SOLAR HEATING AND COOLING 
 
 OF RESIDENTIAL BUILDINGS 
 
 SIZING, INSTALLATION 
 
 AND OPERATION 
 
 OF SYSTEMS 
 
 1980 EDITION 
 
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 ENERGY 
 iFFICIENOr 
 
 U.S. DEPARTMENT OF COMMERCE 
 Economic Development Administration 
 
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£**&,$>.■ So y/*./??a 
 
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 SOLAR HEATING AND COOLING 
 
 OF RESIDENTIAL BUILDINGS 
 
 SIZING, INSTALLATION 
 
 AND OPERATION 
 
 OF SYSTEMS 
 
 1980 EDITION 
 
 Prepared by 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 
 COLORADO STATE UNIVERSITY 
 
 Si S 
 
 
 U.S. Department of Commerce 
 Philip M. Klutznick, Secretary 
 
 Luther H. Hodges, Jr., Deputy Secretary 
 
 8 ' Robert T. Hall , Assistant Secretary 
 
 g, for Economic Development 
 
 1 
 
 & 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 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 
 technicians 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 contribute 
 substantially to the reduction of fuel imports, lead to increased 
 production of housing, and create opportunities for expanded employment. 
 
 (jU* 
 
 ^ b^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/solarheatingcoolOOunit 
 
PREFACE 
 
 This manual was prepared for use as a text for a training course on 
 solar heating and cooling of residential buildings. The content level 
 is appropriate for practitioners in the building industry and it is 
 assumed that participants have a basic understanding of conventional 
 heating systems. The course and text are directed toward sizing, 
 installation, operation, and maintenance of solar systems for space 
 heating and hot water supply, and solar cooling is treated only briefly. 
 
 The present manual is a revision of an earlier edition of the same 
 title, prepared in 1976 and printed by the U.S. Government Printing 
 Office in October 1977. This edition was initially planned only to 
 update the original manual, but as the task progressed, it became 
 evident that reorganization and rewriting were desirable. 
 
 As a text for training courses, the modular structure of this 
 manual allows flexibility in presentation. Within reasonable limits, 
 the modules may be presented in a different order from that arranged in 
 this text, and some modules may be deleted so that courses can be 
 shortened to fit a limited schedule. 
 
 The solar systems described in this manual are primarily for 
 residential applications and one- and two-story off ice- type buildings. 
 Although the types of solar systems described are appropriate for 
 various sizes of buildings, the reader should be advised that perform- 
 ance prediction procedures included in this manual may not be applicable 
 to large commercial and multi-story office buildings. 
 
 The training course curriculum and this manual for Sizing, 
 Installation, and Operation of Systems 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 
 various 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: 
 Dan S. Ward, Susumu Karaki , George 0. G. Ldf, Charles C. Smith, C. Byron 
 Winn, Milton E. Larson and Ivan E. Valentine. Michael Z. Lowenstein, 
 visiting professor from Adams State College, also assisted in preparing 
 the manual, as did Ralph J. Johnson and H. W. Anderson of the NAHB 
 Research Foundation. The present edition was revised and rewritten by 
 Susumu Karaki and George 0. G. Lof. 
 
 Development of the training course and preparation of the original 
 manual were made possible by a matching grant from the Economic 
 Development 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 ENERGY CONSERVATION IN RESIDENTIAL BUILDINGS 
 
 MODULE 3 INTRODUCTION TO PASSIVE DESIGNS 
 
 MODULE 4 INTRODUCTION TO LIQUID SYSTEMS 
 
 MODULE 5 INTRODUCTION TO AIR SYSTEMS 
 
 MODULE 6 SOLAR RADIATION 
 
 MODULE 7 SOLAR COLLECTORS 
 
 MODULE 8 COMPONENTS OF LIQUID SYSTEMS 
 
 MODULE 9 COMPONENTS OF AIR SYSTEMS 
 
 MODULE 10 DOMESTIC HOT WATER SYSTEMS 
 
 MODULE 11 INSTALLATION AND OPERATION OF LIQUID SOLAR HEATING SYSTEMS 
 
 MODULE 12 INSTALLATION AND OPERATION OF AIR SOLAR HEATING SYSTEMS 
 
 MODULE 13 HEATING LOAD CALCULATIONS 
 
 MODULE 14 SOLAR SYSTEM SIZING 
 
 MODULE 15 ECONOMIC CONSIDERATIONS 
 
 MODULE 16 OPERATIONAL CHECK-OUT 
 
 MODULE 17 INTRODUCTION TO SOLAR COOLING 
 
 MODULE 18 FUTURE PROSPECTS FOR SOLAR HEATING AND COOLING SYSTEMS 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION 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 
 
 SUGGESTED COURSE SCHEDULE 1-1 
 
 COURSE SYLLABUS 1-4 
 
1-1 
 
 OBJECTIVES 
 
 This training course is designed to develop the capability of each 
 trainee to size, install, operate and maintain solar heating and cooling 
 systems for residential and small office-type buildings. Specific 
 objectives of the course are to: 
 
 1. Develop fundamental knowledge of different types of solar 
 systems and their components. 
 
 2. Differentiate between experimental and proven systems. 
 
 3. Size solar systems for heating space and service water. 
 
 4. Calculate expected performance from a selected solar heating 
 system. 
 
 5. Recognize proper installation procedures. 
 
 6. Measure and evaluate system performance. 
 
 7. Identify maintenance items for different types of solar 
 systems. 
 
 SUGGESTED COURSE SCHEDULE 
 
 The Solar Energy Applications Laboratory at Colorado State 
 University prepared this manual to be used in conjunction with a 
 training course on the practical aspects of solar heating systems for 
 space and service water. In determining curriculum content, a rigorous 
 procedure was followed to develop course standards and needs by practi- 
 tioners in the home-building industry. From established standards and 
 needs, objectives for the course were developed and curricular materials 
 
1-2 
 
 were then prepared. Each module in this manual has specific objectives 
 for the trainees, and examinations may be given to determine levels of 
 achievement. 
 
 So that the order of 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 8 and 9, but they appear also in 
 the sections on heating systems (Modules 11 and 12). When 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 
 during five consecutive days, but a longer period of time may be 
 utilized if desired. A shorter training period will probably neces- 
 sitate deletion of some modules during the presentation. A course 
 arrangement suitable for a five-day program is shown on the following 
 page. The modules are presented in the order arranged in the manual 
 except that Module 16 is presented before Module 15 so that performance 
 data on actual systems may be obtained while operational checks are 
 being made. 
 
1-3 
 
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1-4 
 
 COURSE SYLLABUS 
 
 TOUR OF SOLAR HOUSES 
 
 A pre-course tour of solar houses in the local area is provided to 
 acquaint participants with different styles of homes and practical types 
 of solar systems. The tour is concluded with an informal reception and 
 dinner. After dinner, a brief overview of national solar energy 
 activities is presented. 
 
 MODULE 1 - COURSE OUTLINE 
 
 The purpose of this module is to present the course objectives and 
 to outline the sequence of events which follow. The contents of modules 
 are briefly discussed so that trainees are generally aware of the scope 
 of the training course. 
 
 MODULE 2 - ENERGY CONSERVATION IN RESIDENTIAL BUILDINGS 
 
 Energy conservation in buildings is fundamental and should be 
 applied whenever heating and cooling loads can be economically reduced. 
 The effects of building orientation, shape, external design and internal 
 arrangement as well as effects of landscaping are discussed. Proper 
 practices for installing insulation are described in the module. 
 
 MODULE 3 - INTRODUCTION TO PASSIVE DESIGNS 
 
 An overview of building designs to collect solar heat passively are 
 discussed in the module. It is a brief treatise on passive designs 
 which include direct, indirect and isolated gain types. References to 
 more complete works on passive designs are also provided. 
 
1-5 
 
 MODULE 4 - INTRODUCTION TO LIQUID SYSTEMS 
 
 Discussion of active solar heating systems is divided into liquid 
 and air types. Although there are many common features in the two types 
 of systems, comprehension by trainees is easier by separation. This 
 module is an introduction, and details of operation are discussed after 
 components of both types of systems are described. 
 
 MODULE 5 - INTRODUCTION TO AIR SYSTEMS 
 
 In a manner comparable to Module 4, principal features of air 
 systems are described. Details of operation are presented in Module 12. 
 
 MODULE 6 - SOLAR RADIATION 
 
 Knowledge of the nature of solar radiation, its distribution in 
 time and its variability with weather conditions are of fundamental 
 importance in the design of solar heating and cooling systems. 
 Explanations of atmospheric effects and hourly, daily, monthly and 
 seasonal variations are given. 
 
 MODULE 7 - SOLAR COLLECTORS 
 
 Design and operational characteristics of presently available 
 flat-plate collectors are described in this module. Features of good 
 collector design for both liquid and air types are described. Factors 
 which indicate the performance of solar collectors are explained. 
 
 MODULE 8 - COMPONENTS OF LIQUID SYSTEMS 
 
 In addition to solar collectors the important components of liquid- 
 type solar systems are thermal storage, controls, heat exchangers, 
 
1-6 
 
 and pumps. Installation and operational characteristics of these 
 components are described. 
 
 MODULE 9 - COMPONENTS OF AIR SYSTEMS 
 
 Storage, controls, blowers and ducts for air systems are described 
 in this module. The essential features of thermal energy transport 
 through pebble beds are explained, and basic control functions are 
 presented. 
 
 MODULE 10 - DOMESTIC HOT WATER SYSTEMS 
 
 Detailed descriptions of several types of solar water heaters are 
 presented in this module. Advantages and disadvantages of each are 
 explained, and sizing, installation, operation and maintenance features 
 are included. 
 
 MODULE 11 - INSTALLATION AND OPERATION OF LIQUID SOLAR HEATING SYSTEMS 
 
 Basic operation of liquid- type solar systems is described in 
 detail. Principles of assembly and control which lead to effective 
 system performance are explained. 
 
 MODULE 12 - INSTALLATION AND OPERATION OF AIR SOLAR HEATING SYSTEMS 
 
 Basic operation of air-type solar systems is described separately 
 from liquid-type systems. Principles of proper installation and control 
 of these types of systems are explained. 
 
1-7 
 
 MODULE 13 - HEATING LOAD CALCULATIONS 
 
 The thermal energy load of a building is needed to calculate the 
 expected contributions of solar thermal systems. A "short" method for 
 calculating building heat loss rate and heating load is described. 
 
 MODULE 14 - SOLAR SYSTEM SIZING 
 
 A simple procedure called the relative areas method is presented 
 for estimating the performance of solar heating systems. Rules are 
 given for sizing the system relative to collector area. Effects of 
 collector tilt and orientation on system performance are also shown. 
 
 MODULE 15 - ECONOMIC CONSIDERATIONS 
 
 Procedures for determining total life-cycle costs of solar and 
 conventional heating systems are presented. When the total life-cycle 
 cost of a solar system is less than the total life-cycle cost of a 
 conventional heating system, there is a total life-cycle cost saving and 
 the system is considered to be cost effective. 
 
 MODULE 16 - OPERATIONAL CHECK-OUT 
 
 Procedures for determining whether systems are operating properly 
 after installation are described in this module. Items for particular 
 attention are identified. 
 
 MODULE 17 - INTRODUCTION TO SOLAR COOLING 
 
 Several solar cooling alternatives are described. Principal among 
 them are absorption chillers, desiccant types and Rankine cycle systems. 
 
1-8 
 
 MODULE 18 - FUTURE PROSPECTS FOR SOLAR HEATING AND COOLING SYSTEMS 
 
 Many new types of equipment for solar heating and cooling systems 
 are undergoing research, development and testing. Some components which 
 have hopeful prospects for future use in systems are described. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 2 
 
 ENERGY CONSERVATION IN RESIDENTIAL BUILDINGS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
2-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 2-1 i 
 
 INTRODUCTION .... 
 OBJECTIVES .... 
 SITING AND LANDSCAPING . 
 BUILDING SHAPE AND ORIENTATION 
 BUILDING DESIGN 
 
 ROOM ARRANGEMENT 
 
 WINDOWS . 
 
 AIR LOCKS . 
 INSULATION 
 
 INSULATION RATINGS 
 
 MOISTURE CONTROL 
 
 INSULATING EXTERIOR WALLS 
 
 INSULATING CEILINGS . 
 
 INSULATING FLOORS . 
 
 INSULATING DUCTS AND PIPES 
 STORM DOORS AND WINDOWS . 
 WEATHER STRIPPING AND CAULKING 
 OTHER ENERGY CONSERVATION MEASURES 
 
 "SET-BACK" THERMOSTATS . 
 
 FURNACE ADJUSTMENTS . 
 
 FIREPLACE .... 
 
 DOMESTIC WATER HEATERS . 
 REFERENCES .... 
 
 2-1 
 
 2-1 
 
 2-2 
 
 2-4 
 
 2-4 
 
 2-4 
 
 2-6 
 
 2-7 
 
 2-7 
 
 2-7 
 
 2-8 
 
 2-9 
 
 2-12 
 
 2-12 
 
 2-15 
 
 2-15 
 
 2-16 
 
 2-16 
 
 2-16 
 
 2-17 
 
 2-17 
 
 2-18 
 
 2-19 
 
2-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 2-1 Siting and Landscaping ....... 2-3 
 
 2-2 Sheltering a Building from Winds with Trees or Fence . 2-3 
 
 2-3 General Interior Room Arrangement ..... 2-5 
 
 2-4 Effect of Overhang above South-Facing Window . . . 2-6 
 
 2-5 Air Lock (Vestibule) 2-7 
 
 2-6 Wall Insulation 2-10 
 
 2-7 Insulating Around Fenestrations ..... 2-11 
 
 2-8 Insulating Basement Walls ...... 2-11 
 
 2-9 Insulating Walls of Unvented Crawl Spaces . . . 2-13 
 
 2-10 Insulating Floors Over Vented Crawl Spaces or Unheated 
 
 Basements . . . . . . . . . . 2-13 
 
 2-11 Floor Insulation End Treatment ..... 2-14 
 
 2-12 Perimeter Insulation of Concrete Slabs on Grade . . 2-14 
 
2-1 
 
 INTRODUCTION 
 
 Regardless of the energy source used for heating and cooling 
 buildings, appropriate energy conservation measures should be included 
 in all buildings to reduce the use of energy and consequently the cost 
 of heating and cooling. Energy requirements in buildings may be reduced 
 in a number of ways. Factors such as building shape and orientation can 
 affect heating and cooling loads. Landscaping should be planned to 
 protect the building from winds, utilize solar gain in winter, and 
 provide shade in the summer. Buildings should be oriented to avoid 
 entrances on windy sides and have vestibules or air locks to minimize 
 infiltration of cold air. Insulation should be provided, storm doors 
 and windows should be added and cracks around window and door frames 
 should be caulked. These and other energy conservation measures 
 appropriate for residential buildings are discussed in this module. 
 
 OBJECTIVES 
 
 The purpose of this module is to describe energy conservation 
 measures that are appropriate for new buildings and some that are 
 appropriate for existing buildings. The participants should be able to: 
 
 1. Recognize siting and environmental factors for a building 
 which will affect energy requirements for space conditioning. 
 
 2. Recognize features of building design which can minimize heat 
 losses in winter and heat gains in summer. 
 
 3. Identify energy conservation measures that are appropriate for 
 new buildings and those that are appropriate for existing 
 buildings. 
 
