table Page 
 
 12-1 Values of P/X (d,r,n) for Discount Rate of 
 
 Percent 12-6 
 
 12-2 Values of P/X (d,r,n) for Discount Rate of 
 
 4 Percent 12-7 
 
 12-3 Values of P/X (d,r,n) for Discount Rate of 
 
 6 Percent 12-8 
 
 12-4 Values of P/X (d,r,n) for Discount Rate of 
 
 8 Percent 12-9 
 
 12-5 Values of P/X (d,r,n) for Discount Rate of 
 
 10 Percent 12-10 
 
 12-6 Values of P/X (d,r,n) for Discount Rate of 
 
 12 Percent 12-11 
 
 12-7 Present Worth Factors (P) 12-16 
 
 12-8 Typical Equipment and Material Prices (in 1978) 
 
 for Liquid-Heating Systems ..... 12-22 
 
 12-9 Installation Time Estimates for Typical Liquid- 
 Heating Systems ....... 12-23 
 
 12-10 Typical Equipment and Material Prices (in 1978) 
 
 for Air-Heating Systems ...... 12-23 
 
 12-11 Installation Time Estimates for Typical Air- 
 Heating Systems ....... 12-24 
 
 12-12 Equipment Costs for Components of Domestic Water 
 
 Heaters (1978 prices) 12-25 
 
 12-13 Estimates of Installation Times for Domestic Water 
 
 Heaters 12-25 
 
 12-14 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i)J" m " 1 Mortgage Term (m) = 10 years 12-33 
 
 12-15 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 15 years 12-34 
 
 12-16 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-d+i)- 3 """ 1 " 1 Mortgage Term (m) = 20 years 12-35 
 
12-v 
 
 Table Page 
 
 12-17 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 25 years 12-36 
 
 12-18 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 30 years 12-37 
 
12-1 
 
 OBJECTIVES 
 
 The objectives of this module are to describe methods for 
 determining solar heating costs on a life-cycle basis and on a cash-flow 
 basis and for comparing these costs with those of non-solar systems. 
 The participant of this workshop should be able to: 
 
 1. Estimate the installed cost of a solar system. 
 
 2. Calculate the total life-cycle cost of a solar heating system. 
 
 3. Estimate the economic feasibility of a solar system. 
 
 INTRODUCTION 
 
 Solar heating systems require higher capital costs than 
 conventional systems, and economic evaluations invariably involve cost 
 comparisons between the two systems. Comparisons which do not account 
 for future fuel cost savings for heating are both misleading and un- 
 favorable to solar systems. By accounting for capital and operating 
 costs of heating alternatives over a period of time, deemed to be the 
 "life" of the systems, the relative economic merits of "paying for 
 hardware" or "paying for energy" can be assessed. Thus, life-cycle 
 costing methods have generally been used to make economic comparisons, 
 although speculative assumptions for the rates of increase in energy 
 prices, discount rates, costs for goods and services, property tax, and 
 insurance must be used in the analysis. Credit is taken for income tax 
 deductions allowable for property tax payments and mortgage (loan) 
 interest payments. While life-cycle cost analysis is a fair method for 
 
12-2 
 
 comparing solar and non-solar systems, consider annual cash flow 
 differences between the two types of heating systems. Both methods are 
 explained in this module. 
 
 The economic principles in this module have been presented in 
 sufficient detail for verification by financial specialists. Much of 
 this material, such as the development of equations for discounted cash 
 flow, need not be learned by the trainee. By following the examples in 
 the work sheets and using the charts and tables in this module, calcula- 
 tions are simplified. Solar heating practitioners concerned mainly with 
 selecting and installing solar heating systems may seldom need economic 
 information other than the costs of equipment and installation labor. 
 Other material in this module can be, however, useful and important for 
 those who are reponsible for making decisions and providing recommenda- 
 tions on the most economical methods for the heating of buildings. 
 
 FACTORS IN ANALYSES 
 
 The total cost of a solar heating system, over its useful life, 
 includes (1) capital and installation costs or mortgage payments on 
 money borrowed to pay for the installed system, (2) fuel cost for the 
 auxiliary unit, (3) operating and maintenance (0 and M) costs, and (4) 
 income tax credits for initial investment and for annual interest and 
 property tax payments. With a non-solar heating system the capital and 
 and M costs are small but fuel costs are high (and rising steadily). 
 A solar system has large capital costs, lower fuel costs, and non- 
 negligible and M costs. A comparison is necessary to determine 
 whether a solar system is economical compared to a non-solar system, and 
 
12-3 
 
 the comparison is usually made for a selected number of years, which is 
 
 estimated to be the "life" of a system. A life-cycle cost analysis is 
 
 first explained followed by an annual cash-flow analysis. 
 
 The yearly cash flow for a residential solar heating system is: 
 
 Yearly cost _ Mortgage + Auxiliary + Property + Insurance (12-l'J 
 with solar payment % fuel cost tax increase premium ^ * 
 
 . Operating Maintenance _ Income tax savings for 
 costs cost interest and taxes paid 
 
 whereas for a non-solar system, 
 
 Yearly cost _ Fuel + Operating and (\?-i\ 
 
 for non-solar cost maintenance costs *■ ' 
 
 In commercial buildings there are other factors such as depreciation of 
 equipment and salvage value to be considered. 
 
 The sum of the yearly cash flows over the "life" of the system can 
 be construed as the life-cycle cost of the system, and the costs of the 
 solar and non-solar systems can be compared over an equal life-time of n 
 years, to determine which system would be more expensive. Cash flow 
 calculations should include inflation, with fuel costs probably increas- 
 ing more rapidly than costs of general goods and services (at least in 
 the near-term). The use of different inflation factors for the items in 
 Equation (12-1) or (12-2) in effect gives more weight to some cost items 
 than to others, say fuel costs over mortgage payments as an example, 
 particularly if mortgage payment is fixed and fuel cost rises. 
 
 Because the sum of annual cash flows for both solar and non-solar 
 systems would in effect add different value dollars each year as a 
 consequence of inflation, a more appropriate economic comparison is made 
 on the basis of present worth, which discounts future expenditures 
 
12-4 
 
 to the value of first year dollars. Hence, when the present worth of 
 future annual expenditure is computed, and these values are added, 
 equivalent-value dollars are being considered. When the inflation and 
 discount factors are taken into consideration in a life-cycle cost 
 analysis, Equations (12-1) and (12-2) may be rewritten as follows: 
 
 C T (solar) = (AC a )E 1 + C Q E o + C m E m + (l-F)Lc f E f (12-3) 
 
 and 
 
 C Tr (non-solar) = C E + C E + Lc.E. (12-4) 
 
 IL ocomcm ff 
 
 where A is the collector area, ft 2 , 
 
 Cj is the total life-cycle cost of the solar system, $, 
 
 Cj C is the total life-cycle cost of the non-solar system, $, 
 
 C is the installed cost of the solar system per unit 
 collector area, $/ft 2 , 
 
 C is the first year operating cost for the solar system, 
 $/yr, 
 
 C is the first year operating cost for the non-solar system, 
 oc $/yr, 
 
 C is the first year maintenance cost for the solar system, 
 m $/yr, 
 
 c is the first year maintenance cost for the non-solar 
 mc system, $/yr, ' 
 
 c f is the first year fuel cost per unit of delivered heat, 
 T $/MMBtu, 
 
 E-, is an economic factor which accounts for downpayment, 
 mortgage interest rate, insurance rate, property tax rate, 
 income tax saving, inflation rate, and market discount 
 rate, 
 
 E is an economic factor which accounts for inflation rate of 
 operating cost and market discount rate, 
 
 E is an economic factor which accounts for inflation rate 
 of maintenance cost and market discount rate, 
 
 E f is an economic factor which accounts for fuel inflation 
 rate and market discount rate, 
 
12-5 
 
 F is the fraction of annual heat provided by the solar system, 
 
 L is the annual heating load for the building, MMBtu. 
 
 The economic factors, E , E , and E-: are the sums of annual 
 
 o m f 
 
 compounded inflation factors discounted annually to present worth. The 
 present worth of the sum of an annuity over a life-time of n years 
 inflated at a constant rate and discounted at a constant rate can be 
 written as: 
 
 P/X(d,r,n) = (1+d) " (1+r) for d 4 r (12-5) 
 
 (l+d) n (d-r) 
 
 and 
 
 P/X(d,r,n) = n/(l+r) for d = r (12-6) 
 
 where P is the present value of an annuity over n years, 
 
 X is the first year cost, 
 
 d is the discount rate, 
 
 r is the inflation rate, 
 
 n is the years of analysis or life of the system. 
 The notation (d,r,n) after P/X indicates that the value of P/X refers to 
 values of d, r, and n, placed in the appropriate terms in Equations 
 (12-5) and (12-6). Tables of P/X values are provided in this module for 
 an appropriate range of d, r, and n in Tables 12-1 through 12-6. 
 The economic factors can now be expressed as: 
 
 E Q = P/X(d,r Q ,n) years, (12-7) 
 
 E m = p / x ( d >V n ) years ' (12 ' 8) 
 
 E f = P/X(d,r f ,n) years. (12-9) 
 
 The economic factor E-. is slightly more involved and is expressed 
 
 as: 
 
12-6 
 
 Table 12-1 
 Values of P/X (d, r, n) for Discount Rate of Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 10.0 
 
 11.464 
 
 13.181 
 
 14.487 
 
 15.937 
 
 17.549 
 
 11 
 
 11.0 
 
 12.808 
 
 14.972 
 
 16.645 
 
 18.531 
 
 20.655 
 
 12 
 
 12.0 
 
 14.192 
 
 16.870 
 
 18.977 
 
 21.384 
 
 24.133 
 
 13 
 
 13.0 
 
 15.618 
 
 18.882 
 
 21.495 
 
 24.523 
 
 28.029 
 
 14 
 
 14.0 
 
 17.086 
 
 21.015 
 
 24.215 
 
 27.975 
 
 32.393 
 
 15 
 
 15.0 
 
 18.599 
 
 23.276 
 
 27.152 
 
 31.772 
 
 37.280 
 
 16 
 
 16.0 
 
 20.157 
 
 25.673 
 
 30.324 
 
 35.950 
 
 42.753 
 
 17 
 
 17.0 
 
 21.762 
 
 28.213 
 
 33.750 
 
 40.545 
 
 48.884 
 
 18 
 
 18.0 
 
 23.414 
 
 30. 906 
 
 37.450 
 
 45.599 
 
 55.750 
 
 19 
 
 19.0 
 
 25.117 
 
 33.760 
 
 41.446 
 
 51.159 
 
 63.440 
 
 20 
 
 20.0 
 
 26.870 
 
 36.786 
 
 45.762 
 
 57.275 
 
 72.052 
 
 21 
 
 21.0 
 
 28.676 
 
 39.993 
 
 50.423 
 
 64.002 
 
 81.669 
 
 22 
 
 22.0 
 
 30.537 
 
 43.392 
 
 55.457 
 
 71.403 
 
 92.503 
 
 23 
 
 23.0 
 
 32.453 
 
 46.996 
 
 60.893 
 
 79.543 
 
 104.603 
 
 24 
 
 24.0 
 
 34.426 
 
 50.816 
 
 66.765 
 
 88.497 
 
 188.155 
 
 25 
 
 25.0 
 
 36.459 
 
 54.865 
 
 73.106 
 
 98.347 
 
 133.334 
 
 26 
 
 26.0 
 
 38.553 
 
 59.156 
 
 79.954 
 
 109.182 
 
 150.334 
 
 27 
 
 27.0 
 
 40.710 
 
 63.706 
 
 87.351 
 
 121.100 
 
 169.374 
 
 28 
 
 28.0 
 
 42.931 
 
 68.528 
 
 95.339 
 
 134.210 
 
 190.699 
 
 29 
 
 29.0 
 
 45.219 
 
 73.640 
 
 103.966 
 
 148.631 
 
 214.583 
 
 30 
 
 30.0 
 
 47.575 
 
 79.058 
 
 113.283 
 
 164.494 
 
 241.333 
 
12-7 
 
 Table 12-2 
 Values of P/X (d, r, n)_ for Discount Rate of 4 Percent 
 
 Years ! 
 
 
 Ar 
 
 inual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 8.111 
 
 9.210 
 
 10.492 
 
 11.462 
 
 12.537 
 
 13.727 
 
 11 
 
 8.760 
 
 10.083 
 
 11.655 
 
 12.865 
 
 14.222 
 
 15.845 
 
 12 
 
 9.385 
 
 10.947 
 
 12.841 
 
 14.321 
 
 16.004 
 
 17.918 
 
 13 
 
 9.986 
 
 11.804 
 
 14.049 
 
 15.833 
 
 17.889 
 
 20.258 
 
 14 
 
 10.563 
 
 12.652 
 
 15.281 
 
 17.404 
 
 19.883 
 
 22.777 
 
 15 
 
 11.118 
 
 13.492 
 
 16.536 
 
 19.035 
 
 21.991 
 
 25.491 
 
 16 
 
 11.652 
 
 14.323 
 
 17.816 
 
 20.728 
 
 24.222 
 
 28.413 
 
 17 
 
 12.166 
 
 15.147 
 
 19.120 
 
 22.487 
 
 26.580 
 
 31.561 
 
 1 18 
 
 12.659 
 
 15.963 
 
 20.449 
 
 24.314 
 
 29.076 
 
 34.950 
 
 19 
 
 13.134 
 
 16.771 
 
 21.804 
 
 26.210 
 
 31.714 
 
 38.600 
 
 20 
 
 13.590 
 
 17.571 
 
 23.185 
 
 28.180 
 
 34.506 
 
 42.531 
 
 21 
 
 14.029 
 
 18.364 
 
 24.592 
 
 30.225 
 
 37.458 
 
 46.764 
 
 22 
 
 14.451 
 
 19.149 
 
 26.027 
 
 32.349 
 
 40.581 
 
 51.322 
 
 23 
 
 14.857 
 
 19.926 
 
 27.489 
 
 34.555 
 
 43.883 
 
 56.232 
 
 24 
 
 15.247 
 
 20.696 
 
 28.979 
 
 36.846 
 
 47.377 
 
 61.519 
 
 25 
 
 15.622 
 
 21.459 
 
 30.498 
 
 39.224 
 
 51.071 
 
 67.213 
 
 26 
 
 15.983 
 
 22.214 
 
 32.046 
 
 41.695 
 
 54.979 
 
 73.344 
 
 27 
 
 16.330 
 
 22.962 
 
 33.623 
 
 44.260 
 
 59.113 
 
 79.448 
 
 28 
 
 16.663 
 
 23.703 
 
 35.232 
 
 46.924 
 
 63.485 
 
 87.059 
 
 29 
 
 16.984 
 
 24.436 
 
 36.871 
 
 49.690 
 
 69.109 
 
 94.718 
 
 30 
 
 17.292 
 
 25.163 
 
 38.541 
 
 52.563 
 
 73.000 
 
 102.965 
 
12-8 
 
 Table 12-3 
 Values of P/X (d s r, n) for Discount Rate of 6 Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 7.360 
 
 8.319 
 
 9.434 
 
 10.277 
 
 11.208 
 
 12.238 
 
 11 
 
 7.887 
 
 9.027 
 
 10.377 
 
 11.414 
 
 12.575 
 
 13.874 
 
 12 
 
 8.384 
 
 9.715 
 
 11.321 
 
 12.573 
 
 13.993 
 
 15.603 
 
 13 
 
 8.853 
 
 10.383 
 
 12.264 
 
 13.753 
 
 15.464 
 
 17.430 
 
 14 
 
 9.295 
 
 11.033 
 
 13.208 
 
 14.956 
 
 16.991 
 
 19.360 
 
 15 
 
 9.712 
 
 11.664 
 
 14.151 
 
 16.182 
 
 18.575 
 
 21.399 
 
 16 
 
 10.106 
 
 12.277 
 
 15.094 
 
 17.430 
 
 20.220 
 
 23.553 
 
 17 
 
 10.477 
 
 12.873 
 
 16.038 
 
 18.703 
 
 21.926 
 
 25.83C 
 
 18 
 
 10.828 
 
 13.452 
 
 16.981 
 
 19.999 
 
 23.697 
 
 28.236 
 
 19 
 
 11.158 
 
 14.015 
 
 17.925 
 
 21.320 
 
 25.535 
 
 30.777 
 
 20 
 
 11.470 
 
 14.562 
 
 18.868 
 
 22.665 
 
 27.442 
 
 33.463 
 
 21 
 
 11.764 
 
 15.093 
 
 19.811 
 
 24.036 
 
 29.421 
 
 36.30C 
 
 22 
 
 12.042 
 
 15.609 
 
 20.755 
 
 25.433 
 
 31.474 
 
 39.298 
 
 23 
 
 12.303 
 
 16.111 
 
 21.698 
 
 26.857 
 
 33.605 
 
 42.466 
 
 24 
 
 12.550 
 
 16.598 
 
 22.642 
 
 28.307 
 
 35.817 
 
 45.813 
 
 25 
 
 12.783 
 
 17.072 
 
 23.585 
 
 29.784 
 
 38.112 
 
 49.35C 
 
 26 
 
 13.003 
 
 17.532 
 
 24.528 
 
 31.290 
 
 40.493 
 
 53.087 
 
 27 
 
 13.211 
 
 17.979 
 
 25.472 
 
 32.823 
 
 42.965 
 
 57.03E 
 
 28 
 
 13.406 
 
 18.414 
 
 26.415 
 
 34.386 
 
 45.530 
 
 61.207 
 
 29 
 
 13.591 
 
 18.836 
 
 27.358 
 
 35.978 
 
 48.191 
 
 65.615 
 
 30 
 
 13.765 
 
 
 
 19.246 
 
 28.302 
 
 37.601 
 
 50.953 
 
 70.272 
 
12-9 
 
 Table 12-4 
 Values of P/X (d, r, n) for Discount Rate of 8 Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 ; 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 6.710 
 
 7.550 
 
 8.525 
 
 9.259 
 
 10.070 
 
 10.965 
 
 11 
 
 7.139 
 
 8.127 
 
 9.293 
 
 10.185 
 
 11.183 
 
 12.297 
 
 12 
 
 7.536 
 
 8.676 
 
 10.046 
 
 11.111 
 
 12.316 
 
 13.679 
 
 13 
 
 7.904 
 
 9.200 
 
 10.786 
 
 12.037 
 
 13.470 
 
 15.111 
 
 14 
 
 8.244 
 
 9.700 
 
 11.513 
 
 12.963 
 
 14.645 
 
 16.597 
 
 15 
 
 8.559 
 
 10.177 
 
 12.225 
 
 13.889 
 
 15.842 
 
 18.137 
 
 16 
 
 8.851 
 
 10.632 
 
 12.926 
 
 14.815 
 
 17.061 
 
 19.735 
 
 17 
 
 9.122 
 
 11.066 
 
 13.611 
 
 15.741 
 
 18.303 
 
 21.392 
 
 18 
 
 9.372 
 
 11.479 
 
 14.285 
 
 16.667 
 
 19.568 
 
 23.110 
 
 19 
 
 9.604 
 
 11.874 
 
 14.947 
 
 17.593 
 
 20.856 
 
 24.892 
 
 20 
 
 9.818 
 
 12.250 
 
 15.596 
 
 18.519 
 
 22.169 
 
 26.740 
 
 21 
 
 10.017 
 
 12.609 
 
 16.233 
 
 19.444 
 
 23.505 
 
 28.656 
 
 22 
 
 10.201 
 
 12.951 
 
 16.858 
 
 20.370 
 
 24.866 
 
 30.643 
 
 23 
 
 10.371 
 
 13.277 
 
 17.472 
 
 21.296 
 
 26.253 
 
 32.704 
 
 24 
 
 10.529 
 
 13.589 
 
 18.074 
 
 22.222 
 
 27.665 
 
 34.841 
 
 25 
 
 10.675 
 
 13.885 
 
 18.666 
 
 23.148 
 
 29.103 
 
 37.058 
 
 26 
 
 10.810 
 
 14.169 
 
 19.246 
 
 24.074 
 
 30.568 
 
 39.356 
 
 27 
 
 10.935 
 
 14.438 
 
 19.815 
 
 25.000 
 
 | 32.060 
 
 41.740 
 
 28 
 
 11.051 
 
 14.696 
 
 20.374 
 
 35.926 
 
 33.580 
 
 44.212 
 
 29 
 
 11.158 
 
 14.942 
 
 20.923 
 
 26.852 
 
 35.127 
 
 46.775 
 
 30 
 
 11.258 
 
 15.176 
 
 21.461 
 
 27.778 
 
 36.704 
 
 ! 49.433 
 
12-10 
 
 Table 12-5 
 Values of P/X (d, r, n) for Discount Rate of 10 Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 6.145 
 
 6.884 
 
 7.739 
 
 8.382 
 
 9.091 
 
 9.872 
 
 11 
 
 6.495 
 
 7.355 
 
 8.366 
 
 9.139 
 
 10.000 
 
 10.961 
 
 12 
 
 6.814 
 
 7.796 
 
 8.971 
 
 ; 9.882 
 
 10.909 
 
 12.069 
 
 13 
 
 7.103 
 
 8.209 
 
 9.554 
 
 10.611 
 
 11.818 
 
 13.197 
 
 14 
 
 7.367 
 
 8.596 
 
 10.116 
 
 11.377 
 
 12.727 
 
 14.346 
 
 15 
 
 7.606 
 
 8.958 
 
 10.657 
 
 12.030 
 
 13.636 
 
 15.516 
 
 16 
 
 7.824 
 
 9.297 
 
 11.179 
 
 12.721 
 
 14.545 
 
 16.708 
 
 17 
 
 8.022 
 
 9.614 
 
 11.681 
 
 13.399 
 
 15.455 
 
 17.920 
 
 18 
 
 8.201 
 
 9.911 
 
 12.166 
 
 14.064 
 
 16.365 
 
 ! 19.155 
 
 19 
 
 8.365 
 
 10.190 
 
 12.632 
 
 14.717 
 
 17.273 
 
 20.413 
 
 20 
 
 8.514 
 
 10.450 
 
 13.082 
 
 15.359 
 
 18.182 
 
 21.693 
 
 21 
 
 8.649 
 
 10.695 
 
 13.515 
 
 15.989 
 
 19.091 
 
 ! 22.997 
 
 22 
 
 8.772 
 
 10.923 
 
 13.933 
 
 16.607 
 
 20.000 
 
 24.324 
 
 23 
 
 8.883 
 
 11.137 
 
 14.335 
 
 17.214 
 
 20.909 
 
 25.675 
 
 24 
 
 8.985 
 
 11.337 
 
 14.723 
 
 17.810 
 
 21.818 
 
 27.051 
 
 25 
 
 9.077 
 
 11.525 
 
 15.097 
 
 18.396 
 
 22.727 
 
 28.452 
 
 26 
 
 9.161 
 
 11.701 
 
 15.457 
 
 18.970 
 
 23.636 
 
 29.878 
 
 27 
 
 9.237 
 
 11.865 
 
 15.804 
 
 19.534 
 
 24.545 
 
 31.331 
 
 28 
 
 9.307 
 
 12.019 
 
 16.138 
 
 20.088 
 
 25.455 
 
 32.809 
 
 29 
 
 9.370 
 
 12.613 
 
 16.461 
 
 20.632 
 
 26.364 
 
 34.315 
 
 30 
 
 9.427 
 
 12.299 
 
 16.771 
 
 21.166 
 
 27.273 
 
 35.848 
 
12-11 
 
 Table 12-6 
 Values of P/X (d, r, n) for Discount Rate of 12 Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 5.650 
 
 6.303 
 
 7.057 
 
 7.822 
 
 8.244 
 
 8.929 
 
 11 
 
 5,938 
 
 6.690 
 
 7.571 
 
 8.243 
 
 8.990 
 
 9.821 
 
 12 
 
 6.194 
 
 7.045 
 
 8.059 
 
 8.841 
 
 9.722 
 
 10.714 
 
 13 
 
 6.424 
 
 7.372 
 
 8.520 
 
 9.418 
 
 10.441 
 
 11.607 
 
 14 
 
 6.628 
 
 7.672 
 
 8.956 
 
 9.975 
 
 11.148 
 
 12.500 
 
 15 
 
 6.811 
 
 7.949 
 
 9.369 
 
 10.511 
 
 11.842 
 
 13.393 
 
 16 
 
 6.974 
 
 8.203 
 
 9.760 
 
 11.029 
 
 12.523 
 
 14.286 
 
 17 
 
 7.120 
 
 8.436 
 
 10.130 
 
 11.528 
 
 13.192 
 
 15.179 
 
 18 
 
 7.250 
 
 8.651 
 
 10.480 
 
 12.009 
 
 13.850 
 
 16.071 
 
 19 
 
 7.366 
 
 8.849 
 
 10.812 
 
 12.473 
 
 14.495 
 
 16.964 
 
 20 
 
 7.469 
 
 9.031 
 
 11.125 
 
 12.920 
 
 15.129 
 
 17.857 
 
 21 
 
 7.562 
 
 9.198 
 
 11.422 
 
 13.352 
 
 15.752 
 
 18.758 
 
 22 
 
 7.645 
 
 9.352 
 
 11.703 
 
 13.768 
 
 16.363 
 
 19.643 
 
 23 
 
 7.718 
 
 9.493 
 
 11.969 
 
 14.169 
 
 16.964 
 
 20.536 
 
 24 
 
 7.784 
 
 9.623 
 
 12.221 
 
 14.556 
 
 17.554 
 
 21.429 
 
 25 
 
 7.843 
 
 9.743 
 
 12.459 
 
 14.929 
 
 18.133 
 
 22.321 
 
 26 
 
 7.896 
 
 9.853 
 
 12.684 
 
 15.288 
 
 18.702 
 
 23.214 
 
 27 
 
 7.943 
 
 9.954 
 
 12.898 
 
 15.635 
 
 19.261 
 
 24.107 
 
 28 
 
 7.984 
 
 10.047 
 
 13.100 
 
 15.970 
 
 19.810 
 
 25.00 
 
 29 
 
 8.022 
 
 10.132 
 
 13.291 
 
 16.292 
 
 20.349 
 
 25.893 
 
 30 
 
 8.055 
 
 10.211 
 
 13.472 
 
 16.603 
 
 20.879 
 
 26.786 
 
12-12 
 
 E 1 = a + [(1 - t)p + h)]P/X(d,g,n) + 
 
 (1 - ofUri - t) P/ ! X (d,0,m) m P/X (d,i,m )-. ( 12 - 1Q \ 
 U aJLU tJ P/X (i,0, m) Ct; P/X (0,i,m) J U ^ 1U; 
 
 where 
 
 a is the downpayment rate in the terms of the loan, and fixed 
 mortgage payment is assumed, 
 
 t is the effective income tax rate of the owner, 
 
 p is the property tax rate based on initial capital cost 
 (first year market value), 
 
 h is the insurance premium rate, 
 
 g is the inflation rate for general cost of goods and 
 services (general inflation rate), 
 
 i is the interest rate of the loan, 
 
 m is the term (years) of the loan. 
 
 Values of P/X (a,b,c) may be determined from Tables 12-1 through 12-6 by 
 referring to the appropriate values in the tables as indicated by the 
 terms in the parentheses following P/X. For example, P/X (d,0,m) may be 
 determined by consulting the appropriate discount rate d, rate of annual 
 increase 0, (zero), and years m. 
 
 EXAMPLE 12-1 
 
 Determine the economic factors for costs of operation, maintenance, 
 
 and fuel, E , E , and E^, if the annual rate of increase for operating 
 o m f 
 
 cost, r , is 10 percent, annual rate of increase for maintenance, r , is 
 * o r m 
 
 6 percent, annual rate of increase for fuel, r f , is 12 percent, and the 
 discount rate is 8 percent for a life span of 20 years. 
 Solution: 
 
 E Q = P/X (8,10,20) = 22.169 (from Table 12-4) 
 E m = P/X (8,6,20) = 15.596 (from Table 12-4) 
 E f = P/X (8,12,20) = 26.740 (from Table 12-4) 
 
12-13 
 
 EXAMPLE 12-2 
 
 Determine the economic factor for interest, insurance, taxes, and 
 other costs, E-, , if the terms of the loan are m = 25 years, i = 10 
 percent, and a = 20 percent downpayment. The property tax rate, p, is 3 
 percent and insurance rate, h, is 0.3 percent of market value, general 
 inflation, g, is 6 percent, and the effective income tax rate is 35 
 percent. The market discount rate, d, is 8 percent. 
 Solution: 
 
 For Equation (12-10), find appropriate P/X values from the 
 tables. 
 
 P/X (d,g,n) = P/X (8,6,20) = 15.596 
 P/X (d,0,m) = P/X (8,0,25) = 10.675 
 P/X (i,0,m) = P/X (10,0,25) = 9.077 
 P/X (d,i,m) = P/X (8,10,35) = 29.103 
 P/X (0,i, m) = P/X (0,10,25) = 98.347 
 a = 0.20 
 t = 0.35 
 p = 0.03 
 h = 0.003 
 Thus, 
 
 E 1 = 0.20 + [(l-.35)(0.03)+0.003](15.596) 
 
 + (l-0.2)[(l-.35) 1§$7 + (0 - 35) 9XW ] 
 E 1 = 1.245 (ans) 
 
 EXAMPLE 12-3 
 
 Determine the present values of life-cycle costs of a solar system, 
 a non-solar system and the savings with a solar system, given the 
 following information: 
 
12-14 
 
 A = 500 ft 2 
 
 
 r = 6% 
 m 
 
 
 C = 26 $/ft 2 
 
 a 
 
 
 r f = 12% 
 
 
 C = 87 $/yr 
 
 o J 
 
 
 m = 25 years 
 
 
 C oc = 20 $/yr 
 
 
 i = 10% 
 
 
 C = 100 $/yr 
 
 
 a = 20% down 
 
 
 C mc = 10 $/yr 
 
 
 p = 3% of market value 
 
 
 F = 0.68 
 
 
 h = 0.3% of market value 
 
 
 c f = 10.25 R/MMBtu 
 
 
 g = 6% 
 
 
 L = 130 MMBtu 
 
 
 t = 35% 
 
 
 r = 10% 
 
 
 
 
 d = 8% 
 
 
 Solution: 
 
 
 
 
 The equation to 
 
 apply 
 
 for the solar system is 
 
 Equation 
 
 (12-13). 
 
 
 
 
 From Example 12-1, E = 
 
 22.169, E m = 15.596, E f = 26.740. 
 
 
 From Example 12-2, E-, = 
 
 1.245 
 
 
 
 Therefore, 
 
 
 
 
 C T = (500)(26)(1.245) + (87)(22.169) + (100)(15. 596) 
 
 + (1 - .68)(130)(10. 25X26.740) 
 C-p = $31,075 present value (total cost) over 20 years 
 
 of life 
 The equation to apply to the non-solar system is Equation 
 
 (12-4) 
 
 C K = (20X22.169) + (20)(15.596) + (130)(10.25)(26.740) 
 
 C TC = $36,230 present value (total cost) over 20 years 
 
 of life 
 
 The cost of the non-solar is clearly larger than the cost of 
 
 the solar system. The difference, or savings realizable with the solar 
 
 system, is: 
 
12-15 
 
 Present value = c . - = 36 230 . 31 75 = $5155 
 of savings TC T ' ' 
 
 While in Example 12-3 the present values of the total costs for 
 systems and life time savings are determinable, the calculations are 
 restricted to fixed annual increases, fixed discount rates, fixed 
 property tax and insurance rates, and fixed income tax rates for the 
 owner. These rates are, of course, uncertain in future years and highly 
 variable. If variable rates are to be applied, a detailed year-by-year 
 analysis of cash flow and present worth discounting must be carried out, 
 using the basic form of Equations (12-1) and (12-2). 
 
 Annual cash flows are calculated for a system and the annual cost 
 
 may be discounted to present value. The cost in a future year may be 
 
 discounted to present worth by multiplying the cost by the present worth 
 
 factor, P, in: 
 
 P = — i- - (12-11) 
 
 (l+d) q 
 
 where 
 
 q is any year in the analysis period from 1 to n 
 
 d is the market discount rate 
 Values of P for practical ranges of d and q are tabulated in Table 12-7. 
 