2-2 
 
 SITING AND LANDSCAPING 
 
 Energy requirements for space conditioning can be influenced by 
 building orientation. During winter the south sides of buildings can be 
 utilized for direct solar heating of the rooms. During summer the 
 building walls can be shaded to reduce cooling loads. Achieving both 
 maximum exposure to sunshine during the winter and effective shading 
 during the summer can also be aided by proper site selection and careful 
 landscaping around the building. 
 
 During the winter, most of the solar energy entering a building 
 occurs between the hours of 9 a.m. and 3 p.m. In the summer months, 
 solar heating begins earlier in the day and continues longer in the 
 afternoons, but south-facing windows and walls can be effectively shaded 
 by external building features such as roof overhangs. The east and west 
 walls can be shaded by trees to minimize heat gains as illustrated in 
 Figure 2-1. 
 
 Heating loads are affected by the amount of cold air that 
 infiltrates into the building. Infiltration through cracks is signif- 
 icantly increased by winds that impact on building walls, so wind 
 barriers can reduce the amount of infiltration. Common wind barriers 
 are fences and trees along north sides of the building sites as 
 illustrated in Figures 2-1 and 2-2. Other techniques are to slope and 
 extend the roof close to the ground toward the north and to build earth 
 berms either against the building or along the north side to minimize 
 exposure of the building walls to high winds. 
 
2-3 
 
 Coniferous 
 Trees 
 
 Fence 
 
 Coniferous 
 
 Deciduous Trees 
 
 ?- ifc .1?'" 
 
 Deciduous 
 Trees 
 
 / ! \ 
 
 Figure 2-1. Siting and Landscaping 
 
 North Wind 
 
 Figure 2-2. Sheltering a Building from Winds with Trees or Fence 
 
2-4 
 
 BUILDING SHAPE AND ORIENTATION 
 
 A building with small wall and ceiling area per unit floor area 
 will normally have small heat transmission losses. The building shape 
 which best satisfies these requirements is a hemisphere, but a hemi- 
 spherical shape for residential buildings is encumbered by limited room 
 arrangements and aesthetic appeal. The ratio of wall area to unit floor 
 area for circular-shaped buildings is larger but still preferable to 
 rectangular-shaped buildings. The wall area of a square building is 13 
 percent greater than a circular building with equivalent floor space and 
 wall height. Wall areas of rectangular buildings with large aspect 
 ratios can be much larger than buildings with square floor plans, but 
 when solar gains and heat losses are considered, an optimum shape often 
 turns out to be a rectangular building with the longer side facing south 
 (and north) (Ref. 1). In cool and temperate regions of the country, 
 rectangular buildings with length-to-width ratios of 1.1 to 1.3 have 
 been found to be suitable. This means that for a typical residential 
 building with about 1575 ft 2 floor area, the side dimensions would be 
 35 ft and 45 ft, with the longer side facing south. The wall area of 
 such a rectangular building is larger than that in a square building by 
 less than one percent, but the 13 percent greater wall area on the south 
 side results in increased solar gain during the day. 
 
 BUILDING DESIGN 
 
 ROOM ARRANGEMENT 
 
 The layout of a residential building is usually based on minimizing 
 construction costs. Other criteria for design may include functional 
 
2-5 
 
 utilization of space, high aesthetic appeal, and low energy cost for 
 heating and cooling. A single design may not be able to meet all 
 criteria, so an acceptable building design usually requires tradeoffs. 
 However, if high priority is placed on achieving low heating costs, 
 there are some general recommendations for room arrangement that may be 
 considered. 
 
 Space which is not occupied for many hours of the day, such as 
 mechanical equipment rooms, corridors, closets, utility rooms and 
 bathrooms, can be maintained at a lower temperature than other living 
 space, so locating them on the north side of the building as in 
 Figure 2-3 may be suitable. If building orientation is restricted, a 
 garage on the north side of the building can serve also as buffer space. 
 Living and bedroom space may be arranged along the south side where 
 there is natural lighting and solar gain through the windows during the 
 day. 
 
 r 
 
 J UTILITY 
 
 ^ r ^ 
 
 j j CLOSETS, STAIRS, 
 
 } ROOM 
 
 HALLWAY, BATH 
 
 | KITCHEM || INTERIOR jj j 
 DINING II WARM ROOMS || 
 
 ! v ^ - y i 
 
 jj BEDROOMS i 
 
 | LIVING SPACE 
 i 
 
 ' 1 
 II 1 
 
 1 
 
 II 1 
 
 _ 
 
 i 
 
 N 
 
 Figure 2-3. General Interior Room Arrangement 
 
2-6 
 
 WINDOWS 
 
 A large amount of heat is lost in winter through windows. There 
 can be more than 10 times greater heat loss through double-glazed 
 windows per square foot of area than through well-insulated walls. 
 Therefore, unless the building is specifically designed to utilize solar 
 gains through south-facing windows (passive heating), it is generally 
 not advisable to adopt large window areas. 
 
 Properly designed roof overhangs above south- facing windows, as 
 shown in Figure 2-4, can reduce solar heating of the rooms during summer 
 and take advantage of low sun angles in winter. For effective shading, 
 the summer sun should be blocked out during the hours of 9 a.m. to 
 3 p.m. Since north windows can have no useful solar gain during winter 
 months to offset the heat losses, the sizes of windows on the north wall 
 should be small. 
 
 Summer 
 Sun Position 
 
 Winter 
 Sun Position 
 
 v vysi/\h_ J I . ■ . . . . — , . . , 
 
 Figure 2-4. Effect of Overhang above South-Facing Window 
 
2-7 
 
 Cracks around window frames are also primary sources for 
 infiltration. Tightly fitted windows are a prime requisite for reducing 
 heat losses. 
 
 AIR LOCKS 
 
 Heat losses can be reduced by adding storm doors. Alternatively, 
 an air lock, or vestibule, shown in Figure 2-5 helps to reduce the 
 volume of cold air entering the room each time the exterior door is 
 opened. The air lock can be added to the outside of the building as 
 shown in Figure 2-5 or built inside the enclosure. Wingwalls protruding 
 from the exterior wall can be useful in reducing wind impact on 
 doorways, and storm doors are effective in reducing infiltration and 
 heat transmission losses. 
 
 Shrubs 
 
 Cold 
 
 ^ssssssssssssssss^ s sssssa 
 
 K\V\\VVV\\ 
 
 ■ - '••'■ I '.' : ' . — ~~* 
 
 Figure 2-5. Air Lock (Vestibule) 
 
 INSULATION 
 
 INSULATION RATINGS 
 
 Insulation is rated by an "R" value. The greater the R value, the 
 higher is the resistance to heat flow. Thus, there will be less heat 
 flow through R-ll insulation than R-4 insulation. 
 
2-8 
 
 Insulation is usually available in batts (blankets) or loose fill, 
 but there are also preformed foam sheets and liquid foam material that 
 may be mixed with air and pumped into building walls. Insulation batts 
 are generally available in ratings of R-4 (1.5 inches), R-ll 
 (3.5 inches), R-19 (6 inches), and R-22 (7 inches). If more than R-22 
 is desired, batts can be combined to make up the desired R value. For 
 example, an R-ll combined with an R-19 will result in insulation 
 thickness of about 10 inches with an R-30 insulating value. Loose-fill 
 insulation is rated according to thickness such as R-2 per inch or R-3 
 per inch. 
 
 Resistance to heat flow in insulation material is achieved by 
 trapped bubbles of air. Compacted insulation generally has a lower R 
 value than loosely placed insulation, but if air movement can occur 
 freely through or around the insulation, the resistance to heat flow is 
 reduced considerably. Moist or wet insulation loses much or all of its 
 insulating value. 
 
 MOISTURE CONTROL 
 
 To protect insulation from becoming wet, vapor barriers are used to 
 reduce the flow of air and water vapor through the interior wall 
 material and condensation within the insulation as cooling occurs. The 
 vapor barrier is applied adjacent to or facing the interior surface. 
 
 Insulation batts may be purchased with or without a vapor barrier. 
 When combining batts, or adding batts to existing insulation, additional 
 vapor barriers should not be used beyond the one recommended. If batts 
 without vapor barriers are not available and batts are to be combined, 
 the vapor barrier in the second layer should be extensively perforated 
 
2-9 
 
 or slit to prevent trapping moist air between vapor barriers and causing 
 possible condensation. 
 
 When loose-fill material is used for insulation, a vapor barrier 
 may be provided on the inside face of the building frame with about a 
 2-mil-thick plastic sheet. Foil-back gypsum board may be substituted 
 for a thin film vapor barrier. 
 
 In some locations, a separate vapor barrier may be considered in 
 addition to the one on the batt insulation. The importance of a second 
 vapor barrier depends upon the winter climate. It generally is 
 advisable where outdoor air temperatures are low. However, in many 
 regions the air is very dry at low temperatures and unless humidifiers 
 are used inside the building, there may not be a problem. 
 
 INSULATING EXTERIOR WALLS 
 
 When batt (blanket) insulation with a vapor barrier is used to 
 insulate exterior walls, the batts should be installed between studs so 
 that the face touches the outside sheathing or siding. Working from the 
 top downward, the vapor barrier is stapled to the studs (approximately 
 8-in spacing). At the top and bottom ends, the batts should be cut 
 either to fit snugly against the top and bottom plates, as shown in 
 Figure 2-6(a), or slightly overlength, as shown in Figure 2-6(b). 
 Electrical wiring, junction boxes, switch boxes and plumbing may often 
 be located in exterior walls. Special effort should be made to insulate 
 around or behind them to prevent an opening in the insulation which can 
 allow air circulation and reduce the effectiveness of the insulation. 
 
 If loose-fill insulation is used, a plastic sheet vapor barrier is 
 most appropriate. Considerable care should be exercised in placing 
 
2-10 
 
 Figure 2-6. Wall Insulation 
 
 loose insulation to avoid large air pockets, particularly around 
 electrical wiring and conduits in the wall. 
 
 Plastic (foam) insulation is also available for injection into wall 
 spaces. Most have acceptably high R values when dry, but shrinkage in 
 the drying or setting process may create air gaps in some types, thereby 
 reducing their effective R value. 
 
 Cracks around windows and door jambs should be sealed and insulated 
 as shown in Figure 2-7. The vapor barrier should be on the inside face 
 of the wall. 
 
 In many older buildings, there is often inadequate insulation or 
 none at all, and economical alternatives are to use loose-fill material 
 or to inject foam. When carefully treated, walls with no prior 
 insulation can be adequately insulated, but if some insulation material 
 already exists in the walls, additions may be difficult. 
 
 Concrete or masonry walls can be insulated on the inside face by 
 use of furring strips as shown in Figure 2-8. With 2x2 (1-5/8x1-5/8) 
 furring strips, R-4 insulation can be provided. 
 
2-11 
 
 Cover All Insulated Cracks 
 With Vapor Barrier 
 
 Stuff All Cracks Around 
 Doors and Windows 
 
 Figure 2-7. Insulating Around Fenestrations 
 
 Masonry 
 or Concrete 
 
 Figure 2-8. Insulating Basement Walls 
 
2-12 
 
 INSULATING CEILINGS 
 
 Either batt or loose insulation may be used above ceilings. If 
 ceiling joists are constructed of 2 x 4 lumber, R-ll batt insulation may 
 be placed between joists, and this material may be covered with another 
 layer of R-ll or R-19 batt insulation to achieve R-22 or R-30 ceiling 
 insulation. 
 
 An attic should be well ventilated and well insulated. Insulation 
 should not block eave vents. If interior wall spaces are open to the 
 attic, they should be blocked off to prevent cold air from circulating 
 into the wall spaces. 
 
 INSULATING FLOORS 
 
 Floors over crawl spaces may be insulated, or if the crawl space is 
 unvented, the foundation walls may be insulated as shown in Figure 2-9. 
 The latter is generally less expensive, but a vapor barrier must cover 
 the ground in the crawl space to prevent moisture damage to the 
 insulation. Floors over vented crawl spaces or over unheated basements 
 may be insulated by one of two alternative methods suggested in 
 Figure 2-10. Insulation is held in place by wire supports. 
 
 The sill plate on foundations or on basement walls is particularly 
 susceptible to formation of gaps and large amounts of infiltration. The 
 cracks below and above the sill plate should be carefully sealed. Band 
 joists should be insulated by one of the two methods shown in 
 Figure 2-11. 
 
 Floor slabs on grade should be insulated around the perimeter by 
 either of the two methods shown in Figure 2-12. The rigid insulation 
 should extend downward or along the base of the slab a minimum distance 
 of 2 feet. 
 
2-13 
 
 nCi-. 'V-o.0. c 
 
 
 .CJ 
 
 Joe 
 
 
 Vapor Barrier- 
 
 ?.'-o - 
 
 Figure 2-9. Insulating Walls of Unvented Crawl Spaces 
 
 Vapor Barrier Side 
 
 Figure 2-10. Insulating Floors Over Vented Crawl 
 Basements 
 
 Spaces or Unheated 
 
2-14 
 
 End of Insulation Blanket Pushed Up 
 or Short Piece at Header 
 
 Figure 2-11. Floor Insulation End Treatment 
 
 ■ o" ■ ' ■ " ' .^Y I A ' 8- 1 
 
 rV:i?i*.':0r.°.ip3 
 
 Rigid Insulation 
 
 <rss* 
 
 nsulation -^ 
 
 Figure 2-12. Perimeter Insulation of Concrete Slabs on Grade 
 
2-15 
 
 INSULATING DUCTS AND PIPES 
 
 Heating and cooling ducts and pipes in unheated spaces should be 
 well insulated. Joints of ducts should be sealed before applying the 
 insulation, either with duct tape or preferably with silicone sealant. 
 Although 1 to 2 inches of insulation is normal, thicker insulation may 
 be desirable in cold climates. 
 
 On cold pipes and ducts, closed-cell insulation should be used, as 
 fiber insulation can be ruined by moisture condensation. Insulation of 
 pipes and ducts in solar systems is discussed in a separate module. 
 
 STORM DOORS AND WINDOWS 
 
 Storm doors and windows are available in a wide variety of designs 
 and costs. The basic purpose is the creation of dead air spaces which 
 increase resistance to heat flow. In this regard, storm doors are less 
 effective than storm windows because they are opened more frequently and 
 they must be looser fitting than storm windows. Nevertheless their use 
 will decrease the amount of air infiltration and increase resistance to 
 heat flow. Storm doors that can be used as screen doors in summer are 
 popularly used, with interchangeable glass and screen sections. If the 
 exterior door has glass insets, storm doors are beneficial. Weather 
 stripping is also useful in decreasing infiltration, and the cost is 
 small if installed by the homeowner. 
 
 Storm windows with metal frames should have thermal breaks. Wood 
 frames conduct less heat to the outside than metal frames, but wood- 
 framed windows are more expensive. 
 
2-16 
 
 WEATHER STRIPPING AND CAULKING 
 
 When a house is well insulated, and storm doors and windows are 
 provided, the largest heat loss is the infiltration of cold air into the 
 rooms and the equal volume of warm air leaking out of the building. 
 Caulking of cracks in the building envelope decreases infiltration. 
 Particularly troublesome are cracks or openings along the sill plate on 
 foundations and basement walls and cracks around windows and door 
 frames. 
 
 Weather stripping is available in a wide variety of materials to 
 suit many different types of windows and doors. Weather stripping 
 sliding doors may be difficult and aid from specialists may be required. 
 Durability is an important consideration in the selection of weather 
 stripping material. 
 
 OTHER ENERGY CONSERVATION MEASURES 
 
 "SET-BACK" THERMOSTATS 
 
 Setting the thermostat to maintain a lower temperature in 
 unoccupied rooms can save energy. Thermostats may be "set back" either 
 manually or automatically but clock-driven thermostats are also 
 available. With the latter types, thermostats may be set back automat- 
 ically to a desired setting any time in the evening and raised to a 
 higher level in the early morning. Prices of clock-driven thermostats 
 vary widely, and the advantages of each type should be clearly 
 understood before purchase. 
 