 ENERGY COSTS 
 
 The conversion of unit costs of energy to dollars per million Btu 
 ($/MMBtu) with various furnace efficiencies is shown in Figure 12-1 for 
 natural gas, propane, and No. 2 fuel oil. The conversion of electrical 
 energy costs to dollars per million Btu for resistance heating and heat 
 
12-16 
 
 Table 12-7 
 Present Worth Factors CP) 
 (use for Worksheet LCA-4) 
 
 
 Discount Rate 
 
 
 Year of 
 Analysis 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 .943 
 
 .935 
 
 .926 
 
 .917 
 
 .909 
 
 .901 
 
 .893 
 
 .885 
 
 .877 
 
 .870 
 
 .862 
 
 2 
 
 .890 
 
 .873 
 
 .857 
 
 .842 
 
 .826 
 
 .812 
 
 .797 
 
 .783 
 
 .769 
 
 .756 
 
 .743 
 
 3 
 
 .840 
 
 .816 
 
 .794 
 
 .772 
 
 .751 
 
 .731 
 
 .712 
 
 .693 
 
 .675 
 
 .658 
 
 .641 
 
 4 
 
 .792 
 
 .763 
 
 .735 
 
 .708 
 
 .683 
 
 .659 
 
 .636 
 
 .613 
 
 .592 
 
 .572 
 
 .552 
 
 5 
 
 .747 
 
 .713 
 
 .681 
 
 .650 
 
 .621 
 
 .593 
 
 .567 
 
 .543 
 
 .519 
 
 .497 
 
 .476 
 
 6 
 
 .705 
 
 .666 
 
 .630 
 
 .596 
 
 .564 
 
 .535 
 
 .507 
 
 .480 
 
 .456 
 
 .432 
 
 .410 
 
 7 
 
 .665 
 
 .623 
 
 .583 
 
 .547 
 
 .513 
 
 .482 
 
 .452 
 
 .425 
 
 .400 
 
 .376 
 
 .354 
 
 8 
 
 .627 
 
 .582 
 
 .540 
 
 .502 
 
 .467 
 
 .434 
 
 .404 
 
 .376 
 
 .351 
 
 .327 
 
 .305 
 
 9 
 
 .592 
 
 .544 
 
 .500 
 
 .460 
 
 .424 
 
 .391 
 
 .361 
 
 .333 
 
 .308 
 
 .284 
 
 .263 
 
 10 
 
 .558 
 
 .508 
 
 .463 
 
 .422 
 
 .386 
 
 .352 
 
 .322 
 
 .295 
 
 .270 
 
 .247 
 
 .227 
 
 11 
 
 .527 
 
 .475 
 
 .429 
 
 .388 
 
 .350 
 
 .317 
 
 .287 
 
 .261 
 
 .237 
 
 .215 
 
 .195 
 
 12 
 
 .497 
 
 .444 
 
 .397 
 
 .356 
 
 .319 
 
 .286 
 
 .257 
 
 .231 
 
 .208 
 
 .187 
 
 .168 
 
 13 
 
 .469 
 
 .415 
 
 .368 
 
 .326 
 
 .290 
 
 .258 
 
 .229 
 
 .204 
 
 .182 
 
 .163 
 
 .145 
 
 14 
 
 .442 
 
 .388 
 
 .340 
 
 .299 
 
 .263 
 
 .232 
 
 .205 
 
 .181 
 
 .160 
 
 .141 
 
 .125 
 
 15 
 
 .417 
 
 .362 
 
 .315 
 
 .275 
 
 .239 
 
 .209 
 
 .183 
 
 .160 
 
 .140 
 
 .123 
 
 .108 
 
 16 
 
 .394 
 
 .339 
 
 .292 
 
 .252 
 
 .218 
 
 .188 
 
 .163 
 
 .141 
 
 .123 
 
 .107 
 
 .093 
 
 17 
 
 .371 
 
 .317 
 
 .270 
 
 .231 
 
 .198 
 
 .170 
 
 .146 
 
 .125 
 
 .108 
 
 .093 
 
 .080 
 
 18 
 
 .350 
 
 .296 
 
 .250 
 
 .212 
 
 .180 
 
 .153 
 
 .130 
 
 .111 
 
 .095 
 
 .081 
 
 .069 
 
 19 
 
 .331 
 
 .277 
 
 .232 
 
 .194 
 
 .164 
 
 .138 
 
 .116 
 
 .098 
 
 .083 
 
 .070 
 
 .060 
 
 20 
 
 .312 
 
 .258 
 
 .215 
 
 .178 
 
 .149 
 
 .124 
 
 .104 
 
 .087 
 
 .073 
 
 .061 
 
 .051 
 
 21 
 
 .294 
 
 .242 
 
 .199 
 
 .164 
 
 .135 
 
 .112 
 
 .093 
 
 .077 
 
 .064 
 
 .053 
 
 .044 
 
 22 
 
 .278 
 
 .226 
 
 .184 
 
 .150 
 
 .123 
 
 .101 
 
 .083 
 
 .068 
 
 .056 
 
 .046 
 
 .038 
 
 23 
 
 .262 
 
 .211 
 
 .170 
 
 .138 
 
 .112 
 
 .091 
 
 .074 
 
 .060 
 
 .049 
 
 .040 
 
 .033 
 
 24 
 
 .247 
 
 .197 
 
 .158 
 
 .126 
 
 .102 
 
 .082 
 
 .066 
 
 .053 
 
 .043 
 
 .035 
 
 .028 
 
 25 
 
 .233 
 
 .184 
 
 .146 
 
 .116 
 
 .092 
 
 .074 
 
 .059 
 
 .047 
 
 .038 
 
 .030 
 
 .024 
 
12-17 
 
 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 
 
 Dollars/Energy Unit 
 Natural Gas- Price/100 ft 3 #2 Fuel Oil-Price/gallon 
 Propane -Price /gal Ion 
 
 Figure 12-1. Energy Cost per Million Btu for Natural Gas, 
 Propane, and No. 2 Fuel Oil 
 
12-18 
 
 5 6 7 8 9 
 
 Electricity 4/kWh 
 
 Figure 12-2. Energy Cost per Million Btu for Electricity 
 
12-19 
 
 pumps with various coefficients of performance is shown in Figure 12-2. 
 To determine the cost per million Btu of heat generated from furnaces, 
 electric resistance heaters, or heat pumps, follow the unit cost of 
 energy, found on the horizontal axis of the graphs, vertically to the 
 appropriate line on the graph and read the cost in dollars along the 
 vertical axis. For example, if No. 2 fuel oil cost is one dollar per 
 gallon, and the furnace efficiency is 60 percent, the energy cost is 
 $12.00/MMBtu or $1.20 per therm. If the furnace is more efficient, say 
 70 percent, the energy cost is $10.29 MMBtu. Similarly, if electricity 
 cost is five cents per kilowatt-hour (<t/kWh), and resistance heating is 
 used at 100 percent efficiency, the energy cost is $14.65/MMBtu. If a 
 heat pump is used, and the COP of the heat pump is 2, the energy cost is 
 $7.32/MMBtu. 
 
 The cost of energy will increase in future years, and an estimate 
 of the rate of increase is subject not only to inflation rates of goods 
 and services, but also to economic and political decisions of the 
 Federal Government and the governments of other nations. One expects, 
 however, the rate of fuel cost increases to be different from general 
 inflation rates and higher by a few percent, at least for the immediate 
 future. 
 
 INFLATION RATES 
 
 The increases in costs per unit of energy several years in the 
 future in terms of cents per gallon of oil, cents per kilowatt-hour of 
 electricity, cents per hundred cubic feet of natural gas, or dollars per 
 therm, can be estimated on the basis of annual percentage increases over 
 current costs. The multiplying factors for current energy costs to 
 
12-20 
 
 determine future costs are shown in Figure 12-3. The horizontal axis is 
 the number of years beyond the current year. The vertical axis is the 
 multiplying factor over current costs, and is simply the interest 
 compounded annually, (1 + i) n , where i is the interest rate and n is 
 years. 
 II 
 
 8 
 
 10 12 14 16 18 20 22 24 26 28 
 Years Beyond the First 
 
 Figure 12-3. Inflation Factors 
 
 For example, if the current cost of electricity is expected to 
 increase at a rate of 6 percent each year for the next 12 years, Figure 
 12-3 shows that at the end of 12 years, the electricity cost will 
 double. If the current electricity cost is 5 cents per kilowatt-hour, 
 equivalent to $14.65 per million Btu, the cost will be 10 cents per 
 kilowatt-hour and $29.30 per million Btu in 12 years. 
 
12-21 
 
 SOLAR SYSTEM COSTS 
 
 There is considerable uncertainty about the installed costs of 
 solar heating systems, and there is insufficient information available 
 to substantiate published reports. System costs based on research 
 projects and demonstration projects funded by the Federal Government are 
 misleading, because the total costs of such projects may include con- 
 siderable design and engineering. In some instances, instrumentation 
 for monitoring the performance of experimental systems and the cost of 
 developing alternative components are included. The costs reported in 
 popular magazines and newspaper accounts are likewise misleading, be- 
 cause they are often based on systems which have been designed and 
 assembled by the owner on a do-it-yourself basis. Installation labor, 
 normally a major cost item, is seldom included. 
 
 Guidelines are provided in this section to estimate the total 
 installed cost of a solar system including equipment and installation 
 labor. Of these two items, equipment costs are the larger and easier to 
 estimate, largely by consulting manufacturer's literature and price 
 lists. Estimating labor costs is more difficult because it depends upon 
 the type of installation, location of the house, experience of the 
 installer, and other factors. Ranges in equipment price and estimates 
 of man-hours for installation of systems in new buildings are listed 
 below to provide cost-estimating guidelines. There may be specific 
 items of equipment which have lower costs than those listed, and some 
 which are more expensive. The prices may not be representative of any 
 single project. 
 
12-22 
 
 EQUIPMENT AND INSTALLATION TIME ESTIMATES 
 Liquid-Heating Systems 
 
 Table 12-8 
 
 Typical Equipment and Material Prices (in 1978) 
 for Liquid-Heating Systems 
 
 Item 
 
 Unit 
 
 
 Price Range 
 (in dollars 
 
 
 
 Low 
 
 Medium 
 
 High 
 
 Flat-plate collectors and 
 mounting hardware 
 
 ft 2 
 
 10 
 
 15 
 
 24 
 
 Storage tank 
 
 750-1200 gal 
 capacity 
 
 1000 
 
 1500 
 
 2500 
 
 Pumps and motor 
 
 10-20 gpm 
 
 80 
 
 180 
 
 350 
 
 Heat exchanger 
 
 each 
 
 200 
 
 300 
 
 400 
 
 Controls and sensors 
 
 each 
 
 500 
 
 750 
 
 1500 
 
 Piping (3/4-inch copper) 
 
 ft 
 
 .45 
 
 .60 
 
 .80-. 85 
 
 Valves 
 
 each 
 
 20 
 
 30 
 
 45 
 
 *1isc. fittings 
 
 - 
 
 200 
 
 250 
 
 350 | 
 
 Expansion tank 
 
 - 
 
 60 
 
 80 
 
 100 
 
 Insulation 
 
 - 
 
 500 
 
 750 
 
 1000 
 
 DHW Preheat tank 
 
 each 
 
 80 
 
 100 
 
 150 
 
12-23 
 
 Table 12-9 
 Installation Time Estimates for Typical Liquid-Heating Systems 
 
 Item 
 
 Unit 
 
 Time (man-hours) 
 
 Low 
 
 Medium High 
 
 Collectors and flashing 
 
 400-500 ft 2 
 
 40 
 
 60 
 
 80 
 
 Storage tank 
 
 each 
 
 8 
 
 10 
 
 12 
 
 Piping loops 
 
 all 
 
 40 
 
 60 
 
 80 
 
 DHW preheat subsystem 
 
 - 
 
 8 
 
 12 
 
 20 
 
 Insulation 
 
 all 
 
 16 
 
 20 I 30 
 
 Controls 
 
 - 
 
 8 
 
 12 16 
 
 Testing and balancing 
 
 " 
 
 10 
 
 15 | 20 
 
 i 
 i 
 
 Air- Heating Systems 
 
 Table 12-10 
 
 Typical Equipment and Material Prices (in 1978) 
 for Air-Heating Systems 
 
 Item 
 
 Unit 
 
 Price Range 
 (in dollars) 
 
 Low 
 
 Medium 
 
 [ High 
 
 Flat-plate collectors and 
 mounting hardware 
 
 ft 2 
 
 10 
 
 15 
 
 24 
 
 Storage containers 
 
 ft 3 
 
 0.5 
 
 1 
 
 1.5 
 
 Gravel 
 
 ton 
 
 3 
 
 4 
 
 5 
 
 Blower and motor 
 
 each 
 
 150 
 
 175 
 
 200 
 
 Control and sensors 
 
 set 
 
 500 
 
 750 
 
 1500 
 
 Motorized dampers 
 
 each 
 
 115 
 
 125 
 
 150 
 
 [Heat exchanger 
 
 each 
 
 45 
 
 60 
 
 80 
 
 |DHW Preheat tank 
 
 each 
 
 80 
 
 100 
 
 150 
 
 ! Ducts 
 
 bulk 
 
 2000 
 
 2500 
 
 3500 
 
 Insulation 
 
 bulk 
 
 500 
 
 750 
 
 1000 
 
 Miscellaneous 
 
 - 
 
 200 
 
 300 
 
 400 
 
12-24 
 
 Table 12-11 
 Installation Time Estimates for Typical Air-Heating Systems 
 
 Item 
 
 Unit 
 
 Time (man-hours) 
 
 Low 
 
 Medium 
 
 High 
 
 Collectors 
 
 400-500 ft 2 
 
 40 
 
 60 
 
 80 
 
 Storage unit 
 
 each 
 
 20 
 
 25 
 
 30 
 
 Ducting 
 
 all 
 
 50 
 
 75 
 
 100 
 
 Controls 
 
 - 
 
 8 
 
 12 
 
 16 
 
 DHW preheat subsystem 
 
 - 
 
 8 
 
 12 
 
 20 
 
 Insulation 
 
 - 
 
 16 
 
 20 
 
 30 
 
 Testing and balancing 
 
 - 
 
 10 
 
 15 
 
 20 
 
 Domestic Water Heaters 
 
 There are numerous manufacturers marketing complete systems for 
 domestic water heating. Prices of "packaged units" vary from about 
 $1500 to about $4000 with a median price of about $2500. Solar water 
 heaters may also be assembled from components supplied from different 
 manufacturers. Price ranges of components are listed in Table 12-12. 
 
 Installed cost of a "packaged" solar domestic hot water unit 
 appears to be approximately the same as the installed cost of a system 
 assembled with individually selected components. Manufacturers of 
 packaged systems supply an integrated set of components which mainly 
 saves time in designing and purchasing the components separately. 
 Because components are pre-arranged to fit together, some savings in 
 assembly time can be expected. Time required for installation of solar 
 hot water systems will depend on background experience of the installer, 
 and estimates are provided in Table 12-13. 
 
12-25 
 
 Table 12-12 
 Equipment Costs for Components of Domestic Water Heaters (1978 prices) 
 
 Item 
 
 Unit 
 
 Price Range 
 (in dollars) 
 
 Low 
 
 Medium 
 
 High 
 
 Flat-plate collectors 
 and mounting hardware 
 
 ft 2 
 
 10 
 
 15 
 
 24 
 
 Preheat tank 
 
 80- gal Ion 
 capacity 
 
 100 
 
 200 
 
 250 
 
 Pump and motor 
 assembly 
 
 each 
 
 80 
 
 120 
 
 150 
 
 Heat exchanger 
 
 each 
 
 200 
 
 300 
 
 400 
 
 Controls and sensors 
 
 set 
 
 100 
 
 150 
 
 200 
 
 Piping (1/2- inch copper) 
 
 ft 
 
 .40 
 
 .50 
 
 .75 
 
 Valves 
 
 each 
 
 20 
 
 30 
 
 45 
 
 Miscellaneous fittings 
 
 bulk 
 
 30 
 
 40 
 
 50 
 
 Expansion tank 
 
 each 
 
 60 
 
 80 
 
 100 
 
 Insulation 
 
 bulk 
 
 80 
 
 100 
 
 120 
 
 Table 12-13 
 Estimates of Installation Times for Domestic Water Heaters 
 
 Item 
 
 Unit 
 
 Tii 
 
 ne (man-hours) 
 
 Low 
 
 Medium 
 
 High 
 
 Collectors and flashing 
 
 2-4 collector 
 units 
 
 4 
 
 8 
 
 12 
 
 Preheater tank 
 
 1 
 
 1 
 
 2 
 
 2 
 
 Piping loops, pumps, valves 
 
 all 
 
 8 
 
 12 
 
 16 
 
 Insulation 
 
 - 
 
 2 
 
 4 
 
 6 
 
 Controls 
 
 - 
 
 1 
 
 2 
 
 3 
 
 Filling, testing, and 
 adjusting 
 
 _ 
 
 2 
 
 4 
 
 6 
 
 For packaged units, subtract 
 20 percent from total 
 
 Total 
 
 (with 20% 
 
 subtracted) 
 
 14 
 
 26 
 
 37 
 
12-26 
 
 TYPICAL INSTALLED COSTS 
 
 Space Heating System - Liquid Collectors 
 
 An estimate for the installed cost of a typical liquid-heating 
 system in a new building with 400 ft 2 of collectors is outlined below 
 using the median values in Tables 12-8 and 12-9. 
 
 Collectors 
 Storage Tank 
 Pipe Loops 
 
 equipment 400 ft 2 x $15/ft 2 
 
 installation 60 hrs x $15/hr 
 
 equipment 
 
 installation 10 hrs x $15/hr 
 
 equipment 
 
 installation 60 hrs x $15/hr 
 
 DHW Subsystem equipment 
 
 installation 12 hrs x $15/hr 
 
 $6,000 
 900 
 
 1,500 
 150 
 
 2,070 
 900 
 
 280 
 180 
 
 5. 
 
 Controls 
 
 equipment 
 
 installation 12 hrs x $15/hr 
 
 
 750 
 180 
 
 6. 
 
 Insulation 
 
 materials 
 
 installation 20 hrs x $15/hr 
 
 
 750 
 300 
 
 7. 
 
 Testing and 
 balancing 
 
 
 
 
 225 
 
 
 
 
 Total Estimated Costs 
 
 14 
 
 ,185 
 
 
 
 
 Breakdown of costs: 
 Equipment & materials 
 Labor 
 
 11 
 2 
 
 ,350 
 ,835 
 
 
 Ins 
 
 tailed 
 
 cost/unit collector area 
 
 $35.46/ft 2 
 
 Space Heating System - Air Collectors 
 
 An estimate of the installed cost of a typical air-heating system 
 in a new building with 400 ft 2 of collectors is outlined below using the 
 median values in Tables 12-10 and 12-11. 
 
12-27 
 
 1. 
 
 Collectors 
 
 equipment 
 installation 
 
 400 ft 2 X $15/ft 2 
 60 hrs x $15/hr 
 
 $6 
 
 ,000 
 900 
 
 2. 
 
 Pebble Bed 
 
 Container 
 
 Gravel 
 
 Assembly 
 
 300 ft 3 x $l/ft 3 
 15 tons x $4/ton 
 25 hrs x $15/hr 
 
 
 300 
 
 60 
 
 375 
 
 3. 
 
 Duct, Pumpers 
 & blowers 
 
 equipment 
 installation 
 
 75 x $15/hr 
 
 3 
 
 1 
 
 ,175 
 ,125 
 
 4. 
 
 DHW Subsystem 
 
 equipment 
 installation 
 
 12 x $15/hr 
 
 
 385 
 180 
 
 5. 
 
 Controls 
 
 equipment 
 installation 
 
 12 hrs x $15/hr 
 
 
 750 
 180 
 
 6. 
 
 Insulation 
 
 materials 
 installation 
 
 20 hrs x $15/hr 
 
 
 750 
 300 
 
 7. 
 
 Testing and 
 balancing 
 
 
 15 hrs x $15/hr 
 
 
 225 
 
 Total Estimated Costs 
 
 Breakdown of costs: 
 Equipment & materials 
 Labor 
 
 14,705 
 
 11,420 
 3,285 
 
 Installed cost/unit collector area $36.76/ft 2 
 
 Domestic Water Heaters 
 
 Two estimates for the installed cost of a typical solar domestic 
 hot water system in a new building with 60 ft2 of collectors are pro- 
 vided below. One estimate is for the installed cost of a "packaged" 
 unit, and the second is for assembling a system from separately 
 purchased components. 
 
Complete 
 Complete 
 
 12-28 
 
 equipment (3 modules = 60 ft 2 ) 
 installation 26 hrs x $15/hr 
 
 Total Estimated Cost 
 Installed cost/unit collector area 
 
 $2500 
 320 
 
 $2890 
 
 $48.17/ft 2 
 
 1. 
 
 Collectors 
 
 and 
 
 flashing 
 
 equipment (3 modules) 
 
 60 ft 2 x $15/ft 2 
 installation 8 hrs x $15/hr 
 
 
 $ 900 
 120 
 
 2. 
 
 Preheater 
 tank 
 
 equipment 
 
 installation 2 hrs x $15/hr 
 
 
 200 
 30 
 
 3. 
 
 Pumps and 
 motor 
 
 equipment (2) 
 
 installation (included in pi pi 
 
 ng) 
 
 240 
 
 4. 
 
 Heat 
 exchanger 
 
 equipment 
 
 installation (included in piping) 
 
 300 
 
 5. 
 
 Piping 
 
 materials 
 
 installation 12 hrs x $15/hr 
 
 
 340 
 180 
 
 6. 
 
 Insulation 
 
 materials 
 
 installation 4 hrs x $15/hr 
 
 
 100 
 60 
 
 7. 
 
 Controls and 
 sensors 
 
 equipment 
 
 installation 2 hrs x $15/hr 
 
 
 150 
 30 
 
 8. 
 
 Filling, 
 testing and 
 adjusting 
 
 4 hrs x $15/hr 
 
 Total Estimated Costs 
 
 
 60 
 $2,710 
 
 
 
 Breakdown of costs: 
 Equipment and materia 
 Installation 
 
 tls 
 
 2,230 
 480 
 
 
 Ins 
 
 tailed cost/unit collector area 
 
 
 $45.17/ft 2 
 
12-29 
 
 MORTGAGE PAYMENTS 
 
 The largest portion of the annual cost of a solar system is the 
 repayment of the loan obtained to install the system. The loan may be 
 based on the total building costs or separately on the solar system 
 alone. In either event, a downpayment of up to 30 percent may be 
 required to obtain the loan. 
 
 The annual mortgage payments can be calculated from the mortgage 
 interest rate and term of the loan using the curves of Figure 12-4. To 
 illustrate the use of Figure 12-4, suppose that a solar system with 400 
 square feet of collectors costs $14,185. A 25-year loan is obtained to 
 purchase and install the system with interest at 10 percent, which 
 requires a 20 percent downpayment. The annual mortgage payment on the 
 loan is calculated as follows: 
 
 Annual 
 
 Mortgage = (System cost - downpayment)x(Annual repayment factor) 
 
 (from Figure 12-4) 
 
 or 
 
 $ 1248 = (14,185 - 2837) x (0.11) 
 
 TAX CREDIT 
 
 A major item of income tax credit is the legislation passed by the 
 Federal Government, effective January 1980 through 1985, which allows a 
 maximum credit of $4000 from the owner's Federal income tax liability. 
 The credit allowance is 40 percent of the first $10,000 of the cost of a 
 qualified solar system. In some states there are additional income tax 
 credits or deductions provided to owners of solar systems. A list 
 
12-30 
 
 
 0.21 
 
 
 0.20 
 
 
 0. 
 
 19 
 
 TJ 
 
 
 
 Q> 
 
 
 
 IB 
 
 £ 
 
 
 
 O 
 
 
 
 k- 
 
 
 
 w 
 
 
 
 o 
 m 
 
 0. 
 
 17 
 
 >N 
 
 
 
 CD 
 
 
 
 C 
 
 o 
 
 0. 
 
 16 
 
 IS 
 
 
 
 c 
 
 
 
 o 
 
 0. 
 
 15 
 
 h_ 
 
 
 
 o 
 
 
 
 
 
 
 o 
 
 
 
 u 
 Ll_ 
 
 0. 
 
 14 
 
 ^_ 
 
 
 
 c 
 
 
 
 <r> 
 
 
 
 £ 
 
 0. 
 
 13 
 
 >» 
 
 
 
 o 
 
 
 
 Q. 
 
 
 
 <D 
 
 
 
 or 
 
 0. 
 
 12 
 
 o 
 
 
 
 3 
 
 
 
 C 
 
 
 
 C 
 < 
 
 0. 
 
 1 1 
 
 0.10 
 0.09 
 0. 
 
 Repayment 
 
 Factor 
 
 n tef e_stL- Rate 
 
 _. nv^ -Ye a! r s^bf E |_p a n 
 
 ^An ri u a h R e Rd y me n tnbn 
 
 @|C^l:nletes^25 
 
 
 Figure 12-4. Repayment on Loan 
 
12-31 
 
 of state provisions prepared by the National Solar Heating and Cooling 
 Information Center is appended to this module. 
 
 PROPERTY TAXES 
 
 Property taxes are usually based on a fraction of the assessed 
 value of the solar system. The method of assessment and the tax rate 
 vary from state to state and sometimes from county to county within a 
 state. The office of the county treasurer can provide detailed informa- 
 tion on assessment practices and the tax rate. Usually, the assessed 
 value is a fraction of the market value of the property, and the tax 
 rate is applied to the assessed value. The amount of property tax on 
 the solar system can be calculated as follows: 
 
 ./ y = (System cost)x(Fraction of assessed value)x(tax rate) 
 
 INSURANCE 
 
 Insurance rates on houses with a solar system, at present, are the 
 same as for houses without solar systems. The solar equipment is there- 
 fore usually insured at a rate equivalent to that applicable to all the 
 conventional components of the building. The basic insurance rate 
 depends upon the type of house construction and location of the building 
 within or outside a city or town. The insurance rate for a compre- 
 hensive homeowners policy differs from the rate for a straight fire 
 insurance policy, and the insurance rates for earthquake and flood 
 damage (which are federally subsidized) are the only special insurances 
 available for owners of buildings. Information on various insurance 
 
12-32 
 
 rates is available from local insurance agents. Very few insurance 
 companies have established insurance rates for solar systems. Damage to 
 the contents of a building resulting from leaks in piping or storage 
 tanks or damage to the solar system resulting from flooding by natural 
 causes is based on comprehensive or flood insurance rates. Although 
 there are many factors to be considered, the annual premium on insurance 
 for houses with solar systems is less than one percent of the value of 
 the house and contents, and ranges from 0.3 to about 0.6 percent. 
 
 ADDITIONAL INCOME TAX CREDITS 
 
 The "savings" on state and Federal income taxes for property tax 
 and interest paid on the mortgage can be substantial, depending upon the 
 "tax bracket" of the homeowner. The amount of interest paid annually on 
 the mortgage decreases with the number of years remaining on the 
 mortgage. The portion of annual mortgage which is paid as interest can 
 be determined from Tables 12-14 through 12-18. The use of the tables 
 is illustrated in the following example. 
 
 Let us assume that a loan of $11,348 has been secured with a term 
 of 25 years and 10 percent interest. The annual mortgage payment was 
 computed in the previous section to be $1248. Of that mortgage payment, 
 90.8 percent, or $1133, is for interest in the first year. From Table 
 12-17, line 1, at the interest rate of 10 percent, the number 0.908 
 indicates the fraction of the mortgage payment which is interest on the 
 money borrowed and payable in the first year. Mortgages are usually 
 repaid monthly, but for this analysis annual payment figures will 
 
12-33 
 
 Table 12-14 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = 1-Cl+fr Mortgage Term (m) - 10 years 
 
 YEAR 
 
 
 
 
 
 INTEREST 
 
 RATE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (j) 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 1 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 2 
 
 .408 
 
 .456 
 
 .500 
 
 .540 
 
 .576 
 
 .609 
 
 .639 
 
 .667 
 
 .692 
 
 .716 
 
 3 
 
 .373 
 
 .418 
 
 .460 
 
 .498 
 
 .533 
 
 .566 
 
 .596 
 
 .624 
 
 .649 
 
 .673 
 
 4 
 
 .335 
 
 .377 
 
 .417 
 
 .453 
 
 .487 
 
 .518 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 5 
 
 .295 
 
 .334 
 
 .370 
 
 .404 
 
 .436 
 
 .465 
 
 .493 
 
 .520 
 
 .544 
 
 .568 
 
 6 
 
 .253 
 
 .287 
 
 .319 
 
 .350 
 
 .379 
 
 .407 
 
 .433 
 
 .457 
 
 .481 
 
 .503 
 
 7 
 
 .208 
 
 .237 
 
 .265 
 
 .292 
 
 .317 
 
 .341 
 
 .364 
 
 .387 
 
 .408 
 
 .428 
 
 8 
 
 .160 
 
 .184 
 
 .206 
 
 .228 
 
 .249 
 
 .269 
 
 .288 
 
 .307 
 
 .325 
 
 .342 
 
 9 
 
 .110 
 
 .127 
 
 .143 
 
 .158 
 
 .174 
 
 .188 
 
 .203 
 
 .217 
 
 .231 
 
 .244 
 
 10 
 
 .057 
 
 .065 
 
 .074 
 
 .083 
 
 .091 
 
 .099 
 
 .107 
 
 .115 
 
 .123 
 
 .130 
 
12-34 
 
 Table 12-15 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i )J _rn - 1 Mortgage Term (m) = 15 years 
 
 YEAR 
 (j) 
 
 INTEREST RATE 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 1 
 
 .583 
 
 .638 
 
 .685 
 
 .725 
 
 .761 
 
 .791 
 
 .817 
 
 .840 
 
 .860 
 
 .877 
 
 2 
 
 .588 
 
 .612 
 
 .660 
 
 .701 
 
 .737 
 
 .768 
 
 .795 
 
 .819 
 
 .840 
 
 .859 
 
 3 
 
 .531 
 
 .585 
 
 .632 
 
 .674 
 
 .710 
 
 .742 
 
 .771 
 
 .796 
 
 .818 
 
 .837 
 
 4 
 
 .503 
 
 .556 
 
 .603 
 
 .644 
 
 .681 
 
 .714 
 
 .743 
 
 .769 
 
 .792 
 
 .813 
 
 5 
 
 .473 
 
 .525 
 
 .571 
 
 .612 
 
 .650 
 
 .683 
 
 .713 
 
 .739 
 
 .763 
 
 .785 
 
 6 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 7 
 
 .408 
 
 .456 
 
 .500 
 
 .540 
 
 .576 
 
 .609 
 
 .639 
 
 .667 
 
 .692 
 
 .716 
 
 8 
 
 .373 
 
 .418 
 
 .460 
 
 .498 
 
 .533 
 
 .566 
 
 .596 
 
 .624 
 
 .649 
 
 .673 
 
 9 
 
 .335 
 
 .377 
 
 .417 
 
 .453 
 
 .487 
 
 .518 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 10 
 
 .295 
 
 .334 
 
 .370 
 
 .404 
 
 .436 
 
 .465 
 
 .493 
 
 .520 
 
 .344 
 
 .568 
 
 11 
 
 .253 
 
 .287 
 
 .319 
 
 .350 
 
 .379 
 
 .407 
 
 .433 
 
 .457 
 
 .481 
 
 .503 
 
 12 
 
 .208 
 
 .237 
 
 .265 
 
 .292 
 
 .317 
 
 .341 
 
 .364 
 
 .387 
 
 .408 
 
 .428 
 
 13 
 
 .160 
 
 .184 
 
 .206 
 
 .228 
 
 .249 
 
 .269 
 
 .288 
 
 .307 
 
 .325 
 
 .342 
 
 14 
 
 .110 
 
 .127 
 
 .143 
 
 .158 
 
 .174 
 
 .188 
 
 .203 
 
 .217 
 
 .231 
 
 .244 
 
 15 
 
 .057 
 
 .065 
 
 .074 
 
 .083 
 
 .091 
 
 .099 
 
 .107 
 
 .115 
 
 .123 
 
 .130 
 
12-35 
 
 Table 12-16 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = 1-Cl+ir"" 1 " 1 Mortgage Term (m) = 20 years 
 
 YEAR 
 (J) 
 
 INTEREST RATE 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 1 
 
 .688 
 
 .742 
 
 .785 
 
 .822 
 
 .851 
 
 .876 
 
 .896 
 
 .913 
 
 .927 
 
 .939 
 
 2 
 
 .669 
 
 .723 
 
 .768 
 
 .806 
 
 .836 
 
 .862 
 
 .884 
 
 .902 
 
 .917 
 
 .930 
 
 3 
 
 .650 
 
 .704 
 
 .750 
 
 .788 
 
 .820 
 
 .847 
 
 .870 
 
 .889 
 
 .905 
 
 .919 
 
 4 
 
 .629 
 
 .683 
 
 .730 
 
 .769 
 
 .802 
 
 .830 
 
 .854 
 
 .875 
 
 .892 
 
 .907 
 
 5 
 
 .606 
 
 .661 
 
 .708 
 
 .748 
 
 .782 
 
 .812 
 
 .837 
 
 .859 
 
 .877 
 
 .893 
 
 6 
 
 .583 
 
 .638 
 
 .685 
 
 .725 
 
 .761 
 
 .791 
 
 .817 
 
 .840 
 
 .860 
 
 .877 
 
 7 
 
 .558 
 
 .612 
 
 .660 
 
 .701 
 
 .737 
 
 .768 
 
 .795 
 
 .819 
 
 .840 
 
 .859 
 
 8 
 
 .531 
 
 .585 
 
 .632 
 
 .674 
 
 .710 
 
 .742 
 
 .771 
 
 .796 
 
 .818 
 
 .837 
 
 9 
 
 .503 
 
 .556 
 
 .603 
 
 .644 
 
 .681 
 
 .714 
 
 .743 
 
 .769 
 
 .792 
 
 .813 
 
 10 
 
 .473 
 
 .525 
 
 .571 
 
 .612 
 
 .650 
 
 .683 
 
 .713 
 
 .739 
 
 .763 
 
 .785 
 
 11 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 12 
 
 .408 
 
 .456 
 
 .500 
 
 .540 
 
 .576 
 
 .609 
 
 .639 
 
 .667 
 
 .692 
 
 .716 
 
 13 
 
 .373 
 
 .418 
 
 .460 
 
 .498 
 
 .533 
 
 .566 
 
 .596 
 
 .624 
 
 .649 
 
 .673 
 
 14 
 
 .335 
 
 .377 
 
 .417 
 
 .453 
 
 .487 
 
 .518 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 15 
 
 .295 
 
 .334 
 
 .370 
 
 .404 
 
 .436 
 
 .465 
 
 .493 
 
 .520 
 
 .544 
 
 .568 
 
 16 
 
 .253 
 
 .287 
 
 .319 
 
 .350 
 
 .379 
 
 .407 
 
 .433 
 
 .457 
 
 .481 
 
 .503 
 
 17 
 
 .208 
 
 .237 
 
 .265 
 
 .292 
 
 .317 
 
 .341 
 
 .364 
 
 .387 
 
 .408 
 
 .428 
 
 18 
 
 .160 
 
 .184 
 
 .206 
 
 .228 
 
 .249 
 
 .269 
 
 .288 
 
 .307 
 
 .325 
 
 .342 
 
 19 
 
 .110 
 
 .127 
 
 .143 
 
 .158 
 
 .174 
 
 .188 
 
 .203 
 
 .217 
 
 .231 
 
 .244 
 
 20 
 
 .057 
 
 .065 
 
 .074 
 
 .083 
 
 .091 
 
 .099 
 
 .107 
 
 .115 
 
 .123 
 
 .130 
 
12-36 
 
 Table 12-17 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i )J-m-l M 0r tgage Term (m) = 25 years 
 
 YEAR 
 (j) 
 
 INTEREST RATE 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 1 
 
 .767 
 
 .816 
 
 .854 
 
 .884 
 
 .908 
 
 .926 
 
 .941 
 
 .953 
 
 .962 
 
 .970 
 
 2 
 
 .753 
 
 .803 
 
 .842 
 
 .874 
 
 .898 
 
 .918 
 
 .934 
 
 .947 
 
 .957 
 
 .965 
 
 3 
 
 .738 
 
 .789 
 
 .830 
 
 .862 
 
 .888 
 
 .909 
 
 .926 
 
 .940 
 
 .951 
 
 .960 
 
 4 
 
 .722 
 
 .774 
 
 .816 
 
 .850 
 
 .877 
 
 .899 
 
 .917 
 
 .932 
 
 .944 
 
 .954 
 
 5 
 
 .706 
 
 .758 
 
 .801 
 
 .836 
 
 .865 
 
 .888 
 
 .907 
 
 .923 
 
 .936 
 
 .947 
 
 6 
 
 .688 
 
 .742 
 
 .785 
 
 .822 
 
 .851 
 
 .876 
 
 .896 
 
 .913 
 
 .927 
 
 .939 
 
 7 
 
 .669 
 
 .723 
 
 .768 
 
 .806 
 
 .836 
 
 .862 
 
 .884 
 
 .902 
 
 .917 
 
 .930 
 
 8 
 
 .650 
 
 .704 
 
 .750 
 
 .788 
 
 .820 
 
 .847 
 
 .870 
 
 .889 
 
 .905 
 
 .919 
 
 9 
 
 .629 
 
 .683 
 
 .730 
 
 .769 
 
 .802 
 
 .830 
 
 .854 
 
 .875 
 
 .892 
 
 .907 
 
 10 
 
 .606 
 
 .661 
 
 .708 
 
 .748 
 
 .782 
 
 .812 
 
 .837 
 
 .859 
 
 .877 
 
 .893 
 
 11 
 
 .583 
 
 .638 
 
 .685 
 
 .725 
 
 .761 
 
 .791 
 
 .817 
 
 .840 
 
 .860 
 
 .877 
 
 12 
 
 .558 
 
 .612 
 
 .660 
 
 .701 
 
 .737 
 
 .768 
 
 .795 
 
 .819 
 
 .840 
 
 .859 
 
 13 
 
 .531 
 
 .585 
 
 .632 
 
 .674 
 
 .710 
 
 .742 
 
 .771 
 
 .796 
 
 .818 
 
 .837 
 
 14 
 
 .503 
 
 .556 
 
 .603 
 
 .644 
 
 .681 
 
 .714 
 
 .743 
 
 .769 
 
 .792 
 
 .813 
 
 15 
 
 .473 
 
 .525 
 
 .571 
 
 .612 
 
 .650 
 
 .683 
 
 .713 
 
 .739 
 
 .763 
 
 .785 
 
 16 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 17 
 
 .408 
 
 .456 
 
 .500 
 
 .540 
 
 .576 
 
 .609 
 
 .639 
 
 .667 
 
 .692 
 
 .716 
 
 18 
 
 .373 
 
 .418 
 
 .460 
 
 .498 
 
 .533 
 
 .566 
 
 .596 
 
 .624 
 
 .649 
 
 .673 
 
 19 
 
 .335 
 
 .377 
 
 .417 
 
 .453 
 
 .487 
 
 .518 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 20 
 
 .295 
 
 .334 
 
 .370 
 
 .404 
 
 .436 
 
 .465 
 
 .493 
 
 .520 
 
 .544 
 
 .568 
 
 21 
 
 .253 
 
 .287 
 
 .319 
 
 .350 
 
 .379 
 
 .407 
 
 .433 
 
 .457 
 
 .481 
 
 .503 
 
 22 
 
 .208 
 
 .237 
 
 .265 
 
 .292 
 
 .317 
 
 .341 
 
 .364 
 
 .387 
 
 .408 
 
 .428 
 
 23 
 
 .160 
 
 .184 
 
 .206 
 
 .228 
 
 .249 
 
 .269 
 
 .288 
 
 .307 
 
 .325 
 
 .342 
 
 24 
 
 .110 
 
 .127 
 
 .143 
 
 .158 
 
 .174 
 
 .188 
 
 .203 
 
 .217 
 
 .231 
 
 .244 
 
 25 
 
 .057 
 
 .065 
 
 .074 
 
 .083 
 
 .091 
 
 .099 
 
 .107 
 
 .115 
 
 .123 
 
 .130 
 
12-37 
 
 Table 12-18 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i) J " m ' 1 Mortgage Term (m) = 30 years 
 
 YEAR 
 it) 
 
 INTEREST RATE 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 1 
 
 .826 
 
 .869 
 
 .901 
 
 .925 
 
 .943 
 
 .956 
 
 .967 
 
 .974 
 
 .980 
 
 .985 
 
 2 
 
 .815 
 
 .859 
 
 .893 
 
 .918 
 
 .937 
 
 .952 
 
 .963 
 
 .971 
 
 .978 
 
 .983 
 
 3 
 
 .804 
 
 .850 
 
 .884 
 
 .910 
 
 .931 
 
 .946 
 
 .958 
 
 .967 
 
 .974 
 
 .980 
 
 4 
 
 .793 
 
 .839 
 
 .875 
 
 .902 
 
 .924 
 
 .940 
 
 .953 
 
 .963 
 
 .971 
 
 .977 
 
 5 
 
 .780 
 
 .828 
 
 .865 
 
 .894 
 
 .916 
 
 .934 
 
 .947 
 
 .958 
 
 .967 
 
 .974 
 
 6 
 
 .767 
 
 .816 
 
 .854 
 
 .884 
 
 .908 
 
 .926 
 
 .941 
 
 .953 
 
 .962 
 
 .970 
 
 7 
 
 .753 
 
 .803 
 
 .842 
 
 .874 
 
 .898 
 
 .918 
 
 .934 
 
 .947 
 
 .975 
 
 .965 
 
 8 
 
 .738 
 
 .789 
 
 .830 
 
 .862 
 
 .888 
 
 .909 
 
 .926 
 
 .940 
 
 .951 
 
 .960 
 
 9 
 
 .722 
 
 .774 
 
 .816 
 
 .850 
 
 .877 
 
 .899 
 
 .917 
 
 .932 
 
 .944 
 
 .954 
 
 10 
 
 .706 
 
 .758 
 
 .801 
 
 .836 
 
 .865 
 
 .888 
 
 .907 
 
 .923 
 
 .936 
 
 .947 
 
 11 
 
 .688 
 
 .742 
 
 .785 
 
 .822 
 
 .851 
 
 .876 
 
 .896 
 
 .913 
 
 .927 
 
 .939 
 
 12 
 
 .669 
 
 .723 
 
 .768 
 
 .806 
 
 .836 
 
 .862 
 
 .884 
 
 .902 
 
 .917 
 
 .930 
 
 13 
 
 .650 
 
 .704 
 
 .750 
 
 .788 
 
 .820 
 
 .847 
 
 .870 
 
 .889 
 
 .905 
 
 .919 
 
 14 
 
 .629 
 
 .683 
 
 .730 
 
 .769 
 
 .802 
 
 .830 
 
 .854 
 
 .875 
 
 .892 
 
 .907 
 
 15 
 
 .606 
 
 .661 
 
 .708 
 
 .748 
 
 .782 
 
 .812 
 
 .837 
 
 .859 
 
 .877 
 
 .893 
 
 16 
 
 .583 
 
 .638 
 
 .685 
 
 .725 
 
 .761 
 
 .791 
 
 .817 
 
 .840 
 
 .860 
 
 .877 
 
 17 
 
 .558 
 
 .612 
 
 .660 
 
 .701 
 
 .737 
 
 .768 
 
 .795 
 
 .819 
 
 .840 
 
 .859 
 
 18 
 
 .531 
 
 .585 
 
 .632 
 
 .674 
 
 .710 
 
 .742 
 
 .771 
 
 .796 
 
 .818 
 
 .837 
 
 19 
 
 .503 
 
 .556 
 
 .603 
 
 .644 
 
 .681 
 
 .714 
 
 .743 
 
 .769 
 
 .792 
 
 .813 
 
 20 
 
 .473 
 
 .525 
 
 .571 
 
 .612 
 
 .650 
 
 .683 
 
 .713 
 
 .739 
 
 .763 
 
 .785 
 
 21 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 22 
 
 .408 
 
 .456 
 
 .500 
 
 .540 
 
 .576 
 
 .609 
 
 .639 
 
 .667 
 
 .692 
 
 .716 
 
 23 
 
 .373 
 
 .418 
 
 .460 
 
 .498 
 
 .533 
 
 .566 
 
 .596 
 
 .624 
 
 .649 
 
 .673 
 
 24 
 
 .335 
 
 .377 
 
 .417 
 
 .453 
 
 .487 
 
 .518 
 
 .548 
 
 .575 
 
 .600 
 
 .624 
 
 25 
 
 .295 
 
 .334 
 
 .370 
 
 .404 
 
 .436 
 
 .465 
 
 .493 
 
 .520 
 
 .544 
 
 .568 
 
 26 
 
 .253 
 
 .287 
 
 .319 
 
 .350 
 
 .379 
 
 .407 
 
 .433 
 
 .457 
 
 .481 
 
 .503 
 
 27 
 
 .208 
 
 .237 
 
 .265 
 
 .292 
 
 .317 
 
 .341 
 
 .364 
 
 .387 
 
 .408 
 
 .428 
 
 28 
 
 .160 
 
 .184 
 
 .206 
 
 .228 
 
 .249 
 
 .269 
 
 .288 
 
 .307 
 
 .325 
 
 .342 
 
 29 
 
 .110 
 
 .127 
 
 .143 
 
 .158 
 
 .174 
 
 .188 
 
 .203 
 
 .217 
 
 .231 
 
 .244 
 
 30 
 
 .057 
 
 .065 
 
 .074 
 
 .083 
 
 .091 
 
 .099 
 
 .107 
 
 .115 
 
 .123 
 
 .130 
 
12-38 
 
 suffice. In the eleventh year, the interest paid during the year is 
 
 (0.791) x ($1248), or $987. The income tax savings on a Federal or 
 
 state return for interest and taxes would be: 
 
 , Income . _ , Interest and. w /Tax rate based, 
 tax credit taxes on net income' 
 
 The Federal income tax return provides credit for state income 
 
 taxes paid and many states allow credit for Federal income taxes. Thus 
 
 the full credit for tax savings resulting from payment of interest is 
 
 not simply the sum of state and Federal tax savings. The net effective 
 
 rate for states allowing credit is: 
 
 Net 
 fcff a r+u, a \ - r Federal. . / State . , Federal. , State . 
 (Effective) - ( ) + ( tflx ) 2( ^) x ( ) 
 
 Kate 
 
 For states which do not give credit, the net effective rate is: 
 
 Net 
 /"Effective 1 = ( F e d era l\ + ( State \ » -f / FederaK , State . 
 
 Rate x rate ^ ax ra "te tax rate^ Hax rate^ 
 
 If the income tax rate on a Federal tax return is 25 percent and on 
 a state tax return is 10 percent, the net effective rate is (0.25 + 
 0.10 - 2 x 0.25 x 0.10) = 0.30, or 30 percent. The net annual income 
 tax savings realized on the Federal and state taxes for interest paid is 
 (0.30) x ($1133), or $340 in the first year and (0.30) x ($987) or $296 
 in the eleventh year. 
 
 OPERATING COSTS 
 
 The cost of operating a solar heating system, including the cost 
 for operating the auxiliary unit in the system, is the cost of electric 
 energy required to operate the pumps, central heat distribution fan, 
 valves, and controller in a hydronic system, and the blowers, motorized 
 
12-39 
 
 dampers, and controller in an air system. The amount of energy used to 
 collect, store, and distribute solar energy varies from system to system 
 in the range from 5 to 10 percent of the total solar energy collected. 
 The lower values in the range apply to low-head systems with small 
 pressure drops, and air systems with single blowers with small pressure 
 drops. The higher values in the range apply to high-head systems with 
 large pressure drops, small systems with large pumps, and air systems 
 with two blowers. 
 
 The operating cost of a non-solar system is considerably less than 
 that for a solar system. Although the blower size for distributing air 
 to the rooms is the same, the power requirement is less for a non-solar 
 system because the pressure drop in the system is lower. As an approxi- 
 mation, the energy required to operate a non- solar system is two to 
 three percent of the total annual heating load. 
 
 MAINTENANCE COSTS 
 
 The maintenance costs for solar systems are unknown because there 
 is insufficient long-term experience with various systems to indicate an 
 appropriate maintenance cost. While there is one air system that has 
 operated continuously for over 20 years, on which the maintenance cost 
 has been negligible, it can be expected that all solar systems should 
 receive annual preventive maintenance requiring about one man-day per 
 year. Liquid systems may require somewhat more frequent maintenance 
 than once a year. For the purpose of economic analysis, maintenance 
 costs can be estimated at about $100 for the first year and escalated 
 annually at a selected inflation rate. 
 
12-40 
 
 ECONOMIC ANALYSIS WORKSHEETS 
 
 Included in this section are "short" forms and "long" forms for 
 calculating life-cycle costs of solar and conventional heating systems. 
 The short form enables direct calculation of the present worth of cumu- 
 lative costs over a predetermined life of the system, e.g. 20 years. 
 The long form enables year-by-year calculations and allows flexibility 
 in the analysis because annual inflation rates can be changed for any 
 item. In using the short form the inflation rates remain constant for 
 the total period of analysis. Calculation procedures are explained 
 through detailed worksheets in the following sections. 
 
 WORKSHEET LCA-1 
 
 Worksheets LCA-1 (2 sheets) are data sheets to facilitate the 
 computations. Technical, economic, and cost data are listed on the 
 worksheets. 
 
 > 
 WORKSHEET LCA-2 
 
 Worksheet LCA-2 outlines step-by-step procedure for calculating 
 life-cycle costs of both the solar and non-solar systems. The economic 
 factors, E values, are determined from Tables 12-1 through 12-6. 
 
12-41 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project 
 
 Building Data 
 
 1. Annual space heating load 
 
 2. Annual DHW heating load 
 
 3. Total H and DHW load (add lines 1 & 2) 
 
 Economic Data 
 
 11. C , installed cost of solar system per 
 
 unit area 
 
 12. r^, estimated auxiliary fuel inflation 
 
 rate 
 
 13. r , r , estimated electric energy 
 
 inflation 
 
 14. g, r , estimated general inflation 
 
 m rate 
 
 15. p, property tax rate (based on 
 
 market value) 
 
 16. h, insurance premium rate 
 
 17. Federal income tax rate for owner 
 
 18. State income tax rate for owner 
 
 19. t, effective income tax rate 
 
 {i.e., (line 17) + (line 18) 
 - [2 x (line 17) x (line 18)]} 
 
 20. d, market discount rate 
 
 MMBtu/yr 
 MMBtu/yr 
 MMBtu/yr 
 
 Solar System Data 
 
 
 
 4. 
 
 Collector area 
 
 
 ft2 
 
 5. 
 
 Fraction of annual heating load 
 supplied from solar 
 
 
 decimal 
 
 Energy 
 
 Prices 
 
 
 
 6. 
 
 c , current energy cost for electrici 
 e (use Figure 12-2) <t/kWh 
 
 ty 
 
 $/MMBtu 
 
 7. 
 
 c f , c f , current cost of fuel 
 T (uSe Figure 12-1 or 12-2) 
 
 
 $/MMBtu 
 
 Terms c 
 
 if Loan 
 
 
 
 8. 
 
 m, term of the loan for solar system 
 
 
 yrs 
 
 9. 
 
 a, downpayment % 
 
 
 decimal 
 
 10. 
 
 i, interest rate on loan % 
 
 
 decimal 
 
 _$/ft2 
 % 
 
 % 
 
 % 
 
 decimal 
 decimal 
 decimal 
 decimal 
 
 decimal 
 decimal 
 
12-42 
 
 Worksheet LCA-1 
 Sheet 2 of 2 
 
 Solar System Cost Items 
 
 21. Installed cost (line 4 x line 11) $ 
 
 22. Federal tax credit for solar 
 (40% of first $10,000 of 
 
 system cost) $ 
 
 23. Downpayment (line 21 x line 9) $ 
 
 24. Amount of loan (line 21 - line 23) $ 
 
 25. Annual mortgage payment (multiply line 
 24 by annual mortgage rate from 
 
 Figure 12-4) $/yr 
 
 26. C f , first year cost of auxiliary heating 
 
 (line 3 x (1-line 5) x line 7) $/yr 
 
 27. First year property tax (line 21 x 
 
 line 15) $/yr 
 
 28. First year insurance premium 
 
 (line 21 x line 16) $/yr 
 
 29. C , first year cost of operating the 
 
 solar system (line 3 x (a value 
 
 between .05 and .10) x line 6) $/yr 
 
 30. C , first year maintenance cost 
 
 m (estimate) $/yr 
 
 Non-Solar System Cost Items 
 
 31. C.p , first year cost of fuel for non- 
 
 solar system (line 3 x line 7) $/yr 
 
 32. C , first year cost of operating 
 
 non-solar system (line 3 x 
 
 .01 x line 6) $/yr 
 
12-43 
 
 Worksheet LCA-2 
 Sheet 1 of 2 
 
 LIFE-CYCLE COST ANALYSIS 
 Total Cost for Solar System 
 
 33. n, total years of analysis yrs 
 
 34. A, collector area (line 4 of LCA-1) ft 2 
 
 35. L, annual heat load (line 3 of LCA-1) MMBtu 
 
 36. F, fraction of annual heat provided 
 
 by the solar system (line 5 of 
 
 LCA-1) decimal 
 
 37. P/X (d,g,n) (See Tables 12-1 
 
 through 12-6) 
 
 38. P/X (d,0,m) (See Tables 12-1 
 
 through 12-6) 
 
 39. P/X (i,0,m) (See Tables 12-1 
 
 through 12-6) 
 
 40. P/X (d,i,m) (See Tables 12-1 
 
 through 12-6) 
 
 41. P/X (0,i,m) (see Tables 12-1 
 
 through 12-6) 
 
 A9 z+Nr P/X (d,i ,m) n , line 19 x line 40 A 
 
 **' WL P/X (0,i,m) J ' l line 41 ; 
 
 A o n ^xr P/X (d > 0,m) 1 .. r (l-line 19) x (line 38) -, 
 
 **• u l;l P/X (i,0,m) J "' L line 41 J 
 
 44. Add line 42 and line 43 
 
 45. 1 - a (1 - line 9) 
 
 46. Multiply: line 44 x line 45 
 
 47. (l-t)(p) + h 
 
 (1 - line 19)(line 15) + (line 16) 
 
 48. Multiply: line 47 x line 37 
 49. 
 
 E-,^ = (line 9) + (line 48) + (line 46) 
 P/X (d,r o ,n) (see 
 12-1 through 12-6) 
 P/X (d,r m ,n) i 
 through 12-6) 
 
 50. E Q = P/X (d,r Q ,n) (see Tables 
 
 51. E m = P/X (d,r ,n) (see Tables 12-1 
 m m 
 
12-44 
 
 Worksheet LCA-2 
 Sheet 2 of 2 
 
 52. E f = P/X (d,r f ,n) (See Tables 12-1 
 
 through 12-6) 
 
 53. (A)(C XE-.) = (line 34 x line 11 x line 49) $ 
 
 a J. 
 
 54. C E n = (line 29 x line 50) $ 
 
 oo 
 
 55. C E = (line 30 x line 51) $ 
 
 mm 
 
 56. (l-F)(L)(c f )(E f ) = ( )( )( )( ) 
 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 57. C T = line 53 + line 54 + line 55 + line 56 - line 22 
 
 Total Cost for Non-Solar System 
 
 58. C E = line 32 x line 50 $ 
 
 OC 
 
 59. Lc fc E f = line 35 x line 7 x line 52 $ 
 
 (maintenance cost neglected) 
 
 60. C TC = line 58 + line 59 $ 
 
 Present Value of Life-Cycle Cost Savings 
 With Solar System 
 
 61. Savings = (line 60 - line 57) 
 
12-45 
 
 WORKSHEET LCA-3 
 
 In Worksheet LCA-3, column [1] is the year into the future for 
 which the analysis may be made. 
 
 Column [2] is the annual mortgage payment (see Worksheet LCA-1, 
 line 25). If the mortgage payment is a fixed annual amount, the payment 
 for all future years would be the same as the first year. 
 
 Column [3] is the fraction of the mortgage payment which is paid as 
 interest. The fraction decreases with increasing years and may be 
 determined from Tables 12-14 through 12-18 for the particular interest 
 rate and term of the mortgage. 
 
 Column [4] is the portion of the mortgage which is paid as interest 
 and is the product of column [2] times column [3]. 
 
 Column [5] is auxiliary fuel cost. Because fuel cost is expected 
 to increase, the first year fuel cost should be increased in subsequent 
 years. The first year fuel cost is the amount on line 26, Worksheet 
 LCA-1. The second year fuel cost is determined by multiplying the first 
 year cost by (1 + r f ), (for r f see line 12 of Worksheet LCA-1). For 
 example, if the first year fuel cost is $400 and the fuel inflation rate 
 is 15 percent, the second year cost is ($400 x 1.15 -) $460. The fuel 
 cost for each succeeding year is determined by multiplying the previous 
 year by (1 + fuel inflation rate). Note that the inflation rate may be 
 changed for any year in the period of analysis. 
 
 Column [6] is the annual property tax. The first year tax is 
 calculated on line 27 on Worksheet LCA-1 and succeeding years can be 
 escalated by the general inflation rate, g. 
 
 Column [7] is the annual insurance premium, which is determined on 
 line 28 of Worksheet LCA-1 for the first year. Succeeding years may be 
 
12-46 
 
 increased by a fixed or variable rate as desired. If no other guideline 
 is available, insurance rates may be assumed to increase at the assumed 
 general inflation rate. 
 
 Column [8] is the annual operating cost. The first year cost is 
 estimated on line 29 of Worksheet LCA-1. Costs for succeeding years may 
 be increased according to the fuel (electric) inflation rate. 
 
 Column [9] is the annual maintenance cost. The first year cost is 
 on line 30 of LCA-1. Maintenance costs may be increased annually 
 according to general inflation rates of items of replacement, such as 
 motorized valves, pumps, or domestic hot water tanks. Such costs may be 
 added in the future year when replacement is expected. 
 
 Column [10] is the income tax savings calculated by the product of 
 the effective tax rate (on line 19 of Worksheet LCA-1) and the sum of 
 annual interest paid, in column [4], plus property taxes, column [6]. 
 
 Column [11] is the annual expense of solar system and is determined 
 by: Column [2] + column [5] + column [6] + column [7] + column [8] + 
 column [9] - column [10]. The first year cash flow is calculated by 
 adding the down payment and subtracting the Federal tax credit. 
 
12-47 
 
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12-48 
 
 WORKSHEET LCA-4 
 
 Worksheet LCA-4 is used to compare life-cycle and cash-flow 
 analyses for solar and non-solar systems. 
 
 Column [1] is the year of analysis. 
 
 Column [2] is the total fuel and operating cost for the non-solar 
 system. The first year cost is the total of lines 31 and 32 on Work- 
 sheet LCA-1. The costs in succeeding years are determined by multiply- 
 ing the cost of fuel for the previous year (1 + r f ) and the cost for 
 operation for the previous year by (1 + r ). 
 
 Column [3] is the cumulative annual cash flow for the non-solar 
 system. 
 
 Column [4] is the present worth factor, determined from Table 12-7. 
 
 Column [5] is the present worth of the annual cost for a non-solar 
 system. 
 
 Column [6] is the annual cost of the solar system, transferred from 
 column [11] of Worksheet LCA-3. 
 
 Column [7] is the cumulative annual cash flow for the solar system. 
 
 Column [8] is the present value of the annual cost of the solar 
 system determined by multiplying column [6] by column [4]. 
 
 Column [9] is the present worth of savings with a solar system and 
 is determined by column [5] - column [8]. 
 
 Column [10 is the cumulative present worth of savings with a solar 
 system and is the running sum of column [9]. 
 
 Column [11] is the cumulative savings in cash flow and is 
 determined by column [3] - column [7]. 
 
12-49 
 
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12-50 
 
 EXAMPLE 12-4 
 
 Determine the life-cycle cost and energy cost savings of a 
 liquid-heating solar system 500 square feet of collectors. Assume 
 the following data apply: 
 
 1. F, annual solar fraction is 0.68. 
 
 2. Parasitic energy requirement is 7.5 percent of the solar 
 energy collected. 
 
 3. c , current electrical energy cost is 5.0 <t/kWh. 
 
 4. A 25-year loan at 10 percent is obtainable with 20 percent 
 down. 
 
 5. Cost of solar system is $17.25/ft 2 for collector-related 
 costs plus $7,285 for costs not related to collector area. In 
 terms of collector area, the cost is $17.25 + (7285/500) or 
 31.82 $/ft 2 of collector. 
 
 6. r f , fuel inflation rate is 15 percent. 
 
 7. g, general inflation rate is 7 percent. 
 
 8. Homeowners insurance is available for a premium of 0.3 percent 
 of insured value. 
 
 9. Property tax is levied on an assessed value which is 30 percent 
 of market and the mil levy is 100. This is equivalent to a 
 property tax levied as (0.30 x 0.1), or 3 percent of market 
 value. 
 
 10. The owner's Federal income tax rate is 32 percent and the 
 state tax is 8 percent. 
 
 11. Maintenance cost is $100 for first year. 
 
 12. Use a market discount rate of 10 percent. 
 
12-51 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project 
 
 Building Data 
 
 1. Annual space heating load 
 
 2. Annual DHW heating load 
 
 3. Total H and DHW load (add lines 1 & 2) 
 
 Solar System Data 
 
 4. Collector area 
 
 5. Fraction of annual heating load 
 supplied from solar 
 
 Energy Prices 
 
 6. c , current energy cost for electricity 
 
 e (use Figure 12-2) £~,QC /kWh 
 
 7. c f , c f , current cost of fuel C^ilJ 
 
 T TC (use Figure 12-1 or 12-2) 
 
 Terms of Loan 
 
 8. m, term of the loan for solar system 
 
 9. a, downpayment ^0 % 
 
 10. i, interest rate on loan f % 
 
 Economic Data 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 IQ3Ll3i M MBtu/yr 
 
 Q\,Q M MBtu/yr 
 
 \21 .,3 M MBtu/yr 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 17. 
 18. 
 19. 
 
 C , installed cost of solar system per 
 unit area 
 
 r.p, estimated auxiliary fuel inflation 
 rate 
 
 r , r , estimated electric energy 
 inflation 
 
 g» r. estimated general inflation 
 
 m 
 
 rate 
 
 p, property tax rate (based on 
 market value) 
 
 h, insurance premium rate 
 
 Federal income tax rate for owner 
 
 State income tax rate for owner 
 
 t, effective income tax rate 
 {i.e., (line 17) + (line 18) 
 - [2 x (line 17) x (line 18)]} 
 
 20. d, market discount rate 
 
 S'OO ft 2 
 
 / (o K d ec i ma 1 
 
 \4-.L5 $ /MMBtu 
 U-OO $/MMBtu 
 
 ^5" y rs 
 Q .£Q decimal 
 , \Cl d ecimal 
 
 
 \S 
 
 1 
 
 iQ 3 d ecimal 
 
 0±0&3l d ecimal 
 
 0,3^- d ecimal 
 
 Q i Q& d ec i ma 1 
 
 Oi 3S decimal 
 
 O i I O d ecimal 
 
12-52 
 
 Worksheet LCA-1 
 Sheet 2 of 2 
 
 Solar System Cost Items 
 
 21. Installed cost (Jine 4 x line 11) 
 
 22. Federal tax credit for solar 
 (40% of first $10,000 of 
 system cost) 
 
 23. Downpayment (line 21 x line 9) 
 
 24. Amount of loan (line 21 - line 23) 
 
 25. Annual mortgage payment (multiply line 
 24 by annual mortgage rate from 
 Figure 12-4) 
 
 26. Cp, first year cost of auxiliary heating 
 
 (line 3 x (1-line 5) x line 7) 
 
 27. First year property tax (line 21 x 
 line 15) 
 
 28. First year insurance premium 
 (line 21 x line 16) 
 
 29. C , first year cost of operating the 
 
 solar system (line 3 x (a value 
 between .05 and .10) x line 6) 
 
 30. C , first year maintenance cost 
 
 (estimate) 
 
 Non-Solar System Cost Items 
 
 31. Cp , first year cost of fuel for non- 
 
 solar system (line 3 x line 7) 
 
 32. C , first year cost of operating 
 
 non-solar system (line 3 x 
 .01 x line 6) 
 
 IS,<\\0 $ 
 
 3/£2 
 
 $ 
 
 \4 0O $ /yr 
 _lll_J/yr 
 
 4r7_$/yr 
 4 V $ /yr 
 
 l^ 2 ^ $ /yr 
 \0O $ /yr 
 
 1 5"tT^$ /yr 
 / J $ /yr 
 
12-53 
 
 Worksheet LCA-2 
 Sheet 1 of 2 
 
 LIFE-CYCLE COST ANALYSIS 
 Total Cost for Solar System 
 
 33. n, total years of analysis d^O y rs 
 
 34. A, collector area (line 4 of LCA-1) 55 Q f t 2 
 
 35. L, annual heat load (line 3 of LCA-1) U^iL 3 M MBtu 
 
 36. F, fraction of annual heat provided 
 
 by the solar system (line 5 of , „ 
 
 LCA-1) ■ (c o d ecimal 
 
 37. P/X (d,g,n) (See Tables 12-1 
 
 through 12-6) \4r.lCd 
 
 38. P/X (d,0,m) (See Tables 12-1 
 
 through 12-6) ^ % Q 7 / 
 
 39. P/X (i,0,m) (See Tables 12-1 n 
 through 12-6) ^-d 7 / 
 
 40. P/X (d,i,m) (See Tables 12-1 
 
 through 12-6) 33 . 7J / 
 
 41. P/X (0,i, m) (see Tables 12-1 ^^ _ , .- 
 through 12-6) IV j^r/ 
 
 /i9 /4-\r P/X (d,i,m) n _ / line 19 x line 40 N /] a<^ I 
 
 42 - (t)[ p/x (o;i,m) ] - ( — mm } U >0 ^> ' 
 
 a* (^ f N f P/X (d,0,m)i ... r (l-line 19) x (line 38) -, 
 43 - (1 " t)L P/X (i,0,m) J " L line 41 J 
 
 44. Add line 42 and line 43 Q t 73] 
 
 45. 1 - a (1 - line 9) j] , % 
 
 46. Multiply: line 44 x line 45 Q x SlLSL 
 
 47. (l-t)(p) + h A ,^ c 
 
 (1 - line 19)(line 15) + (line 16) Oj Q32z> 
 
 48. Multiply: line 47 x line 37 fl. 3 \^ 
 
 49. E 2 = (line 9) + (line 48) + (line 46) | t [()/\- 
 
 50. E Q = P/X (d,r ,n) (see Tables 
 
 12-1 through 12-6) %% , (j 5 £ 
 
 P/X (d,r ,n) (see Tables 12-1 
 
 through 12-6) \ V , \k 
 
12-54 
 
 Worksheet LCA-2 
 Sheet 2 of 2 
 
 52. E f = P/X (d,r f ,n) (See Tables 12-1 
 through 12-6) 
 
 53. (A)(C a )(E 1 ) = (line 34 x line 11 x line 49) 
 
 54. C o E Q = (line 29 x line 50) 
 
 55. C E = (line 30 x line 51) 
 
 mm 
 
 56. (l-F)(L)(c f )(E f ) = (.33)( ^.3 )(l3.o^(jg.^ I 4,-333 $ 
 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 57. C T = line 53 + line 54 + line 55 + line 56 - line 22 
 
 A-OC'f $ 
 
 SAlAt 
 
 iiL^lg $ 
 
 Total Cost for Non-Solar System 
 
 58. C rt E = line 32 x line 50 
 
 OC 
 
 59. Lc f Ex = line 35 x line 7 x line 52 
 
 (maintenance cost neglected) 
 
 60. C JC = line 58 + line 59 
 
 Present Value of Life-Cycle Cost Savings 
 With Solar System 
 
 61. Savings = (line 60 - line 57) 
 
 5~4-4- $ 
 
 44; 44 3$ 
 
 ±£JkLl$ 
 
12-55 
 
 EXAMPLE 12-5 
 
 Determine the life-cycle cost over 20 years of an air-heating solar 
 space and water-heating system with 400 square feet of collectors. 
 Calculate both the cumulative savings in cash flow and present worth of 
 cumulative savings over the 20 years. Assume the following: 
 
 1. F, annual solar fraction is 0.50. 
 
 2. Parasitic energy requirement is 7.5 percent of the solar 
 energy collected to store and distribute the heat. 
 
 3. c , current electrical energy cost is 5$/kWh. 
 
 4. A 30-year loan at 10 percent is obtainable with 10 percent 
 down-payment. 
 
 5. Cost of the solar system is $17.25/ft 2 for collector-related 
 costs plus $7805 for costs not related to collector area. In 
 terms of collector area, the cost is [17.25 + (7805/400)] = 
 $36.76/ft2. 
 
 6. r f , full inflation rate will vary, and let us assume a 40 
 
 percent increase over the next 2 years, dropping to 25 percent 
 for the following 2 years, 15 percent for the following 4 
 years, and 8 percent for the balance of the years to 20 years. 
 
 7. g, general inflation rate will be affected by the fuel 
 inflation rate and will tend to follow its pattern. Assume 12 
 percent for 2 years, 10 percent for the next 2 years, 8 
 percent for the following 4 years, and 6 percent for the 
 balance of the years. 
 
 8. Homeowner's insurance is available for a premium of 0.3 
 percent of insured value for the first year (use system cost) 
 and will increase according to the general inflation rate. 
 
 9. Property tax for the first year is 3 percent of market value 
 and will increase steadily at 7 percent per year. 
 
 10. The owner's Federal income tax rate is 25 percent now but will 
 increase to 45 percent over the 20 years of analysis. Assume 
 a linear rate of increase, i.e. one percent per year. There 
 is no state income tax. 
 
 11. Maintenance cost will be $100 per year for the first 5 years, 
 which will increase to $150 for the following 5 years. In the 
 11th year there will be a motor replacement necessary which 
 will cost $300, but thereafter the maintenance cost remains at 
 $150/yr. 
 
12-56 
 
 12. Assume a steady market discount rate of 10 percent over the 
 20-year period. 
 
 The annual cash flow for the solar system is calculated on Worksheet 
 LCA-3. If the inflation scenario is realistic, the cost for heating the 
 building in the year 2000 can be 12 times larger than present for the 
 conventional heating system and 4 to 5 times larger with the solar plus 
 auxiliary system. 
 
 According to the calculations, by the third year, the cost of 
 heating with the solar plus auxiliary system is about the same as heat- 
 ing with auxiliary alone and with the solar system there is a 50 percent 
 reduction in consumption of fuel oil. This observation is borne out in 
 the calculations shown on Worksheet LCA-4, where cumulative present 
 worth of savings over twenty years is calculated, and for comparison, 
 cumulative savings of annual cash flow are also shown. The cumulative 
 savings of cash flow is not a realistic value because, although "dollar" 
 savings are added each year to determine the total savings, the value of 
 the dollar changes each year because of inflation. The cumulative 
 present worth column sums devalued dollars, and provided a realistic 
 economic scenario has been applied, the owner of this solar house can 
 expect to save a significant amount of money each year beyond the third 
 year by installing the solar system. At the same time, consumption of 
 heating fuel is reduced by about one-half. 
 