2-17 
 
 FURNACE ADJUSTMENTS 
 
 Furnaces in many homes are operating at efficiencies far below 
 normal. Rather than operating at the 60 to 70 percent efficiencies 
 attainable in well adjusted and maintained equipment, furnaces commonly 
 operate at only 40 to 50 percent efficiency. Under these conditions, 
 fuel consumption is 30 to 35 percent higher. Representatives of local 
 utility companies and qualified HVAC contractors can clean and adjust 
 furnaces to operate at improved efficiencies. 
 
 To check combustion efficiencies, a flue gas analysis and a stack 
 temperature measurement are made. The carbon dioxide content in the 
 stack gas should be above a certain concentration, about 14 percent, and 
 stack temperatures should not be above a certain level, depending upon 
 the fuel source. Adjustments to the combustion air flow rate, possibly 
 changing the orifice in the fuel line, and cleaning of the burner jets 
 will usually improve furnace efficiencies. 
 
 There are a number of devices on the market which can be attached 
 to the furnace stacks. Their use is often claimed to result in substan- 
 tial efficiency. The local utility company or a qualified individual 
 should be consulted before purchase and installation of such devices. 
 Local code officials should also be consulted to determine if a 
 particular device is permitted in local buildings, and inquiries about 
 fire and health hazards that might be related to use of the device 
 should be made. 
 
 FIREPLACE 
 
 Fireplaces should not be installed without a flue damper, but even 
 with dampers that are closed during periods of nonuse, significant 
 
2-18 
 
 amounts of room air will be drawn up the fireplace chimney along with 
 combustion air when the fireplace is in use. When room air is drawn 
 into the fireplace and up the chimney, cold air must enter the building 
 elsewhere to replace it; infiltration and heating loads are thus 
 increased. 
 
 There are a number of fireplace designs that minimize exhausting of 
 room air and provide net heating of the rooms. Common features of such 
 designs involve direct supply of combustion air to the fireplace from 
 outside, glass doors which prevent room air entry to the fireplace and 
 chimney, and controlled circulation of room air around the fireplace, 
 entering from below and returning to the room from above. 
 
 DOMESTIC WATER HEATERS 
 
 Energy use for domestic water heating can be minimized by setting 
 the thermostat to maintain a moderately low water temperature. 
 Satisfactory water temperature will depend upon volume and frequency of 
 use. Many automatic dishwashers are provided with separate heating 
 elements so hot water supplied at a temperature of about 120°F is 
 satisfactory. Dishwashers without heating elements may require a higher 
 water temperature from the hot water tank. Although heat losses from 
 hot water tanks contribute to heating of conditioned space in winter, 
 these losses increase the cooling load during the summer. Heat loss can 
 be reduced by use of insulating jackets which fit over the exterior of 
 the tanks. Batt insulation may also be used, but obstruction of air 
 vents in gas- or oil -fueled water heaters and stack draft hoods must be 
 carefully avoided. 
 
2-19 
 
 REFERENCES 
 
 1. Olgyay, V.V. (1963) Design with Climate. Princeton University 
 Press, Princeton, N.J. 
 
 2. Crowther, R. L. (1977) Sun Earth. A. B. Hirschfield Press, Inc., 
 Denver, Colorado. 
 
 3. Arizona State University (1975) Solar Oriented Architecture. ASU 
 College of Architecture, Research Report prepared for AIA Research 
 Corporation and NBS. 
 
 4. Mazria, E. , (1979) The Passive Solar Energy Book , Rodale Press, 
 Emmaus, Pennsylvania. 
 
 5. NAHB Research Foundation, Inc., (1979) Insulation Manual, 
 Rockville, Maryland. 
 
 6. National Bureau of Standards, (1975) Making the Most of Your 
 Energy Dollars in Home Heating and Cooling. U. S. Department of 
 Commerce, NBS. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 3 
 
 INTRODUCTION TO PASSIVE DESIGNS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
3-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 
 Page 
 3- ii 
 3- i i i 
 
 INTRODUCTION 
 
 OBJECTIVES 
 
 TYPES OF PASSIVE DESIGNS .... 
 
 DIRECT GAIN 
 
 INDIRECT GAIN 
 
 Masonry Walls .... 
 
 Water Walls 
 
 Sunspace ..... 
 
 ISOLATED GAIN 
 
 COMBINATION SYSTEMS 
 
 MEASURING THE PERFORMANCE OF PASSIVE SYSTEMS 
 REFERENCES 
 
 3-1 
 
 3-1 
 
 3-2 
 
 3-2 
 
 3-10 
 
 3-10 
 
 3-17 
 
 3-20 
 
 3-24 
 
 3-27 
 
 3-29 
 
 3-32 
 
3-ii 
 
 LIST OF FIGURES 
 
 Figure 
 
 3- 
 
 ■1( 
 
 ^a) 
 
 3- 
 
 ■1( 
 
 » 
 
 3- 
 
 •2( 
 
 'a) 
 
 3- 
 
 •2( 
 
 » 
 
 3- 
 
 ■2< 
 
 [c) 
 
 3- 
 
 ■2( 
 
 [d) 
 
 3- 
 
 3( 
 
 'a) 
 
 3- 
 
 •3( 
 
 » 
 
 3- 
 
 •3( 
 
 !c) 
 
 3- 
 
 ■4 
 
 
 3- 
 
 ■5( 
 
 'a) 
 
 3- 
 
 ■5( 
 
 » 
 
 3- 
 
 ■6( 
 
 'a) 
 
 3- 
 
 ■6( 
 
 » 
 
 3- 
 
 ■6( 
 
 'c) 
 
 3- 
 
 ■7( 
 
 'a) 
 
 3- 
 
 ■7( 
 
 [b) 
 
 3- 
 
 ■7( 
 
 'c) 
 
 3- 
 
 ■8< 
 
 'a) 
 
 3- 
 
 ■8( 
 
 [b) 
 
 3- 
 
 ■8( 
 
 'c) 
 
 3- 
 
 ■9( 
 
 'a) 
 
 3- 
 
 ■91 
 
 » 
 
 3- 
 
 ■9( 
 
 'c) 
 
 Direct Gain Through a South-Facing Wall . 
 Direct Gain Through Roof .... 
 
 Building Using Direct Gain Passive Heating 
 Floor Plan ...... 
 
 Winter Mode Operation .... 
 
 Summer Mode Operation .... 
 
 Direct Gain Heating of a Two-Story Duplex 
 Floor Plan ...... 
 
 Side View of Duplex ..... 
 
 Thermal Wall Design ..... 
 
 The Trombe Wall in the Heating Mode 
 The Trombe Wall in the Ventilating Mode . 
 Passively Heated Home with Trombe Walls . 
 Upper and Lower Floor Plans 
 Cross-Sections Through House . 
 Building Designed with a Water Wall 
 Floor Plan ...... 
 
 Section Through the Building and South Elevat 
 
 Attached Greenhouse Dwelling . 
 
 Floor Plans ...... 
 
 Cross-Section of Attached Greenhouse Dwelling 
 Design of Combination Sunspace-Isolated Gain 
 Floor Plans ...... 
 
 Cross-Section of House .... 
 
 on 
 
 Page 
 
 3-3 
 
 3-3 
 
 3-6 
 
 3-6 
 
 3-7 
 
 3-7 
 
 3-8 
 
 3-9 
 
 3-9 
 
 3-11 
 
 3-13 
 
 3-13 
 
 3-16 
 
 3-16 
 
 3-17 
 
 3-19 
 
 3-19 
 
 3-20 
 
 3-21 
 
 3-22 
 
 3-22 
 
 3-25 
 
 3-25 
 
 3-26 
 
3-iii 
 
 Figure Page 
 
 3-10(a) Doug Kelbaugh House 3-27 
 
 3-10(b) Cross-Section of the Kelbaugh House . . . 3-28 
 
 3-ll(a) A View of the South and East Walls of the Hunn 
 
 Residence ......... 3-30 
 
 3-ll(b) Floor Plans and Heat Distribution System in the 
 
 Hunn Residence ........ 3-30 
 
 LIST OF TABLES 
 
 Table Page 
 
 3-1 Cost Estimate of the Space and DHW Heating 
 
 Systems ......... 3-31 
 

3-1 
 
 INTRODUCTION 
 
 Passive solar heating is accomplished by building designs that 
 utilize solar energy without primary dependence on mechanical means to 
 collect, transport and distribute solar heat to the rooms. The designs 
 feature large areas of glass on the south walls of buildings and thermal 
 mass inside the building for energy storage and distribution. Depending 
 upon the area of glass used and the thickness and volume of thermal 
 mass, passive heating can provide an appreciable portion of the space 
 heating needs within a building. 
 
 Passive designs require considerations to heat flow and heat 
 transfer within the building to prevent overheating during sunny days. 
 The layout of rooms within the building, window locations, and the 
 placement of storage can affect the amount of useful heating provided by 
 the sun. 
 
 OBJECTIVES 
 
 The objectives of this module are to: 
 
 1. Introduce trainees to different types of passive designs. 
 
 2. Describe the functions of various elements of a passively 
 heated building. 
 
 3. Provide appraisals of the performance of some passively heated 
 designs. 
 
3-2 
 TYPES OF PASSIVE DESIGNS 
 
 There are many different concepts for passive heating designs which 
 may be classified into the following types: 
 
 A. Direct Gain 
 
 B. Indirect Gain 
 
 1. Masonry Wall 
 
 2. Water Wall 
 
 3. Attached sunspace 
 
 C. Isolated Gain 
 
 Effective designs may be created by combining the different types such 
 as indirect solar heating with thermal walls and direct gain through 
 some south- facing windows. 
 
 DIRECT GAIN 
 
 Building designs that allow heating by penetration of solar energy 
 directly into the living space and the building enclosure are called 
 direct gain. The designs feature large south-facing windows, although 
 windows facing toward the east or west may also be used if heat is 
 desired earlier in the day or later in the afternoon. The windows are 
 generally double glazed to reduce heat losses and improve net heat gain 
 during the day. A single glazed window can result in net energy loss. 
 It is desirable, and in severe climates, necessary, to insulate the 
 windows at night using shutters or insulated curtains to reduce heat 
 losses. Overhangs are desirable design features so that windows are 
 shaded during the summer. Schematics of direct gain structures are 
 shown in Figures 3-l(a) and 3-l(b). 
 
3-3 
 
 Figure 3-l(a). Direct Gain Through a South-Facing Wall 
 
 Figure 3-l(b). Direct Gain Through Roof 
 
3-4 
 
 Solar energy is converted to heat within the building and stored in 
 the interior masonry walls and floors. To be effective, the masonry 
 must be sufficiently thick to store most of the heat energy received 
 during the day for release during the night. Unless they are designed 
 properly, the interiors of direct gain buildings may overheat during the 
 day, making it necessary to ventilate for maintenance of comfortable 
 temperatures. There are two reasons for the overheating. Some of the 
 incident sunlight is converted to heat on the surfaces of furniture and 
 other low-mass objects from which heat is transferred to the room air. 
 In addition, to conduct heat into the massive storage walls (and floor), 
 their surface temperatures must become high enough to enable substantial 
 heat conduction into the interior of the masonry walls. The warm 
 surface will convect heat to the room air while heat is also conducted 
 into storage. 
 
 Overheating can be minimized and effective coupling of solar energy 
 into storage can be achieved by using the following guidelines: 
 
 1. Solar radiation should be received directly by the storage 
 walls and floor. 
 
 2. The ratio of storage area to glass area should be 3 to 5. 
 
 3. There should be high thermal conductivity in the storage mass. 
 
 4. There should be a large amount of thermal mass. 
 
 If the ratio of storage surface area to glass area is less than 
 about 3, and the walls are about 8 inches thick, ventilation may 
 frequently be necessary to prevent overheating. Increasing the wall 
 thickness does not significantly decrease overheating. As the ratio of 
 storage surface area to glass area is increased, the amount of 
 
3-5 
 
 discomfort from overheating is reduced, and if a ratio as large as 9 can 
 be achieved, temperature fluctuations may be limited to a range of 12°F 
 to 15°F. 
 
 An example of direct gain heating is a building designed by 
 J. Morgan, New York, New York (Ref. 1), shown in Figure 3-2(a). The 
 building is located in Bucks County, Pennsylvania, and is primarily a 
 weekend retreat. The two-bedroom house has a floor space of about 
 1000 ft 2 . The structure is conventional wood frame, well insulated, and 
 the masonry floor has perimeter insulation. The south wall can be 
 shaded in the summer, and cross-ventilation is possible by opening the 
 windows on both the north and south sides. 
 
 The house is on a south-facing slope which permits terracing of the 
 north and south parts of the building. Living spaces are along the 
 south side and the bedrooms are to the north side as shown in 
 Figure 3-2(b). 
 
 Sunlight is admitted into the building through the windows and 
 translucent skylight panels as indicated in Figure 3-2(c). Light 
 through the skylight panels is diffused over the masonry surfaces. At 
 night (after approximately 3 p.m.), insulated hatches, operating on 
 small electric motors, cover the skylight. Also, motor-operated drapes 
 cover the south windows. 
 
 During the summer a retractable fabric awning shades the south 
 windows and by opening the windows on the north and south sides, cross- 
 ventilation can cool the rooms as indicated in Figure 3-2(d). The open 
 floor plan facilitates ventilation. 
 
 The building is located in a climate with an average of 5300 
 degree-days and solar radiation which averages 600 to 700 Btu/(ft 2 «day) 
 
3-6 
 
 Figure 3-2(a). Building Using Direct Gain Passive Heating 
 
 STUDIO 
 
 UJ 
 
 AS SHELF 
 
 _• AWNING 
 
 SHADED TERRACE 
 
 STONE SLAB MANTEL/ 1 * I — | ^wmgSI r, 
 
 FLUE HEAT REFLECTOR^ HH \ SIOtlESLAl 
 
 — pr — i 1 — t i_i j i 
 
 FLOOR FLAGSTONE ON CONCRETE^ THRUOUT ^ 'TCHEN 
 
 STORAGE 
 
 SCREENED 
 PORCH 
 
 el. 334 
 
 VESTIBULE 
 
 DINING 
 TERRACE 
 
 \o 
 
 SECTION 
 
 RETRACTABLE FABRIC AWNINGS 
 
 FLOOR PLAN ot el. 342 
 5 10 15 feet 
 
 Figure 3-2(b). Floor Plan 
 
3-7 
 
 CEILING HATCHES OPEN ON SUNNY 
 DAYS, WARMING THERMAL MASS. 
 
 (9) STOVE AND/OR FIREPLACE HEAT 
 ^ OCCUPANTS AND THERMAL MASS; 
 
 HEAT FROM FLUE GASES REFLECTED 
 
 INTO ROOM. 
 
 (3) SOUTH WALL HAS INSULATED 
 SHADES AND NIGHT DRAPERY 
 TO RESIST HEAT LOSS. 
 
 (2) NORTH WALL AWNING WINDOWS 
 COVERED BY INSULATED WINTER 
 FLAPS. 
 
 (g) WEATHERSTRIPPED DOORS ISOLATE 
 W THE UNHEATED AREAS OF THE HOUSE. 
 
 HEAVY CURTAIN ISOLATES BEDROOMS 
 FROM MAIN ROOM AT NIGHT. 
 