12-57 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project 
 
 So 
 
 (\r 
 
 11 
 
 Building Data 
 
 1. Annual space heating load 
 
 2. Annual DHW heating load 
 
 3. Total H and DHW load (add lines 1 & 2) 
 
 Solar System Data 
 
 4. Collector area 
 
 5. Fraction of annual heating load 
 supplied from solar 
 
 Energy Prices 
 
 6. c , current energy cost for electricity 
 
 (use Figure 12- 2) _ff_<t/kWh 
 
 7. c f , c f , current cost of fuel Co]) 
 
 TC (use Figure 12-1 or 12-2) 
 
 Terms of Loan 
 
 8. m, term of the loan for solar system 
 
 9. a, downpayment }/) % 
 
 10. i, interest rate on loan tO % 
 
 Economic Data 
 
 11. c a , 
 
 12. r f5 
 
 13. r_, 
 14. 
 15. 
 
 installed cost of solar system per 
 unit area 
 
 estimated auxiliary fuel inflation 
 rate 
 
 , r , estimated electric energy 
 inflation 
 
 r , estimated general inflation 
 m rate 
 
 p s property tax rate (based on 
 market value) 
 
 16. h, insurance premium rate 
 
 17. Federal income tax rate for owner 
 
 18. State income tax rate for owner 
 
 19. t, effective income tax rate 
 
 {i.e., (line 17) + (line 18) 
 - [2 x (line 17) x (line 18)]} 
 
 20. d, market discount rate 
 
 \(lt. 3 M MBtu/yr 
 
 g L Q M MBtu/yr 
 
 3^ 3 M MBtu/yr 
 
 too 
 
 ft : 
 
 CufLQ. d ecimal 
 
 W-t>5 $ /MMBtu 
 M • CO $/MMBtu 
 
 3>0 
 
 yrs 
 
 Q< \Q d eci ma 1 
 flAO d ecimal 
 
 M(XV\ #3 % 
 \}<KY\<L<> % 
 
 4O3 d ecimal 
 
 « 2> d ecimal 
 
 fi,2,t>~ d ecimal 
 
 Q d ecimal 
 
 Q 1 2 5 d e c i ma 1 
 OilO d ecimal 
 
12-58 
 
 Worksheet LCA-1 
 Sheet 2 of 2 
 
 Solar System Cost Items 
 
 21. Installed cost (line 4 x line 11) 
 
 22. Federal tax credit for solar 
 (40% of first $10,000 of 
 system cost) 
 
 23. Downpayment (line 21 x line 9} 
 
 24. Amount of loan (line 21 - line 23) 
 
 25. Annual mortgage payment (multiply line 
 24 by annual mortgage rate from 
 Figure 12-41 
 
 C 
 
 26. C f , first year cost of auxiliary heating 
 T (line 3 x (1-line 5) x line 7) 
 
 27. First year property tax (line 21 x 
 line 15). 
 
 28. First year insurance premium 
 (line 21 x line 16) 
 
 29. C , first year cost of operating the 
 
 solar system (line 3 x (a value 
 between .05 and .10) x line 6 ) 
 
 30. C , first year maintenance cost 
 
 m (estimate) 
 
 4,Oq6 $ 
 
 IA1Q $ 
 
 \Ao3 $ /yr 
 
 "7 7£ $ /yr 
 
 Non-Solar System Cost Items 
 
 31. C» , first year cost of fuel for non- 
 
 solar system (line 3 x line 7) 
 
 32. C , first year cost of operating 
 
 non-solar system (line 3 x 
 .01 x line 6) 
 
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 44- 
 
 J/yr 
 
 5^L_$/yr 
 J/yr 
 
 too 
 
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 .$/yr 
 
 11 
 
 $/yr 
 
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 3 
 
 S- O Q. O 
 
 CU i— 
 
 •r- CU — ' O 
 
 CU o 
 
 U. OO <V)U 
 
 CNJ 
 
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Worksheet LCA-1 
 Sheet 1 of 2 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project 
 
 Building Data 
 
 1. Annual space heating load 
 
 2. Annual DHW heating load 
 
 3. Total H and DHW load (add lines 1 & 2) 
 
 Solar System Data 
 
 4. Collector area 
 
 5. Fraction of annual heating load 
 supplied from solar 
 
 Energy Prices 
 
 6. 
 7. 
 
 c , current energy cost for electricity 
 
 (use Figure 12-2) 
 
 cVkWh 
 
 c f , c f , current cost of fuel 
 
 TC (use Figure 12-1 or 12-2) 
 
 Terms of Loan 
 
 8. m, term of the loan for solar system 
 
 9. a, downpayment % 
 
 10. i, interest rate on loan % 
 
 Economic Data 
 
 11. C , installed cost of solar system per 
 
 unit area 
 
 12. r f , estimated auxiliary fuel inflation 
 
 rate 
 
 13. r , r , estimated electric energy 
 
 inflation 
 
 14. g, r , estimated general inflation 
 
 m rate 
 
 15. p, property tax rate (based on 
 
 market value) 
 
 16. h, insurance premium rate 
 
 17. Federal income tax rate for owner 
 
 18. State income tax rate for owner 
 
 19. t s effective income tax rate 
 
 {i.e., (line 17) + (line 18) 
 - [2 x (line 17) x (line 18)]} 
 
 _MMBtu/yr 
 _MMBtu/yr 
 MMBtu/yr 
 
 ft 2 
 
 decimal 
 
 _$/MMBtu 
 $/MMBtu 
 
 _yrs 
 
 _decimal 
 decimal 
 
 $/ft : 
 
 decimal 
 decimal 
 decimal 
 decimal 
 
 20. d, market discount rate 
 
 decimal 
 decimal 
 
Worksheet LCA-1 
 Sheet 2 of 2 
 
 Solar System Cost Items 
 
 21. Installed cost (line 4 x line 11) $ 
 
 22. Federal tax credit for solar 
 (40% of first $10,000 of 
 
 system cost) $ 
 
 23. Downpayment (line 21 x line 9) $ 
 
 24. Amount of loan (line 21 - line 23) $ 
 
 25. Annual mortgage payment (multiply line 
 24 by annual mortgage rate from 
 
 Figure 12-4) $/yr 
 
 26. C f , first year cost of auxiliary heating 
 
 (line 3 x (1-line 5) x line 7) $/yr 
 
 27. First year property tax (line 21 x 
 
 line 15) Myr 
 
 28. First year insurance premium 
 
 (line 21 x line 16) $/yr 
 
 29. C , first year cost of operating the 
 
 solar system (line 3 x (a value 
 
 between .05 and .10) x line 6) $/yr 
 
 30. C , first year maintenance cost 
 
 (estimate) $/yr 
 
 Non-Solar System Cost Items 
 
 31. Cc , first year cost of fuel for non- 
 
 solar system [line 3 x line 7) $/yr 
 
 32. C , first year cost of operating 
 
 non-solar system (line 3 x 
 
 .01 x line 6) $/yr 
 
Worksheet LCA-2 
 Sheet 1 of 2 
 
 LIFE-CYCLE COST ANALYSIS 
 Total Cost for Solar System 
 
 33. n, total years of analysis 
 
 34. A, collector area (line 4 of LCA-1) 
 
 35. L, annual heat load (line 3 of LCA-1) 
 
 36. F, fraction of annual heat provided 
 
 by the solar system (line 5 of 
 LCA-1) 
 
 37. P/X (d.g.n) 
 through 12-6 
 
 38. P/X (d,0,m) 
 through 12-6 
 
 39. P/X (i,0,m) 
 through 12-6 
 
 40. P/X (d,i,m) 
 through 12-6 
 
 41. P/X (0,i,m) 
 through 12-6 
 
 See Tables 12-1 
 
 See Tables 12-1 
 
 See Tables 12-1 
 
 See Tables 12-1 
 
 see Tables 12-1 
 
 ne 40 
 
 _yrs 
 ft 2 
 
 MMBtu 
 
 decimal 
 
 Ao / + \ r P/X (d,i,m) -i . / line 19 x lii 
 
 **' ^ JL P/X (0,i,m) J " l line 41 
 
 /l-5 m + N[- P/X (d,0,m)- | .. r ( l-line 19) x (line 38) -, 
 
 43 - u " t)L p/x (i,o,m) J - L mrtvi J 
 
 44. 
 45. 
 46. 
 47. 
 
 48. 
 49. 
 50. 
 
 51. 
 
 Add line 42 and line 43 
 
 1 - a (1 - line 9) 
 
 Multiply: line 44 x line 45 
 
 (l-t)(p) + h 
 
 (1 - line 19)(line 15) + (line 16) 
 
 Multiply: line 47 x line 37 
 
 E, = (line 9) + (line 48) + (line 46) 
 
 E o = P/X ( d >V n) 
 
 (see Tables 
 12-1 through 12-6) 
 
 E m = P/X (d,r ,n) (see Tables 12-1 
 m m 
 
 through 12-6) 
 
Worksheet LCA-2 
 Sheet 2 of 2 
 
 52. E f = P/X (d,r f ,n) (See Tables 12-1 
 through 12-6) 
 
 53 
 
 . (A)(CJ(E 1 ) = (line 34 x line 11 x line 49) 
 
 54. C E Q = (line 29 x line 50) _____ 
 
 55. C E = (line 30 x line 51) 
 
 mm 
 
 56. (l-F)(L)(c f )(E f ) = ( )( )( )( ) 
 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 57. C T = line 53 + line 54 + line 55 + line 56 - line 22 
 
 Total Cost for Non-Solar System 
 
 58. C,E = line 32 x line 50 
 
 OC 
 
 59. Lc f E f = line 35 x line 7 x line 52 
 
 1 (maintenance cost neglected) 
 
 60. C JC = line 58 + line 59 
 
 Present Value of Life-Cycle Cost Savings 
 With Solar System 
 
 61. Savings = (line 60 - line 57) 
 
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APPENDIX 
 
ALASKA 
 
 TAX INCENTIVES 
 
 Alaska allows a 10% residential fuel conservation credit of up to $200 per individual or married 
 couple for money spent on the following: 1) insulation; 2) insulating windows; 3) labor related to 
 items 1 and 2; 4) alternate energy systems which are not dependent on fossil fuel, including 
 solar, wind, tidal, and geothermal. Expires 12/31/82 (Chapter 94, Laws of 1977). 
 
 Contact State Department of Revenue 
 Income Tax Division 
 Pouch SA 
 
 continue State Office Building 
 Juneau, AK 99811 
 (907) 465-2326 
 
 GRANTS AND LOANS 
 
 This act creates the Alaska Renewable Research Corporation. The Corporation is funded by a 
 portion of the state's proceeds from mineral leases, rentals, bonuses, and royalties. Most of 
 the Corporation's budget is used as venture capital for new businesses involved in renewable 
 resources such as forest products, fisheries, agriculture and renewable energy resources. Up 
 to 10% of every annual appropriation may be used as grants to the same types of enterprises 
 (Chapter 179, Laws of 1978). 
 
 Contact Alaska Renewable Research Corporation 
 Box 1647 
 
 Juneau, AK 99802 
 (907) 465-4616 
 
 Suite One 
 313 "E" Street 
 Anchorage, AK 99501 
 (907) 272-2500 
 
 This law establishes an Alternative Power Resource Revolving Loan Fund in the Department of 
 Commerce and Economic Development. The fund shall be used to develop energy production 
 from sources other than fossil or nuclear fuel. This includes wind, water and solar devices. 
 Loans may not exceed $10,000 (Chapter 29, Laws of 1978). 
 
 Contact Division of Business Loans 
 
 Department of Commerce & Economic Development 
 
 Pouch D 
 
 Juneau, AK 99811 
 
 (907) 465-2510 
 
 (907) 274-6693 (Anchorage) 
 
 (907) 452-8182 (Fairbanks) 
 
 NATIONAL 
 m .SOLAR u 
 
 INFORMATION COWER 
 
 im? 
 
 3/30/80 
 
 The Center is operated by the Franklin Research Center tor the U S. Department ol Housing and Urban Development and the 
 U S Department ol Energy The listings contained herein are based on information known by the Center at the time ol print- 
 ing Periodic updates are available. For more information, please contact us at P.O. Box 1607, Rockville. MD 20850 or call toll 
 Iree (800) 523-2929. In Pennsylvania call (800) 462-4983. In Alaska and Hawaii call (800) 523-4700. 
 
ARIZONA 
 
 TAX INCENTIVES 
 
 Individuals may claim an income tax credit equal to 35% of the cost of a solar energy device 
 through 1983. Thereafter the percentage decreases 5% per year until the credit expires on 
 12/31/89. The maximum credit is $1,000. Home builders may claim the credit on new speculative 
 solar homes in lieu of the purchaser. The credit is available at the same rates for commercial 
 and industrial solar installations. All credits include carry forward provisions (Chapter 93, Laws 
 of 1975; Chapter 129, Laws of 1976; Chapter 112, Laws of 1978; Chapter 146, Laws of 1979). 
 
 Solar energy devices are exempt from property taxes through 12/31/89 (Chapter 165, Laws of 
 1974; Chapter 146, Laws of 1979). Solar energy devices are exempt from Transaction Privilege 
 and Use Taxes through 12/31 /89 (Chapter 42, Laws of 1977; Chapter 146, Laws of 1979). A 25% 
 credit is allowed for residential insulation and ventilation devices, such as insulating doors and 
 windows. Maximum credit is $100. Credit expires 12/31/84 (Chapter 112, Laws of 1978). 
 
 Contact State Department of Revenue 
 Box 29002 
 Phoenix, AZ 85038 
 (602) 255-3381 
 
 LAND USE 
 
 Provides authority for local governments to regulate solar access (Chapter 94, Laws of 1979). 
 
 Contact Local planning commission or zoning board 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 Local building codes may include provisions requiring that new, single-family residences be 
 
 designed to facilitate future installation of solar heating equipment (Chapter 94, Laws of 1979). 
 
 Contact Local building official 
 
 ARKANSAS 
 
 TAX INCENTIVES 
 
 An energy conservation income tax deduction is available to any individual, fiduciary or cor- 
 poration. Eligible items include insulation and energy conservation adjustments made to 
 buildings constructed before 1/1/79. Also eligible are these additions made to new or existing 
 buildings: devices using solar energy, bioconversion energy, geothermal energy, hydroelectric 
 energy (for mechanical or electrical power) for space heating or cooling or water heating; 
 devices using wind energy; and devices creating energy from woodburning in stoves, furnaces, 
 or fireplaces with controllable drafts and dampers. Deductions exceeding income may be car- 
 ried forward until exhausted. Eligible expenditures must be made before 12/31/84. The Com- 
 missioner of Revenue may promulgate regulations for the administration of the deduction (Act 
 535,1977; Act 742, 1979; Act 59, 1980). 
 
 Contact State Department of Revenue 
 Income Tax Section 
 7th and Wolfe Streets 
 Little Rock, AR 72201 
 (501) 371-2193 
 
 CALIFORNIA 
 
 TAX INCENTIVES 
 
 California provides personal income tax credit of 55% of the cost of a solar energy system, up 
 to a maximum of $3000. If a system is installed in other than a single-family dwelling and the 
 cost exceeds $6000, the credit equals 25% of the cost, or $3000, whichever is greater. In both, 
 single-family dwellings and other buildings, the cost of energy-conserving devices installed in 
 conjunction with the solar enorqv system may also be included in the total cost used to 
 
calculate the tax credit. If a federal credit is claimed, the state credit is reduced by the amount 
 of the federal credit. The same provisions apply to corporate taxpayers. Taxpayers who partial- 
 ly own and partially lease a solar system from a public utility are also eligible for the credit. 
 The system must meet the criteria of the California Energy Commission. Eliglible expenses for 
 credit include attorney's fees, compensation, and recording fees associated with obtaining a 
 solar easement. Credit expires 12/31/80 (Chapter 168, Laws of 1976; Chapter 1082, Laws of 1977; 
 Chapter 1154, Laws of 1978; Chapter 816, Laws of 1979). 
 
 Contact Franchise Tax Board 
 Attn: Correspondence 
 Sacramento, CA 95807 
 (916) 355-0370 
 
 GRANTS AND LOANS 
 
 This law creates the Solar Energy Demonstration Loan Program and provides $2000 interest- 
 free loans for solar space heating and domestic hot water systems in areas where a state of 
 emergency has been declared (Chapter 1 and Chapter 7, Laws of 1978). 
 
 Contact Department of Housing and Community Development 
 Division of Research and Policy Development 
 921 10th Street, Fifth Floor 
 Sacramento, CA 95814 
 (916) 445-4728 
 
 The maximum loan available to veterans for home mortgages is increased to $60,000 if the 
 home is equipped with a solar energy system (Chapter 1243, Laws of 1978; Chapter 48, Laws of 
 1979). 
 
 Contact Department of Veterans' Affairs 
 1227 "O" Street 
 P.O. Box 1559 
 Sacramento, CA 95807 
 (916) 445-2347 
 
 or any local district office of the 
 Department of Veterans' Affairs 
 
 LAND USE 
 
 Anyone who owns, occupies, or controls real estate is prohibited from allowing a tree or shrub 
 to cast a shadow on a solar collector between 9:30 a.m. and 2:30 p.m. Trees casting a shadow 
 before the installation of a collector are excluded (Chapter 1366, Laws of 1978). 
 
 This law declares that any restriction on real property purporting to prohibit the installation and 
 use of a solar energy system is void and unenforceable. It recognizes solar easements and 
 prescribes their contents. City and county governments may not prohibit or restrict solar 
 energy systems except to ensure the public health. The law requires that new subdivision 
 maps be designed to accommodate passive solar energy systems to the maximum extent 
 possible. It permits city and county governments to require the dedication of solar easements 
 before approving the map (Chapter 1154, Laws of 1978). 
 
 Contact Local planning or zoning body 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 Any city or county may require that new buildings subject to the State Housing Law be con- 
 structed in a manner that permits the installation of solar heating (Chapter 670, Laws of 1976). 
 
 Contact Local building inspector 
 
 The California Energy Commission is required to adopt regulations and standards governing 
 solar energy equipment (Chapter 1081, Laws of 1977). 
 
 Contact California Energy Commission 
 1111 Howe Avenue 
 Sacramento. CA 95825 
 (916) 3?2-3690 
 
COLORADO 
 
 TAX INCENTIVES 
 
 Alternative energy devices will be assessed for real estate tax at 5% of their value. Eligible 
 devices must use solar or geothermal energy, renewable biomass, or wind resources. Passive 
 solar designs are included, but devices for the direct combustion of wood are ineligible. The 
 exemption expires 12/31/89 (Chapter 344, Laws of 1975; Chapter 363, Laws of 1979). 
 
 Contact Local tax assessor 
 
 Creates an income tax deduction for alternative energy devices. Eligible deductions include the 
 cost of solar, wind, geothermal, or renewable biomass systems. Passive solar designs are in- 
 cluded to the extent that construction costs exceed those of conventional designs. Devices for 
 the direct combustion of wood do not qualify. Corporate taxpayers may use the deduction in 
 lieu of depreciation (Chapter 512, Laws of 1977; Chapter 374, Laws of 1979). 
 
 Contact Colorado Department of Revenue 
 Capitol Annex Building 
 1375 Sherman Street 
 Denver, CO 80203 
 (303) 839-2801 
 
 LAND USE 
 
 Solar easements are recognized and their contents are prescribed. They are subjected to the 
 same conveyancing and recording requirements as other easements. Any unreasonable 
 restriction on real estate, based on aesthetic considerations and effectively prohibiting or 
 restricting the installation and use of a solar energy device, is declared void and unenforceable 
 (Chapter 326, Laws of 1975; Chapter 358, Laws of 1979). 
 
 This law authorizes local governments to regulate uses of land in planning and zoning regula- 
 tions to assure access to direct sunlight for solar energy devices. Special exceptions to zoning 
 regulations may be granted to protect solar access. Subdivision regulations may be altered to 
 protect solar access. Effective 1/1/80 (Chapter 306, Laws of 1979). 
 
 Contact Local zoning board or planning commission 
 
 CONNECTICUT 
 
 TAX INCENTIVES 
 
 Municipalities are authorized to exempt windmills, waterwheels and solar heating, cooling or 
 electrical systems from real estate tax. Installation must occur before 10/1/91. The exemption 
 will be effective for 15 years after installation. Passive solar energy systems, constructed or in- 
 stalled after 10/1/80 may also be exempted. Systems must meet standards of the Office of 
 Policy and Management (Public Act 76-409; Public Act 77-490; Public Act 79-479). 
 
 Solar collectors are exempt from sales tax through 10/1 /82 (Public Act 77-457) 
 
 Contact Commissioner of Revenue Services 
 92 Farmington Avenue 
 Hartford, CT 06115 
 (203) 566-7120 
 
 GRANTS AND LOANS 
 
 This law requires the Commissioner of Economic Development to establish an energy conser- 
 vation loan fund. The Commissioner shall make low-cost loans from this fund for insulation, 
 energy conservation materials and alternate energy devices to be installed in residential 
 buildings containing not more than four dwelling units. Alternate energy devices are those 
 which use solar radiation, wind, water, or geothermal resources for space heating or cooling, 
 water heating or generation of electricity. Loans can range from $400 to $3000. The State Bond 
 Commission may authorize the issuance of bonds to fund the loan program (Public Act 79-509). 
 
The law authorizes the Department of Economic Development to make loans for industrial ap- 
 plications of energy conservation techniques, solar, wind, hydro, biomass or other forms of 
 renewable energy (Public Act 79-520). 
 
 Contact Department of Economic Development 
 210 Washington Street 
 Hartford, CT 06115 
 (203) 566-4555 
 
 This law authorizes the Connecticut Housing Financing Authority to make and insure loans for 
 energy conservation improvements and installation of renewable energy systems for space 
 heating and cooling, water heating, and electricity in residential buildings. Renewable energy 
 sources eligible include wind, solar, water and biomass (Public Act 79-578). 
 
 Contact Connecticut Housing Financing Authority 
 190 Trumbull Street 
 Hartford, CT 06103 
 (203) 525-9311 
 
 LAND USE 
 
 The zoning commission of each city, town, or borough is authorized to regulate development to 
 encourage energy efficiency and the use of renewable forms of energy, including solar (Public 
 Act 78-314). 
 
 Contact Local planning or zoning body 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Office of Policy and Management is required to establish standards for solar energy 
 
 systems (Public Act 76-409; Public Act 79-479). 
 
 Contact Office of Policy and Management 
 20 Grand Street 
 Hartford, CT 06115 
 (203) 566-5765 
 
 DELAWARE 
 
 TAX INCENTIVES 
 
 This law provides an income tax credit of $200 for solar energy devices designed to produce 
 domestic hot water. Systems must meet HUD Intermediate Minimum Property Standards Sup- 
 plement for Solar Heating and Domestic Hot Water Systems. Systems must be warranted ac- 
 cording to criteria set out in the law (Chapter 512, Laws of 1978). 
 
 Contact Division of Revenue 
 State Office Building 
 820 French Street 
 Wilmington, DE 19801 
 (302) 571-3360 
 
 FLORIDA 
 
 TAX INCENTIVES 
 
 Effective 7/1/79, solar energy systems are exempt from sales and use tax until 6/30/84 (Chapter 
 
 339, Laws of 1979). 
 
 Contact Florida Department of Revenue 
 Sales Tax Division 
 Carlton Building 
 Tallahassee, FL 32304 
 (904) 488-6800 
 
LAND USE 
 
 Solar easements are recognized and subject to the same requirements as other easements; 
 the contents are prescribed (Chapter 309, Laws of 1978). 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Florida Solar Energy Center is required to establish standards for solar energy systems 
 (Chapter 246, Laws of 1976). 
 
 Contact Florida Solar Energy Center 
 300 State Road 401 
 Cape Canaveral, FL 32920 
 (305) 783-0300 
 
 The law stipulates that no single-family dwelling shall be constructed unless it is designed to 
 facilitate future installation of a solar hot water system (Chapter 361, Laws of 1974). 
 
 Contact Local building inspector 
 
 All solar energy systems manufactured or sold in Florida must meet the standards established 
 by the Florida Solar Energy Center (Chapter 309, Laws of 1978). 
 
 Contact Bureau of Codes and Standards 
 2571 Executive Center Circle 
 Tallahassee, FL 32301 
 (904) 488-3581 
 
 GEORGIA 
 
 TAX INCENTIVES 
 
 Real estate owners may claim a refund of sales tax paid for the purchase of solar equipment. 
 Expires 7/1/86 (Act 1030, 1976; Act 1309, 1978). 
 
 Contact State Department of Revenue, Sales Tax Division 
 309 Trinity-Washington Building 
 Atlanta, GA 30334 
 (404) 656-4065 
 
 Any county or municipality may exempt solar heating and cooling equipment and machinery 
 used to manufacture solar equipment from property taxes. Expires 7/1/86 (Georgia Constitu- 
 tion, Article VII, Section 1, Paragraph IV). 
 
 Contact Local city council or county board of supervisors 
 
 LAND USE 
 
 Solar easements are recognized and subject to the same requirements as other easements; 
 the contents are prescribed (Act 1446, 1978). 
 
 HAWAII 
 
 TAX INCENTIVES 
 
 A 10% income tax credit is provided to individuals and corporations who purchase solar energy 
 devices that are placed in service by 12/31/81. The law also provides property tax exemptions 
 for solar energy systems through 12/31/81. This exemption also applies to any non-nuclear and 
 non-fossil fuel system and to any improvement that increases the efficiency of systems which 
 use fossil fuel (Act 189, 1976). 
 
 Contact State Tax Department 
 P.O. Box 259 
 Honolulu, HI 96809 
 (808) 548-3270 
 
IDAHO 
 
 TAX INCENTIVES 
 
 This law allows an income tax deduction for a solar heating/cooling or solar electrical system 
 installed in the taxpayer's residence. The deduction equals 40% of the cost in the first year and 
 20% of the cost in each of the next 3 years; the maximum deduction in any year is $5000. This 
 deduction also applies to systems fueled by wind, geothermal energy, wood, or wood pro- 
 ducts. Built-in fireplaces qualify if they have control doors, regulated draft, and heat ex- 
 changers that deliver heated air to substantial portions of the residence (Chapter 212, Laws of 
 1976). 
 
 Contact State Tax Commission 
 5257 Fairview 
 Boise, ID 83722 
 (208) 384-3290 
 
 LAND USE 
 
 Solar easements are recognized and are made subject to the same requirements as other 
 easements; the contents are prescribed (Chapter 294, Laws of 1978.) 
 
 ILLINOIS 
 
 TAX INCENTIVES 
 
 A property owner who installs a solar or wind energy system may claim an alternate valuation 
 for property taxes. The property is assessed twice: with the solar or wind energy system and 
 also as though it were equipped with a conventional system. The lesser of the two 
 assessments is used to compute the tax due. Owners must file a claim with the local Board of 
 Assessors. (Public Act 79-943, 1975; Public Act 80-430, 1977). 
 
 Contact Local assessor or board of assessors 
 
 GRANTS AND LOANS 
 
 This law establi?hes a $5 million research, development, and demonstration program for non- 
 coal, non-nuclear energy (Public Act 80-432, 1977). 
 
 Contact Illinois Institute of Natural Resources 
 325 West Adams 
 Room 300 
 
 Springfield, IL 62706 
 (217) 785-2800 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Illinois Institute of Natural Resources is required to establish guidelines and regulations 
 for solar energy systems (Public Act 80-430, 1977). 
 
 Contact Illinois Institute of Natural Resources 
 325 West Adams 
 Room 300 
 
 Springfield, IL 62706 
 (217) 785-2800 
 
 INDIANA 
 
 TAX INCENTIVES 
 
 The law permits the property owner who installs a solar heating and cooling system to. have 
 property assessment reduced by the difference between the assessment of the property with 
 the system and the assessment of the property without the system. The owner must apply to 
 the county auditor (Public Law 15, 1974; Public Law 68, 1977). 
 
 Contact Local assessor or board of assessors 
 
An income tax credit is created for individuals, corporations, and partnerships that install solar 
 or wind energy systems for heating space or water or for generating electricity. For single- 
 family dwellings the credit equals 25% of eligible expenditures to a maximum of $3,000. For 
 other buildings the credit equals 25% of expenditures to a maximum of $10,000. Credit ex- 
 ceeding tax liability may be carried forward until exhausted. Expenditures must be made by 
 12/31/82. The Department of Revenue shall promulgate rules to implement the credit, including 
 performance and quality standards for qualifying systems. (Public Law 20, 1980). 
 
 Contact Indiana Department of Revenue 
 202 State Office Building 
 Indianapolis, IN 46204 
 (317) 232-2101 
 
 IOWA 
 
 TAX INCENTIVES 
 
 Installation of a solar energy system will not increase the assessed, actual, or taxable values of 
 property for 1979-1985 (Section 441.21, Code of 1979). 
 
 Contact Local assessor or board of assessors 
 
 GRANTS AND LOANS 
 
 This law establishes a loan and grant fund for property improvements and mortgages for low- 
 income families. Solar energy systems qualify as improvements (Chapter 1086, Laws of 1978). 
 
 Contact Iowa Housing Finance Authority 
 218 Liberty Building 
 Des Moines, IA 50319 
 (515) 281-4058 
 
 KANSAS 
 
 TAX INCENTIVES 
 
 The individual taxpayer is allowed an income tax credit of 25% of the cost of a residential solar 
 energy system to a maximum of $1000. A solar energy installation on business or investment 
 property receives a credit equal to 25% of the system cost, $3000, or that year's tax bill, 
 whichever is the least amount. The cost of an installation on business or investment property 
 can be amortized over 60 months. Wind energy systems are also covered by this law. Credit ex- 
 pires 7/1/83. (Chapter 434, Laws of 1976; Chapter 346, Laws of 1977). 
 
 If a solar system supplies 70% of the energy for heating and cooling, the property owner may 
 be reimbursed for 35% of his property tax for up to 5 consecutive years. Applies through 1985. 
 Claims must be filed with the Department of Revenue (Chapter 345, Laws of 1977; Chapter 419, 
 Laws of 1978). 
 
 Provides an income tax deduction of 50% (maximum $500) of the cost of insulating residential 
 buildings owned by the taxpayer. The deduction can be applied separately to each residential 
 building owned and insulated by the taxpayer. To qualify, a building must have been con- 
 structed before 7/1/77. The insulating materials must meet minimum standards for energy con- 
 servation in new buildings prescribed by the Federal Housing Administration (Chapter 410, 
 Laws of 1978). 
 
 Contact State Department of Revenue 
 P.O. Box 692 
 Topeka, KS 66601 
 (913) 296-3909 
 
 LAND USE 
 
 Solar easements are recognized and are subject to the same requirements as other 
 easements; the contents are prescribed (Chapter 277, Laws of 1977). 
 
 
LOUISIANA 
 
 TAX INCENTIVES 
 
 Solar energy equipment installed in owner-occupied residential buildings or in swimming pools 
 are exempt from property tax (Act 591, 1978). 
 
 Contact Local parish tax assessor 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The law requires the Department of Natural Resources and Development to adopt regulations 
 
 and standards governing solar energy devices (Act 542, 1978). 
 
 Contact Department of Natural Resources and Development 
 P.O. Box 44396 
 Baton Rouge, LA 70804 
 (504) 342-4500 
 
 MAINE 
 
 TAX INCENTIVES 
 
 Solar space or water heating systems are exempt from property tax for 5 years after installa- 
 tion. Eligible taxpayers must apply to the local Board of Assessors. Purchasers of solar energy 
 systems may also receive a sales tax rebate from the Office of Energy Resources (Chapter 542, 
 Laws of 1977). 
 
 Contact (for property tax) Local assessor or board of assessors. 
 
 Contact (for sales tax) Office of Energy Resources 
 
 55 Capitol Street 
 Augusta, ME 04330 
 (207) 289-3811 
 
 This law creates an income tax credit for solar, wind, and wood energy systems which provide 
 space or Wcter heating or electrical or mechanical power. Fireplaces and woodstoves not 
 operating as central heating systems are ineligible. Both active and passive solar systems 
 qualify. The credit equals the lesser of $100 or 20% of eligible expenditures. Retroactive to 
 1/1/79 (Chapter 557, Laws of 1979). 
 
 Contact Bureau of Taxation 
 
 Department of Finance and Administration 
 State Office Building 
 Augusta. ME 04333 
 (207) 289-2076 
 
 LAND USE 
 
 Local governments are permitted to enact zoning ordinances to protect access to direct 
 
 sunlight for solar energy use (Chapter 418, Laws of 1979). 
 
 Contact Local zoning or planning group 
 
 Planning boards are permitted to protect solar access in new developments through subdivi- 
 sion regulations. These may include restrictive covenants, height restrictions, and setback re- 
 quirements (Chapter 435, Laws of 1979). 
 
 Contact Local planning board 
 
 MARYLAND 
 
 TAX INCENTIVES 
 
 A solar energy unit will be assessed at no more than a conventional system needed to serve 
 
 the building (Chapter 509, Laws of 1975; Chapter 509, Laws of 1978). 
 
 Contact Local assessor or board of assessors 
 
10 
 
 Baltimore City and any other city or county may offer property tax credits for the use of solar 
 systems in any type of building. Credit may be applied over a 3-year period (Chapter 740, Laws 
 of 1976). 
 
 Contact Local city or county department of revenue 
 
 LAND USE 
 
 Solar easements are recognized as a lawful restriction on land (Chapter 934, Laws of 1977). 
 
 GRANTS AND LOANS 
 
 This law authorizes the city of Baltimore to issue $2 million in municipal bonds. The proceeds 
 from the sale of bonds shall be used for energy conservation loans and loan guarantees to im- 
 prove residential buildings in the city. The bond issue requires an ordinance of the Baltimore 
 City Council and the approval of the electorate of the city (Chapter 12, Laws of 1979). 
 
 MASSACHUSETTS 
 
 TAX INCENTIVES 
 
 Solar energy systems are exempt from property tax for 20 years from the date of installation 
 
 (Chapter 734, Laws of 1975; Chapter 388, Laws of 1978). 
 
 Contact Local assessor or board of assessors 
 
 A personal income tax credit of 35% of the cost of renewable energy equipment is created. The 
 equipment must be installed in the taxpayer's principal residence in the state. Maximum credit 
 is $1000. Eligible equipment must use solar energy for space heating or cooling or water 
 heating or must use wind energy for any nonbusiness residential purpose. If a federal income 
 tax credit or grant is received by the taxpayer, the state credit will be reduced. The credit ex- 
 pires 12/31/83. 
 
 Sales of equipment for residential solar energy systems, wind power systems, or heat pumps 
 are exempt from sales tax. Wood-fueled central heating systems installed in a person's prin- 
 cipal residence in the state and costing more than $900 are exempt from sales tax through 
 12/31/83. Eligible furnaces must be approved by the State Fire Marshall or Building Code Com- 
 issioner (Chapter 796, Laws of 1979). 
 
 Corporations may deduct the cost of a solar or wind energy system from income. The system 
 will also be exempt from tangible property tax (Chapter 487, Laws of 1977). 
 
 Contact State Department of Corporations & Taxation 
 100 Cambridge Street 
 Boston MA 02204 
 (617) 727-4201 (income tax) 
 (617) 727-4601 (sales tax) 
 
 GRANTS AND LOANS 
 
 Banks and credit unions are authorized to make loans with extended maturation periods and in- 
 creased maximum amounts for home improvements, including solar energy systems. Banks 
 may lend up to $15,000. and credit unions may lend up to $12,000 (Chapter 28, Laws of 1977; 
 Chapter 260, Laws of 1977; Chapter 73, Laws of 1978). 
 
 Contact Local bank or credit union 
 
 MICHIGAN 
 
 TAX INCENTIVES 
 
 This law exempts solar, wind, or water energy conversion devices from real and personal pro- 
 perty tax. An application must be filed with local tax assessor, who will submit it to the state 
 tax commission for certification. Authority to exempt expires 7/1/85, but exemptions made by 
 that time stay in force (Public Act 135. 1976). 
 
11 
 
 Contact Local Government Services 
 Treasury Building 
 Lansing, Ml 48922 
 (517) 373-3232 
 
 Proceeds from sales of solar, wind, or water energy conversion devices used for heating, cool- 
 ing, or electrical generation in new or existing residential or commercial buildings are excluded 
 from business activities tax. Expires 1/1/85 (Public Act 132, 1976). 
 
 Tangible property used for solar, wind, or water energy devices is excluded from excise tax if it 
 is used to heat, cool, or electrify a new or existing commercial or residential building. Expires 
 1/1/85 (Public Act 133, 1976). 
 
 Income tax credit may be claimed for a residential solar, wind, or water energy device that is 
 used for heating, cooling, or electricity. This includes devices designed to use the difference 
 between water temperatures in a body of water. Energy conservation measures installed in 
 connection with such devices are also eligible; these include insulation, water-flow reduction 
 devices, and some wood furnaces. Swimming pool heaters are eligible only if 25% or more of 
 their heating capacity is used for residential purposes. The credit is refundable. The law in- 
 structs the Department of Commerce to establish system eligibility standards within 180 days of 
 the law's passage. To be eligible, expenditures must be made by 12/31/83. The rate of credit 
 changes annually. For 1980, the rate for single-family dwellings is 25% of the first $2000 spent, 
 plus 15% of the next $8000 spent. In 1980, the rate for other buildings is 25% of the first $2000, 
 plus 15% of next $13,000 (Public Act 605, 1978; Public Act 41, 1979). 
 
 Contact State Department of Treasury 
 State Tax Commission 
 State Capitol Building 
 Lansing, Ml 48922 
 (517) 373-2910 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Department of Commerce is required to formulate standards for solar energy systems 
 
 (Public Act 605, 1979). 
 
 Contact Energy Extension Service 
 
 Michigan Energy Administration 
 Department of Commerce 
 P.O. Box 30228 
 Lansing, Ml 48909 
 (517) 373-6430 
 
 MINNESOTA 
 
 TAX INCENTIVES 
 
 The market value of solar, wind, or agriculturally derived methane gas systems used for 
 heating, cooling, or electricity in a building or structure is excluded from property tax. The in- 
 stallations must be done prior to 1/1/84 (Chapter 786, Laws of 1978). 
 
 Contact Local assessor or board of assessors 
 
 This law provides an individual income tax credit of 20% of the first $10,000 spent on renewable 
 energy source equipment installed on a Minnesota building of six dwelling units or less. Eligi- 
 ble expenditures include: those eligible as federal renewable energy source property (solar, 
 wind, and geothermal); earth-sheltered dwellings; equipment producing ethanol, methanol or 
 methane for fuel, but not for resale; passive solar energy systems. Excess credit can be car- 
 ried forward through 1984. Federal regulations of the U.S. Internal Revenue Service shall be us- 
 ed to administer relevant portions of the credit. Expenditures must be made between 1/1/79 
 and 12/31/82 (Chapter 303, Laws of 1979). 
 
12 
 
 Contact Department of Revenue 
 
 Centennial Office Building 
 658 Cedar Street 
 St. Paul, MN 55145 
 (612) 296-3781 
 
 LAND USE 
 
 Zoning ordinances may provide for the protection of solar access for solar energy systems. 
 Solar easements are recognized and the contents are prescribed; they are enforceable in civil 
 actions. Depreciation resulting from easements (but not any appreciation) shall be included in 
 revaluation for property tax (Chapter 786, Laws of 1978). 
 
 Contact (for zoning) Local planning or zoning body 
 
 Local governments are prohibited from preventing earth-sheltered construction as long as it 
 otherwise complies with local zoning ordinances. Variances can be given to facilitate earth- 
 sheltered construction. An appropriation of $20,000 is made to conduct a study of impediments 
 to earth-sheltered construction (Chapter 2, Special Session, Laws of 1979). 
 
 Contact Minnesota Energy Agency 
 
 980 American Center Building 
 150 E. Kellogg Boulevard 
 St. Paul, MN 55101 
 (612) 296-5120 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Building Code Division of the Department of Administration is required to promulgate per- 
 formance standards for solar energy systems (Chapter 333, Laws of 1976). 
 
 Contact Minnesota Department of Administration 
 Building Code Division 
 408 Metro Square Building 
 St. Paul, MN 55101 
 (612) 296-4639 
 
 MISSISSIPPI 
 
 TAX INCENTIVES 
 
 Labor, property or services used in the construction of solar energy heating, lighting, or electric 
 generating facilities used by universities, colleges, or junior colleges are exempted from sales 
 tax. Expires 1/1/83 (§27-65-105 of the Mississippi Code). 
 
 Contact Mississippi Tax Commission 
 Sales Tax Division 
 P.O. Box 960 
 Jackson, MS 39205 
 (601) 354-6274 
 
 MISSOURI 
 
 LAND USE 
 
 This law declares that the right to use solar energy is a property right, but it cannot be ac- 
 quired by eminent domain. Solar easements are recognized and subjected to the same con- 
 veyancing and recording requirements as other easements. The contents are mandated 
 (§442.021 of the Missouri Code). 
 
13 
 
 MONTANA 
 
 TAX INCENTIVES 
 
 Energy systems using non-fossil fuel energy (such as solar, wind, solid wastes, decomposition 
 of organic wastes, solid wood wastes, and small scale hydroelectric) installed in an income tax- 
 payer's dwelling before 12/31/82 are eligible for an income tax credit of 10% of the first $1000 
 and 5% of the next $3000. If a federal tax credit is also claimed, the state credit is reduced to 
 5% of the first $1000 and 2 1/2% of the next $3000 (Chapter 548, Laws of 1975; Chapter 574, Laws 
 of 1977; Chapter 652, Laws of 1979), 
 
 This law provides individual or corporate income tax deductions for energy conservation im- 
 provements, including storm windows and insulation. It applies to all types of buildings at the 
 following rates: 
 
 Residential buildings Non-residential buildings 
 
 100% of 1st $1000 100% of 1st $2000 
 
 50% of 2nd $1000 50% of 2nd $2000 
 
 20% of 3rd $1000 20% of 3rd $2000 
 
 10% of 4th $1000 10% of 4th $2000 
 
 (Chapter 576, Laws of 1977). 
 
 Contact State Department of Revenue 
 Income Tax Section 
 Sam Mitchell Building 
 Helena, MT 59601 
 (406) 449-2837 
 
 This law provides a 10-year real estate tax exemption for capital investments in non-fossil forms 
 of energy generation as defined in the state income tax law (Montana Code Annotated 15-32- 
 102). The maximum exemptions are $20,000 for a single-family dwelling and $10,000 for other 
 buildings (Chapter 639, Laws of 1979). 
 
 Contact S'ate Department of Revenue 
 Property Assessment Division 
 Sam Mitchell Building 
 Helena, MT 59601 
 (406) 449-2808 
 
 GRANTS AND LOANS 
 
 This law permits utility companies to install and finance energy conservation materials and non- 
 fossil forms of energy generation systems. The interest rate on energy conservation loans can 
 be no less than two percentage points below the discount rate on 90-day commercial paper in 
 the Ninth Federal Reserve District. The interest rate on non-fossil energy loans shall be 5% to 
 7% annually. Financial institutions may lend money for energy conservation materials and non- 
 fossil energy systems at no less than two percentage points below the Federal Reserve rate. 
 Any interest foregone by not charging the prevailing rate of interest for home improvement 
 loans may be claimed as a credit against energy producer's license tax by a utility, or against 
 corporation license tax by a financial institution (Montana Code Annotated 15-32-107). 
 
 Contact Local lending institution or utility company 
 
 This law amends the Montana Code (MCA90-4-101) to permit the Department of Natural 
 Resources and Conservation to participate in commercial as well as non-commercial projects 
 under its renewable resources research, development and demonstration program (Chapter 
 624, Laws of 1979). 
 
 Contact Energy Division 
 
 Department of Natural Resources and Conservation 
 Capitol Station 
 Helena, MT 59601 
 (406) 449-3940 
 
14 
 
 LAND USE 
 
 This law recognizes solar easements and subjects them to the same conveyancing and re- 
 cording requirements as other easements. The contents ar prescribed (Chapter 524, Laws of 
 1979). 
 
 NEBRASKA 
 
 LAND USE 
 
 This law recognizes solar easements and prescribes their contents. Easements can be enforc- 
 ed in a civil suit. Local governments may include solar access considerations in their zoning or- 
 dinances and development plans. Variances from other ordinances may be granted to facilitate 
 solar access (Legislative Bill 353, 1979). 
 
 Contact Local zoning board or planning commission 
 
 NEVADA 
 
 TAX INCENTIVES 
 
 This law establishes a property tax allowance on solar, wind, geothermal, water-powered, or 
 solid waste energy systems in residential buildings. The property tax allowance equals the dif- 
 ference in tax on the property with the energy system and the tax on the property without the 
 energy system. The allowance may not exceed the tax accrued or $2000, whichever is less. 
 Claims are to be filed with the county assessor (Chapter 345, Laws of 1977). 
 
 Contact Local county assessor 
 
 LAND USE 
 
 This law formally recognizes solar easements and prescribes their contents. The easement will 
 run with the land upon transfer of title but can terminate upon expiration or release (Chapter 
 314, Laws of 1979). 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Nevada Department of Energy is required to establish energy conservation standards, in- 
 cluding provisions on the design and construction of solar, geothermal, wind or other 
 renewable energy systems. Standards must then be included in all city and county building 
 codes (Chapter 17, Laws of 1979). 
 
 Contact Nevada Department of Energy 
 1050 E. Williams 
 Suite 405 
 Capitol Complex 
 Carson City, NV 89710 
 (702) 885-5157 
 
 NEW HAMPSHIRE 
 
 TAX INCENTIVES 
 
 Cities and towns are enabled to grant property tax exemptions to property owners with solar 
 heating, cooling, or hot water systems and will decide the amount of the exemption and the 
 manner of determination. An application for the exemption must be filed with the local 
 assessor (Chapter 391, Laws of 1975; Chapter 5202, Laws of 1977). 
 
 Contact Local assessor or board of assessors 
 
15 
 
 NEW JERSEY 
 
 TAX INCENTIVES 
 
 Solar heating and cooling systems, including sea thermal gradients and wind-powered 
 systems, are exempt from property tax. Systems must be certified under the State Uniform 
 Construction Act on forms designated by the Division of Taxation. Systems must meet stan- 
 dards established by the State Department of Energy. Expires 12/31/82 (Chapter 256, Laws of 
 1977). 
 
 Contact Local assessor or board of assessors 
 
 Solar energy devices designed to provide heating, cooling, electrical or mechanical power are 
 exempt from sales tax. These systems must meet the standards established by the state 
 Department of Energy (Chapter 465, Laws of 1977). 
 
 Contact State Division of Taxation 
 Tax Counselors 
 P.O. Box 999 
 Trenton, NJ 08646 
 (609) 292-6400 
 
 LAND USE 
 
 Solar easements are recognized and subject to the same requirements as other easements; 
 the contents are prescribed (Chapter 152, Laws of 1978). 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Division of Energy Planning and Conservation of the State Department of Energy is re- 
 quired to adopt standards for solar energy systems (Chapter 256, Laws of 1977). 
 
 Contact Department of Energy 
 101 Commerce Street 
 Newark, NJ 07102 
 (201) 648-3290 
 
 NEW MEXICO 
 
 TAX INCENTIVES 
 
 This law provides for an income tax credit of 25% of the cost of a solar energy system or a 
 maximum of $1000. It is available for solar energy systems which heat or cool the taxpayer's 
 residence and for swimming pool heating systems. The criteria of the Solar Heating and Cool- 
 ing Demonstration Act of 1974 (42 USC 5506) must be met. Credit in excess of the taxes due wil 
 be refunded (Chapter 12, Laws of 1975; Chapter 170, Laws of 1978; Chapter 353, Laws of 1979). 
 
 Individuals may claim an income tax credit for a solar energy system used in an irrigation 
 pumping system. The system design must be approved by the Energy Resources Board prior 
 to installation, and it must result in a 75% reduction in the use of fossil fuel. This law is not ap- 
 plicable if federal credit were claimed or if credit were claimed for this equipment under other 
 provisions of the state law. Credit in excess of the taxes due will be refunded (Chapter 114, 
 Laws of 1977). 
 
 Contact State Department of Taxation & Revenue 
 Income Tax Division 
 P.O. Box 630 
 Santa Fe, NM 87503 
 (505) 827-3221 
 
 LAND USE 
 
 The right to use solar energy is a property right of landowners; disputes regarding access will 
 be settled by rule of prior appropriation (Chapter 169, Laws of 1977). 
 
16 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 This law directs the New Mexico Solar Energy Research and Development Institute to develop 
 
 performance standards for solar energy equipment (Chapter 347, Laws of 1977). 
 
 Contact New Mexico Solar Energy 
 
 Research and Development Institute 
 
 Box 3 SOL 
 
 New Mexico State University 
 
 Las Cruces, NM 88003 
 
 (505) 646-1846 
 
 NEW YORK 
 
 TAX INCENTIVES 
 
 This law provides a property tax reduction for owners of solar or wind energy systems. Passive 
 systems qualify to a limited extent. The reduction of assessment is equal to the difference be- 
 tween assessment of the property with the energy system and assessment of the property 
 without the system. The system must conform to guidelines of the state energy office and 
 must be instal'ed before 7/1/88. The exemption is good for 15 years after it is granted (Chapter 
 322, Laws of 1977; Chapter 220, Laws of 1979). 
 
 Contact Local assessor or board of assessors 
 
 LAND USE 
 
 This law recognizes solar easements and subjects them to the same conveyancing and record- 
 ing requirements as other easements. The contents are prescribed (Chapter 705, Laws of 1979). 
 
 This law amends the general city law, the village law, and the town law to make the protection 
 of solar access a valid purpose of zoning regulations. Effective 1/1/80. Before 9/30/80 the state 
 energy office must issue guidelines to assist local governments in implementing the act 
 (Chapter 742, Laws of 1979). 
 
 Contact Local zoning board or 
 
 New York State Energy Office 
 Agency Building 2 
 Empire State Plaza 
 Albany, NY 12223 
 (518) 474-8181 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 This law requires that the Commissioner of the State Energy Office promulgate guidelines and 
 
 definitions for solar energy systems (Chapter 322, Laws of 1977). 
 
 Contact New York State Energy Office 
 Agency Building 2 
 Empire State Plaza 
 Albany, NY 12223 
 (518) 474-8181 
 
 NORTH CAROLINA 
 
 TAX INCENTIVES 
 
 This law provides for a corporate and individual income tax credit of 25% of the cost of a solar 
 heating, cooling, or hot water system. There is a maximum credit of $1000 per unit or building. 
 Although this credit may be taken only once, the amount of credit may be spread over 3 years. 
 The system may be in any type of building, and it must meet the performance criteria of the 
 U.S. Secretary of the Treasury or the North Carolina Secretary of Revenue (Chapter 792, Laws 
 of 1977; Chapter 892, Laws of 1979). 
 
 
17 
 
 Contact State Department of Revenue 
 Income Tax Division 
 P.O. Box 25000 
 Raleigh, NC 27640 
 (919) 733-3991 
 
 Buildings with solar heating or cooling systems shall be assessed as though they had a con- 
 ventional system. Expires 12/1/85 (Chapter 965, Laws of 1977). 
 
 Contact Local assessor or board of assessors 
 
 NORTH DAKOTA 
 
 TAX INCENTIVES 
 
 This law provides for an income tax credit for solar or wind energy devices. The credit is 5% 
 per year for 2 years. The system must provide heating, cooling, mechanical, or electrical power 
 (Chapter 537, Laws of 1977). 
 
 Contact State Tax Commission 
 Income Tax Division 
 Capitol Building 
 Bismarck, ND 58505 
 (701 ) 224-3450 
 
 Solar heating or cooling systems in any building are exempt from property tax for 5 years after 
 installation (Chapter 508, Laws of 1975). 
 
 Contact Local assessor or board of assessors 
 
 LAND USE 
 
 Solar easements are recognized and subject to the same requirements as other easements; 
 the contents are prescribed (Chapter 425, Laws of 1977). 
 
 OHIO 
 
 TAX INCENTIVES 
 
 Solar, wind, and hydrothermal energy systems installed through 12/31/85 are exempt from real 
 estate tax. A corporate franchise tax credit of 10% of the cost of a solar or wind energy system 
 is created. The law creates a sales tax exemption for materials sold to a construction contrac- 
 tor for use in a solar, wind, or hydrothermal energy system. Sales of these systems are exempt 
 from sales tax; components and labor costs are also covered by the exemption. This exemp- 
 tion is valid through 12/31/85. 
 
 A personal income tax credit of 10% of the cost of a solar, wind, or hydrothermal energy 
 system is created. The system must be installed in a building that is owned and occupied as a 
 dwelling, or owned and operated by the taxpayer in Ohio. The credit includes a two-year carry 
 toward provision and a maximum credit of $1000. To qualify for any of these tax advantages, the 
 taxpayer's system must provide space heating or cooling, hot water, industrial process heat, 
 mechanical or electrical energy and must meet guidelines estabished by the Department of 
 Energy. Passive designs are included to a limited extent (Amended Substitute House Bill 154, 
 1979). 
 
 Contact (for income and Ohio Tax Commission 
 
 franchise tax information) Income Tax Division 
 
 1030 Freeway Drive 
 Columbus, OH 43229 
 (614) 466-7910 
 
18 
 
 Contact (for sales tax 
 information) 
 
 Contact (for guidelines) Ohio Department of Energy 
 
 30 E. Broad Street, 3<ilh Floor 
 Columbus, OH 43215 
 (614) 466-7915 
 
 Ohio Tax Commission 
 Sales Tax Division 
 30 W. Broad Street 
 Columbus, OH 43215 
 (614) 466-7350 
 
 LAND USE 
 
 This law recognizes solar easements and subjects them to the same requirements as other 
 easements. The contents are prescribed (Amended Substitute House Bill 154, 1979). 
 
 OKLAHOMA 
 
 TAX INCENTIVES 
 
 Individuals may claim an income tax credit for solar energy devices used to heat, cool, or fur- 
 nish electrical or mechanical power at their principal residence. The credit is equal to 25% of 
 the cost of the system or a maximum of $2000. Although this credit may be taken only once, the 
 amount of credit may be spread over 3 years. Expires on 1/1/88 (Chapter 209, Laws of 1977). 
 
 Contact State Tax Commission 
 Income Tax Division 
 2501 Lincoln Boulevard 
 Oklahoma City, OK 73194 
 (405) 521-3125 
 
 OREGON 
 
 TAX INCENTIVES 
 
 This law exempts, in addition to solar systems, geothermal, wind, water and methane gas 
 energy systems from real estate tax until 1/1/98. Property owned or leased by persons produc- 
 ing, transporting, or distributing energy is not included (Chapter 196, Laws of 1977; Chapter 670, 
 Laws of 1979). 
 
 Contact Local assessor or board of assessors. 
 
 An income tax credit is provided for owners, tenants, and lessors of property used as a prin- 
 cipal or secondary residence. The credit equals 25% of the cost of alternative energy devices 
 using solar, water, wind, or geothermal resources for 10% of the energy requirements of the 
 dwelling unit or 50% of the water heating requirements of the unit. Maximum credit is $1000 per 
 dwelling unit. A carry forward provision is included. Systems must be certified by the Depart- 
 ment of Energy before a credit may be claimed (Chapter 196, Laws of 1977; Chapter 670, Laws 
 of 1979). 
 
 This law provides an income tax credit for weatherization materials installed in the taxpayer's 
 principal residence, including a mobile or floating home or a unit of a nuiltifamily dwelling. A 
 list of qualifying items is available from the Department of Energy or the Department of 
 Revenue Items must be installed before 1/1/85. The credit equals 25% of the cost of eligible 
 items to a maximum of $125. A 5-year carry forward provision is included (Chapter 534. Laws of 
 1979). 
 
 This law provides a corporation excise tax credit for commercial lending institutions making 
 loans at 6 1/2% interest or less for the installation of certified alternative energy devices. Max- 
 imum loans are $10,000 for home improvement loans. The tax credit is equal to the difference 
 between 6 1/2% and the average interest rate for home improvement loans made in a previous 
 calendar year (Chapter 483, Laws of 1979). 
 
49 
 
 This law creates a corporate income tax credit of 35% of the cost of energy conservation 
 facilities. The credit is claimed at a rate of 10% for the first two years and 5% for each of the 
 next three years. A carry forward provision is included. 
 
 Energy conservation facilities means facilities used in trade or business and employing or pro- 
 cessing renewable energy sources to: (1) replace a substantial part of an existing use of elec- 
 tricity, petroleum, or natural gas; (2) provide initial use of energy where such resources would 
 have been used; (3) generate electricity to replace an existing source of electricity or provide a 
 new source of electricity; or (4) perform a process that obtains energy resources from material 
 that would otherwise be solid waste. Renewable energy resources include, but are not limited 
 to straw, forest slash, wood waste or other forms of forest waste, industrial or municipal waste, 
 solar energy, wind power, water power or geothermal energy (Chapter 512, Laws of 1979). 
 
 Contact State Department of Revenue 
 State Office Building 
 Salem, OR 97310 
 (503) 378-3366 
 
 GRANTS AND LOANS 
 
 This law creates a loan fund for alternate energy projects and authorizes the Director of the 
 Department of Energy to sell bonds to finance the loan fund (Chapter 732, Laws of 1977). 
 
 Contact Oregon Department of Energy 
 Room 111 
 
 Labor & Industries Building 
 Salem, OR 97310 
 (503) 378-4128 
 
 To finance a domestic solar energy system, veterans can obtain a loan in excess of the max- 
 imum allowed under the War Veterans Fund. The system must provide at least 10% of the 
 home's energy requirements and must meet performance criteria established by the State 
 Department of Energy (Chapter 315, Laws of 1977). 
 
 Contact State Department of Veterans' Affairs 
 3000 Market Street Plaza 
 Suite 522 
 Salem, OR 97310 
 (503) 378-6438 
 
 LAND USE 
 
 This law enables local governments to regulate solar access in comprehensive plans, zoning 
 ordinances, and subdivision regulations. Solar easements are recognized and their contents 
 are prescribed. Private restrictions prohibiting the use of solar energy are void and unen- 
 forceable if the provision is executed after 10/3/79 (Chapter 671, Laws of 1979). 
 
 Contact Local zoning board or planning commission 
 
 STANDARDS AND REGULATION OF CONSTRUCTION 
 
 The Department of Energy is required to adopt rules prescribing performance criteria for solar 
 energy systems (Chapter 196, Laws of 1977). 
 
 Contact Oregon Department of Energy 
 Room 111 
 
 Labor & Industries Building 
 Salem, OR 97310 
 (503) 378-4128 
 
20 
 
 RHODE ISLAND 
 
 TAX INCENTIVES 
 
 Solar heating or cooling systems in residential or non-residential buildings shall be assessed at 
 no more than the value of a conventional system necessary to serve the building. Law expires 
 4/1/97 (Chapter 202, Laws of 1977). 
 
 Contact Local assessor or board of assessors 
 
 SOUTH DAKOTA 
 
 TAX INCENTIVES 
 
 This law provides property tax assessment credit for renewable resource energy systems 
 (solar, wind, geothermal, and biomass). For residential property the amount of the credit 
 equals the assessed value of the property with the system, minus the assessed value of the 
 property without the system, but not less than the actual installation cost of the system. The 
 credit for systems in commercial buildings is equal to 50% of the cost of installation. For 
 residential buildings, full credit is given for 5 years. For the next 3 years, the credit is 75%, 
 50%, and 25% of the full credit. For commercial buildings, full credit is given for 3 years, and 
 for the next 3 years credit is 75%, 50%, and 25% of the full credit. Taxpayers must aoply to the 
 county auditor (Chapter 74, Laws of 1978). 
 
 Contact Local county auditor 
 
 TENNESSEE 
 
 TAX INCENTIVES 
 
 Solar or wind energy systems for heating, cooling, or electrical power shall be exempt from 
 property taxation. Law expires 1/1/88 (Chapter 837, Laws of 1978). 
 
 Contact Local assessor or board of assessors 
 
 GRANTS AND LOANS 
 
 Provides loans to low- and moderate-income persons to make energy conserving im- 
 provements, including the installation of solar hot water systems (Chapter 884, Laws of 1978). 
 
 Contact Tennessee Housing Development Authority 
 Hamilton Bank Building 
 Nashville, TN 37219 
 (615) 741-3023 
 
 LAND USE 
 
 This law recognizes solar easements and prescribes their contents. They are subjected to the 
 same general requirements as other easements. The Tennessee Energy Authority is directed 
 to prepare a sample solar easement for use in Tennessee. Local governments are empowered 
 to protect solar access through zoning regulations (Chapter 259, Laws of 1979). 
 
 Contact (for sample Tennessee Energy Authority 
 
 easement) Suite 707 
 
 Capitol Boulevard Building 
 Nashville, TN 37219 
 (615) 741-2994 
 
 Contact (for zoning) Local zoning or planning body 
 
 TEXAS 
 
 TAX INCENTIVES 
 
 The legislature is allowed to exempt solar- or wind-powered energy devices from property tax. 
 (Chapter 719. Laws of 1975). (Article VIII, Sec. 2(a) of Texas Constitution). 
 
21 
 
 This law exempts solar and wind energy devices from real estate tax assessments. The 
 devices must be used for thermal, mechanical or electrical energy. The Comptroller of Public 
 Accounts shall develop guidelines to assist tax assessors in carrying out this law. Effective 
 1/1/80 (Chapter 107, Laws of 1979). 
 
 This law provides a franchise tax exemption for corporations exclusively engaged in manufac- 
 turing, selling, or installing solar energy devices for heating, cooling, or electrical power 
 (Chapter 584, Laws of 1977). 
 
 Solar energy systems used for heating, cooling, or electrical power are exempt from sales tax. 
 Corporations may deduct from taxable capital the amortized cost of a solar energy device over 
 a period of 60 months or more. 
 
 Contact Comptroller of Public Accounts 
 Capitol Station 
 Drawer SS 
 Austin, TX 78775 
 (512) 475-2206 
 
 UTAH 
 
 LAND USE 
 
 This law recognizes solar easements as a property interest. Easements must be in writing and 
 they will run with the land in perpetuity unless terminated upon stated conditions. Enforcement 
 may be by injunction or other civil action (Chapter 82, Laws of 1979). 
 
 VERMONT 
 
 TAX INCENTIVES 
 
 Towns may enact a property tax exemption for alternate energy systems. Systems exempted 
 are grist mills, windmills, solar energy systems, and devices to convert organic matter to 
 methane. All components are exempt, including land on which the facility is situated, up to 
 one-half acre (Act 226, 1976). 
 
 Contact Local assessor or board of assessors 
 
 Wood-fired central heating and solar or wind systems for heating, cooling, or electrical power 
 are eligible for income tax credit if they are installed in the taxpayer's dwelling before 7/1/83. 
 The credit is equal to 25% of the cost of the system or $1000, whichever is less. Businesses 
 may deduct 25% of the cost of the system or $3000, whichever is less (Act 210, 1978). 
 
 Contact State Tax Department 
 Income Tax Division 
 State Street 
 Montpelier, VT 05602 
 (802) 828-2517 
 
 VIRGINIA 
 
 TAX INCENTIVES 
 
 Any county, city, or town may exempt solar energy equipment used for heating, cooling, or 
 other applications from property tax. The State Board of Housing must certify the system. The 
 exemption is good for not less than 5 years (Chapter 561. Laws of 1977). 
 
 This law creates a separate class of tangible personal property for local taxation. The class in- 
 cludes energy conversion equipment purchased by a manufacturer for the purpose of changing 
 the energy source of a plant from oil or gas to coal, wood, or alternative energy resources Co- 
 generation equipment is also included. Tax years covered are those beginning after 7/1/79. 
 This class oj property may be taxed at a rate different from the rate on other tangible personal 
 
22 
 
 property, but not higher than the rate on machinery and tools. To be eligible, equipment must 
 have been purchased after 12/31/74 (Chapter 351, Laws ot 1979). 
 
 Contact Local taxing authority 
 
 LAND USE 
 
 This law subjects solar easements to the same fegal requirements as other easements and 
 
 mandates contents of the agreement (Chapter 323, Laws of 1978). 
 
 WASHINGTON 
 
 TAX INCENTIVES 
 
 Solar water and space heating or solar power systems are exempt from property taxation. 
 Claims must be filed with the county assessor The exemption is valid for 7 years. Claims must 
 be filed by 12/31/81 (Chapter 364, Laws of 1977). 
 
 Contact Local county assessor 
 
 GRANTS AND LOANS 
 
 This law authorizes municipally or privately owned utility companies to establish programs to 
 perform energy audits, to recommend improvements and to arrange the installation and financ- 
 ing of energy conservation materials in residential buildings. (Chapter 239. Laws of 1979). 
 
 Contact Local utility company 
 
 LAND USE 
 
 This law permits local governments to regulate protection of solar access in comprehensive 
 plans and zoning ordinances. It recognizes easements, covenants and other restrictions on trie 
 use of real property, created to protect access to sunlight. The contents of easements are 
 mandated and they are subjected to the same conveyancing and recording requirements as 
 other easements. Some remedies for interference with a solar easement are authorized 
 (Chapter 170E-1, Laws of 1979). 
 
 Contact Local planning commission or zoning board 
 
 WISCONSIN 
 
 TAX INCENTIVES 
 
 The cost of alternative energy systems owned and installed by corporations on property in 
 Wisconsin between 4/20/77 and 12/31/84 may be used as a tax deduction in the year paid for. 
 may be depreciated, or may be amortized over 5 years. This law covers solar, waste conversion 
 and wind systems certified by the Department of Industry, Labor and Human Relations (Chapter 
 313, Laws of 1977). 
 
 Contact State Department of Revenue 
 Income Tax Division 
 P.O. Box B910 
 Madir.on, Wl .13708 
 (608) 266-1^11 
 
 GRANTS AND LOANS 
 
 This law creates a program to subsidize the cost of an alternative energy system purchased by 
 individuals If the building on which the system is installed was on the local tax rolls before 
 4/20/77. the rate of refund will be: 24% in 1979 and 1980, 18% in 1981 and 1982: 12% in 1983 and 
 1984. Eligible expenses must exceed $500, but the subsidy will not be calculated on more than 
 $10,000 Eligible systems are: 1) solar systems used for space heating or cooling, crop drying, 
 electricity or water heating: 2) waste conversion energy systems including equipment which 
 converts waste into usable forms of energy, but excluding solid-fuel consuming devices used 
 for residential purposes; and 3) wind energy systems that convert wind energy into other 
 usable forms of energy All systems must meet standards of the Department of Labor, Industry 
 and Human Relations (Chapter 34. Laws of 1979). 
 
23 
 
 Contact Department of Industry, Labor & Human Relations 
 201 E. Washington 
 
 Rm. 101, Safety and Buildings Division 
 Madison, Wl 53702 
 (608) 266-1149 
 

 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 13 
 
 OTHER ECONOMIC CONSIDERATIONS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
13-i 
 
 TABLE OF CONTENTS 
 
 
 
 
 
 Page 
 
 LIST OF FIGURES ... 13-i i 
 
 OBJECTIVES .... 
 
 m 
 
 m 
 
 
 13-1 
 
 INTRODUCTION .... 
 
 • 
 
 • 
 
 
 13-1 
 
 BREAKEVEN COST .... 
 
 • 
 
 • 
 
 
 13-2 
 
 EXAMPLE 13-1 . 
 
 • 
 
 • 
 
 
 13-2 
 
 SOLUTION .... 
 
 ■ 
 
 • 
 
 
 13-3 
 
 PAYBACK 
 
 • 
 
 • 
 
 
 13-3 
 
 EXAMPLE 13-2 . 
 
 • 
 
 • 
 
 
 13-4 
 
 SOLUTION .... 
 
 • 
 
 • 
 
 
 13-4 
 
 ECONOMIC OPTIMUM COLLECTOR AREA 
 
 • 
 
 • 
 
 
 13-6 
 
 EXAMPLE 13-3 . 
 
 • 
 
 > 
 
 
 13-8 
 
 Solar System 
 
 • 
 
 • 
 
 
 13-8 
 
 Economic Parameters . 
 
 • 
 
 • 
 
 
 13-9 
 
 SOLUTION .... 
 
 • 
 
 • 
 
 
 13-9 
 
 REFERENCES .... 
 
 
 
 
 13-11 
 
13-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 13-1 Nomograph for Determining SPB and DPB . . . 13-5 
 13-2 Concept of Optimum Collector Area .... 13-7 
 
13-1 
 
 OBJECTIVES 
 
 The objectives in this module are to: 
 
 1. Determine the cost of solar thermal energy delivered from a 
 system. 
 
 2. Establish cost effectiveness of a system. 
 
 3. Determine an economic optimum collector area for a system. 
 
 INTRODUCTION 
 
 In a preceding module, two procedures are described for calculating 
 the total life-cycle cost (TLCC) of solar heating systems and the TLCC 
 of conventional heating systems. If the TLCC of the solar system is 
 less than the TLCC of a conventional system, the solar system is con- 
 sidered to be cost effective. The first procedure described yields the 
 TLCC of both solar and conventional systems directly but assumes con- 
 stant interest, inflation, and discount rates during the period of 
 analysis. The second procedure, although more tedious in calculation, 
 allows TLCC determinations with variable rates of interest, inflation, 
 and discount in any year according to an economic "scenario". In both 
 methods, discount, inflation, and interest rates can be treated in 
 "real" terms, or alternatively, discount and inflation rates can be 
 treated in marginal terms relative to the general inflation rate for 
 goods and services. 
 