 DECEMBER 21 
 
 © 
 
 Figure 3-2(c). Winter Mode Operation 
 
 JUNE 21 
 
 Figure 3-2(d). Summer Mode Operation 
 
3-8 
 
 during the winter. Solar heat is expected to supply about 40 percent of 
 the total seasonal space heating demand. 
 
 Design for direct gain heating of a two-story duplex in an urban 
 setting is shown in Figure 3-3. The building was designed by J. Migani, 
 Teamworks, Cambridge, Massachusetts (Ref. 1). The building is 
 constructed of concrete block walls with foam insulation and stucco 
 applied to the exterior. The floors and roof are precast concrete 
 slabs, which provide additional heat storage mass. 
 
 Figure 3-3(a). Direct Gain Heating of a Two-Story Duplex 
 
DOUBLE GLAZING 
 
 NIGHT INSULATING 
 
 SHUTTERS 
 
 3-9 
 
 -AWNING FRAME- 
 SUMMER 
 
 MASONRY WALLS 
 
 SECOND FLOOR 
 
 REDWOOD DECK 
 
 REDWOOD DECK 
 •DOUBLE GLAZING 
 
 IVlOT WATER HEATER 
 
 BASEMENT 
 
 Figure 3-3(b). Floor Plan 
 
 GLASS 
 AIR SPACE 
 CURVED LOUVER 
 
 SUMMER SUN 
 
 REFLECTIVE SURFACE 
 
 TARGET AREA- PRIMARY 
 THERMAL STORAGE 
 TRANSOM OVER 
 BEDROOM DOOR TO 
 FACILITATE MOVEMENT 
 OF SOLAR HEATED AIR 
 8NATURAL VENTILATION 
 
 SUMMER SUN SCREEN 
 
 AWNING FRAME 
 
 *->' 
 
 TARGET AREA - 
 PRIMARY THERMAL 
 STORAGE 
 
 REFLECTIVE SUN CONTROdj 
 LOUVERS - ANGLE TO BE H 
 ADJUSTED MONTHLY 
 
 
 NOTE .MASONRY WALLS 
 SERVE AS 
 SECONDARY 
 THERMAL STORAGE 
 
 TARGET AREA- 
 ' PRIMARY THERMAL 
 STORAGE 
 
 WINTER 
 SUN 
 
 Figure 3-3(c). Side View of Duplex 
 
3-10 
 
 The south-wall windows consist of two panes of glass with curved 
 reflective louvers between them. By positioning the louvers, sunlight 
 can be reflected onto the ceiling or closed off effectively from 
 entering the rooms. If floor heating is desired, the louvers may be 
 turned to let the sun shine directly on the floor. By reflecting 
 sunlight to the ceiling, the surface of the storage mass is heated 
 directly, and conversion to heat by the furniture is minimized. A ratio 
 of storage surface to glass area of about 5 is achieved in this design, 
 including east and west walls and the party wall. 
 
 The duplex is located in Connecticut where heating degree days 
 average about 5800 and cloudy days are prevalent during the winter. 
 Solar energy is expected to contribute about 45 percent of the total 
 space heating needs in this building. 
 
 INDIRECT GAIN 
 
 Indirect gain passive designs utilize a storage mass placed between 
 the glass wall and the heated space. In this way the storage mass acts 
 as a thermal filter, absorbing the excess solar heat during the day and 
 delivering it to the rooms in the evening and at night. Indirect gain 
 designs can be characterized by at least three different types; masonry 
 wall, water wall and sunspace. 
 
 Masonry Walls 
 
 The concept of using a masonry wall immediately adjacent to the 
 glass wall was developed by Felix Trombe and his associates in the south 
 of France in the late 1960's, and a masonry wall is frequently referred 
 
3-11 
 
 to as a "Trombe" wall. Instead of absorbing heat into masonry walls 
 after sunlight has entered the rooms as in direct gain designs, a 
 masonry wall is placed adjacent to the south-facing windows within the 
 enclosure. The principle of the Trombe wall for heating room air is 
 illustrated in Figure 3-4. As the air between the glass and masonry 
 wall is heated it rises and enters the room through a vent at the top of 
 the wall. The number and size of vents can be varied. Room air enters 
 the lower vent and is heated as it rises between the window and the 
 masonry wall. Not all of the solar heat is transferred to the air; some 
 is stored in the wall. As heat is conducted through the masonry wall 
 and the room-side wall temperature becomes greater than the room air 
 
 TRANSPARENT 
 COVER OR GLASS 
 
 / I OR 2 \ 
 ^COVERS/ 
 
 HEAT 
 STORAGE WALL 
 MASONRY OR 
 
 LIQUID IN 
 CONTAINERS 
 
 Figure 3-4. Thermal Wall Design 
 
3-12 
 
 temperature, air in the room is heated by convection as shown in Figure 
 3-5(a). Heat is also radiated into the room from the wall, transferring 
 heat to interior walls, furniture, and occupants. If the room becomes 
 too warm during the day, the lower vents can be closed to stop the 
 circulation of air between the window and the wall. If the inside wall 
 surface becomes too warm, the window can be shaded, or an insulating 
 curtain can be drawn across the inside wall to stop radiant heating of 
 interior walls. Venting to the outside is also possible as shown in 
 Figure 3-5(b). At night, as the air in the space between wall and 
 glass cools, the direction of circulation reverses and if the upper vent 
 is not closed, heat would be lost from continued circulation of the room 
 air. 
 
 During the summer the outside vents are opened to allow the heated 
 air to exhaust outdoors, as shown in Figure 3-5(b), and some cooling by 
 ventilation can be achieved by drawing cool air from the north side of 
 the building through the rooms. 
 
 Properly designed masonry walls share the following features: 
 
 1. The wall must be of a dark color on the window side. 
 
 2. The window should be double glazed and may be insulated at 
 night. 
 
 3. The storage wall should be of such material that the rate of 
 heat delivery to the living area should be reasonably low, or 
 movable insulation may be installed between the storage wall 
 and the living space to control the rate of heat transfer to 
 the living space. 
 
 4. Rooms that are not adjacent to the storage wall will need 
 additional heat. 
 
3-13 
 
 VENT OPEN 
 
 HEAT DELIVERY BY 
 CONVECTION 
 
 CONVECTION 
 
 RADIATION 
 
 Figure 3-5(a). The Trombe Wall in the Heating Mode 
 
 VENT CLOSED 
 
 OUTSIDE 
 AIR 
 
 Figure 3-5(b). The Trombe Wall in the Ventilating Mode 
 
3-14 
 
 5. A reasonable storage capacity for the wall is about 
 30 Btu/(°F«ft 2 ) for any location. This amounts to about a 
 1-foot-thick concrete wall. 
 
 6. Typical net gains of 40,000 to 70,000 Btu/(year-ft 2 ) are 
 possible. 
 
 7. Vents are provided to cool the south face of the wall and to 
 provide circulation of heat to the rooms during the day. 
 
 The wall thickness need not be greater than 1 foot for any location. If 
 vents through the wall to the living space are used, then dampers over 
 the upper vents may be advisable to prevent circulation through the 
 vents at night which will cool the room air. 
 
 An experimental building was constructed in Odeillo, France, in 
 1967. The south wall of the building is approximately 2 feet thick, and 
 painted with black acrylic along the glass side of the wall. There are 
 two glazings on a steel frame with a space of approximately 5 inches 
 between the glass and the wall. The distance between the vents is 
 approximately 11.5 feet. A group of buildings constructed by Trombe in 
 1974 uses the same materials as the first building, but the thickness of 
 the wall was reduced to 1.2 feet and the distance between vents to 
 7.2 feet. The thinner wall reduced the time for heat to be conducted 
 through it by 5 to 6 hours. The time required to conduct heat through 
 the 2-foot wall was 14 to 16 hours, reduced to 9 to 10 hours for the 
 1.2-ft wall. The daily solar collection efficiencies for the 1967 house 
 ranged between 32 and 40 percent during the winter, and the collection 
 efficiencies for the 1974 houses are lower by about 10 percent. The 
 solar wall contributed about 70 percent of the total heating needs in 
 the 1967 house. 
 
3-15 
 
 An example of a recent house with Trombe walls (and a sun porch) 
 designed by Adolphus Chester, Architectural Design Branch, TVA, for 
 western Virginia is shown in Figure 3-6(a) (Ref. 1). The house is built 
 into a southward-sloping hillside and faces east of south. There are 
 900 ft 2 of heated space on the upper level and 900 ft 2 more on the lower 
 level, 540 ft 2 of which are heated. Upper and lower level floor plans 
 are shown in Figure 3-6(b). 
 
 The Trombe walls of this house are unvented, and all the heating of 
 the rooms must take place by convection and radiation from the inner 
 wall surface. The Trombe wall is made of reinforced concrete and filled 
 concrete block 12 inches thick, covered by 2 layers of fiberglass- 
 reinforced plastic. Two sections through the house are shown in 
 Figure 3-6(c). The sun porch provides some heat to a masonry wall which 
 borders the kitchen, and the concrete floor slab is 6 inches thick. 
 Adjustable louvers over the sun porch can be used to control solar 
 penetration on the kitchen wall and in the sun porch. 
 
 In a climate with 4100 degree-days and net annual heating load of 
 25 million Btu, the annual solar fraction is expected by the designer to 
 be about 74 percent. Auxiliary heat is provided by a wood stove and an 
 electric heat pump. 
 
 Cooling is expected by cross-ventilation. Windows which penetrate 
 the Trombe wall are provided to allow air to flow into the rooms. A 
 potential problem is overheating of the rooms during times of the year 
 when heating load is small because an outdoor vent is not provided for 
 the Trombe wall . 
 
3-16 
 
 Figure 3-6(a). Passively Heated Home with Trombe Wall 
 
 
 LOWER PLAN VIEW 
 
 Figure 3-6(b). Upper and Lower Floor Plans 
 
3-17 
 
 JUNE 21 
 
 ..DEC. 21 
 
 TRIPLE GLAZIN 
 2X6 WALL 
 STYROFOAM INSULATION 
 
 SUN CONTROL DEVICES 
 OPERABLE VENTS 
 —GREENHOUSE/SUN PORCH 
 OPERABLE VENTS 
 
 MASS TROMBE WALL 
 GLAZING (2 LAYERS) 
 
 SECTION AA 
 
 JUNE 21 
 
 ..- DEC. 21 
 
 MASS TROMBE WALL 
 WOtiD BOX PASS THROUGH 
 V^'WOOD STOVE 
 
 SUN CONTROL DEVICES 
 
 GLAZING (2 LAYERS) 
 INSULATING SLAB 
 
 SECTION BB 
 
 Figure 3-6(c). Cross-Sections Through House 
 
 Water Walls 
 
 In place of a masonry wall, containers of water (or other liquid) 
 can be placed adjacent to the windows. A water wall can absorb heat 
 more rapidly than a masonry wall and has greater heat capacity per ft 3 
 of material, but heated liquid in a container sets up convective 
 currents inside the container so the room-side surfaces of the 
 containers can become nearly as warm as the side facing the sun. 
 Therefore, there can be more room heating during the day from a water 
 wall than a masonry wall. Control measures for water walls are external 
 shading, control of upper and lower vents through the water wall, and 
 operable vents to the outside. 
 
3-18 
 
 Extravagant heat losses during non-sunshine hours are prevented by 
 insulation of the windows adjacent to the water wall. 
 
 An example of a building with a water wall is shown in 
 Figure 3-7(a). The house was designed by Victor Habib, One Design, 
 Inc., for a mountain region in Virginia. The climate averages 
 6000 degree-days of heating, but with energy conservation measures, the 
 building heat load is limited to about 20 million Btu per year. 
 
 The floor plan of the house is shown in Figure 3-7(b) and the 
 section through the building and the south elevation are shown in Figure 
 3-7(c). There are three sections of water walls totalling 192 ft 2 , and 
 there are 45 ft 2 of south-facing windows for direct gain heating. The 
 containers are fiberglass troughs which stack together tightly, and are 
 blackened on the window side. The total capacity of the troughs is 
 
 about 480 gallons, or 2.5 gallons per square foot of window area. The 
 
 (R) 
 window is single glazed, with a Roll Door Movable Insulation V[y on the 
 
 outside. The sliding doors retract into modified ceiling pre-fab roof 
 
 trusses to expose the glass area to sunshine. 
 
 A potential weakness of this design is that the rooms on the north 
 side will receive little benefit from the water walls unless circulation 
 from the warmer rooms is augmented by fans. In recognition of this 
 problem, rooms requiring less heat are arranged on the north side. 
 One-half to two-thirds of the heating needs is expected by the designer 
 to be provided from solar energy. 
 
 Summer cooling is planned by ventilation with an attic fan. To 
 prevent heating of the water wall during the day, the roll doors are to 
 be kept in a closed position. 
 
3-19 
 
 Figure 3-7(a). Building Designed with a Water Wall 
 
 DOUBLE DOOR / 
 
 REAR ENTRY->-~ 
 PROTECTED BY 
 GARAGE 
 
 FIREPLACE WITH 
 OUTSIDE AIR 
 INTAKE 
 
 AIR LOCK ENTRY 
 
 water wall 
 "roll door" 
 
 MODULE 
 REFLECTIVE TERRACE 
 
 Figure 3-7(b). Floor Plan 
 
3-20 
 
 AUTOMATIC ELECTRIC 
 OPERATOR LIGHT 
 ACTIVATED 
 
 STANDARD ARKANSAS 
 
 ^FRAMC TRUSS MODIFIED 
 JDVER "ROLL DOOR" 
 
 ^SS=^- TRACK s?' -^--SjSJ 
 
 ^, . ■ -,. . .. .y. VJI ,,- J ,wy'.. , 1....- A\.<K.- .. . .... - . .. ,. I- W-- ' .,.V..*L- ■■ ; - ■■ ■ [P-— 
 
 rrr' : -' ,;r -' ■'• ■ '■• ■ " ^^—- - „■ ■■—;■■> ■' -■ ■ ■ -• ■ ■ ■■■■■■/ INS 
 
 "ROLL DOOR" 
 MOVABLE INSULATION 
 
 "WATER WALL" 
 DIRECT RADIATION 
 
 INDIRECT RADIATION 
 FLUCTUATES ONLY 
 2.5" BETWEEN 
 
 L 
 
 ROOMS 
 
 
 R-38 
 INSULATION 
 
 SECTION 
 
 "ROLL DOOR MOVABLE INSULATION" 
 ROLLS UP TO EXPOSE "WATER WALL" 
 PASSIVE COLLECTORS DURING 
 WINTER DAYS ONLY- 
 
 ROLL DOOR MODULES 
 
 SOUTH ELEVATION 
 
 Figure 3-7(c). Section Through the Building and South Elevation 
 
 Sunspace 
 
 A sunspace is used to collect solar heat in a secondary space, 
 separate from the living area, but connected to it by a common wall 
 which serves as the thermal mass storage for solar heat. The space may 
 
 be used as a greenhouse, atrium, sun porch, or sun room. Masonry or 
 
 i 
 
 concrete floors and walls, rock beds, water container, or covered pools 
 of water may serve as thermal storage. Air temperature within the sun 
 space may be allowed to vary more widely than in the living space, but 
 for greenhouses, both minimum and maximum temperatures must be 
 maintained if plant life is to survive. As with other passive heating 
 devices, shading should be provided to prevent overheating during the 
 
3-21 
 
 summer, and movable insulation should be used to prevent excessive heat 
 losses during winter. 
 