 The concept of life-cycle costs applied to residential systems is 
 probably too complex for the average homeowner; also, determination of 
 cost effectiveness is susceptible to assumed energy inflation and 
 
13-2 
 
 discount rates. Therefore, there may be some utility in appraising the 
 economic value of solar systems by alternative approaches presented in 
 this module. 
 
 BREAKEVEN COST 
 
 Instead of attempting to predict the rates of inflation explicitly 
 in the analysis, a simple approach is a calculation of the breakeven 
 cost of the solar system. Breakeven occurs when the cost of energy 
 delivered by the solar system is equal to the cost of the conventional 
 energy it displaces and is usually calculated in terms of a uniform 
 annual cost. In simplest terms, inflation and discount rates are 
 ignored, and the uniform annual cost of the solar system is considered 
 to consist of annual mortgage repayment (principal plus interest) and 
 operating costs. More complex breakeven analysis would include other 
 annual costs such as property taxes, insurance, and maintenance minus an 
 annual credit for income tax saving on interest paid on the mortgage. 
 The simple calculation assumes that property taxes, insurance, and 
 maintenance costs are offset by an annual income tax credit on the 
 interest paid (at least in the first few years). A breakeven cost 
 calculation is illustrated by the following example. 
 
 EXAMPLE 13-1 
 
 2 
 
 A solar heating system with 400 ft of collectors costs $14,000 
 
 o 
 ($35/ft ). After taking a Federal income tax credit of $4,000 and a 
 
 State income tax credit of $1,000, a 30-yr loan is negotiated for the 
 
 balance of $9,000 at 10 percent interest rate. The solar system will 
 
13-3 
 
 provide an annual average useful thermal energy of 65 million Btu. 
 Determine a (simple) breakeven cost for the solar system. 
 
 SOLUTION 
 
 At 10 percent interest, a 30-yr loan will necessitate a uniform 
 annual payment of $955 to repay the $9,000 loan. Since the average net 
 annual energy delivery is $65 MMBtu, the solar energy cost, or breakeven 
 cost, is $14.69/MMBtu. In terms of various types of conventional energy 
 used for heating, the breakeven prices of the conventional fuels are: 
 
 Type of Furnace 
 
 Electrical resistance 
 
 Oil furnace at 60 percent efficiency 
 (140,000 Btu/gal) 
 
 Propane furnace at 70 percent efficiency 
 (90,000 Btu/gal) 
 
 Natural gas furnace at 70 percent efficiency 
 (1,000 Btu/ft 3 ) 
 
 Breakeven Price 
 5.0<t/kWh 
 $1.23/gal 
 
 $0.93/gal 
 
 $1.03/100ft 3 
 
 PAYBACK 
 
 Another economic measure for a solar system is the number of years 
 (elapsed time) required for accumulated energy cost savings to equal 
 initial investment (payback period). The calculation may be made with 
 or without consideration to escalation of energy prices and market 
 discount rate. If inflation and discount rates are ignored, the result 
 of the calculation is called simple payback (SPB) period. If inflation 
 and discount are both considered, the result is called discounted 
 
13-4 
 
 payback (DPB) period. In equation form, simple payback period may be 
 determined as follows: 
 
 SPB(yrs) = „— . ■— - %*?*"« 
 
 (Annual Energy Cost Savings - Annual and M Costs) 
 
 (13-1) 
 
 Discounted payback period is the period between initial investment and 
 the time when the sum of net energy savings, appropriately inflated and 
 discounted, equals the initial investment. A nomograph to determine 
 both simple payback and discounted payback periods is provided in Figure 
 13-1. Its use is illustrated in Example 13-2. 
 
 EXAMPLE 13-2 
 
 Determine the simple payback period for a solar system with a net 
 investment cost (after tax credits) of $8,000 which delivers 80 MMBtu of 
 useful solar energy annually. The annual operating and maintenance 
 costs total $172, and the conventional fuel displaced is electricity at 
 5<t/kWh. Determine also the discounted payback period if the fuel in- 
 flation rate is 15 percent and discount rate is 10 percent. 
 
 SOLUTION 
 
 The annual energy cost savings is 
 
 80 x 10 6 Btu $0.05 „ 4.,™ 
 3423 Btu/kWh x kWh * 11/z ' 
 
 The operating cost is computed on the basis of 7 percent operating 
 
 energy requirement and a small amount is added for maintenance to total 
 
 $172. Then the simple payback period is 
 
13-5 
 
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 rlOx I0 4 
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 800 
 
 600 
 
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 Discounted Payback Period, yrs 
 
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 Figure 13-1. Nomograph for Determining SPB and DPB 
 
13-6 
 
 CDD _ 80000 
 
 SPB - 1172 _ 172 = 8 years 
 
 Using the nomograph of Figure 13-1, the solid line connecting $1000 
 annual savings with $8000 investment cost leads to a simple payback of 8 
 years as calculated above. Also, following the dashed horizontal line 
 to curve (T) , the discounted payback period is 7.6 years. If the fuel 
 inflation rate and discount rate are both 10 percent, the payback period 
 is slightly longer, as indicated by the intercept of the horizontal 
 dashed line and curve (?) . Other combinations of inflation rates and 
 10 percent discount rate may be read from the nomograph by interpolating 
 between the appropriate curves. 
 
 ECONOMIC OPTIMUM COLLECTOR AREA 
 
 There is, in most situations, an economically optimum collector 
 area in the sense that annual heating cost with a combined solar and 
 conventional energy system is minimum for a specific solar system size. 
 However, optimum area, (A*), is dependent upon the economic assumptions 
 made in the analysis. Using the life-cycle cost approach, the concept 
 of optimum collector area is illustrated in Figure 13-2. 
 
 The curve labeled LCC is the life-cycle cost for the solar system 
 alone, LCC is the life-cycle cost for conventional energy required as 
 auxiliary to the heating system. The sum of LCC and LCC is the total 
 life-cycle cost for the system, TLCC. As collector area increases, LCC 
 increases (nearly linearly with collector area) and LCC decreases 
 because solar energy supplies an increasing fraction of the total heat 
 requirements. Depending upon the shape of the two curves, there will 
 
13-7 
 
 o 
 
 I- 
 
 C/) 
 O 
 o 
 
 UJ 
 
 _J 
 O 
 
 >- 
 
 o 
 
 I 
 
 UJ 
 
 u_ 
 
 TLCC 
 
 LCC 
 
 LCC 
 
 COLLECTOR AREA, A 
 CONCEPT OF OPTIMUM COLLECTOR AREA 
 
 Figure 13-2. Concept of Optimum Collector Area 
 
 generally be a minimum point in the TLCC curve, and the collector area 
 corresponding to the minimum is labeled the optimum collector area, A*. 
 The determination of A* is readily made by using the first 
 procedure for computing TLCC described in the previous module and a 
 simple equation-based method for determining the solar fraction such as 
 the relative areas method described in Module 6. The TLCC of the solar/ 
 auxiliary system is given by Equation (12-3) and is repeated below: 
 
 TLCC = C T (solar) - (ACJE-, + C E + CE + (l-F)Lc f E., 
 I a 1 oo mm ff 
 
 The minimum point in the TLCC curve occurs where 
 
 (13-2) 
 
 C a E l " Lc f E f & = ° 
 
 (13-3) 
 
13-8 
 
 The functional relationship of annual solar fraction F and collector 
 
 area A is expressed in the relative areas method (Module 6) as 
 
 F = C;L + c 2 £n(^-) (13-4) 
 
 o 
 
 Thus, 
 
 dF .. c 2 
 
 (13-5) 
 
 and by substituting into Equation (13-3) 
 
 I— r\ I— L* jp L. jj 
 
 a* = -Vr 1 ( 13_6 ) 
 
 a L l 
 
 where L is the total building heating load (MMBtu) 
 
 c f is cost of conventional energy (cost/MMBtu) 
 
 c ? is a location dependent constant (dimensionless) 
 
 E f is the economic factor for fuel cost 
 
 E-. is the economic factor for the system 
 
 2 
 C is unit cost of the solar system (cost/ft ) 
 a 
 
 The use of Equation (13-6) is illustrated by the following example. 
 
 EXAMPLE 13-3 
 
 Determine the optimum collector area for a liquid-heating solar 
 system on a building located in Washington, D.C., and calculate the 
 annual solar fraction the optimum system will provide: The following 
 information is given: 
 
 Solar System 
 
 1. Liquid-heating collectors: F R (ta) = 0.75 
 
 F R U L = 1.00 Btu/(hr-ft 2 -°F) 
 
13-9 
 
 2. Building UA = 450 Btu/(hr-°F) 
 
 3. Auxiliary Heating - Electrical Energy 
 
 Economic Parameters 
 
 1. Electrical energy cost, c f = 5<t/kWh = $14.65/MMBtu 
 
 ?* 
 
 2. System cost, C = $28/ft 
 
 a 
 
 3. Mortgage terms: downpayment, a = 0.20 
 
 period of loan, m = 25 yrs 
 interest rate, i = 12 percent 
 
 4. Property tax rate, p = 0.02 
 
 5. Insurance premium rate, h = 0.003 
 
 6. General inflation rate, g = 0.06 
 
 7. Fuel escalation rate, r f = 0.12 
 
 8. Market discount rate, d = 0.10 
 
 9. Owner's income tax rate, t = 0.35 
 
 10. Life-cycle analysis period, n = 20 years 
 
 SOLUTION 
 
 From Module 12, 
 
 E f = P/X(d,r f ,n) = 21.693 
 
 E 1 = a + [(l-t)p+h]P/x(d,g,n) + 
 
 (1 °° [(1 t} P/X(i,o,m) + (t) P/X(o,i,m) ] 
 E 1 = 0.2 + [(l-0.35)(0.02) + 0.003]13.082 + 
 (l-0.2)[(l-0.35) ^|g + (0.35) II73I7] 
 
 x System cost consists of $1000 fixed costs plus incremental costs of 
 $28/ft 2 . 
 
be: 
 
 13-10 
 
 E 1 = 1.076 
 
 C f = $14.65/MMBtu 
 
 L = < UA >bldg x 24 Hiy X D ° 
 
 L = 450 x 24 x 4224 = 45.62 MMBtu 
 
 c 2 = 0.271 (from Module 6) 
 
 A * _ 0.271 x 45.62 x 14.65 x 21.693 
 28 x 1.076 
 
 A* = 130 ft 2 of collectors 
 
 Using the relative areas method the solar fraction is calculated to 
 
 A = 0.237(450) = 24 2 
 M o . 75-1. 0(. 307) ^ 1 TX 
 
 F = .520 + .271 £n(130/241) = 0.35 
 
13-11 
 
 REFERENCES 
 
 1. Barley, CD. and Winn, C.B. (1978) "Optimal Sizing of Solar 
 Collectors by the Method of Relative Areas", Solar Energy , Vol. 21, 
 No. 4, pp. 279-289. 
 
 2. Barley, CD. (1979) "Load Optimization in Solar Space Heating 
 Systems," Solar Energy , Vol. 23, No. 2, pp. 149-156. 
 
 3. Brandemuehl , M.J. and Beckman, W.A. (1979), "Economic Evaluation 
 and Optimization of Solar Heating Systems", Solar Energy , Vol. 23, 
 No. 1, pp. 1-10. 
 
 4. Ruegg, R.T. , McConnaughey, Sav, G.T. , and Hockenbery, K.A. (1978), 
 Life Cycle Costing. ABS Building Science Series 113, U.S. Dept. of 
 Commerce, September. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE M 
 
 INSTALLATION OF SOLAR SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
14-1 
 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 14- ii 
 
 OBJECTIVE 14-1 
 
 INTRODUCTION 14-1 
 
 INSTALLATION OF STORAGE VESSELS 14-2 
 
 WATER TANKS 14-2 
 
 PEBBLE BEDS 14-5 
 
 INSTALLATION OF COLLECTORS 14-6 
 
 PLUMBING AND DUCTING 14-8 
 
 ADAPTING TO EXISTING HEATERS 14-11 
 
 ELECTRIC SERVICE 14-13 
 
14-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 14-1 Support for Vertical Water Storage Tanks . . 14-3 
 
 14-2 Connecting Collector to Header .... 14-9 
 
 14-3 Recommended Arrangement for Retrofit Installations 
 
 with a Central Air Circulation System . . . 14-11 
 
 14-4 Air-Heating Solar System for Retrofit 
 
 Installations 14-12 
 
14-1 
 
 OBJECTIVE 
 
 The objective of this module is to explain preferred installation 
 practices for solar systems. At the end of this module the trainee 
 should be able to: 
 
 1. Identify a logical sequence for installing solar systems for 
 new and retrofit construction. 
 
 2. Recognize items of specific concern for retrofit 
 installations. 
 
 INTRODUCTION 
 
 The cost of labor to install a solar system is a substantial 
 portion of the total solar system cost. Careful planning of the instal- 
 lation can significantly lower costs and improve the economic viability 
 of a solar space conditioning and domestic water heating system. There 
 are many important considerations in the installation of a system which 
 affect not only initial costs, but operating, maintenance, and repair 
 costs as well, and the latter factors can, in the long term, be as 
 important as the first cost if the systems are not properly installed. 
 
 Whether the system is being installed in a new structure or is 
 being retrofitted in an existing building, there are many common con- 
 cerns. Other factors apply specifically to retrofit installations which 
 may limit the options for locating storage tanks and other equipment 
 inside the building, or mounting collectors on the roof. Scheduling the 
 installation of the several parts of a solar heating system, whether for 
 new or retrofit construction, is an important part of overall planning. 
 An awareness of major factors when designing and planning system layouts 
 
14-2 
 
 should result in minimum expense for installation, optimum operation, 
 and low maintenance costs. 
 
 INSTALLATION OF STORAGE VESSELS 
 
 The first component of a solar system which should be installed in 
 a new building is the solar storage vessel. The important factors of 
 concern are foundation and footings, scheduling construction of the 
 storage unit, placement of prefabricated tanks, anchoring the vessel, 
 leak testing, insulating, and placing control sensors in the vessel. 
 Many of these items are common to water tanks and pebble beds, and new 
 and retrofit situations. However there are some important differences 
 between water tanks and pebble beds that affect installation methods. 
 
 WATER TANKS 
 
 Several types of water containers are suitable for storage of 
 solar-heated water. Regardless of the type of vessel used, the founda- 
 tion must be adequate to support the weight of the tank when filled with 
 water. If a cylindrical tank is placed vertically, the weight will be 
 supported by the total area of the foundation. A typical arrangement is 
 
 shown in Figure 14-1. 
 
 3 
 The weight of water is 62.4 lb/ft , so a tank which is 6 ft high 
 
 2 
 filled with water has a water load of about 375 lb/ft . With an ad- 
 ditional weight of about 300 lb for the steel tank, the total load on 
 
 2 
 the foundation is about 390 lb/ft . A concrete foundation at least 6 
 
 inches thick, reinforced with a 6- in. heavy wire mesh, is recommended to 
 
 support the load. The type of soil beneath the foundation should also 
 
14-3 
 
 FOUNDATION 
 
 BOTTOM INSULATION AND SUPPORT SCHEME FOR 
 WATER STORAGE TANK 
 
 Figure 14-1. Support for Vertical Water Storage Tanks 
 
 be considered. Sandy soil or gravel will cause no settlement problems, 
 but if the soil contains a large amount of clay, expansion will take 
 place when the soil becomes moist, and lift the foundation despite the 
 weight of the water tank. In such cases, there should be a control 
 joint in the concrete around the tank separating the foundation from the 
 basement floor to prevent uncontrolled cracking of the foundation caused 
 either by soil settlement or expansion. 
 
 Cylindrical water tanks are sometimes placed horizontally and 
 supported by two or more saddle footings which rest on the foundation. 
 The load of the water tank is concentrated at the saddles and the unit 
 load will be larger than the load under a vertical tank. The foundation 
 should be poured for the projected area of the tank so that the load on 
 individual footings will be spread over the entire concrete pad. 
 
14-4 
 
 It is recommended that storage tanks not be buried beneath the 
 basement or garage because access for replacement or maintenance is 
 difficult and expensive. Underground tanks outside the building meet 
 with less objection, but tanks should preferably be placed above grade 
 for accessibility. If there is no choice for placement except under- 
 ground, the insulation on the tank must be completely protected from 
 moisture penetration. There should also be provision for drainage in 
 case of leakage from the tanks or from surface or ground water. Because 
 of these factors, unless the tank can be placed inside the building, a 
 separate underground chamber to house the storage tank is recommended. 
 
 All storage tanks should be inspected carefully for damage before 
 and after placement. Although inspection may be difficult if a pre- 
 insulated tank is purchased, pre-instal lation inspection may detect 
 flaws so that unnecessary and costly replacement after installation can 
 be avoided. 
 
 There should be at least 10 inches of fiberglass insulation, or 
 equivalent, around a water tank to prevent excessive heat losses. It is 
 desirable to achieve at least an R-30 insulation value. While heat 
 losses from tanks placed within the heated envelope are distributed into 
 the building and are utilized, these losses are uncontrolled and may 
 contribute to overheating portions of the building, which is wasteful 
 use of solar heat. 
 
 All tanks should be leak- tested after the piping is installed and 
 connections are made and before insulation is applied. If the solar 
 system is unpressurized, leak detection by filling the storage tank is 
 satisfactory. However, if the system is to be pressurized the tanks 
 should be pressure-tested. 
 
14-5 
 
 The control sensor(s) should be placed in the tank before 
 insulation is applied to the outside of the tank. An immersion well is 
 suitable for thermistors, whether vertical or horizontal tanks are used. 
 
 PEBBLE BEDS 
 
 The foundation for rock storage boxes must be able to support a 
 
 2 
 load of 500 to 600 lb/ft depending upon the size and depth of pebbles 
 
 used. Pebbles of 0.75- to 1.5-in. sizes weigh approximately 100 to 120 
 
 lb/ft . In retrofit applications, constructing a container for a pebble 
 
 bed is less difficult than installation of a water tank. However, 
 
 placement of gravel into the box may pose some difficulties. In new 
 
 construction, the pebbles should be placed before the subfloor is laid 
 
 above the rock box. Considerable expense for gravel placement can be 
 
 spared if the rocks can be loaded into the box directly from above 
 
 rather than with a conveyor after the flooring has been placed. 
 
 The control sensor at the bottom of storage can be attached to the 
 supporting screen after gravel has been placed, by reaching through the 
 bottom port. In many systems, this sensor is mounted in the duct sup- 
 plying cold air from storage and from the rooms to the collector. If a 
 control sensor is needed at the top of the rock bed, likewise, the 
 sensor can be inserted through the top port. 
 
 It is important that rock containers be air tight. All corners and 
 joints in the box should be sealed from the inside with a pliable seal- 
 ant. Many suitable sealant materials are available. Because sealing a 
 pebble bed container from the outside is difficult, careful sealing 
 during initial construction is very important. 
 
14-6 
 
 Rock containers should be insulated at least to R-13. Less 
 insulation is required for pebble-bed containers than for water tanks 
 because the rate of heat conduction from the pebbles to the walls is 
 low, and most of the heat lost through the walls comes from air cir- 
 culating along the walls inside the storage container. Nevertheless, 
 because the wall area of a container is large, insulation is needed to 
 minimize these heat losses. 
 
 Locating storage in an existing building may be difficult without 
 sacrificing valuable living space. Storage boxes for rocks can be 
 located in the backyard above grade if desired. An underground rock bed 
 may also be constructed, but the exterior should be sealed from moisture 
 and the walls should be insulated to minimize heat losses. By far the 
 most desirable location for a pebble bed is inside the heated space. 
 
 INSTALLATION OF COLLECTORS 
 
 The cost of installing collectors varies widely with design. Some 
 manufacturers design collectors to minimize installation time and cost, 
 while other manufacturers give little or no consideration to the in- 
 stallation process; although their collector costs may be low, the 
 installation costs may be very high. Some manufacturers of liquid 
 collectors provide plumbing fittings on the collector frame which are 
 sturdy enough to be torqued with a pipe wrench. Other manufacturers 
 simply provide a pipe stub protruding loosely from the frame and leave 
 the problem of making piping connections to the installer. While col- 
 lectors with prefitted connections may be more expensive than those 
 without connections, the total installed cost of the former may be 
 
14-7 
 
 considerably less than the latter. Similarly, collectors with 
 provisions for anchoring the modules to the roof and for surface and 
 edge flashing designed to fit the collectors can result in considerable 
 time saving during installation. Air collectors with internal mani- 
 folding can result in considerable installation cost reduction compared 
 to collectors that require two roof penetrations and separate ducting 
 for each collector module. 
 
 Collectors are normally mounted on the roof of a building to 
 minimize overall labor and material costs. In new construction, roof 
 trusses should be angled at a suitable pitch, and collectors can be 
 mounted either directly on the sheathing or integrally with the roof 
 trusses. For retrofit construction, the pitch of the roof may not be at 
 the desired angle, and collector tilt may have to be adjusted with 
 standoffs above the finished roofing. If standoffs are used, a minimum 
 spacing between the collector and the finished roofing is usually re- 
 quired by building codes. The spacing required will vary with location. 
 Costs for mounting collectors with standoffs may be considerably higher 
 than costs for mounting collectors directly on the roof. Wind and snow 
 loads for standoff mounting will be larger than normal and the struc- 
 tural adequacy of roof trusses should be checked. 
 
 Rack-mounted collectors are suitable for flat roofs and placement 
 on the ground. For ground-level installations, safeguards such as 
 fences must be provided around the collector. An advantage of a rack- 
 mounted array is that collectors can be assembled at ground level. A 
 disadvantage, especially of the air types, is that duct runs and 
 connections may be expensive. 
 
14-8 
 
 PLUMBING AND DUCTING 
 
 After installing the collectors, pipe and duct connections are 
 required. Headers must be connected to liquid collectors and ducts from 
 manifolds to air collectors. Depending upon the type of collectors and 
 arrangement of the array, headers and ducts may be connected to each 
 collector or groups of collectors. For domestic water heating, requir- 
 ing only a few collectors, headers may be connected to each module; but 
 for space heating systems, collectors are usually interconnected in a 
 two- or three-high array. In such arrangements, interconnection of 
 collectors must be made during assembly. 
 
 If the absorber metal and piping in liquid collectors are of the 
 same material, connections from the header to the collector may be made 
 as illustrated in Figure 14-2. The "bent tube" arrangement allows 
 thermal expansion and contraction of the header without creating exces- 
 sive stress at the connectors. If, however, the absorber and pipe are 
 dissimilar metals, a dielectric (non-metallic) coupling must be used. 
 In that case, the offset between header and collector connections should 
 be less than shown in Figure 14-2 to avoid crimping the flexible hose 
 connections. 
 
 Headers should be sloped to drain. For closed loop systems, a 
 slope of 1/4 in. for each 10 feet of header is adequate, but for drain- 
 down systems, a slope of 2 in. for each 10 feet is desirable. Headers 
 should be covered with a hood, the base of which is flashed and the top 
 of which should be easily removable for access to the header 
 connections. 
 
14-9 
 
 HEADER 
 
 SWEAT TO FLARE 
 CONNECTION 
 
 FLARED 
 MALE ELBOW 
 
 SOLAR COLLECTOR 
 
 Figure 14-2. Connecting Collector to Header 
 
 Copper and high temperature plastic (CPVC) pipe are commonly used 
 in solar installations. Of the two, copper is preferable, but if CPVC 
 piping is used, supports must be provided at frequent intervals along 
 horizontal runs so that the pipe will not sag when heated by a warm 
 liquid. Long straight lengths of plastic piping should be avoided 
 wherever possible. All piping should be leak- tested with water and 
 pressurized to specified limits. Pipes in the collector loop, including 
 the manifold, should be insulated with at least 1 inch of closed cell 
 material . 
 
14-10 
 
 It is extremely important that ducts in air systems be leak- tight, 
 because performance can otherwise be significantly affected. Unlike in 
 liquid systems, leaks are not easily detected, but if warm air escapes 
 from a collector loop, cold air must enter the system elsewhere to make 
 up for the air leak. Because leaks are difficult to avoid in a complex 
 arrangement of collector arrays, the best practice is to position the 
 blower in the loop so that air leakage is into the collector array. 
 This infiltration into the collector provides pre- heated ventilating air 
 to the building, which ultimately escapes through cracks and openings. 
 If warm air leaks out of the collector array, cold air must enter the 
 building, thus increasing the normal amount of infiltration and 
 discomfort. 
 
 Ducts may be made of fiberglass ductboard or sheet metal with 
 insulation on the inside or outside, with external insulation usually 
 being preferred. Ductboard can be taped to seal the joints, and metal 
 ducts may be joined with drive clips and hard casted or covered with 
 duct tape. Bends and elbows should contain turning vanes to minimize 
 pressure losses and fan power consumption. 
 
 Connections between ductwork and blowers should be made with 
 flexible (usually fabric) sections to dampen noise from vibrating 
 blowers and motors, and for ease of removing the blower for service and 
 maintenance. Connections between the ducts and storage box should be 
 flexible to allow for differential movement of the storage box relative 
 to the ducts. 
 
14-11 
 
 ADAPTING TO EXISTING HEATERS 
 
 Solar heating systems are readily adaptable to air distribution 
 systems. While baseboard convectors are prevalent in many non-solar 
 hydronic systems, flat-plate collectors will not perform well with such 
 systems so fan-coil units are usually preferred. A water-to-air coil 
 can be installed in the cold air return duct of an existing warm air- 
 heating system as illustrated in Figure 14-3. Usually the blower is an 
 integral part of a furnace, whether fuel -fired or electric, and for 
 electric furnaces the automatic controls must be reconnected so that the 
 
 COLD AIR RETURN 
 
 AIR HEATING 
 DUCT COIL 
 
 EXISTING 
 DUCTS 
 
 HOT AIR TO 
 BUILDING 
 
 Figure 14-3. 
 
 Recommended Arrangement for Retrofit Installations 
 with a Central Air Circulation System 
 
14-12 
 
 blower is independent of the heating element. Locating the heating coil 
 ahead of the blower, as shown in Figure 14-3, is preferred so that air 
 is pre-heated by the solar system. However, if the blower motor is in 
 the air stream, its life may be reduced because it is subjected to a 
 high temperature environment. Alternatively a type B (higher tempera- 
 ture operation) motor may be used. Generally, the location of the 
 water- to-air heating coil is dependent upon the duct arrangement. 
 
 A two-blower arrangement for a retrofit air solar system might be 
 arranged as shown in Figure 14-4. The existing blower will have to be 
 decoupled from the heating element control and reconnected to the 
 central solar system controller. 
 
 NEW CONSTRUCTION 
 EXISTING SYSTEM 
 
 ^ / HOT AIR TO 
 fWf BUILDING 
 
 \ 
 \ 
 
 REMOVE \ 
 
 EXISTING | 
 RETURN 
 
 DUCT ' 
 
 SECTION / 
 
 / 
 / 
 
 / 
 
 / 
 
 ROOM AIR 
 RETURN 
 
 Figure 14-4. Air-Heating Solar System for Retrofit Installations 
 
14-13 
 
 ELECTRIC SERVICE 
 
 Connections to the control box, pumps, and blowers are usually 120 
 V A.C. single-phase power. Electrical connections to valves and damper 
 motors are normally 24 volts, and transformers are provided with the 
 controller. Low voltage wiring is also appropriate for thermostats. 
 
 Control panels should be located conveniently for easy access 
 during installation and maintenance. Control devices are usually field- 
 wired according to instructions provided by the system (or controller) 
 manufacturer. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 15 
 
 OPERATIONAL CHECK-OUT 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
15-i 
 
 TABLE OF CONTENTS 
 
 OBJECTIVE .... 
 INTRODUCTION . 
 GENERAL PROCEDURE . 
 
 VISUAL INSPECTION . 
 
 FINAL CHECK 
 
 OPERATIONAL CHECK-OUT 
 
 PERFORMANCE TEST 
 AIR SYSTEMS 
 
 INSPECTION CHECK LIST - COLLECTORS 
 
 INSPECTION CHECK LIST - PEBBLE-BED HEAT STORAGE UNIT. 
 
 START-UP PROCEDURES - AIR HANDLER 
 
 PERFORMANCE CHECK . 
 
 PERFORMANCE ANALYSIS 
 LIQUID SYSTEMS . 
 
 PUMPS 
 
 HEAT EXCHANGER . 
 
 ANTIFREEZE SOLUTION 
 
 LIQUID LEVELS . 
 
 CORROSION INHIBITOR 
 
 DRAIN-DOWN SYSTEMS . 
 Collector Loop . 
 Storage Tank 
 Sensors and Controls 
 
 Page 
 
 15-1 
 
 15-1 
 
 15-2 
 
 15-2 
 
 15-3 
 
 15-4 
 
 15-4 
 
 15-6 
 
 15-6 
 
 15-7 
 
 15-8 
 
 15-11 
 
 15-13 
 
 15-14 
 
 15-15 
 
 15-16 
 
 15-16 
 
 15-17 
 
 15-18 
 
 15-18 
 
 15-18 
 
 15-19 
 
 15-20 
 
15-ii 
 
 Page 
 
 PERFORMANCE CHECK 15-21 
 
 PERFORMANCE ANALYSIS 15-23 
 
 APPENDIX A15-1 
 
15-1 
 
 OBJECTIVE 
 
 The objective of this module is to acquaint the trainee with: 
 
 1. The importance of thorough check-out of a completed solar 
 heating system. 
 
 2. The general procedure for checking the proper functioning of 
 the system. 
 
 3. The information for adjusting the controls in a solar heating 
 system to achieve effective and dependable operation. 
 
 INTRODUCTION 
 
 The numerous components in a solar heating system, with their 
 interconnection and interdependence, require thorough checking for 
 proper functioning before final completion and acceptance. Although 
 there are substantial differences in systems, a reasonably standard 
 procedure of inspection, functional checking, and adjustment can be 
 applied in most installations. Where check-out instructions of the 
 system designer and/or manufacturer are available, they should be 
 closely followed. Step-by-step directions are included in installation 
 manuals provided by a few suppliers of complete solar heating systems. 
 Specific directions for installation, adjustment, and checking are also 
 usually supplied by manufacturers of solar system controllers. The 
 installer's use of a complete check list or form is recommended as the 
 best protection against omissions, subsequent operation problems, 
 customer complaints, expensive damage, and costly service calls. 
 
15-2 
 
 GENERAL PROCEDURE 
 
 VISUAL INSPECTION 
 
 The first step in a practical check-out procedure is a visual 
 comparison of the completed system with construction drawings and manu- 
 facturers' instructions. Fluid flow patterns, sizes and locations of 
 ducts and piping, and sealing of duct joints should be verified. Elec- 
 trical' connections on controls, sensors, and motors should be checked 
 for integrity and conformity with plans. The collector installation 
 should be inspected for alignment, tight connections, properly posi- 
 tioned piping and ductwork, and security of collector support and 
 perimeter flashing. 
 
 After completion of the visual inspection of the idle system, 
 various observations should be made when the equipment is operated in 
 each required mode. Generally, the following checks will usually be 
 necessary: 
 
 1. Observation of leakage of liquids or air at any point in the 
 system, while running in each operating mode; 
 
 2. Verification of proper functioning of all moving parts and 
 controls, including motors, pumps, fans, motorized valves and 
 dampers, manual valves and dampers, check valves and dampers, 
 fuel valves, electrical switches and relays, thermostats and 
 their contacts, draining and venting valves and fittings, and 
 any other adjustable components in the system; 
 
 3. Liquid levels and compositions; 
 
15-3 
 
 4. Cleanliness and freedom from obstructions in flow channels for 
 liquids and air; 
 
 5. After initial operation, cleanliness of filters in liquid 
 and air circuits; 
 
 6. Verification of proper control settings and their proper 
 action (turning on, turning off) in actuating motors, valves, 
 and dampers; 
 
 7. Detailed check of proper functioning of safety and limiting 
 devices and designs, such as complete drain-down of water from 
 collectors and piping in drain-down systems, automatic valves 
 for draining, venting, and bleeding liquid systems, overheat 
 protection devices such as pressure relief valves and sensor 
 actuated drain valves, and any other system protection 
 devices; 
 
 8. Complete check of auxiliary heating and distribution system. 
 The check-out procedure outlined above should be followed prior to 
 
 final insulation of the principal system components and piping unless 
 insulation is part of the equipment such as in internally insulated air 
 ducts. The heat storage unit may, however, be insulated prior to final 
 system check. 
 
 FINAL CHECK 
 
 Following the testing and the repair and correction of faults which 
 may be found, insulation should be applied to components and inter- 
 connections in the system, as recommended or required. A final check on 
 the proper functioning of all moving parts and control functions should 
 then be made to eliminate possibility of malfunction accidentally caused 
 
15-4 
 
 by damage during the insulation process, and as a double check on system 
 functions. This final check-out may advantageously be done in collabo- 
 ration with the system owner so that he may understand its operation. 
 
 OPERATIONAL CHECK-OUT 
 
 Of particular importance is the careful use of manufacturer's and 
 designer's check-out instructions in verifying and correcting the in- 
 stallation and operation of each system and its components. Procedures 
 are provided by some suppliers of complete solar heating systems, and 
 the manufacturers of the principal components usually supply check-out 
 information on their own products. Collectors, pumps, motorized valves 
 and dampers, and control subsystems are examples. 
 
 In checking operations in various modes, it is usually necessary 
 for the system installer to simulate one or more conditions not pre- 
 vailing at the time of testing. If the sun is obscured, for example, 
 solar collector checking requires imposing some type of artificial 
 condition to actuate the appropriate components. The supplier of the 
 controller or of the complete system usually offers instructions on 
 simulating each operating mode by making jumper connections across 
 sensor terminals. Sensor control settings must be verified, however, by 
 observations under actual conditions. 
 
 PERFORMANCE TEST 
 
 The third major checking procedure is the measurement of heat 
 delivery from the solar heating system. Although only a few systems are 
 provided with convenient and accurate facilities for solar system effi- 
 ciency checking, the installer can usually make a reasonably reliable 
 
15-5 
 
 determination of performance. By comparing the measured results with 
 design values, the quality of the system and its installation can be 
 verified. As indicated in more detail below, measurement of inlet and 
 outlet collector temperatures, and measurement or estimate (based on 
 measured pressures) of collector fluid flow rate near noon on a sunny 
 day will provide sufficient information for at least a minimum evalua- 
 tion of system performance. 
 