 A building which utilizes a greenhouse for solar heat gain is shown 
 in Figure 3-8(a). Floor plans for upper and lower levels are shown in 
 Figure 3-8(b) and a cross-section is shown in Figure 3-8(c). The 
 building was designed by Fuller Moore of Oxford, Ohio, located in 
 southwestern Ohio. The building has 1600 ft 2 of living area and is 
 in a region with 4800 heating degree-days. Annual heating load is 
 expected to be about 36 million Btu. 
 
 Figure 3-8(a). Attached Greenhouse Dwelling 
 
3-22 
 
 UNDERGROUND 
 AIR INTAKE 
 
 O 
 
 5! 
 
 ''Goroge" Door Provides 
 f Shade When Open 
 
 Of 
 
 I 
 
 =>i 
 
 Ol 
 
 II 
 
 r AMILY/ 
 STUDY/ 
 
 FAf, 
 
 ST 
 
 BEDROOM 
 
 12X12 
 
 JbptionoT Wall 
 
 al 
 ■^ 
 
 DINING 
 10X12 
 
 
 b a 
 
 ID a 
 
 a 
 
 □ 
 
 ALTERNATE ENTRY ipj> 
 
 Ol — fc 
 
 UNDERGRO 
 AIR INTA 
 
 LIVING 
 0X12 
 
 UPPER 
 LEVEL 
 
 Q 
 
 r 
 
 £ 
 
 J, 10X18 
 I 
 
 SUN- l 
 
 TEMPERED 
 
 BREEZEWAY 
 
 Garoge Doo 
 
 <3^ 
 
 L J 
 
 GARAGE 
 20X24 
 
 
 Figure 3-8(b). Floor Plans 
 
 LOWER 
 LEVEL 
 
 ROLL- DOWN BAMBOO SHADE - 
 
 Figure 3-8(c). Cross-Section of Attached Greenhouse Dwelling 
 
3-23 
 
 When heating is required, the greenhouse collects solar heat and 
 the occupant must raise the roll-down reflective insulation shade. 
 Solar heat is absorbed in the floor and common wall of the greenhouse 
 and also in the plant beds if provided. By opening the bedroom windows 
 and the door to the living space, convective circulation is expected to 
 take place into the living space, down through the stairwell to the 
 level below, through the bedrooms and back to the greenhouse. At night, 
 the occupant closes the doors and windows and rolls down the shade, 
 covering the greenhouse glazing. 
 
 Additional collecting area is provided by 142 ft 2 of attic 
 collector. When needed, ceiling dampers are opened in the living space 
 and a small fan circulates air from the greenhouse. An automatic damper 
 between the greenhouse and attic collector is connected to the fan 
 control. Auxiliary heating is provided by a wood stove, and there are 
 also electric resistance baseboard units located in the lower level. 
 More than 50 percent of the heating needs is expected by the designer to 
 be supplied by solar heat. 
 
 Cooling by augmented ventilation is accomplished by using the attic 
 collector section as the thermal generator. Manual vents are opened at 
 the ridge line, heated air rises through the open vent and circulation 
 through the living space is created by opening the ceiling vents. The 
 sun-tempered breezeway is the fresh air supply, and air can pass through 
 the rock bed backfill, through the stairwell into the living room. 
 Unless the house is tightly sealed, however, there will not be 
 sufficient pressure drop between the house and outdoors to circulate air 
 through the rock bed by the thermal chimney effect. By using the attic 
 
3-24 
 
 fan between the greenhouse and the attic vent and opening the windows 
 and door it is hoped that ventilation will be augmented during very hot 
 days. 
 
 ISOLATED GAIN 
 
 In isolated gain designs, solar collection and thermal storage are 
 separated from the living spaces (Ref. 2), so that the solar heating 
 system functions independently of the building. Heat is drawn from the 
 system as needed. A particular approach associated with a sloping 
 building site involves a flat-plate air heating collector with thermo- 
 siphon circulation through the collector and rock bed storage. Rather 
 than employing the building itself for solar collection and storage, as 
 in most passive designs, this concept involves special solar collectors 
 and other components. 
 
 A combination sunspace- isolated gain design is shown in 
 Figure 3-9(a). The 2000 ft 2 building was designed by Gary Cook of Ann 
 Arbor, Michigan, for a climate with 6300 degree-days of heating, located 
 just outside of Ann Arbor. Plans of the first and second floors are 
 shown in Figure 3-9(b), and a section through the building is shown in 
 Figure 3-9(c). The prototype of this design is the home of Paul Davis 
 in New Mexico. 
 
 Manually operated dampers control the thermocirculation heating of 
 the rock bed and living space. For daytime heating, air can pass 
 through the top and bottom plenums of the rock bed to heat the rooms 
 directly from the collectors. During the night, thermocirculation of 
 air through the pebble bed extracts heat from the rocks and delivers it 
 to the rooms. There are 1500 ft 3 of rocks in the rock bed, extending 
 
3-25 
 
 Figure 3-9(a). Design of Combination Sunspace-Isolated Gain 
 
 30Z3T 
 
 PA 
 
 KIT 
 
 DiN. RM 
 
 □r u 
 
 N T RY MECH. 
 1 IL 
 
 TEH 
 
 J-^-\ fsolar Htq. 
 
 f *• J R.A. Venls 
 
 ''■Wood Furn. /Fireplace 
 
 STOR. BATH 
 
 ! IS 
 
 LIVING ROOM U |_ 
 
 STDY 
 
 2* 
 
 Supply Air Solor 
 
 brVtesTV 
 
 GREENHOUSE 
 (Brick Paving) 
 
 u Y 
 
 
 [mmxnxa 
 
 FIRST FLOOR 
 
 PTLfTE 
 
 r ' "■ i i! j L 'W^ 
 
 MBR 
 
 BR 
 
 i u 
 
 J 
 
 BR 
 
 £^entrO 
 
 STDY./REC 
 
 VELUX OPERABLE SKYLIGHT-^ 
 
 D D D D 
 
 ^ddddddddddlV 
 
 SECOND FLOOR 
 
 Figure 3-9(b). Floor Plans 
 
3-26 
 
 CONTINUOUS RIDGE VENT 
 
 OPERABLE VELUX 
 SKYLIGHT (4) — 
 
 OPERABLE PELLA 
 AWNING WINDOW " 
 
 DARK BRICK 
 
 45 CUBIC YDS. 4-5 ROCK 
 HEAT STORAGE 
 
 -METAL REFLECTOR AND COVER PANEL - CORRUGATED 
 
 THERMOSIPHON- 
 COLLECTOR TO STORAGE 
 
 O THERMOSIPHON- 
 <- STORAGE TO LIVING 
 
 ■2 HOT AIR RISES TO BEDROOMS " 
 SUPPLY AIR FROM LIVING 
 
 4 DIRECT GAIN TO FLOOR AND 
 
 BACK WALL 
 C OVERHANG SHADES AND PROVIDES 
 
 VENTILATION SUPPLY AIR 
 
 Figure 3-9(c). Cross-Section of House 
 
 the entire length of the building, and 432 ft 2 of double-glazed 
 collectors which supply solar heat to the rock bed. 
 
 There is a sizable greenhouse area provided at the first floor 
 level, with a 9-inch concrete and brick floor and a 4-inch brick party 
 wall. Heat circulates through the building into the upper level, down 
 the stairwell and back through the French doors of the living level. 
 The designer expects solar energy to provide about 75 percent of the 
 annual heating needs. 
 
 Cooling is by ventilation through windows which can be opened on 
 all sides of the building. The greenhouse can be shaded and a skylight 
 can be opened to enhance ventilation. 
 
3-27 
 
 COMBINATION SYSTEMS 
 
 A combination of Trombe wall, direct gain, and an attached 
 greenhouse is utilized in the Kelbaugh house in Princeton, New Jersey. 
 The building, with a greenhouse on the south side, is shown in 
 Figure 3-10(a) and a cross section is shown in Figure 3-10(b). During 
 the winter of 1975-76 it was estimated that 72 percent of the heating 
 needs was provided by the solar system. The indoor temperature varia- 
 tions were about 3°F to 6°F during a 24-hour period with a seasonal high 
 and low of 68°F and 58°F at the first floor level and 72°F and 62°F at 
 the second level. The average temperature at the first floor level was 
 about 63°F, and at the second level the average temperature was 67°F. 
 The thermostat setting was varied between 60°F and 64°F during the 
 daytime and was lowered to 58°F during the night. 
 
 Figure 3-10(a). Doug Kelbaugh House 
 
3-28 
 
 1) Winter sun angle 
 
 2) Two glazings of double strength 
 window glass 
 
 3) Concrete wall 15 inches thick 
 
 4) Air space between inner glazing 
 and concrete wall 
 
 5) Lower air vent 
 
 6) Top air vent 
 
 7) Air circulation path 
 
 8) Radiation from the solar wall to 
 the interior 
 
 Conventional hot air furnace ducts 
 Heavily insulated house skin, 
 average U = 0.05 
 
 11) Attached greenhouse 
 
 12) Black concrete floor 
 13] Cellar 
 
 14) Summer sun angle 
 
 15) Exhaust fans 
 
 16) North windows for natural 
 ventilation 
 
 17) Greenhouse shades 
 
 18) Solar water heater (to be added) 
 
 Figure 3-10(b). Cross-Section of the Kelbaugh House 
 
 After the 1975-76 season, modifications were made to the Kelbaugh 
 house to minimize heat losses (especially in the greenhouse) and to 
 reduce the temperature differences between the two floors of the house. 
 These modifications included shuttering of windows, installation of a 
 door at the top of the first floor stairs, adding thermal mass to the 
 greenhouse, and installing an insulating curtain between the greenhouse 
 and the rest of the house. The thermal stratification persisted and it 
 is concluded that the Trombe wall is oversized for the second story. 
 
 A combination house utilizing a forced ventilated Trombe wall, rock 
 bed storage, direct gain, and active DHW system is the Hunn residence in 
 Los Alamos, New Mexico, shown in Figure 3-ll(a). The solar wall is made 
 
3-29 
 
 of slump block one foot thick with double glazing. A blower circulates 
 air between the wall and glazing and stores the heat in a rock bed for 
 heat storage. In effect, the Trombe wall is a set of vertical solar 
 collectors for an active system. A three-zone, forced air distribution 
 system is connected to the storage unit as shown in Figure 3-ll(b) and a 
 separate flat-plate collector array is used for domestic hot water. A 
 detailed cost estimate of the system is listed in Table 3-1. 
 
 Observations made by the owner during the first year of operation 
 indicated that when the Trombe wall was fully charged, temperatures of 
 85°F to 90°F were attained on the inner surface. Under these circum- 
 stances, it was comfortable in the room even when the room air 
 temperature was as low as 65°F. However, if the temperature of the 
 interior surface of the wall drops to 60°F to 65°F, then it is uncom- 
 fortably cool even when the room air temperature is as high as 67°F. 
 Operation of the Trombe wall as an active collector has not been 
 successful because of low collection efficiency. 
 
 MEASURING THE PERFORMANCE OF PASSIVE SYSTEMS 
 
 In active solar systems, relatively simple instrumentation can be 
 used to measure the solar energy contribution to the heating load of a 
 structure. For passive designs, measuring the solar heat contribution 
 is much more difficult and is usually estimated by subtracting the 
 measured auxiliary energy from the calculated building heat loss. The 
 calculations, however, are subject to large errors. A few computer- 
 oriented methods for calculating solar contributions are available, but 
 
3-30 
 
 / 
 
 ■i 
 
 1 I L- 
 
 L 
 
 
 Figure 3-ll(a). A View of the South and East Walls of the Hunn Residence 
 
 INDICATES SLUMP 
 BLOCK 
 
 SECOND FLOOR 
 
 ^ST HEATING 
 
 ZONE I RETURN 
 
 HEATING 
 
 Figure 3-ll(b). Floor Plans and Heat Distribution System in the Hunn 
 Residence 
 
3-31 
 
 Table 3-1 
 Cost Estimate of the Space and DHW Heating Systems 
 
 I. SPACE HEATING SYSTEM 
 A. Trombe Wall 
 
 1. 300 ft 2 of 1-ft-thick slump block 
 
 2. Masonry cement, sand, and mortar coloring 
 
 3. Concrete block fill 
 
 4. Concrete footings 
 
 5. Rebar and Durowall reinforcing 
 
 6. Wood framing for glazing 
 
 7. Glazing 
 
 8. Stain 
 
 9. Ductwork 
 
 Subtotal 
 
 Less credit for the 6-in. frame wall that 
 was replaced, 300 ft 2 @ $5.25/ft 2 
 
 Rock Bed Storage 
 
 1. 12 tons washed gravel 
 
 2. Framing 
 
 3. Insulation 
 
 4. Miscellaneous hardware 
 
 5. Angle iron 
 
 Subtotal 
 
 C. Extra Ductwork (including motor-operated dampers 
 and back-draft dampers) 
 
 D. Rock Bed Charging Blower, 500 cfm 
 
 E. Controls (including one Rho Sigma Model 106 
 controller and furnace burner thermostat) 
 
 Subtotal 
 
 Materials 
 
 $ 825 
 233 
 280 
 219 
 231 
 
 62 
 846 
 
 25 
 325 
 
 Installation 
 Labor 
 
 $ 466 
 
 $ 525 
 
 $ 208 
 
 $ 200 
 
 $ 933 
 
 $1262 
 
 208 
 
 300 
 
 80 
 
 96 
 
 $3046 
 
 $1946 
 
 = $4992 
 -1575 
 
 $ 51 
 
 150 
 
 134 
 
 54 
 
 77 
 
 $ 50 
 
 200 
 
 50 
 
 
 $ 300 
 
 $ 240 
 
 $ 20 
 
 $ 60 
 
 $ 320 
 
 766 
 
 1253 
 
 TOTAL ITEM I 
 
 $5436 
 
 II. DOMESTIC HOT WATER SYSTEM 
 
 A. Two Miromit Model 200 flat-plate collectors 
 (single-glazed, water-white crystal glass, 
 20 ft 2 each 
 
 B. Differential controller, Rho Sigma Model 106 
 
 C. Circulating pump, Grundfos Model VSP 20-42 
 
 D. 50-gallon preheater/storage tank with finned 
 tube heat exchanger coil 
 
 E. Associated plumbing (including solenoid vent 
 valves) 
 
 TOTAL ITEM II 
 
 $ 400 
 
 $ 100 
 
 $ 90 
 
 $ 30 
 
 $ 85 
 
 $ 30 
 
 $ 350 
 
 $ 45 
 
 $ 80 
 
 $ 50 
 
 $1005 
 
 255 
 
 $1260 
 
 GRAND TOTAL, SPACE HEATING AND DOMESTIC HOT WATER HEATING 
 
 $6696 
 
3-32 
 
 validation of these methods and computed results is needed. One 
 simplified method for estimating annual solar fractions for indirect and 
 direct gain designs is available, developed by the Los Alamos Scientific 
 Laboratory. Efforts to compare predicted (calculated) solar 
 contributions with measurements are currently underway. 
 
 REFERENCES 
 
 Franklin Research Center (1979) "The First Passive Solar Home 
 Awards", U. S. Government Printing Office, Washington, D. C. 20402, 
 January. 
 
 Mazria, E. , (1979) The Passive Solar Energy Book , Rodale Press, 
 Emmaus, Pennsylvania. 
 
 Passive Solar Heating and Cooling , Conference and Workshop 
 Proceedings May 18-19, 1976, Los Alamos Scientific Laboratory/ U.S. 
 ERDA (Available from: National Technical Information Service, U.S. 
 Department of Commerce, Springfield, Virginia 22151). 
 