 A general blank form for use in checking a complete solar heating 
 system is presented in the Appendix to this module. It includes numer- 
 ous items which might be considered trivial or obvious, but even a minor 
 fault, if overlooked and uncorrected, can cause poor performance, system 
 deterioration, or building damage. Heating practitioners may also 
 notice omissions which, in their experience, should be covered in the 
 check-out process. Since the listing is intended to apply to all types 
 of solar heating systems, some items are not applicable in each case 
 considered. 
 
 Although sometimes difficult, measurement of solar heat collection 
 and delivery to use provides the best assurance of good system per- 
 formance. Fluid temperature rise and flow rate through the collectors, 
 ambient temperature, and solar radiation should be measured. Solar heat 
 collection and collection efficiency can then be calculated. If flow 
 rates cannot be directly measured, they may sometimes be approximated by 
 determining pressure drops across manufactured standard equipment, such 
 as a heat exchanger or collector, in which the pressure-flow relation- 
 ships are known. 
 
15-6 
 
 AIR SYSTEMS 
 
 Among the check-out steps listed in the general procedure, several 
 are particularly important in air systems. Air leakage, damper closure, 
 blower and motor operation, and proper control should be thoroughly 
 checked. Because of their specialized aspects, collectors, storage 
 units, air handlers, and controllers require more than routine 
 attention. 
 
 The collector inspection check list used by installers of a 
 nationally distributed solar air heating system follows: 
 
 INSPECTION CHECK LIST - COLLECTORS ^ 
 
 1. Collector Array: Refer to plans 
 
 2. Holding proper dimension from collector to collector - thus 
 making airtight seal from port to port: Refer to specifica- 
 tions and/or plans. 
 
 3. Used specified material for port and end cap sealant: Refer 
 to specifications and/or plans. 
 
 4. Relief tubes sealed and in place: Refer to specifications. 
 
 5. Confirm location and dimensions of 2 x 8 (W x 7 1/8") 
 frame. 
 
 6. Cap strips installed so proper and airtight seal is 
 accomplished. 
 
 7. Perimeter insulation installed: Refer to specifications 
 and/or plans. 
 
 8. Perimeter flashings installed properly: Refer to 
 specifications and/or plans. 
 
 'Courtesy of The Solaron Corporation, used by permission. 
 
15-7 
 
 9. Connecting Collars: Refer to plans. 
 
 a. Location 
 
 b. Sealed properly 
 
 10. Heat Sensors: Refer to plans. 
 
 a. Installed properly 
 
 b. Correct location 
 
 An inspection list for the pebble-bed heat storage unit specified 
 by the same solar air system manufacturer follows: 
 
 INSPECTION CHECK LIST - PEBBLE-BED HEAT STORAGE UNIT (1) 
 
 1. Location: Refer to plans. 
 
 2. Location of Duct Openings: Refer to plans. 
 
 3. Dimensions of Unit: Refer to plans. 
 
 4. Dimensions of Duct Openings: Refer to plans. 
 
 5. General Construction: Refer to plans. 
 
 a. If construction does not follow plans, make sure 
 modifications are adequate to meet specifications 
 
 b. Check for exposed wood - all combustible surfaces must be 
 covered with a non-combustible material 
 
 6. Check all joints: 
 
 a. Sealed adequately 
 
 b. Correct sealant used (i.e. suitable for temperatures 
 around 180°F) 
 
 ^ ^Courtesy of The Solaron Corporation, used by permission. 
 
15-8 
 
 7. Lower Plenum: Refer to plans. 
 
 a. Proper materials used 
 
 b. Correct dimensions 
 
 c. Correct spacing of bond beam block 
 
 8. Upper Plenum: Refer to plans. 
 Correct Dimensions 
 
 9. Rock: Refer to specifications. 
 
 a. Proper size 
 
 b. Free of foreign materials (clean) 
 
 c. Proper amount 
 
 d. No depressions in rock bed (level on top) 
 10. Storage Unit Lid: Refer to specifications. 
 
 a. Construction 
 
 b. Sealed adequately 
 
 c. Proper sealant used (i.e. suitable for temperatures 
 around 180°F) 
 
 An air handler start-up procedure, which is effectively an 
 installation check list, is shown below. This procedure also verifies 
 the proper functioning of nearly all the elements in the control system. 
 
 START-UP PROCEDURES - AIR HANDLER (1) 
 I. Preliminary Check 
 
 1. Double check all line and low voltage wiring and connections 
 (see wiring diagram for exact wiring hook-up to unit). 
 
 'Courtesy of The Solaron Corporation, used by permission. 
 
15-9 
 
 2. Check all damper positions, both inside air handler and any 
 dampers that might be located elsewhere in the duct system. 
 
 3. Check belt-driven power train (tighten set screws on pulleys, 
 confirm V-belt alignment, etc.). 
 
 4. Check voltage supply to unit. Should voltage not be correct, 
 contact electrician before proceeding with start-up. 
 
 5. Open all registers, diff users and grilles in distribution 
 system. 
 
 II. Start-up on "Sunny Days" 
 
 1. Set heat anticipators in space thermostat. 
 
 a. W-, (first stage heating) set at 0.7 amp. 
 
 b. Wp (second stage heating) set at 0.1 amp. 
 
 2. Set thermostat so W-. is calling for heat. W ? must not be 
 calling for heat at this time. 
 
 NOTE: The use of a jumper between W, and R H at the AU control 
 panel can be used in lieu of setting the thermostat. Before 
 the system is given approval, however, check system operation 
 with the thermostat to insure proper operation. 
 
 3. Set Sub-base switches (if present). 
 
 a. "Fan-Auto" 
 
 b. "System-Heat" 
 
 4. Turn on circuit breakers. 
 
 5. Turn on disconnect feeding the AU air handler. 
 
15-10 
 
 6. Observe unit operation. 
 
 a. The auxiliary furnace blower should be running. There 
 should be no auxiliary heat. 
 
 b. The AU air handler blower should start as long as sensors 
 T and T . have a 45 degree F or greater temperature 
 differential . 
 
 c. Air flow through dampers in the air handler, and BD1 and 
 BD2, should be as shown on your plans (refer to A.E.M. 
 "Control System" schematic). 
 
 d. A temperature differential of less than 45 degrees F will 
 automatically switch the system into a "heat from stor- 
 age" mode. If there is no heat in storage (less than 90 
 degrees F), the control board will automatically by-pass 
 the solar heating circuit and bring on the auxiliary heat 
 source without having W ? in the space thermostat in a 
 "heat" position (closed circuit). 
 
 e. When the rock storage unit has enough heat (greater than 
 
 90 degrees F) available, and the T , T . differential is 
 3 ' co ci 
 
 less than 45 degrees F, the air handler will direct the 
 air flow through the rock storage unit and into the 
 auxiliary furnace. This will be accomplished without the 
 auxiliary heat coming on. 
 
 7. Set the space thermostat so W-. and VL are not calling for heat 
 (open). 
 
 a. The auxiliary furnace blower will cease operating 
 
 b. The AU air handler will continue to operate 
 
15-11 
 
 c. The dampers inside the All air handler will direct the 
 solar heated air to the rock storage unit (see flow 
 schematic on your plan and/or your A.E.M. "Control System" 
 schematic. ) 
 8. Set the space thermostat so W-. and W ? are calling for heat 
 
 (closed circuit). 
 
 a. The auxiliary furnace should operate in a conventional 
 manner 
 
 b. The AU air handler blower will continue to operate 
 
 c. Dampers in the AU unit will direct air through the 
 
 rock storage and into the auxiliary furnace (see flow 
 schematic on your plan and/or "Control System" 
 schematic in your A.E.M. ). 
 
 PERFORMANCE CHECK 
 
 Knowledge of the heat output of a solar air heating system is of 
 value to the owner. If measurement of air flow rate is impossible or 
 impractical, static pressure readings at several places in the system 
 can be used to obtain a reasonably close estimate of flow rate by com- 
 paring measured pressure drop across collectors, air handler, or hot 
 water coil against manufacturer's data. Small holes (1/4- inch diameter) 
 may be drilled or punched through duct walls at the positions shown in 
 the Solar Heating Flow Schematic shown on the next page^ '' Flexible 
 tubing is then inserted for connection to a manometer. 
 
 *■ 'Courtesy of The Solaron Corporation, used by permission. 
 
15-12 
 
 SOLARON 
 COLLECTORS 
 
 U- 
 o 
 
 Solaron Ai 
 
 \Optiona 
 Sum mer Byposs 
 
 ^-Air Plenum 
 
 PROJECT NAME: Typical PrOJPrt DATE.. 
 
 PROJECT TYPE: RES'L X COMM'L IND'l 
 
 AGRI OTHER 
 
 location: Sunbeam Valley, California 
 
 COLLECTOR ARRAY:_2_HIGH X 12 WIDE = 468 SO ft 
 
 serviceman: I Deal Heavenly 
 
 company: SUPERIOR SUNBEAMS, INC. 
 
 PHONE (_) 
 
 BD-2 
 
 Filter 
 
 L___Ajr_i 
 FLOV SCHEMATIC 
 
 = Open 
 P.O. = Partially Optn 
 C = Closed 
 
 SEQUENCE OF OPERATIONS 
 
 HEATING FROM COLLECTOR 
 
 HEATING FROM STORAGE 
 
 STORING HEAT 
 
 HEATING WITH AUX. FURNACE 
 
 WATER HEATING (SUMMER) 
 
 PO 
 
 PO. 
 
 PO. 
 
 
 2^c 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 ON 
 
 Solaron 
 air 
 
 rioodlT 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 ON 
 
 Aux. Furnact 
 
 ON 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 OFF 
 
 OFF 
 
 OFF 
 
 ON 
 
 OFF 
 
 FOR HEAT PUMP SYSTEMS? MD-2 Closed, MD-3 Open, 8D-I Closed 
 
 
 AIR HANDLER 
 
 L SOLAR 
 
 AUX 
 
 Design CFM 
 
 Design Ext. SP 
 
 Fan RPM 
 
 HP 
 
 Motor RPM 
 
 Volt 
 
 Phase 
 
 FLA 
 
 SF 
 
 SFA 
 
 Insul. Class 
 
 Motor Mfg 
 
 Model No 
 
 936 
 
 D.80" 
 
 1160 
 
 1/2 
 
 1725 
 
 115 
 
 1 
 
 fi.n 
 
 1.25 
 6.8 
 
 B 
 GE 
 4T0051 
 
 
 
 
 
 
 
 
 
 
 T, (CFM S0 , ) + T 2 (CFM aux - CFM S0 , ) 
 
 CFMnux 
 
 T, = I30°F 
 T 2 = 68° F 
 T 3 = IIT-F 
 
 TEMPERATURE 6 STATIC PRESSURE MEASUREMENTS 
 
 STORING HEAT| Moto 5 r _ ( J mps - 
 
 HEATING FROM 
 STORAGE 
 
 HEATING FROMJ Motor Amps. 
 COLLECTOR j 5.3 
 
 POINT 
 
 ... . 
 
 °F 
 
 STATIC 
 PRESSURE 
 
 S.P. 
 DIFF. 
 
 POINT 
 
 °F 
 
 STAT 1 C 
 PRESSURE 
 
 S.P. 
 DIFF. 
 
 POINT 
 
 °F 
 
 STATIC 
 PRESSURE 
 
 S.P. 
 DIFF. 
 
 1 
 
 X 
 
 ^0.00" 
 
 X 
 
 
 _ 
 
 0.00" 
 
 
 1 
 
 _ 
 
 -.19" 
 
 
 ) .42" 
 
 2 
 
 138 
 
 -.34" 
 
 
 2 
 
 - 
 
 -.ni" 
 
 
 2 
 
 - 
 
 -.94" 
 
 > .69 
 
 
 3 
 
 132 
 
 + .35" 
 
 3 
 
 130 
 
 -.29" 
 
 
 3 
 
 _ 
 
 -.20" 
 
 
 >.19 
 
 ).14 
 
 > .04" 
 
 4 
 
 68 
 
 + .16" 
 
 4 
 
 68 
 
 -.15" 
 
 4 
 
 - 
 
 -.16" 
 
 
 
 
 5 
 
 66 
 
 + .06" 
 
 
 5 
 
 - 
 
 -.01" 
 
 
 5 
 
 66 
 
 -.34" 
 
 
 >.31 
 
 > .00 
 
 ) .42" 
 
 6 
 
 141 
 
 -.25" 
 
 6 
 
 - 
 
 -.01" 
 
 6 
 
 122 
 
 -.76" 
 
 
 
 
 7 
 
 
 
 
 7 
 
 - 
 
 -.42" 
 
 
 7 
 
 - 
 
 -.21" 
 
 
 ) .60 
 
 ) .48" 
 
 8 
 
 
 
 
 8 
 
 117 
 
 + .18" 
 
 8 
 
 - 
 
 + .27" 
 
 
 
 © COPYRIGHT 2-1978 SOLARON CORP., DENVER, CO. 80222 
 
15-13 
 
 PERFORMANCE ANALYSIS 
 Air Heating System 
 
 A. Collector 
 1. 
 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. Heat delivery rate: 
 
 «c = (%)(V T i )(60) 
 
 Area, A 
 c 
 
 
 ft 2 
 
 Inlet temperature, T. 
 
 
 °F 
 
 Outlet temperature, T 
 
 
 °F 
 
 Pressure drop across blower, Wp 
 
 
 in W.G 
 
 Flow rate, V 
 
 
 cfm 
 
 Air density, p 
 
 .07 
 
 lb/ft 3 
 
 Specific heat, c 
 
 .24 
 
 Btu/(1 
 
 = V . pCpCY^XeO) Btu/hr 
 
 B. Collector Efficiency: 
 
 1. Solar radiation on horizontal 
 
 surface, In Btu/(ft2 . > 
 
 2 
 or on tilted surface, Iy Btu/(ft *hr) 
 
 2. Collector efficiency 
 
 Q c 
 
 h = t-t- x 100 % 
 
 c Vc 
 
15-14 
 
 or sensitive differential pressure gauge. Temperature sensors (glass or 
 dial thermometers, thermocouples, or thermistors) are also inserted 
 through holes at these points. 
 
 A performance analysis form used by installers of a widely used air 
 system, with sample data, is shown on the preceding page^ . Points for 
 measurement of temperature and static pressure are indicated. By com- 
 parison of static pressure differences across the several components 
 with those shown in the manufacturer's engineering data sheets at vari- 
 ous flow rates, actual flow rates may be closely estimated. Heat output 
 may then be calculated by completing the form entitled Performance 
 Analysis, Air Heating System . By use of a simple hand-held meter, solar 
 radiation can also be measured so that collection efficiency, item B2 in 
 the Performance Analysis form, may be calculated. Comparison with 
 manufacturer's performance data may then be made. If a large difference 
 is found, causes should then be investigated. 
 
 LIQUID SYSTEMS 
 
 The principal components of a typical liquid space heating system 
 requiring check-out procedures specific to the liquid type (as compared 
 with air) are 
 
 1. liquid pumps 
 
 2. liquid- to- liquid heat exchanger 
 
 3. valves and piping for draining and venting. 
 
 ^Courtesy of The Solaron Corporation, used by permission. 
 
15-15 
 
 The other system components such as collectors, storage tank, 
 motorized valves, pipe connections, sensors and controllers, all have 
 their counterparts in the air systems previously described. If the 
 supplier of a main component, such as the collector, has provided a 
 complete system design and check-out procedure, those instructions 
 should be followed. In other instances, particularly if large or 
 custom-designed systems are involved, the mechanical engineering 
 designer or consultant may specify a check-out procedure. If no 
 specific inspection list is available, the installer should follow the 
 general guidelines previously outlined, altering them as may be 
 necessary for the specific system involved. 
 
 PUMPS 
 
 With respect to pumps, the installer should check speed (unless 
 directly coupled to motor), and by means of permanent or temporary 
 gauges, the pressure difference from inlet to outlet of the pump. 
 Proper mounting, alignment, and attachment to piping and wiring should 
 also be checked. Noise and vibration should be within acceptable 
 limits. 
 
 By use of the pump speed and the fluid pressure difference, the 
 pump manufacturer's charts or graphs may be used to determine volumetric 
 flow rate. This rate should then be compared with the desired or 
 designed flow rate and, if not in satisfactory agreement, causes for 
 difference should be determined and corrected. 
 
 Because misleading pressure readings may sometimes be obtained at 
 points near pumps, measurements of pressure differences across other 
 components in the system should also be made. Pressure loss through the 
 collector array and across a heat exchanger may be compared with the 
 
15-16 
 
 manufacturer's flow rate-pressure drop data to confirm the flow 
 measurements. If serious discrepancies appear, their cause should be 
 determined. 
 
 HEAT EXCHANGER 
 
 In dual-liquid systems, proper operation of the collector-storage 
 heat exchanger must be verified. Counter flow of the two liquids is 
 essential, so piping connections must be checked to verify the flow of 
 one liquid in a direction opposite to the flow of the other. When 
 operating under conditions such that solar energy is being collected, 
 the inlet and outlet temperature of the collector fluid, the inlet 
 temperature of the storage fluid, and the static pressure at all four 
 points should be measured. If thermometer wells are not provided in the 
 piping, temperature sensors (thermocouples, thermistors or small-bulb 
 thermometers) should be tightly taped to the outside of the pipe in 
 close proximity to the heat exchanger connections. At least 2 inches of 
 pipe insulation should be applied over the temperature sensor along at 
 least 1 foot of pipe length. After they become constant (several 
 minutes) the readings will be sufficiently close to the liquid tempera- 
 tures at those points. Calculation of a heat balance on the exchanger 
 and a comparison of pressure loss with those shown in the manufacturer's 
 data should then be made. 
 
 ANTIFREEZE SOLUTION 
 
 The concentration of antifreeze solution in the collector liquid 
 should be verified by use of a hydrometer such as commonly available 
 
15-17 
 
 for testing automobile radiator coolants. If the test shows inadequate 
 freeze protection, addition of ethylene glycol or propylene glycol as 
 specified by the designer should be made until the concentration is 
 satisfactory. Tables of antifreeze concentration and liquid density may 
 be used if the hydrometer does not show the freezing temperatures 
 directly. Drainage of some liquid from the collector loop may be 
 necessary in order that antifreeze can be added. 
 
 LIQUID LEVELS 
 
 The liquid level both in the collector loop and in the storage tank 
 should be determined by whatever means are provided in the system. 
 Sight gauges, pointer type indicators, inspection ports, and overflow 
 valves or other means may be used, depending on design. 
 
 In a closed collector loop, proper filling and functioning of the 
 expansion tank must be verified, sufficient liquid being present to fill 
 the collector loop and sufficient additional space being available for 
 the enlarged liquid volume when solar heated. Consideration must be 
 given to the temperature of the liquid at which the expansion tank level 
 is noted so that either an increase or decrease in liquid volume can be 
 accommodated. 
 
 If a non-aqueous liquid is used in the collector loop, such as a 
 silicone oil, its quantity and quality should be checked. Normal proce- 
 dure would involve filling of the system by the installer, from a known 
 supply of the chemical. In case of doubt, some chemical or physical 
 property of the liquid which the manufacturer recommends for identifica- 
 tion should be ascertained. 
 
15-18 
 
 CORROSION INHIBITOR 
 
 If a corrosion inhibitor is used in the storage liquid, the most 
 satisfactory procedure for insuring protection is careful compliance 
 with designer's instructions when the inhibitor is first added to the 
 system. If later verification of the quantity and quality of the addi- 
 tive is required, a chemical or physical test of a sample of the solu- 
 tion should be made by the installer. In some cases, a sample may have 
 to be supplied to a testing laboratory for checking. In exceptional 
 cases, the most economical procedure may be the draining and recharging 
 of the storage unit, with properly measured additives. 
 
 DRAIN-DOWN SYSTEMS 
 Collector Loop 
 
 In drain-down systems, careful inspection of all piping and 
 connections must be made to verify the absence of any low points or 
 traps in the system that might prevent complete drainage. Even, hori- 
 zontal runs of pipe should be avoided, slight slope being a much pre- 
 ferred design. Access of air to the collector either through an at- 
 mospheric valve or from the storage tank via an adequately sized pipe 
 must be verified. 
 
 Systems that are designed for collector drainage to occur either 
 when freezing threatens or when the pump ceases operation must be 
 thoroughly and completely checked by dependable and repeated drainage 
 and refilling, without fault. Those that are designed to drain back 
 into the storage tank, either through an open return or siphon return 
 
15-19 
 
 when the pump ceases operation, can be checked by interrupting the power 
 supply to the pump motor. After a minute or so, absence of water out- 
 flow through an opened drain valve located in the collector supply 
 piping above the level of water in the storage tank indicates satisfac- 
 tory collector drainage. The lack of water in the return line from the 
 collector to the storage tank can be similarly verified. In siphon 
 return systems, the opening of the "siphon breaker" air inlet valve at 
 the top of the collector piping assembly must also be verified. This 
 valve must be open whenever electric power is accidentally or purposely 
 interrupted. 
 
 Start-up of the system after drainage must also be checked by 
 restoring power to the pump and to the siphon breaker valve (if the 
 valve is of the electric-operated type). Observation of flow returning 
 to storage, if in a visible location, or verification of normal pres- 
 sures at various points in the circulating loop can confirm satisfactory 
 displacement of air from the collector and piping, and the restoration 
 of normal flow. In the siphon return system, verification of proper 
 functioning of the air bleed valve at the top of the piping array must 
 also be made. 
 
 Storage Tank 
 
 If main storage is operated at a pressure greater than atmospheric 
 pressure and is non-vented (usually because a pressurized hydronic heat 
 distribution system is involved), proper operation of the pressure 
 relief valve (safety valve) on the storage tank must be established. If 
 the valve cannot be tested satisfactorily in place, it should be removed 
 
15-20 
 
 temporarily and tested with measured pressure by use of a pressure test 
 kit. The greater complexity of the piping and valving in this type of 
 system requires verification of complete collector drainage by methods 
 recommended by the designer of the system employed. There is sufficient 
 variation in the designs of these systems, including liquid level con- 
 trol, automatic water make up, check valves, by-pass piping, and motor- 
 ized valves, that there is no standard check-out procedure applicable to 
 all systems. 
 
 Sensors and Controls 
 
 Systems which involve collector drainage only when freezing 
 threatens are usually actuated by a temperature sensor in the collector 
 or in the atmosphere. These controls must be checked by artificially 
 cooling the sensor below the temperature at which it functions to drain 
 the collectors. The application of ice to the sensor should turn off 
 the pump and allow the collector to drain. Removal of the ice will then 
 permit the sensor to warm up and restart the pump. These operations can 
 be visually verified. 
 
 Proper functioning of controls and other components which prevent 
 overheating and/or boiling of fluids in the collector and storage loops 
 must also be verified. Several types of overheat protection devices are 
 commonly used, so the manufacturer's instructions should be carefully 
 followed in the check-out procedure. An excessive temperature condition 
 can usually be electrically simulated by a suitable signal to the con- 
 troller, and the functioning of the overheat protection system observed. 
 Circulation of water from the storage tank through a heat rejection 
 
15-21 
 
 coil, drainage of the collector, draw-off of domestic hot water from the 
 solar pre-heat tank and automatic addition of cold water, and discharge 
 of hot water from the solar hot water storage tank, are the principal 
 methods employed. 
 
 Checking the operation of whatever system is in use is essential. 
 If the overheat sensor is accessible, a small electric heating element 
 can be temporarily applied at the proper point by the installer, thereby 
 checking the entire system in place, including the control elements. If 
 this condition has to be simulated by causing an open circuit or short 
 circuit in the overheat sensor contact in the controller, the sensor 
 itself should be checked by heating prior to installation. Controller 
 manufacturers usually provide check data for all standard elements in 
 the control circuitry. Measurement of electrical resistances can 
 usually provide satisfactory evidence of proper operation. 
 
 PERFORMANCE CHECK 
 
 Following the checking of proper functioning of all components in 
 the system under all conditions of operation, measurement of heat output 
 and efficiency of the system should be made. The following table 
 (Performance Analysis, Liquid Heating System) indicates the measurements 
 needed and the calculations required. The previously described methods 
 for measuring collector flow rate and temperature rise at full and 
 nearly constant solar radiation levels should be conducted simultaneous- 
 ly with measurement of solar radiation intensity. These measurements 
 should be made near mid-day so that conditions are as constant as 
 practical. Calculation of the heat delivery from the collector is a 
 
15-22 
 
 simple multiplication of the temperature rise, flow rate, and heat 
 capacity factors. Dividing this quantity by the solar radiation input 
 rate provides efficiency data. Comparison with the manufacturer's 
 rating data at the temperatures and solar radiation levels corresponding 
 to those applied during the test can then show the degree of agreement 
 with the designed values. Unexplained differences, if any, then need to 
 be investigated and corrected. 
 
15-23 
 
 PERFORMANCE ANALYSIS 
 
 Liquid Heating System 
 
 Collector 
 
 
 1. 
 
 Area, A c 
 
 2. 
 
 Inlet temperature, T. 
 
 3. 
 
 Outlet temperature, T 
 
 4. 
 
 Pressure drop across pump 
 
 5. 
 
 Fluid flow rate, G 
 
 6. 
 
 Specific heat, c 
 p 
 
 7. 
 
 Fluid specific weight, y 
 
 8. 
 
 Heat delivery rate: 
 
 ft 2 
 
 _°F 
 °F 
 
 psi 
 
 gpm 
 
 Btu/(lb-°F) 
 
 lb/gal 
 
 Btu 
 
 Q„ = Gyc (T -T.)(60) , 
 
 x c ' p v o i yv y hr 
 
 Collector Efficiency: 
 
 1. Solar radiation on horizontal n . //£ .2 . ^ 
 surface, L,, or Btu/(ft * hr ^ 
 
 tilted surface, I T Btu/(ft -hr) 
 
 2. Collector efficiency 
 
 Q c 
 n = t4- x loo % 
 
 c n M c 
 
A15-1 
 
 APPENDIX 
 
A15-2 
 
 Inspection Check List 
 
 Project: 
 
 Owner: 
 
 Address: 
 
 Date Inspected: 
 
 Inspector: 
 
 Approved: 
 
 Disapproved: 
 
 Exceptions: 
 
 (refer to Exception Notes) 
 
 Yes No 
 
 Solar Collectors: 
 
 1. Structural strength appears adequate 
 
 2. Are resistant to weather 
 
 3. Are resistant to fire 
 
 4. Provided with an efficiency curve in acceptable form 
 
 5. Have material with potential for outgassing 
 
 6. Are provided with adequate flashing 
 
 7. Meet safety requirements 
 
 8. The glazing is adequate for strength 
 
 9. The glazing appears to have satisfactory durability 
 10. The absorbed material and coating are acceptable 
 
 Energy Transport System: 
 
 1. Expansion or contraction will cause damage 
 
 2. Joints with dissimilar metals are suitably protected 
 
 3. Air distribution system is adequately sized 
 
 4. Filters are placed properly 
 
 5. Pipe and duct hangers are adequate 
 
 6. Valves and dampers are acceptable 
 
 
A15-3 
 
 Yes No 
 
 C. Thermal Storage Units: 
 
 1. Container materials are sufficiently durable 
 
 2. Contamination of air or water is adequately prevented 
 
 3. Materials in storage units are compatible with other 
 units of the system 
 
 D. Heat Transfer Fluids: 
 
 1. Are chemically stable 
 
 2. Are thermally stable 
 
 3. Are non-corrosive 
 
 4. Pose a safety hazard 
 
 5. Have a sufficiently high flash point 
 
 E. Heat Exchangers: 
 
 1. Are suitable with the system 
 
 2. Potable water is suitably protected 
 from non-potable heat source 
 
 3. Heating coils are adequate 
 
 F. Gaskets and Seals: 
 
 1. The system is adequately gasketed for pressure 
 
 2. Ducts are adequately sealed 
 
 G. Insulation and Moisture Protection: 
 
 1. Insulation materials constitute a fire hazard 
 
 2. Materials are thermally stable 
 
 3. Pipe and duct insulation is adequate 
 
 4. Storage is adequately insulated 
 
 H. Hose Couplings: 
 
 1. Are thermally stable 
 
 2. Are compatible with the heat transfer fluid 
 
 3. Are compatible with piping material 
 
 I. Controls: 
 
 1. Fail-safe protection is adequate 
 
 2. Pressure relief devices are adequate 
 
 3. Vacuum relief is provided 
 
 4. Main shut-off valves and switches are identified 
 
 5. Automatic controls are provided 
 
A15-4 
 
 Yes No 
 
 Installation, Operation and Maintenance: 
 
 2. The system is generally maintainable 
 
 Auxiliary Heating and Hot Water Units: 
 
 1. The auxiliary heater is sized adequately to maintain 
 comfort conditions 
 
 2. The auxiliary DHW system is adequate 
 
 Solar System: 
 
 1. Leak tests have been performed 
 
 2. Freeze protection is adequate 
 
 3. Adequate isolation valves have been installed 
 
 4. There is adequate drainage when components are 
 installed and dismantled 
 
 5. There is generally adequate protection from scalding 
 temperatures 
 
 6. Catchments are provided for boil-out and overflow 
 
 of toxic materials 
 
 7. Water hammer arresters are adequate 
 
 8. Air bleeds and vent valves are adequate 
 
 9. Vents, chimneys and ventilation are adequate 
 
 10. Performance estimates are available 
 
 Exception Notes 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 16 
 
 FUNDAMENTALS OF SOLAR COOLING 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
16-i 
 
 TABLE OF CONTENTS 
 
 
 Page 
 
 LIST OF FIGURES 
 
 16- ii 
 
 GLOSSARY OF TERMS 
 
 16-iii 
 
 OBJECTIVE 
 
 16-1 
 
 INTRODUCTION 
 
 16-1 
 
 CATEGORIES OF SPACE COOLING METHODS 
 
 16-1 
 
 DEFINITION OF TERMS 
 
 16-2 
 
 REFRIGERATION SYSTEMS 
 
 16-3 
 
 ABSORPTION REFRIGERATION 
 
 16-5 
 
 Temperature Restrictions .... 
 
 16-6 
 
 Types of Li thium-Bromi de-Absorption 
 Refrigeration Systems .... 
 
 16-7 
 
 SOLAR RANKINE-CYCLE ENGINE .... 
 
 16-8 
 
 HEAT PUMP 
 
 16-10 
 
 EVAPORATIVE COOLING 
 
 16-10 
 
 EVAPORATIVE COOLING THROUGH ROCK BED 
 
 16-10 
 
 EVAPORATIVE COOLING WITH ROOF PONDS AND SPRAYS 
 
 16-11 
 
 DESICCANT COOLING (DEHUMIDIFICATION) 
 
 16-13 
 
 TRIETHYLENE GLYCOL OPEN-CYCLE DESICCANT 
 
 
 SYSTEM 
 
 16-13 
 
 SOLID DESICCANT SYSTEMS 
 
 16-15 
 
 REFRIGERATION COOLING WITH ROCK BED OR WATER STORAGE 
 
 16-15 
 
 REFERENCES 
 
 16-18 
 
16- ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 16-1 Vapor-Compression Air-Conditioner Schematic . 16-4 
 
 16-2 Absorption Air-Conditioner or Chiller — 
 
 Schematic Drawing ...... 16-5 
 
 16-3 Rankine-Cycle Vapor-Compression System . . 16-9 
 
 16-4 Evaporative Cooling with Rock-Bed Storage . 16-12 
 
 16-5 Schematic of Triethylene Glycol (Liquid 
 Desiccant) Open-Cycle Air-Conditioning 
 System . 16-14 
 
 16-6 Solid Desiccant Dehumidification and Cooling 
 
 System ("MEC" System) . . . . . 16-16 
 
16-iii 
 
 GLOSSARY OF TERMS 
 
 absorbent 
 
 A liquid in which a refrigerant can be dissolved or 
 combined 
 
 coefficient 
 of performance 
 
 refrigerant 
 
 ton of 
 refrigeration 
 
 Ratio of heat removal rate (cooling rate) to energy 
 supply rate 
 
 Working fluid in a refrigeration system 
 
 Heat removal at a rate of 12,000 Btu per hour 
 

16-1 
 
 OBJECTIVE 
 
 The objective of this module is to develop understanding of the 
 principles of solar space cooling systems. In order to test whether 
 this objective is met by the trainee, as a minimum level of accomplish- 
 ment, the trainee should be able to: 
 
 1. List the different solar cooling methods and 
 
 2. Describe the operation of solar cooling systems. 
 
 INTRODUCTION 
 
 The withdrawal of heat from the air within a building enclosure 
 which results in a temperature or humidity lower than that of the 
 natural surroundings is termed space cooling or air-conditioning. 
 Cooling methods powered by solar energy are of particular interest in 
 this module. 
 
 CATEGORIES OF SPACE COOLING METHODS 
 
 There are three categories of space cooling methods for residential 
 buildings. They are: 
 
 1. Refrigeration 
 
 2. Evaporative cooling 
 
 3. Desiccant cooling (dehumidification). 
 
 Solar energy may be used as the principal energy supply in some 
 refrigeration systems and in desiccant cooling cycles. Evaporative 
 cooling is only indirectly related to solar in being dependent on 
 
16-2 
 
 climatic factors and in the opportunity for joint use of some of the 
 solar heating equipment. The discussion in this module concerns prin- 
 cipally refrigeration methods. Evaporative and desiccant cooling are 
 also briefly mentioned. 
 
 DEFINITION OF TERMS 
 
 The capacity of a refrigeration machine to cool room air is 
 customarily measured in tons of refrigeration . A ton of refrigeration 
 is the removal of heat at a rate of 12,000 Btu per hour. Another often- 
 used term in connection with refrigeration equipment is coefficient of 
 performance, COP. The COP expresses the effectiveness of a refrigera- 
 tion cooling system as the useful refrigeration effect divided by the 
 net energy supplied to the machine. COP is determined by the simple 
 
 equation below: 
 
 CO p _ Heat energy removed 
 
 Energy supplied from external sources 
 
 The COP of a mechanical vapor-compression refrigeration machine is 
 
 characteristically about two and can be as high as four. The COP of a 
 
 lithium-bromide-water absorption refrigeration machine is about 0.8 and 
 
 more often operates in the range from 0.6 to 0.7. A COP less than 1.0 
 
 means there is more energy supplied to the machine than heat energy 
 
 removed from the room air. From the cooling capacity and COP, the 
 
 energy consumed by the machine to produce the cooling effect can be 
 
 determined by dividing the heat removal rate by the COP. For example, 
 
 with a 3- ton absorption air chiller having a heat removal rate of 36,000 
 
 Btu per hour and a COP of 0.6, the rate of heat supply to the generator 
 
 is 60,000 Btu per hour (36,000 + 0.6). 
 