 Passive Solar, State of the Art , Proceedings of the 2nd National 
 
 Passive Solar Conference, University of Pennsylvania, Philadelphia, 
 
 Pennsylvania, March 16-18, 1978 (Available from: Mid-Atlantic 
 
 Solar Energy Association, 2233 Gray's Ferry Avenue, Philadelphia, 
 Pennsylvania 19146). 
 
 Proceedings of the 1978 Annual Heating AS of ISES , V2.2, Denver, 
 Colorado, August 28-31, 1978 (Available from: American Section of 
 the International Solar Energy Society Inc. , P.O. Box 1416, 
 Killeen, Texas 76541). 
 
 A Survey of Passive Solar Buildings, AIA Research Corporation, 1735 
 New York Avenue Northwest, Washington, D. C. 20006. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 4 
 
 INTRODUCTION TO LIQUID SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
4-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 4-ii 
 
 INTRODUCTION 4-1 
 
 OBJECTIVES 4-1 
 
 SOLAR HEATING AND COOLING SYSTEMS 4-1 
 
 SOLAR COLLECTORS FOR LIQUID HEATING .... 4-5 
 
 THERMAL STORAGE UNITS 4-10 
 
 COLLECTION AND STORAGE OF SOLAR HEAT ..... 4-12 
 
 HEAT DISTRIBUTION 4-15 
 
 AUXILIARY HEATERS 4-17 
 
 AUTOMATIC CONTROLS 4-18 
 
 SOLAR COOLING 4-20 
 
4-ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 4-1 Schematic Diagram of a Simplified Solar Heating 
 
 System 4-2 
 
 4-2 Schematic Arrangement of a Solar Domestic Hot 
 
 Water (DHW) Subsystem 4-4 
 
 4-3 Typical Liquid-Heating Collector with Tubular 
 
 Liquid Passages ....... 4-6 
 
 4-4 Liquid-Heating Collector with Flow Between 
 
 Metal Plates ' 4-6 
 
 4-5 Point Focus Reflecting Type Solar Concentrating 
 
 Collector 4-8 
 
 4-6 Line Focus Reflecting Type Solar Concentrating 
 
 Collector 4-8 
 
 4-7 Fresnel Lens Strip Solar Collector .... 4-9 
 
 4-8 Direct and Diffuse Radiation on a Solar 
 
 Concentrator ........ 4-9 
 
 4-9 Schematic of Corning Glass Works Evacuated 
 
 Tube Solar Collector 4-11 
 
 4-10 Schematic of Owens-Illinois Evacuated Tube 
 
 Solar Collector 4-11 
 
 4-11 Drain-Down System for Solar Collection and 
 
 Storage ......... 4-13 
 
 4-12 Solar Collection in Non-Freezing Liquid and 
 
 Heat Exchange with Water Storage .... 4-14 
 
 4-13 Dual-Liquid Solar Collection with Automatic 
 
 Make-Up Water Supply ...... 4-16 
 
 4-14 Solar Heat to Warm Air Distribution System . . 4-16 
 
 4-15 Typical Use of Auxiliary in Liquid (Hydronic) 
 
 Distribution System ....... 4-18 
 
 4-16 Typical Solar Hot Water Control System . . . 4-19 
 
 4-17 Solar Heating and Cooling System .... 4-21 
 
4-1 
 
 INTRODUCTION 
 
 The purpose of this module is to provide a brief introduction to 
 the types of liquid 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. 
 
 OBJECTIVES 
 
 At the end of this module, the trainee should be able to: 
 
 1. Identify the principal characteristics of liquidtype solar 
 heating and cooling systems. 
 
 2. Describe the basic functions of key components of solar 
 heating and cooling systems employing liquid collection. 
 
 3. Recognize the advantages and limitations of different designs 
 of components and systems. 
 
 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 building design features which permit direct solar entry 
 into the structure, active systems require special equipment for 
 collecting solar energy in liquid or air, storing heat, and distributing 
 
4-2 
 
 heat 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. The differences 
 are sufficient to justify separation of the discussion into two modules. 
 Figure 4-1 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 facilities for providing solar 
 heat to the domestic hot water supply. 
 
 SOLAR 
 
 THERMAL 
 
 STORAGE 
 
 UNIT 
 
 (WATER TANK) 
 
 PUMP 
 
 AUXILIARY 
 HEATER 
 
 (FURNACE 
 
 OR 
 
 BOILER) 
 
 ■$- 
 
 HEAT 
 
 DISTRIBUTION 
 
 SYSTEM 
 
 <Q 
 
 AUTOMATIC PUMP/ BLOWER 
 
 VALVE /DAMPER 
 
 Figure 4-1. Schematic Diagram of a Simplified Liquid Solar System 
 
4-3 
 
 In operation, 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. In general, the solar 
 collector and thermal storage unit can operate independently of heating 
 demands, so solar energy can be collected and stored whenever there is 
 sufficient incident solar radiation. 
 
 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 solar 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. 
 
 Heat delivery to the building can be accomplished 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 where "radiator" 
 surfaces such as baseboard strip heaters (finned tubing) can be used. 
 
4-4 
 
 Service hot water may be solar heated either in a system for that 
 purpose only, or in combination with a space heating system. Figure 4-2 
 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 
 controls actuate the two pumps when the DHW preheat tank is colder than 
 the solar source and heat is transferred in the heat exchanger to the 
 DHW supply. 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 
 
 FROM COLD 
 WATER MAIN 
 
 S 
 
 2 
 < 
 
 H 
 
 u 
 
 O 
 
 o 
 
 Ll) 
 
 < 
 
 -J 
 
 ir 
 
 _l 
 
 o 
 
 o 
 
 crt- 
 
 c_> 
 
 oco 
 
 rr 
 
 _i 
 
 < 
 
 < 
 
 _i 
 
 > 
 
 o 
 
 rr 
 
 CO 
 
 UJ 
 
 
 I 
 
 UJ 
 
 e> 
 o| 
 
 H ° 
 ^ x 
 
 < UJ 
 UJ < 
 
 a 
 
 AUTOMATIC 
 SHUT-OFF 
 VALVE 
 9 
 
 STORAGE 
 DHW PUMP 
 
 d>fe 
 
 PREHEAT 
 DHW PUMP 1 
 
 DHW 
 
 PREHEAT 
 
 TANK 
 
 MIXING 
 J^ VALVE 
 
 TO DHW 
 DISTRIBUTION 
 AND LOAD 
 
 AUXILIARY 
 
 HOT WATER 
 
 TANK 
 
 AUXILIARY ENERGY 
 INPUT TO DHW 
 
 Figure 4-2. Schematic Arrangement of a Solar Domestic Hot Water (DHW) 
 Subsystem 
 
4-5 
 
 the temperature of the preheated water at the desired setting (e.g., 
 140°F). During the summer a solar thermal storage unit provided as part 
 of a space heating system can normally meet nearly 100 percent of the 
 domestic hot water requirements. 
 
 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 4-3 and 4-4 show examples of two liquid-type solar collectors 
 used in solar heating and cooling systems. 
 
 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 is then transferred to a 
 liquid which flows 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 
 
4-6 
 
 SILICONE RUBBER PADS 
 TO ISOLATE ABSORBER PLATE 
 FROM FRAME 
 
 MOUNTING 
 BRACKET 
 
 ABSORBER PLATE 
 WITH 
 SELECTIVE SURFACE 
 
 COPPER TUBES 
 
 TWO COVER GLASSES 
 
 GLASS SEAL 
 TO FRAME 
 
 INLET WATER 
 HEADER 
 
 STEEL FRAMING 
 
 SEMI-RIGID 
 INSULATION 
 
 PLUMBING FITTING 
 
 Figure 4-3. Typical Liquid-Heating Collector with Tubular Liquid 
 Passages 
 
 GLASS COVER 
 
 ABSORBER PLATE 
 
 REFLECTIVE SURFACE 
 
 RIGID FOAM INSULATION 
 
 LIQUID FLOW 
 PASSAGE 
 
 PIPING CONNECTION 
 AND MOUNTING 
 
 Figure 4-4. Liquid-Heating Collector with Flow Between Metal Plates 
 
4-7 
 
 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. 
 
 The collectors in Figures 4-3 and 4-4 are flat-plate liquid heaters 
 representing two commercially available types. They are called flat- 
 plate collectors to distinguish them from concentrating collectors which 
 gather solar radiation falling on a large area and focus the energy onto 
 a smaller absorber area. Concentrating collectors can deliver heat at 
 higher temperatures than flat-plate types and may therefore be used for 
 steam generation and other applications for which such temperatures are 
 necessary. But if used for heat supply at the moderate temperatures 
 needed for space heating and hot water, collector area requirements are 
 comparable to those of the flat-plate type. Examples of concentrating 
 solar collectors of the reflecting type are shown in Figures 4-5 and 4-6 
 and a transmitting lens type is shown in Figure 4-7. 
 
 A technical disadvantage of a concentrating solar collector is that 
 only direct solar radiation can be used. Diffuse radiation resulting 
 from reflections from earth and sky, which is often half and never less 
 than ten percent of that radiation, cannot be focused (see Figure 4-8) 
 and is therefore lost. Most concentrating collectors must also be 
 movable to follow the path of the sun throughout the day. The expense 
 of construction, operation, and maintenance of an accurate, tracking 
 concentrator is usually much too high for use of this type of solar 
 collector in space heating applications. 
 
4-8 
 
 Figure 4-5. Point Focus Reflecting type Solar Concentrating Collector 
 
 Figure 4-6. Line Focus Reflecting Type Solar Concentrating Collector 
 
4-9 
 
 HOUSING 
 
 INSULATION 
 
 Figure 4-7. Fresnel Lens Strip Solar Collector 
 
 T DIFFUSE 
 \ SOLAR 
 i RADIATION 
 
 REFLECTOR 
 
 Figure 4-8. Direct and Diffuse Radiation on a Solar Concentratoi 
 
4-10 
 
 A special type of flat-plate collector comprises a glass tube 
 surrounding a flat or cylindrical absorbing surface. As shown in 
 Figures 4-9 and 4-10, 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. 
 
 THERMAL STORAGE UNITS 
 
 The total absence of solar radiation at night and the continuous 
 need for space heating in cold weather result 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 sufficient mass of 
 solid or liquid in an insulated 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 
 
4-11 
 
 MOLDED PLASTIC MOUNTING 
 WITH MANIFOLD TUBES- 
 
 s / 32 in. THICK 
 PYREX GLASS TUBE 
 
 ABSORBER SUPPORT- 
 CLIPS 
 
 '/» in. OD COPPER 
 TUBING 
 
 '/ w in. THICK COPPER 
 ABSORBER PLATE 
 
 ABSORBER SUPPORT 
 CLIPS ( 6/ABSORBER) 
 
 % in TUBE SPACING 
 MOLDED PLASTIC MOUNTING 
 
 TYPICAL TUBE DETAIL 
 
 Figure 4-9. Schematic of Corning Glass Works Evacuated Tube Solar 
 Collector 
 
 ABSORBER TUBE 
 
 HERMETIC 
 SEAL 
 
 DELIVERY TUBE 
 
 SPRING SUPPORT 
 
 TIP-OFF 
 
 COVER TUBE 
 t = 0.92 
 
 SELECTING COATING 
 a = 0.86, « = 0.07 
 
 FEEDER TUBE 
 
 FLUID FLOW AREA 
 (SUPPLY) 
 
 VACUUM PRESSURE 
 P< I0" 4 torr 
 ABSORBER TUBE 
 
 FLUID FLOW (RETURN) 
 
 Figure 4-10. Schematic of Owens-Illinois Evacuated Tube Solar Collector 
 
4-12 
 
 solidifies, the stored heat is released for use. Because the heat 
 stored by 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 technical difficulties and 
 economic disadvantages, phase-change storage materials are not ready for 
 practical use in active 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. 
 
 COLLECTION AND STORAGE OF SOLAR HEAT 
 
 In nearly all practical liquid solar systems, heat is stored as hot 
 water in a well-insulated tank. If water is also used in the solar 
 collectors in a cold climate, some freeze protection method must be 
 provided. A common arrangement permits the collector to drain into the 
 storage tank whenever operation of the circulating pump stops. 
 Figure 4-11 illustrates this system. When the solar intensity 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 provides a 
 
4-13 
 
 AIR 
 VENT 
 
 INLET 
 MANIFOLD 
 
 S3- 
 
 OUTLET MANIFOLD 
 
 (INTERNAL OR EXTERNAL 
 TO COLLECTOR ARRAY) 
 
 FLOW 
 
 SOLAR 
 THERMAL 
 STORAGE 
 
 Figure 4-11. Drain-Down System for Solar Collection and Storage 
 
 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 pump operation 
 ceases. 
 
 Figure 4-12 shows another method for freeze protection, by which 
 solar heat is collected in a non-freezing liquid, usually a water-glycol 
 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 
 
4-14 
 
 VENT OR RELIEF VALVE 
 
 4 EXPANSION 
 TANK 
 
 Figure 4-12. 
 
 FLOW 
 
 HEAT 
 EXCHANGER 
 
 S3 
 
 VENT 
 
 COLLECTOR 
 PUMP 
 
 HEAT EXCHANGER 
 PUMP 
 
 Solar Collection in Non-Freezing Liquid and Heat Exchange 
 with Water Storage 
 
 of corrosion caused by alternate exposure of the collector tubes to 
 water and air in the drain-down system. The possibility of corrosion 
 and freezing in the drain-down system (in Figure 4-11) can thus be 
 compared with the cost penalty of the exchanger, pump, and additional 
 piping for the design in Figure 4-12. 
 
 Another drawback in the dual fluid system is the temperature loss 
 due to the heat exchanger. Typically the delivery temperature of the 
 collector fluid must be 10°F to 15°F higher than the storage temperature 
 for adequate heat transfer rates to be obtained. The higher temperature 
 results in a decrease in collector efficiency. These factors are 
 discussed in more detail in Module 7. 
 
4-15 
 
 An additional design consideration involving the dual liquid system 
 in Figure 4-12 is the effect of a pump failure or power outage. If 
 circulation ceases, the collector fluid soon begins to boil. A pressure 
 relief mechanism therefore must be included in the system so that steam 
 can be vented and over-pressure will not occur. If liquid loss is 
 excessive, fresh solution will have to be added for operation to 
 continue after power is restored. The automatic liquid make-up arrange- 
 ment shown in Figure 4-13 can partially alleviate this problem, but loss 
 of antifreeze may require manual addition. 
 
 HEAT DISTRIBUTION 
 
 In "hydronic" systems, hot water can be piped from storage to coils 
 imbedded in floors or ceilings (radiant heating) or to "radiators" or 
 fan-coil units or to the common baseboard strip heaters in individual 
 rooms. The operating temperature of baseboard hot water heaters is 
 usually about 180°F, which is too high for use with most 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 most frequently used with solar 
 heating systems. Hot water from the solar storage tank is pumped to a 
 heating coil (finned-tube exchanger) as illustrated in Figure 4-14, and 
 circulating air is heated as it passes through the coil. Warm air is 
 then supplied to the rooms through the conventional distribution system. 
 
4-16 
 
 VENT 
 
 **i MAKE-UP 
 
 WATER 
 
 FLOW 
 
 VENT 
 
 FLOW 
 
 HEAT 
 EXCHANGER 
 
 ^ 
 
 COLLECTOR 
 PUMP 
 
 ^ 
 
 ± 
 
 SOLAR 
 THERMAL 
 STORAGE 
 
 Figure 4-13. 
 
 HEAT EXCHANGER 
 PUMP 
 
 Dual -Li quid Solar Collection with Automatic Make-Up Water 
 Supply 
 
 WARM AIR 
 TO ROOMS 
 
 WARM 
 
 AIR 
 
 FURNACE 
 
 SOLAR 
 
 THERMAL 
 
 STORAGE 
 
 TANK 
 
 ^> 
 
 AA/W, 
 
 i AAAAJ 
 
 _ FUEL OR 
 ELECTRICITY 
 
 HEAT 
 
 TRANSFER 
 
 COIL 
 
 RETURN AIR 
 FROM ROOMS 
 
 Figure 4-14. Solar Heat to Warm Air Distribution System 
 
4-17 
 
 AUXILIARY HEATERS 
 
 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 4-15) 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 automat- 
 ically supplies hot water to air heating coils or to the hydronic 
 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. 
 
 If the building is provided with a warm-air heating system, a warm- 
 air furnace may be used for auxiliary heat supply. This form of 
 auxiliary heat is usually employed when liquid collectors and a liquid- 
 to-air heat exchanger are used for the solar supply, as in Figure 4-14. 
 Electricity or any type of fuel may be supplied to the furnace. 
 Auxiliary heat may also be provided by a heat pump in one of the designs 
 shown in Module 11. 
 
 In an all-liquid solar heating system, with distributed hot water, 
 the auxiliary unit operates as a replacement ; if solar heat either from 
 collector or from storage is insufficient, it is not used and the entire 
 requirement is met by the auxiliary supply. As shown in Figure 4-15, 
 heating is accomplished either with solar or auxiliary energy. If air 
 is heated by transfer from hot water storage, as in Figure 4-14, 
 auxiliary heat may be used as a supplement to "boost" the temperature of 
 
4-18 
 
 SOLAR 
 HEAT 
 
 (STORAGE 
 
 OR 
 COLLECTOR) 
 
 AUTOMATIC 
 VALVE 
 
 AUXILIARY 
 BOILER 
 
 HOT WATER 
 ^ TO HEATING 
 ~ LOAD 
 
 ENERGY INPUT 
 
 *& 
 
 (GAS, ELECTRICITY, etc.) 
 
 RETURN 
 
 V 
 
 PUMP 
 
 Figure 4-15. Typical Use of Auxiliary in Liquid (Hydremic) Distribution 
 System 
 
 the air supply to the rooms. This arrangement is ideal for an air 
 distribution system but is not used in a water loop. 
 
 AUTOMATIC CONTROLS 
 
 To control the temperature in a conventionally heated home, the 
 homeowner needs only to set a thermostat. The same is true for a well- 
 designed solar heating system. However, the controls for solar heating 
 and cooling are necessarily more complex than in a conventional system, 
 because they must control collector and storage pumps or blowers and 
 automatic valves or dampers in addition to the usual functions. An 
 example of a simple control assembly for a solar hot water system is 
 shown in Figure 4-16. 
 
 In nearly all solar hot water and space heating systems, a 
 differential thermostat senses the difference in temperature at 
 
4-19 
 
 FLAT PLATE 
 COLLECTOR 
 
 CHECK 
 VALVE 
 
 
 RELIEF 
 VALVE 
 
 JL 
 
 TO HOUSE 
 
 V^THERMISTOR 
 SENSOR* I 
 
 THERMISTOR 
 SENSOR #2 
 
 DRAIN 
 
 BIBB 
 
 IMMERSION 
 THERMOSTAT 
 (HIGH SET) 
 
 ■ffl 
 
 50 GAL 
 STORAGE 
 
 PUMP 
 
 tXJ: 
 
 
 I BALANCE 
 ! VALVE 
 
 I 
 
 115 VAC_ 
 60 cps 
 
 J_ 
 
 DIFFERENTIAL 
 THERMOSTAT 
 
 ^sH 
 
 i 
 
 r-ekfc: 
 
 30 GAL. 
 
 GAS 
 HEATER 
 
 C: 
 
 \ GAS 
 
 ^? 
 
 .J 
 
 PUMP 
 
 CONTROL 
 
 LINE 
 
 COLD WATER 
 SUPPLY 
 
 ELECTRICAL 
 CONNECTIONS 
 
 s PLUMBING LINES 
 
 Figure 4-16. Typical Solar Hot Water Control System 
 
 collector outlet and in the storage tank. When this difference is more 
 than a few degrees, the circulating pump is operated. The "high set" 
 thermostat (limit control) prevents too high a temperature in the 
 preheat tank by interrupting power to the collector pump. A pressure 
 relief valve protects the system from excessive pressure which might 
 otherwise develop if there is a circulation failure during a sunny 
 period. 
 
 Supply of solar heat to a building is usually controlled by a 
 two-stage thermostat, the normal setting actuating a pump which 
 circulates stored hot water to the rooms or to a central fan-coil 
 exchanger. If the room temperature continues to drop, a second (lower 
 temperature) contact point in the thermostat actuates the supply of fuel 
 or electricity to the auxiliary heater. 
 
4-20 
 
 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 
 
 Several methods can be used for cooling with solar energy. These 
 include absorption refrigeration (lithium bromide-water and ammonia- 
 water systems), Rankine-cycle vapor-compression, desiccant-evaporative 
 cooler combinations, and others. Only the lithium-bromide absorption 
 type is commercial Ty available, and its operation with solar heat has 
 been almost entirely in experimental installations. Although not solar 
 operated, heat pumps are sometimes used in solar heating systems for 
 auxiliary heat supply and for conventional cooling with electric power. 
 
 Design and operation of an absorption cooling system in which 
 solar-heated water is the energy source is illustrated in Figure 4-17. 
 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 
 
 4-21 
 
 AIR TO 
 ROOMS 
 
 AIR 
 
 cp- 
 
 1 
 
 COOLING 
 TOWER 
 
 ^ 
 
 ABSORP 
 TION 
 CHILLER! 
 
 t I 
 
 £7^> 
 
 
 AUXILIARY 
 BOILER 
 
 <S> 
 
 
 t 
 
 COOLING 
 COIL 
 
 HEATING 
 COIL 
 
 AIR FROM 
 ROOMS 
 
 Figure 4-17. Solar Heating and Cooling System 
 
 Other methods of solar cooling are being experimentally 
 investigated, including conventional vapor compression driven by power 
 generated in an on-site engine supplied with steam or organic vapor from 
 a solar collector/ boiler. Experimental desiccant (air-drying) systems 
 in which room air is dehumidified, and the solid or liquid drying agent 
 is regenerated by solar heat are also being studied. None of these 
 systems is at present technically or economically marketable, but 
 considerable development work is being supported by the Federal 
 Government. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 5 
 
 INTRODUCTION TO AIR SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 Page 
 5-ii 
 
 INTRODUCTION 
 
 OBJECTIVES 
 
 AIR-HEATING SOLAR SYSTEMS 
 
 SOLAR COLLECTORS FOR AIR HEATING 
 
 HEAT STORAGE .... 
 COLLECTION AND STORAGE OF SOLAR HEAT 
 
 HEAT DISTRIBUTION . 
 
 AUXILIARY HEATERS . 
 
 AUTOMATIC CONTROLS . 
 
 5-1 
 
 5-1 
 
 5-1 
 
 5-3 
 
 5-5 
 
 5-7 
 
 5-12 
 
 5-12 
 
 5-12 
 
5-ii 
 
 LIST OF FIGURES 
 
 Figure 
 
 5-1 Schematic Diagram of a Air-Heating Solar 
 System (Simplified) ..... 
 
 5-2 Cross-Sectional View Showing Air Flow Through 
 Two Solar Collector Panels in Series 
 
 5-3 Air Flow Diagram 
 
 5-4 Pebble-Bed Heat Storage Unit 
 
 5-5 Air-Heating Solar System . 
 
 5-6 Heating from Collector 
 
 5-7 Storing Heat from Collector 
 
 5-8 Heating from Storage 
 
 5-9 Summer Heating of Domestic Hot Water 
 
 Page 
 
 5-2 
 
 5-4 
 
 5-4 
 
 5-6 
 
 5-7 
 
 5-8 
 
 5-9 
 
 5-10 
 
 5-11 
 
5-1 
 
 INTRODUCTION 
 
 The purpose of this module is to provide a brief introduction to 
 the types of air-heating solar systems that are available and in current 
 use, and to explain the basic functions of the systems and their key 
 components. Air collectors, heat storage in pebble beds, auxiliary heat 
 supply, and system control are described. 
 
 OBJECTIVES 
 
 At the end of this module, the trainee should be able to: 
 
 1. Identify the principal characteristics of air-heating solar 
 systems. 
 
 2. Describe the basic functions of key components of air-heating 
 solar systems. 
 
 3. Recognize the advantages and limitations of different system 
 designs and component types. 
 
 AIR-HEATING SOLAR SYSTEMS 
 
 In the introduction to the discussion of liquid-heating solar 
 systems in Module 4, there is brief mention of air-heating solar, the 
 other principal method for use of solar energy in buildings. 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 5-1 and Figure 4-1. 
 
5-2 
 
 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. Another distinction 
 between the two system types is the direct supply of solar heat from air 
 collectors to load rather than via storage as in most liquid systems. 
 Auxiliary heat is nearly always supplied as a supplement or boost in air 
 systems (Figure 5-1), but in liquid systems having hot water distribu- 
 tion (Figure 4-11), the auxiliary is in parallel rather than in series 
 with the solar supply. 
 
 The most economical type of heat storage unit 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 
 
 BLOWER 
 
 AUTOMATIC 
 DAMPER 
 
 SOLAR 
 
 HEAT 
 
 STORAGE 
 
 UNIT 
 
 It 
 
 AUXILIARY 
 HEATER AND 
 FAN (FURNACE) 
 
 HEAT 
 
 DISTRIBUTION 
 
 SYSTEM 
 
 Figure 5-1. Schematic Diagram of an Air-Heating Solar System 
 (Simplified) 
 
5-3 
 
 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. 
 
 The principles of solar heat collection, storage, distribution, hot 
 water supply, auxiliary requirements, and control, as described under 
 the heading Solar Heating and Cooling Systems in Module 4, apply 
 generally to both air and liquid types, so they are not repeated here. 
 
 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 
 absorber plate. There may also be a difference in absorber plate 
 materials, steel or aluminum normally being used in air collectors, 
 whereas corrosion considerations usually dictate use of copper or 
 stainless steel in liquid types. Figures 5-2 and 5-3 depict a commonly 
 used air collector featuring an internal manifold for air distribution 
 to and from an array of numerous panels. Absorber surface, glazing, 
 bottom insulation, and metal box are similar to those in the liquid 
 type. 
 
 Cool air from a heat storage unit or from the rooms is supplied to 
 the collector, as shown in Figure 5-1, distributed to all the panels in 
 external or internal manifolds, and heated by contact with the hot 
 absorber plates. After passing through one or more series-connected 
 panels, air is delivered from the hot manifold. 
 
5-4 
 
 TEMPERED GLASS 
 COVER 
 
 SELECTIVE COATED 
 ABSORBER PLATE 
 
 AIR CHANNEL 
 
 HOT AIR 
 40°F 
 
 •INTERNAL MANIFOLD AREA 
 
 AIR FLOWS FROM ONE PANEL TO ANOTHER 
 THROUGH THE PORTS AND MANIFOLD AREA 
 
 COLD AIR 
 70° F 
 
 Figure 5-2. Cross-Sectional View Showing Air Flow Through Two Solar 
 Collector Panels in Series 
 
 ABSORBER AIR 
 CHANNEL 
 
 PORTS 
 
 MANIFOLD 
 
 Figure 5-3. Air Flow Diagram 
 
5-5 
 
 Numerous variations in the design of solar air collectors have been 
 investigated. Corrugated, finned, perforated and other modified 
 absorber plate forms have been tested, and there is commercial use of a 
 matrix type in which several layers of slit-and-expanded, blackened 
 aluminum foil is used as the absorber surface with which the air comes 
 in contact. 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. 
 
 There appears to be no advantage and a distinct cost penalty in 
 heating air by use of focusing collectors. Evacuated tube air heaters 
 may, however, reach a commercially practical status after further 
 experimentation and development. 
 
 HEAT STORAGE 
 
 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 on the bin bottom. Depths of 5 to 7 feet 
 are typical, and air supply and withdrawal openings are provided in the 
 top and bottom plenum spaces. Figure 5-4 shows a cut-away view of a 
 pebble bed in a wood bin. 
 
 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 
 
5-6 
 
 HOT AIR 
 CONNECTION 
 
 COLD AIR 
 CONNECTION 
 
 WIRE SCREEN 
 SUPPORTED 
 ON STEEL 
 FRAME. 
 
 in. CONCRETE 
 AGGREGATE 
 
 RIGID INSULATION 
 
 Figure 5-4. Pebble-Bed Heat Storage Unit 
 
 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. 
 Although heat from air collectors could be stored in water and in 
 melted chemical compounds, costs would be considerably higher, separate 
 heat exchangers would be needed, and solar collection efficiency would 
 be reduced by circulation of warmer air to the collector. Pebble beds 
 require considerably more space than these more compact forms of storage 
 (three time the volume of equal heat storage in water), but their 
 advantages far outweigh the added space requirement. 
 
5-7 
 
 COLLECTION AND STORAGE OF SOLAR HEAT 
 
 The collection and storage of heat in a solar air system can be 
 accomplished in a variety of ways. A common type of air- heating solar 
 system is shown in Figure 5-5. The components include: (1) a fixed 
 air-heating solar collector (2) a pebble-bed heat storage unit to and 
 from which heat is transferred by circulating air through the bed (3) a 
 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) an air handling module 
 comprising automatic dampers, filters, and blower(s) (5) a solar hot 
 water heater consisting of an air-to-water heat exchanger and a preheat 
 
 FUEL OR ELECTRICITY 
 
 MOTORIZED 
 DAMPERS 
 
 BLOWER 
 
 X 
 
 ^ 
 
 SUMMER 
 
 BYPASS 
 
 _PLENUM_ 
 
 PEBBLE-BED 
 STORAGE 
 
 PLENUM 
 
 <)- 
 
 BACK- DRAFT 
 DAMPERS 
 
 AUXILIARY 
 i FURNACE 
 
 KD 
 
 WARM AIR 
 
 TO BUILDING 
 
 'HEATING LOAD 
 
 ^ TO DHW 
 LOAD 
 
 -FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 COLD 
 
 WATER 
 
 MAIN 
 
 RETURN AIR 
 
 FROM BUILDING 
 
 Figure 5-5. Air-Heating Solar System 
 
5-8 
 
 storage tank connected to an auxiliary hot water heater and (6) an 
 auxiliary heating unit (usually a warm-air furnace) to provide 
 100 percent back-up space heating when storage temperatures are 
 insufficient to meet demands or when the solar system is not operating. 
 In an air heating system, the collector absorbs solar radiation and 
 converts it to heated air for space heating. Air is circulated from the 
 solar system to the building in the same manner as in most modern warm 
 air heating systems. As air flows from one end of the collector to the 
 other, its temperature normally rises from 70°F to 130°F or 150°F during 
 the mid-part of the day. As shown in Figure 5-6, the building is heated 
 
 L OR ELECTRICITY 
 
 AUXILIARY 
 * FURNACE 
 
 PEBBLE-BED 
 STORAGE 
 
 PLENUM 
 
 _.....,......_.._..... 
 
 BACK- DRAFT 
 DAMPERS 
 
 WARM AIR 
 
 TO BUILDING 
 
 HEATING LOAD 
 
 TO DHW 
 LOAD 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 COLD 
 
 WATER 
 
 MAIN 
 
 ,..tt..£.:jis. .... ■ **,..:>M,,*™'T 
 
 _ RETURN AIR 
 FROM BUILDING 
 
 Figure 5-6. Heating from Collector 
 
5-9 
 
 directly by air from the collector whenever heating is needed during 
 sunny periods. Cool air from the building is returned to the collector 
 for reheating. 
 