16-3 
 
 REFRIGERATION SYSTEMS 
 
 Cooling is achieved in refrigeration systems by removing heat from 
 air or water as it comes in contact with a cold refrigerated surface. 
 That surface is maintained at its low temperature by evaporating a 
 liquid refrigerant at a still lower temperature from the opposite side 
 or face of the surface. Heat absorbed by the evaporating refrigerant is 
 supplied by the air or water being cooled. The most common method for 
 providing the energy necessary for this process is by an electrically 
 powered compressor which raises the pressure of the refrigerant vapor so 
 that it can be condensed to a liquid for subsequent evaporation at lower 
 pressure and temperature as shown in Figure 16-1. 
 
 Conventional vapor-compression refrigeration systems powered by 
 electric motors can be driven by electricity produced in a solar engine 
 of some type, or the compressor can be powered directly by the solar 
 engine, without electricity generation. A system of this type is de- 
 scribed below. 
 
 Another process for supplying refrigerant to a surface through 
 which heat is transferred from air or water being cooled involves the 
 heating of a mixture of refrigerant and an absorbing liquid. The re- 
 frigerant is condensed and evaporated as in the vapor-compression sys- 
 tem, then reabsorbed and returned to the generator where it is again 
 vaporized by heat from fuel. These absorption refrigeration systems may 
 be modified for solar heat supply. Further details are shown in Figure 
 16-2 and in the following sub-section. 
 
 Of the two principal types of commercially available refrigeration 
 units, only the absorption type is driven by solar energy to an appre- 
 ciable extent. Among several types of experimental and commercial 
 
16-4 
 
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 PRESSURE- 
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 ^ 
 
 Air 
 
 to Rooms 
 
 55° 
 
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 if" Low Pressure Refrigerant, 
 Liquid and Vapor, 40° F 
 
 ^ 
 
 CONDENSER 
 
 - — Liquid Refrigerant, 100° F 
 
 Atmosphere 
 
 High Pressure Refrigerant Vapor, I20°F 
 
 Figure 16-1. Vapor-Compression Air-Conditioner Schematic 
 
16-5 
 
 RETURN TO 
 COOLING TOWER 
 
 MM 
 
 WARM AIR 
 OR WATER 
 
 PUMP 
 
 COOLING TOWER WATER 
 
 Figure 16-2. Absorption Air-Conditioner or Chiller -- Schematic Drawing 
 
 absorption machines, the lithium-bromide-water unit is currently (1980) 
 the only one commercially available for residential space cooling by use 
 of solar energy supply. 
 
 ABSORPTION REFRIGERATION 
 
 An absorption refrigeration machine uses heat energy to provide 
 cooling. When a liquid mixture of refrigerant and absorbent is heated, 
 the refrigerant is vaporized from the solution. Refrigerant vapor flows 
 from the generator through a condenser, expansion valve, and evaporator, 
 then into an absorber, where it recombines with the absorbent. In a 
 lithium-bromide-water absorption machine, water is the refrigerant and a 
 lithium-bromide solution is the absorbent. An absorbent is a liquid 
 
16-6 
 
 which combines with or dissolves the refrigerant at low temperatures but 
 will release the refrigerant when heated to higher temperatures. As the 
 refrigerant is absorbed, heat is generated and must be removed by a 
 cooling medium of some type, usually water. 
 
 Operation of a lithium-bromide absorption cycle is explained with 
 the aid of Figure 16-2. Water vapor refrigerant is boiled from the 
 liquid solution in the generator by providing solar heated water to the 
 generator at temperatures between 160°F and 210°F. Vapor leaving the 
 generator enters the condenser, where it is cooled to about 100°F and 
 condensed to liquid by cooling water from an outdoor cooling tower. The 
 condensate passes through a pressure-reducing valve or restrictor into 
 the evaporator (chiller) coil where it cools to about 40°F and vaporizes 
 by absorbing heat from the air or water being chilled. Vaporized re- 
 frigerant then passes to the absorber where it meets concentrated 
 lithium-bromide solution from the generator at a temperature of about 
 100°F. In this absorption process, heat is released and removed by 
 cooling water from the cooling tower. The lithium-bromide solution is 
 returned from the absorber to the generator via a heat exchanger, by a 
 pump or by gravity. The recouperator in the diagram is a heat exchanger 
 which pre-heats the dilute solution as it flows from the absorber to the 
 generator and at the same time cools the hot concentrated solution which 
 flows from the generator to the absorber. 
 
 Temperature Restrictions 
 
 The temperature of the hot water supplied to the generator of a 
 solar-operated lithium-bromide absorption refrigeration machine is 
 usually between 160°F and 210°F. The heat input rate to the generator 
 
16-7 
 
 must be sufficiently high to boil the refrigerant (water) from the 
 solution. If the supply temperature is below 160°F, the heat transfer 
 rate diminishes to a point too low for satisfactory operation. Low 
 temperature in the recouperator can result in crystallization of 
 lithium-bromide in the outlet tube leading from the recouperator to the 
 absorber, eventually extending to the generator as water continues to be 
 boiled off and the concentration of lithium-bromide increases. If the 
 supply temperature is appreciably above 210°F, the heat transfer rate 
 diminishes to a point too low for satisfactory operation (not usually 
 possible because of temperature limitations in the solar collector and 
 storage tank). 
 
 Cooling water temperature is dependent on atmospheric temperature 
 and humidity and is generally a few degrees above the wet-bulb tempera- 
 ture. Design cooling water temperature is normally 80°F, but consider- 
 able variation is common. 
 
 Types of Lithium-Bromide-Absorption Refrigeration Systems 
 
 There are two types of lithium-bromide-water absorption 
 refrigeration systems. In the direct expansion tube, air is circulated 
 from the building to the evaporator coil, where cooling and dehumidifi- 
 cation occur. In the chiller type, water is cooled by circulation 
 through the coil. The chilled water is then pumped through a separate 
 fan-coil unit through which room air is circulated. Chilled water may 
 also be stored in one or two tanks coupled both to the chiller and the 
 water-to-air fan-coil, thereby reducing fluctuations and intermittent 
 chiller operation. 
 
16-8 
 
 Figure 16-2 shows a mechanical pump for return of liquid from 
 absorber to generator. This design is used in a commercial 3-ton 
 chiller. A direct expansion 3-ton air-conditioner has employed a 
 bubble-pump (similar to a coffee percolator tube) to lift the boiling 
 solution from the generator to a vapor-liquid separator, so that the 
 height change provides the pressure difference between generator- 
 condenser on the high pressure side and evaporator-absorber on the 
 low-pressure side. 
 
 SOLAR RANKINE-CYCLE ENGINE 
 
 Instead of driving the compressor of a vapor-compression 
 refrigeration machine with an electric motor, an alternative source of 
 power for the compressor is a solar-powered engine. Solar heat can be 
 used to produce steam or other vapor to drive a turbine. The turbine 
 may be coupled directly to the compressor of a refrigeration machine, as 
 shown in a schematic drawing of a simplified system in Figure 16-3, or 
 an electric generator and motor set may be used to couple the two sys- 
 tems. 
 
 Heat is supplied to a boiler from a solar collector. Fluid in the 
 boiler is vaporized and the vapor drives the rotor of the turbine. The 
 rotating shaft then drives a compressor in a vapor-compression refriger- 
 ation machine which produces the desired cooling effect. Vapor from the 
 turbine is condensed and returned to the boiler. The regenerator is a 
 heat exchanger to recover some of the heat from the vapor leaving the 
 turbine. Working fluids include water (steam), several types of fluor- 
 carbons, chlorinated hydrocarbons, and others. This machine is still in 
 
16-9 
 
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16-10 
 
 experimental and developmental stages and not yet available as a 
 commerical unit. If it becomes commercial, it is probable that this 
 system would be more practical in large sizes (at least 25 tons) than in 
 residential capacities. 
 
 HEAT PUMP 
 
 A heat pump can be used both for heating and for cooling. As a 
 cooling unit, it is essentially a vapor-compression refrigerator which 
 absorbs heat from inside a building and rejects it to the outside air. 
 It is driven by an electric motor, normally supplied with commercial 
 electricity from central station power plants. The principles of 
 operation are described in Module 7. 
 
 EVAPORATIVE COOLING 
 
 EVAPORATIVE COOLING THROUGH ROCK BED 
 
 Air may be cooled by evaporation of water under conditions such 
 that heat for vaporization is supplied by the air. The so-called swamp 
 cooler employs this principle. As an example, ambient air at 100°F 
 dry-bulb temperature and 70°F wet-bulb temperature (relative humidity 22 
 percent) can be evaporatively cooled by water sprays to about 77°F. 
 However, the relative humidity would rise to an uncomfortable 71 
 percent. 
 
 It is evident that evaporative cooling does not require solar 
 energy, so it is not a solar cooling process. However, because the rock 
 bed in an air-heating solar system can be used for heat transfer and 
 cool storage in an evaporative cooling system, this method is sometimes 
 associated with solar cooling. 
 
16-11 
 
 An evaporative cooler coupled with a rock-bed storage unit is shown 
 in Figure 16-4. Night air is evaporatively cooled and circulated 
 through the rock bed to cool the pebbles. During the day, warm air from 
 the building can then be cooled by circulation through the cool pebble 
 bed. Humidity supplied to the night air is thus not introduced to the 
 living space. Dampers are positioned to direct the circulation of air 
 appropriately. When cool air can no longer be delivered from the rock 
 bed, outdoor air may be evaporatively cooled directly and delivered to 
 the rooms. Evaporative cooling is practical only in fairly dry climates 
 where relative humidities and night temperatures are normally low. 
 
 EVAPORATIVE COOLING WITH ROOF PONDS AND SPRAYS 
 
 There are two solar houses, one in California and the other in 
 Arizona, that utilize evaporative cooling and night-time radiation to 
 reduce day-time temperature rise in those structures. Each building has 
 a shallow water pond on a flat roof with sectional i zed retracting in- 
 sulating covers over the pond. By retracting the covers at night, the 
 water cools by evaporation and radiation to the sky. The covers are 
 closed during the day to prevent solar heating of the pond. Heat is 
 absorbed in the water by conduction through the ceiling of the rooms 
 immediately below. 
 
 During the mild winters in these locations, the shallow ponds are 
 used for space heating. The insulating covers are retracted during 
 sunny days to collect solar heat in the pond and closed at night to 
 prevent excessive heat loss. The stored heat is conducted through the 
 metal roof (ceiling) for radiation into the living space below. In 
 
16-12 
 
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16-13 
 
 climates where heating and cooling demands are low, this design may be 
 of interest. 
 
 Roof ponds or sprays are also frequently used in commercial and 
 industrial buildings simply to reduce excessive roof-top temperatures 
 resulting from solar absorption on large area flat roofs. The exposed 
 roof is continuously sprayed or flooded with water so that evaporation 
 can minimize roof-surface temperature. Solar cooling is not involved. 
 
 DESICCANT COOLING (DEHUMIDIFICATION) 
 
 TRIETHYLENE GLYCOL OPEN-CYCLE DESICCANT SYSTEM 
 
 In locations where humidities are high, evaporative cooling can be 
 accomplished if the air is first dehumidified by some means. One system 
 commercially used for air dehumidification is shown schematically in 
 Figure 16-5. Moist room air is dehumidified by contacting it with a 
 solution of triethylene glycol in which moisture is absorbed. The 
 dehumidified air then passes through mist eliminators and then through 
 an evaporative cooler where its temperature is reduced to a comfortable 
 level. The liquid desiccant passing through the absorber picks up 
 moisture from the building air and becomes diluted. Solar heat may be 
 used to regenerate the dilute triethylene glycol solution which is 
 returned to the absorber and recycled. Regeneration is accomplished by 
 spraying the glycol solution into a stream of solar heated air in which 
 moisture evaporated from the glycol solution is exhausted to the 
 atmosphere. If there is insufficient solar heat, an auxiliary heater 
 may be used to heat the air stream. Heat is recovered from the glycol 
 
16-14 
 
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16-15 
 
 solution leaving the stripping column by heat exchange with solution 
 leaving the absorber. 
 
 The system may be operated over a substantial range of air 
 temperatures, but the higher temperatures, in the area of 180°F, result 
 in superior system performance and higher COP's. 
 
 A liquid desiccant open-cycle system in large sizes, using 
 conventional heat sources, is commercially available, but solar opera- 
 tion has been only in limited experiments. This type of system has not 
 been actively considered for residential space cooling systems. 
 
 SOLID DESICCANT SYSTEMS 
 
 Another method for dehumidifying air in preparation for evaporative 
 cooling involves use of solid adsorbents which can be regenerated by 
 heat. Silica gel granules, lithium chloride and calcium chloride 
 crystals, and "molecular sieve" zeolite granules are all commercially 
 used in air-drying applications. Figure 16-6 shows how one of these 
 processes can be adapted to regeneration with solar heat. A combination 
 of dehumidification, air-to-air heat supply from solar and fuel can 
 provide air-conditioning. This and other cycles, employing solar heated 
 water and solar heated air for regeneration, have been experimentally 
 investigated, but no commercial units are available. 
 
 REFRIGERATION COOLING WITH ROCK BED OR WATER STORAGE 
 
 Another cooling process that is not powered by solar energy, but is 
 aided by the solar storage normally used for space heating, employs 
 conventional cooling machines. A heat pump or vapor-compression 
 
16-16 
 
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16-17 
 
 air-conditioner supplies cool air to the storage unit during periods of 
 low electric demand. Off-peak pricing permits lower cost air- 
 conditioning by this night-time cooling of storage which then supplies 
 cool air to the building by heat exchange during the daylight hours when 
 power rates are usually higher. Water tanks may be used, with suitable 
 heat exchangers, or pebble beds can be operated as direct air coolers. 
 The possibility of moisture condensation and odor generation in a pebble 
 bed used as cold storage must, however, be considered and avoided. 
 
16-18 
 
 REFERENCES 
 
 1. American Society of Heating, Refrigeration, and Air Conditioning 
 Engineers, ASHRAE Handbook of Fundamentals, ASHRAE, Inc., New York, 
 1972. 
 
 2. Barber, R.E., "Solar Air Conditioning Systems Using Rankine Power 
 Cycles - Design and Test Results of Prototype Three-Ton Unit", 
 Proceedings, Institute of Environmental Sciences Annual Meeting, 
 Los Angeles, California, April 1975. 
 
 3. Bliss, R.W. , Jr., "The Performance of an Experimental System Using 
 Proceedings, United Nations Conference on New Sources of Energy, 
 Volume 5, pp. 148-158, Rome, 1964. 
 
 4. Chung, R. , Duffie, J. A., and Lof, G.O.G., "A Study of a Solar Air 
 Conditioner", Mechanical Engineering, Volume 85, Number 8, pp. 
 31-35, August 1963. 
 
 5. Close, D.J., et. al., "Design and Performance of a Thermal Storage 
 Air Conditioning System", Institute of Engineering Australia - 
 Mechanical and Chemical Engineering Transcriptions, Volume MC 4, 
 Number 1, pp. 45-54, May 1968. 
 
 6. Duffie, J. A. and Beckman, W.A. , Solar Energy Thermal Processes, J. 
 Wiley and Sons, Inc., New York, 1974. 
 
 7. Hay, H.R. , and Yellott, J. I., "A Naturally Air-Conditioned 
 Building", Mechanical Engineering, Volume 92, pp. 19-25, January 
 1970. 
 
 8. Johnston, R.C.R., "Regenerative Evaporative Air Conditioning with 
 Dehumidifi cation" , AIRAH Transactions, Volume 21, Number 2, pp. 
 29-34. February 1967. 
 
 9. Threlkeld, J.L. , Thermal Environmental Engineering, Second Edition, 
 Prentice-Hall, Inc., New Jersey, 1970. 
 
 10. Ward, D.S., Weiss, T.A. , and Lof, G.O.G., "Preliminary Performance 
 of CSU Solar House I Heating and Cooling System", International 
 Solar Energy Society Congress and Exposition, Los Angeles, 
 California, July 1975. 
 
 11. Wilbur, P.J. and Mitchell, C.E., "Solar Absorption Air Conditioning 
 Alternatives," Solar Energy, Vol. 17, pp. 193-199, 1975. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 DESIGN OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 17 
 
 FUTURE PROSPECTS FOR SOLAR HEATING 
 AND COOLING SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
17-i 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 
 INTRODUCTION . 
 
 OBJECTIVE 
 
 SOLAR COLLECTORS 
 
 SELECTIVE SURFACES . 
 EVACUATED TUBE COLLECTORS 
 TRANSPARENT HONEYCOMBS 
 CONCENTRATING COLLECTORS . 
 
 THERMAL STORAGE 
 
 HEAT EXCHANGER . 
 
 SYSTEMS 
 
 Page 
 
 17- 
 
 ■ii 
 
 17- 
 
 ■ii 
 
 17- 
 
 ■1 
 
 17- 
 
 ■2 
 
 17- 
 
 ■2 
 
 17- 
 
 ■2 
 
 17- 
 
 ■4 
 
 17- 
 
 ■6 
 
 17- 
 
 ■8 
 
 17- 
 
 ■8 
 
 17- 
 
 ■12 
 
 17- 
 
 ■13 
 
17-ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 17-1 Types of Evacuated Tube Collectors .... 17-5 
 
 17-2 Transparent Honeycomb Collector .... 17-7 
 
 17-3 Direct Contact, Li quid- Li quid Heat Exchanger . . 17-13 
 
 LIST OF TABLES 
 
 Table Page 
 
 17-1 Selective Surfaces Characteristics .... 17-3 
 
 17-2 Properties of Phase-Change Heat Storage Materials . 17-10 
 
 17-3 Properties of Possible Collector Fluids . . . 17-14 
 
17-1 
 
 INTRODUCTION 
 
 The solar systems described in this manual are examples of 
 thousands that have been installed in the last three years. Performance 
 data, mainly from well -instrumented systems, indicate that they can 
 function satisfactorily in residential buildings. Air and liquids 
 heated by solar energy in flat-plate collectors provide temperatures 
 suitable for space heating, hot water supply, and cooling by absorption 
 refrigeration. Although heat delivery efficiencies of the various 
 systems differ between them, and fluctuate with climatic conditions, 
 they should average about 30 percent of the solar radiation received. 
 If this average can be improved by better components at equal or lower 
 cost, the improvements are worthwhile. 
 
 A number of new features and components of systems are being 
 investigated, and several might provide substantial improvement in 
 system performance. Flat-plate collectors can be improved with selec- 
 tive coatings or redesigned to produce higher heat collection efficien- 
 cies. Evacuated collectors are inherently more efficient than conven- 
 tional types, and developments which could reduce their cost can have 
 important effects on commercial use. Heat storage in phase-change 
 materials could reduce the space required for the solar heating system, 
 and heat collection and storage by use of two immiscible liquids may 
 result in system simplification and improved performance. If cooling 
 equipment using solar-heated air can be developed, air-heating solar 
 systems could be used throughout the year for heating and cooling. 
 These and other developments may become important in the solar heating 
 and cooling of buildings. 
 
17-2 
 
 OBJECTIVE 
 
 This module contains descriptions of new concepts and developments 
 in solar heating and cooling systems that could improve overall perfor- 
 mance and economy. Its objective is to provide the trainee a basis for 
 anticipating future developments and improvements in the systems de- 
 scribed in this course and to recognize the research and development 
 effort being devoted to component hardware in solar heating and cooling 
 systems. 
 
 SOLAR COLLECTORS 
 
 The component which has the greatest influence on system 
 performance and cost is the solar collector. Improvements in the col- 
 lector which will increase its efficiency and reduce its cost can be 
 particularly important. Among numerous possibilities are durable selec- 
 tive surfaces on absorbers, transparent honeycomb structures between 
 absorbers and glazings, evacuated spaces between absorber surfaces and 
 the glazings, and lower cost materials and assembly methods. 
 
 SELECTIVE SURFACES 
 
 Selective surfaces have high absorptance for solar radiation and 
 low emittance for long-wave radiation. Substitution of such materials 
 for non-selective black paints commonly used can increase solar collec- 
 tion more than the cost difference, therby improving cost effectiveness 
 of the collectors. Although already used in numerous commercially 
 produced collectors, further improvements in optical properties and 
 
17-3 
 
 durability, and reduction in cost, should be possible. Several 
 selective coatings such as copper oxide on copper and black nickel on 
 galvanized steel have been extensively used on solar water heaters in 
 Australia and Israel, but performance and durability have not been 
 completely satisfactory. Black chrome (electro-deposited chromium oxide 
 on nickel-plated steel or copper) is the most widely used selective 
 coating in the United States. Cost reduction could have an important 
 influence on the future market for solar heating systems. It can be 
 expected that virtually all commercial collectors for space heating and 
 hot water supply will be provided with selective absorber coatings in 
 the near future. 
 
 The radiation properties of several selective surfaces are listed 
 in Table 17-1. 
 
 Table 17-1 
 Selective Surfaces Characteristics 
 
 Coating 
 
 Absorptance for 
 
 Emittance for 
 
 
 Solar Radiation 
 
 Thermal Radiation 
 at 200°F 
 
 Chemically Oxidized Copper 
 
 0.90 
 
 0.15 
 
 Converted Zinc 
 
 0.90 
 
 0.071 
 
 Black Nickel 
 
 0.88 
 
 0.066 
 
 Black Chrome 
 
 0.92 
 
 0.085 
 
 Black Anodized Aluminum 
 
 0.93 
 
 0.07 
 
 Chemically Oxidized 
 
 
 
 Stainless Steel 
 
 0.95 
 
 0.10 
 
17-4 
 
 EVACUATED TUBE COLLECTORS 
 
 Removal of nearly all of the air in the space between the absorber 
 and the glazing results in greatly reduced heat loss and a substantial 
 efficiency improvement in solar collectors. There are a number of 
 different designs that are being assembled and tested, and at least 
 three manufacturers produce them in moderate quantities. Evacuated 
 collectors produce more useful heat than equal areas of standard flat- 
 plate collectors under the same sun and weather conditions, because heat 
 conduction and convection through the evacuated space are negligible 
 and, if the absorber coating is a selective surface, the radiation loss 
 is small. Most flat-plate collectors have high efficiency with low 
 inlet fluid temperatures, but have low efficiencies when the fluid 
 temperature is near 200°F. The evacuated tube collector has a signifi- 
 cant advantage when producing high temperature heat and can be used 
 effectively with solar cooling units which require hot water at tempera- 
 tures near 200°F. 
 
 Several types of evacuated tube collectors are shown in Figure 
 17-1. Types A, B, and C are being produced on a semi-commercial scale 
 and are being used in numerous demonstration heating and cooling instal- 
 lations, primarily in the United States and Japan. Types D and E are 
 experimental evacuated tube collectors which have been tested in a few 
 systems. In each design, a selective absorber surface is in an evacu- 
 ated space. Types A, B, and E involve cylindrical-shaped absorber 
 surfaces deposited on interior glass surfaces, while flat metal absorber 
 surfaces are used in Types C and D. Double-walled glass tubes (Dewar 
 flasks) are used in Types A and B, single tubes are used in C and D, and 
 
17-5 
 
 GLASS ENVELOPE, ^VACUUM 
 
 HEAT 
 
 TRANSFER 
 FLUID OUT 
 
 GLASS DELIVERY TUBE 
 
 .TM 
 
 (a) Owens-Illinois Sunpak Double -Walled Evacuated Collector Tube. 
 
 METAL HEAT- 
 TRANSFER I 
 
 -VACUUM 
 
 HEAT TRANSFER FLUID 
 
 (b) General Electric TC-IOO Solartron Double-Walled Evacuated 
 Collector Tube. 
 
 EVACUATING TUBE 
 
 END CAP* 
 
 COLLECTOR TUBE 
 
 (c) Sanyo Single-Walled Evacuated Collector Tube with Unidirectional 
 Flow. 
 
 PYREX GLASS TUBE 
 
 U-SHAPED 
 COPPER TUBE 
 
 (d) Corning Single-Walled Evacuated Collector Tube. 
 
 (e) Philips Mark IV Evacuated Collector Tube (Section) with Flat 
 Glass Cover. 
 
 Figure 17-1. Types of Evacuated Tube Collectors 
 
17-6 
 
 single tubes with flat glass covers are used in E. In all designs 
 except C, the fluid enters and leaves the tube at the same end, and in 
 all designs except A, the fluid conduits are metal tubes (usually 
 copper). In type A, the fluid is in contact only with glass, and in 
 type E, the fluid flows in passages outside the glass tubes. Types A, 
 B, and E, with minor modifications, may be used for air heating as well 
 as water heating. 
 
 Collection efficiencies, based on solar radiation received by the 
 sloping surface within the perimeter of the entire collector array, 
 including space between tubes, are typically about 70 percent at temper- 
 atures for space heating (120°F to 150°F) and about 55 to 60 percent at 
 the higher (200°F) temperatures required by lithium chloride absorption 
 chillers. These efficiencies are substantially higher than good flat- 
 plate collectors, particularly for cooling. Whether the superior effi- 
 ciency justifies their higher current cost is doubtful, but the possi- 
 bilities for manufacturing economies by automated production in large 
 volume sustain commercial interest in this technology. 
 
 TRANSPARENT HONEYCOMBS 
 
 Heat loss from a flat-plate collector can be reduced by subdividing 
 the air space between the absorber plate and the cover glass into small 
 cells by use of a transparent "egg crate" or "honeycomb" structure. 
 Convection movement of air in these small (one-quarter-inch or less) 
 cells is substantially reduced, and thermal radiation from the absorber 
 to the cover is also partially intercepted and suppressed. The trans- 
 parent walls of these cells, however, permit the passage of solar 
 
17-7 
 
 GLASS COVER 
 
 STEEL FRAME 
 
 PIPING 
 CONNECTION 
 
 TRANSPARENT 
 HONEYCOMB 
 
 ABSORBER PLATE 
 
 FIBER GLASS 
 INSULATION 
 
 Figure 17-2. Transparent Honeycomb Collector 
 
 radiation with very little loss, even when obliquely intercepting the 
 rays of the sun. The result of this design addition is increased solar 
 collection efficiency. The principal problem in the use of this concept 
 is achievement of sufficient durability of an economical material. Most 
 transparent plastics cannot withstand the temperatures occasionally 
 encountered when the fluid flow through the absorber is interrupted, 
 melting or other type of failure then being probable. Thin glass honey- 
 combs, as for example by use of a panel of side-by-side thin-walled 
 glass tube sections, have been too costly for practical application. 
 The future prospects for this concept appear to rest on the possibility 
 for developing economical plastic materials and honeycomb structures 
 
17-8 
 
 capable of withstanding the temperatures encountered in efficient solar 
 collectors. If such materials are developed, honeycomb flat-plate 
 collectors appear to have good prospects for practical use. 
 
 CONCENTRATING COLLECTORS 
 
 Concentrating collectors are being experimentally used when very 
 high temperature fluid is needed to drive heat engines or for industrial 
 process heat. If concentrating collectors can be designed to be less 
 costly or more efficient than flat-plate collectors, to operate reli- 
 ably, and to require little maintenance, such collectors also have 
 potential use in space heating systems. Experience thus far has indi- 
 cated otherwise, but there is considerable research underway and new 
 designs for concentrating collectors are being developed. There has 
 been experimental use of a sun-tracking linear focusing collector with a 
 plastic Fresnel lens, and arrays of evacuated tubes with trough-shaped 
 reflectors filling the spaces between tubes have been advertised for 
 sale. Their costs are not competitive with flat-plate collectors in 
 space heating applications nor with evacuated tube collectors (without 
 concentration) for cooling applications. 
 
 THERMAL STORAGE 
 
 Future developments in the selection and application of materials 
 in which heat can be stored by melting or other phase-change process may 
 result in reduction in heat storage volume requirements. Hydrated 
 
17-9 
 
 salts such as sodium sulphate decahydrate (Glauber's salt) and hydrated 
 calcium chloride have been experimentally used, eutectic mixtures of two 
 or more salts (having single melting points) have also been investi- 
 gated, and several types of waxes have been evaluated. Table 17-2 
 contains a list of materials which have been used as phase-change heat 
 storage media. 
 
 The potential advantage of this type of heat storage material is 
 the smaller weight and volume required, compared with water and pebbles, 
 for storage of an equal amount of energy. A second advantage, in some 
 systems, is the storage of most of the energy at a constant temperature, 
 i.e., the melting point of the material. Where volume limitations are 
 very severe, phase-change thermal storage may become economically 
 practical . 
 
 There are a number of disadvantages, however, in the use of these 
 heat storage media. The need for transferring heat into and out of the 
 solid and liquid compounds usually requires their containment in small 
 elements, an inch or two in cross-section. Space between the elements 
 must be provided for circulation of air or water from the solar collec- 
 tor and from the space being heated. Container cost and durability and 
 the added volume of the free space in the storage bin or tank impose 
 design and cost limitations. 
 
 A second disadvantage in most of the phase-change materials 
 developed for solar space heating is their relatively low melting 
 temperature. Although higher collector efficiency is obtained at low 
 temperature, most space heating systems cannot advantageously use water 
 
17-10 
 
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17-11 
 
 or air at the low temperature levels of 90°F to 100°F. Considerably 
 larger heat exchange surfaces or much higher air circulation rates in 
 warm air systems would have to be used. 
 
 Some of the phase-change materials, particularly the hydrated 
 salts, on repeated melting and solidifying may permanently separate into 
 liquid and solid portions, thereby defeating the phase-change heat 
 storage capability. And in air systems, the relatively constant temper- 
 ature of the heat stored is a disadvantage rather than an advantage, 
 because the highly beneficial temperature stratification such as that 
 occurring in pebble beds cannot be achieved. 
 
 The overriding consideration in heat storage selection is cost, and 
 the presently suggested materials all are much more expensive, in as- 
 sembled heat storage units, than tanks of water or bins of rocks. For 
 storing half a million Btu, installed costs of advertised phase-change 
 systems are two to five times as great as systems for sensible heat 
 storage in rock and water. 
 
 Future prospects for practical use of phase-change storage in space 
 heating systems depend on development of improved materials having 
 considerably lower cost, longer life, and transitions in the 120° to 
 160° temperature range. If such materials can be identified and de- 
 veloped, their application could enhance the capability and economy in 
 space heating systems. 
 
 An even more speculative possibility is the storage of solar heat 
 in chemical reactions which absorb energy in the reaction process. By 
 slight alteration in conditions such as the lowering of temperature or 
 pressure, the reaction will reverse so that the stored energy is liber- 
 ated as heat at a temperature near that at which solar collection 
 
17-12 
 
 previously took place. Although such chemical processes are known, none 
 is now a likely candidate for this application. Of particular advan- 
 tage, if such a system can be developed, is the storage of the energy in 
 materials which can be at room temperature. No heat losses or insulated 
 containers would need to be involved. The possibilities for successful 
 development of some such system do not appear promising at this time, 
 but new discoveries might alter this situation. 
 
 HEAT EXCHANGER 
 
 A disadvantage in most liquid- heating solar systems is the 
 temperature difference required for heat transfer to storage by means of 
 a heat exchanger. The collector must operate at a temperature 10°F to 
 20°F higher than if no heat exchanger were used, and heat collection 
 efficiency is therefore adversely affected. 
 
 Now under investigation is a heat exchanger-storage combination 
 unit in which heat is transferred from liquid droplets that transport 
 heat from the collector to water in the storage tank. A liquid that is 
 immiscible with water is pumped through the solar collector and through 
 the storage tank as droplets. If the density of the liquid is sub- 
 stantially different from that of water, the droplets will either rise 
 or descend through the water in the storage tank. A schematic diagram 
 of a heat exchanger-storage unit is shown in Figure 17-3. In this 
 design, the collector liquid is heavier than water. It is delivered to 
 the top of the tank, broken up into droplets at the perforated plate, 
 and collected in the bottom cone. Because of the very large total 
 surface areas of the droplets, the temperature difference between 
 
17-13 
 
 LIQUID 
 
 WATER SURFACE-* 
 
 HOT WATER 
 TO LOAD 
 
 COLD WATER 
 FROM LOAD 
 
 ^ 
 
 PUMP 
 
 TOP OF LIQUID 
 (SURFACE) 
 
 PERFORATED 
 PLATE 
 
 J«<WATER HEAT 
 STORAGE AND 
 LIQUID BUBBLES 
 
 CONICAL 
 BOTTOM 
 
 WATER LIQUID 
 
 INTERFACE 
 
 LIQUID 
 
 Figure 17-3. Direct Contact, Li quid- Li quid Heat Exchanger 
 
 them and the storage water is only about 1°F. Several liquids are 
 candidates for this service, but of those listed in Table 17-3, diethyl 
 phthalate is the only one that has received full-scale testing. 
 Assessment of the future prospects for direct contact, liquid-liquid 
 heat exchange-heat storage use depends on the results of further 
 development work and economic evaluation. 
 
 SYSTEMS 
 
 At present the only commercially available small (3-to^) cooling 
 unit that is operable with solar energy is a lithium-bromide absorption 
 chiller. As mentioned elsewhere in this manual, there are several other 
 solar cooling concepts under development, including heat engine-driven 
 
17-14 
 
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17-15 
 
 vapor-compression machines, absorption chillers with high temperature 
 heat supply from solar concentrators, and desiccant cycles with solar 
 regeneration of the drying agent. Significant effort is also being made 
 in the development of so-called total energy systems, in which high 
 temperature heat from solar energy is used to generate electricity and 
 the low temperature "waste" heat is used to heat and cool a cluster of 
 buildings. Such systems, if economically successful, would probably 
 best be used in grouped facilities such as military bases but, with some 
 variation, might serve a number of homes or apartment complexes. 
 
 In the long term, development of photovoltaic systems for 
 electricity supply to residential buildings is a possibility. Solar 
 electricity could then operate heating and cooling systems as well as 
 other electrical equipment in the building. Whether the cost of photo- 
 voltaic systems will ever be low enough to be competitive with electri- 
 city generated from fossil or nuclear fuels is an open question, but a 
 considerable amount of effort is being devoted to improve efficiency and 
 reduce the costs. 
 
 Other system improvements which should increase the use of solar 
 energy in buildings are hybrid designs consisting of passive as well as 
 active components. As quantitative information and operating results of 
 passive design techniques become available, superior designs can be 
 identified and their cost effectiveness measured. Greater use of direct 
 heating of residential space with passive systems may then decrease size 
 requirements of the active components and thereby reduce overall costs. 
 
 A U. S. GOVERNMENT PRINTING OFFICE : 1980 329-853/6631 
 
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