 Heat is stored by utilizing the heat exchange and heat storage 
 characteristics of dry pebbles, the most practical storage medium for 
 use with air heating collectors. When heat is not needed in the 
 building, solar-heated air is routed through the storage unit as in 
 Figure 5-7, thereby heating the pebbles; cool air, usually at 70°F, 
 returns to the collector for reheating. Temperature stratification in 
 the storage unit assures maximum heat recovery from the solar air 
 collector. 
 
 s 
 
 Bill 
 
 MOTORIZED 
 DAMPERS 
 
 SUMMER 
 
 BYPASS 
 
 PEBBLE-BED 
 STORAGE 
 
 UPLENUMJ 
 
 .^jLj^s*,,.,^.^..^ :■.-, - 
 
 BACK- DRAFT 
 DAMPERS 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY 
 i FURNACE 
 
 WARM AIR 
 
 TO BUILDING 
 
 HEATING LOAD 
 
 TO DHW 
 LOAD 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 COLD 
 
 WATER 
 
 MAIN 
 
 RETURN AIR 
 
 FROM BUILDING 
 
 Figure 5-7. Storing Heat from Collector 
 
5-10 
 
 MOTORIZED 
 DAMPERS 
 
 FUEL OR ELECTRICITY 
 
 BLOWER AUXILIARY 
 
 " FURNACE 
 
 .CZ-L 
 
 SUMMER 
 
 BYPASS 
 
 } 
 
 7 
 
 „ENU 
 
 PEBBLE-BED 
 STORAGE 
 
 PLENUM 
 
 . 
 
 BACK-DRAFT 
 DAMPERS 
 
 ^D 
 
 WARM AIR 
 
 TO BUILDING 
 
 "HEATING LOAD 
 
 TO DHW 
 LOAD 
 
 •FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 COLD 
 
 WATER 
 
 MAIN 
 
 RETURN AIR 
 FROM BUILDING 
 
 Figure 5-8. Heating from Storage 
 
 In the evening and nighttime hours, heat is delivered to the rooms 
 by circulating air from the building through the pebble bed, as in 
 Figure 5-8. Because of temperature stratification in the storage unit, 
 this mode supplies heat to the rooms at the highest available 
 temperature. The system automatically provides auxiliary heating from 
 fuel or electricity when the solar supply is insufficient to meet 
 requirements. 
 
 Domestic hot water can be heated by use of an air-to-water heat 
 exchanger in the hot air duct from the collector. As shown in 
 Figure 5-7, when solar heat is being transferred to storage, heat is 
 
5-11 
 
 also being supplied to the hot water system if needed and if the water 
 pump is running. The temperature of the air passing through the water 
 heating coil is thus usually reduced by a degree or two. When warm air 
 is being supplied from storage to the rooms, Figure 5-8, no water 
 heating occurs because there is no water circulation through the coil. 
 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, as shown in 
 Figure 5-9, and air flow to storage and to the building is blocked. 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY 
 ♦ FURNACE 
 
 WARM AIR 
 
 TO BUILDING 
 
 HEATING LOAD 
 
 TO DHW 
 LOAD 
 
 FUEL OR ELECTRICITY 
 
 AUXILIARY WATER 
 HEATER 
 
 BACK- DRAFT 
 DAMPERS 
 
 RETURN AIR 
 FROM BUILDING 
 
 Figure 5-9. Summer Heating of Domestic Hot Water 
 
5-12 
 
 Nearly 100 percent of typical hot water requirements can thus be met by 
 solar in four to five warm months. Thus solar energy can provide 
 preheated water whenever the collector is in operation. 
 
 At the present time no cooling equipment is commercially available 
 for operation by means of solar heated air. 
 
 HEAT DISTRIBUTION 
 
 Heat is distributed in a solar air system through conventional 
 ductwork associated with a forced warm- air furnace. Air from the 
 collector or from the hot end (usually the top) of the pebble bed is 
 drawn into the auxiliary furnace, heated further if necessary, and pjped 
 to the zones of the building in which heat is required. Simultaneously, 
 air is circulated from the rooms, via cold air return ducts or passages, 
 back to the collector or storage for reheating. 
 
 AUXILIARY HEATERS 
 
 Figures 5-6 and 5-8 show the customary pattern of auxiliary heater 
 use with solar air systems. A gas furnace, oil furnace, or electric 
 resistance coil may be used as required to raise the temperature of 
 solar heated air from collector or storage. Full design capacity must 
 be provided so that comfort can be maintained without solar supply 
 during the coldest weather. As shown in a subsequent module, a heat 
 pump may also be used as auxiliary heat supply, necessitating a by-pass 
 duct which can return air to the heat pump directly without partial 
 heating in the pebble bed. 
 
5-13 
 
 AUTOMATIC CONTROLS 
 
 The only appreciable difference in control equipment and operation 
 in liquid and air systems is the location of one of the sensors in the 
 differential thermostat controlling collector blower operation. Rather 
 than the low temperature sensor being located in the main storage tank 
 as in the liquid system, this sensor is usually mounted in the duct 
 supplying air to the collector. Although ordinarily at about 70°F, the 
 temperature of air supplied to the collector may be considerably higher, 
 particularly in spring and fall. By locating the sensor in the 
 collector return duct, it responds to temperature of air returning 
 either from the rooms or from storage, so proper collector operation is 
 assured. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 6 
 
 SOLAR RADIATION 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 
 COLORADO STATE UNIVERSITY 
 
 FORT COLLINS, COLORADO 
 
6-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 6-ii 
 
 LIST OF TABLES 6-i i i 
 
 GLOSSARY OF TERMS 6-iv 
 
 INTRODUCTION 6-1 
 
 OBJECTIVE 6-1 
 
 UNITS 6-2 
 
 VARIABILITY OF SOLAR ENERGY ON THE EARTH'S SURFACE . . 6-3 
 
 SOLAR CONSTANT 6-3 
 
 THE SOLAR SPECTRUM 6-4 
 
 ENERGY REACHING EARTH 6-4 
 
 MONTHLY VARIATIONS 6-6 
 
 DAILY VARIATIONS 6-8 
 
 HOURLY VARIATIONS 6-9 
 
 EFFECT OF SURFACE TILT 6-9 
 
 EFFECTS OF COLLECTOR ORIENTATION 6-12 
 
 SOLAR DATA FOR SYSTEM DESIGN 6-13 
 
 REFERENCES 6-21 
 
6-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 6-1 Approximate Representation of the Useful Spectrum 
 of Solar Energy for Space Heating and Cooling 
 
 Systems ......... 6-5 
 
 6-2 Atmospheric Effects on Solar Radiation Reaching 
 
 Earth 6-5 
 
 6-3 Energy Intercepted by a Unit-Width Horizontal 
 
 Surface ......... 6-7 
 
 6-4 Monthly Variation of Average Daily Radiation on a 
 
 Horizontal Surface, Boulder, Colorado . . . 6-7 
 
 6-5 Hourly Record of Clear Day Radiation on a Horizontal 
 
 Surface at Fort Collins, Colorado .... 6-10 
 
 6-6 Effect of Tilting the Collector on Energy 
 
 Intercepted ........ 6-10 
 
 6-7(a) Variation of the Angle of Incoming Radiation 
 
 with Season ........ 6-12 
 
 6-7(b) Collector Tilt to Maximize Winter Collection . . 6-12 
 
 6-8 Mean Daily Solar Radiation (Langleys), January . 6-15 
 
 6-9 Mean Daily Solar Radiation (Langleys), February . 6-15 
 
 6-10 Mean Daily Solar Radiation (Langleys), March . . 6-16 
 
 6-11 Mean Daily Solar Radiation (Langleys), April . . 6-16 
 
 6-12 Mean Daily Solar Radiation (Langleys), May . . 6-17 
 
 6-13 Mean Daily Solar Radiation (Langleys), June . . 6-17 
 
 6-14 Mean Daily Solar Radiation (Langleys), July . . 6-18 
 
 6-15 Mean Daily Solar Radiation (Langleys), August . 6-18 
 
 6-16 Mean Daily Solar Radiation (Langleys), September . 6-19 
 
 6-17 Mean Daily Solar Radiation (Langleys), October . 6-19 
 
 6-18 Mean Daily Solar Radiation (Langleys), November . 6-20 
 
 6-19 Mean Daily Solar Radiation (Langleys), December . 6-20 
 
6-iii 
 LIST OF TABLES 
 
 Table Page 
 
 6-1 Energy Units ........ 6-2 
 
 6-2 Energy Conversion Factors ..... 6-3 
 
 6-3 Monthly Variations in Energy on a Horizontal Surface 
 
 Selected Cities, (U.S. )(Btu/ft 2 -day) ... 6-8 
 
 6-4 Mean Daily Solar Radiation (Langleys) . . . 6-14 
 
6-iv 
 
 GLOSSARY OF TERMS 
 
 beam radiation 
 Btu 
 
 calorie 
 
 diffuse radiation 
 
 direct radiation 
 
 infrared radiation 
 
 insolation 
 latitude 
 
 northern hemisphere 
 ozone layer 
 
 ultraviolet radiation 
 
 See "direct radiation" 
 
 British Thermal Unit - the amount of heat 
 required to raise the temperature of one pound 
 of water one degree Fahrenheit 
 
 The amount of heat required to raise the 
 temperature of one gram of water one degree 
 Centigrade 
 
 Radiation that has been scattered in passing 
 through the atmosphere 
 
 Radiation received by a surface directly from 
 the region of the solar disc 
 
 Non-visible radiation just beyond the red end 
 of the visible spectrum 
 
 Solar radiation that is received by a surface 
 
 Angular distance, measured in degrees, north or 
 south from the equator 
 
 Half of the Earth north of the equator 
 
 A layer in the upper atmosphere comprised 
 primarily of the gas ozone (0 3 ) 
 
 Non-visible radiation with short wave lengths 
 just beyond the violet end of the visible 
 spectrum 
 
 visible radiation 
 
 Radiation that is perceptible by the eye 
 
6-1 
 
 INTRODUCTION 
 
 Solar energy starts, of course, with the sun. The sun is a huge 
 nuclear fusion reactor located at an average distance of 93 million 
 miles from earth. It has a surface temperature of about 10,000°F, and 
 gives off energy continuously in the form of electromagnetic radiation 
 with a wide spectrum of wave lengths. Only a small band of wave lengths 
 near and including the visible band is useful for solar collectors and 
 for generating heat for homes. Fortunately this small band contains 
 about 99 percent of the useful solar energy received on earth. 
 
 OBJECTIVE 
 
 The objective of this module is to present the factors which affect 
 the availability of solar radiation at the earth's surface. At the end 
 of this module the trainee should be able to: 
 
 1. Estimate the amount of solar radiation available on the 
 earth's surface on a clear day. 
 
 2. Recognize seasonal variations in solar radiation. 
 
 3. Recognize daily variations in solar radiation. 
 
 4. Differentiate between beam and diffuse radiation. 
 
 5. Estimate the amount of solar energy reaching a collector 
 surface during a typical day of a month. 
 
 6. Recognize the various units used to measure solar energy. 
 
 7. Given conversion factors, convert solar radiation from one set 
 of units to another. 
 
 8. Select the data needed for planning a solar system. 
 
6-2 
 
 UNITS 
 
 The intensity of solar energy is expressed in several different 
 units. In this manual one unit will consistently be used, Btu/ft 2 . 
 However, other units are found in the literature, and it is therefore 
 necessary to be able to convert from one unit to another. Units 
 commonly found are listed in Table 6-1. 
 
 Table 6-1 
 Energy Units 
 
 Abbreviation 
 
 Unit 
 
 Energy Density 
 
 Btu/ft 2 
 
 KJ/m 2 
 Langley (cal/cm 2 ) 
 
 British Thermal Units per square foot 
 Kilo joules 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 foot 
 per hour 
 
 Kilo joules per square meter per hour 
 
 calories per square centimeter per 
 minute 
 
 Watts per square meter 
 
 Table 6-2 gives conversion factors from one set of units to 
 another. An example will show the use of this table. The Climatic 
 Atlas of the United States lists the annual average daily solar 
 
6-3 
 
 Table 6-2 
 Energy Conversion Factors 
 
 To Convert 
 
 into Btu/ft 2 
 
 To Convert into 
 
 Btu/ft 2 -hr 
 
 Multiply 
 
 By. 
 
 Multiply 
 
 By 
 
 Langleys 
 
 3.69 
 
 Langleys/min 
 
 221 
 
 KJ/m 2 
 
 .088 
 
 KJ/m 2 -hr 
 
 .088 
 
 
 
 W/m 2 
 
 .316 
 
 radiation for Boulder, Colorado, as 367 Langleys per day. To obtain the 
 
 value in Btu/(ft 2 *day), 367 Langleys per day are multiplied by the 
 
 conversion factor (3.69) in Table 6-2: 
 
 367 Langleys g Btu/ft 2 . = 354 Btu 
 day Langley ft ZT day 
 
 VARIABILITY OF SOLAR ENERGY ON THE EARTH'S SURFACE 
 
 SOLAR CONSTANT 
 
 The intensity of the sun's energy on a surface varies with distance 
 from the sun. At the average earth-sun distance, out in space, the 
 intensity of solar energy has been determined to be 428 Btu/(ft 2< hr) 
 with a variability of about three percent. The value of 
 428 Btu/(ft 2 -hr) is called the "solar constant." Due to the earth's 
 elliptical orbit around the sun, the distance from the earth to the sun 
 changes during the year so that the energy reaching the outer atmosphere 
 of the earth varies from 410 to 440 Btu/(ft 2 «hr). In addition to the 
 variability in solar radiation that reaches the outer atmosphere around 
 
6-4 
 
 earth due to seasons, there are very large variations in the amount of 
 solar energy available at a particular location on the earth's surface. 
 Radiation reaching the earth's surface is of primary interest for 
 terrestrial applications, and the intensity will vary considerably with 
 latitude, season of the year, and local weather conditions. 
 
 THE SOLAR SPECTRUM 
 
 The radiation from the sun can be separated into three major energy 
 portions as shown in Figure 6-1. The high frequency (short wave length) 
 energy in the radiation spectrum is labeled "ultraviolet" or "UV" and is 
 detected by the human body primarily in terms of sunburn. The medium 
 frequency energy radiation band in the solar spectrum is the visible 
 band. The low frequency (long wave length) radiation band is the 
 "infrared" or "IR" region. The amount of ultraviolet energy in the 
 solar spectrum is small, essentially negligible in terms of useful 
 heating effect. The visible band comprises about 47 to 48 percent of 
 useful radiation for heating and the "near" infrared band makes up the 
 balance. The intensity will vary with latitude, elevation and time of 
 day and year because the amount of radiation that is absorbed and 
 scattered by the atmosphere depends on the thickness of the atmosphere 
 through which solar radiation must penetrate. 
 
 ENERGY REACHING EARTH 
 
 The energy reaching earth is less than the "outer space" intensity. 
 There are a number of factors that cause this reduction as illustrated 
 in Figure 6-2. Some of the energy is reflected back into outer space 
 
6-5 
 
 l 2 
 
 Wavelength, X (^m) 
 
 Figure 6-1. Approximate Representation of the Useful Spectrum of Solar 
 Energy for Space Heating and Cooling Systems 
 
 UPPER 
 ATMOSPHERE 
 
 DUST 
 
 (SCATTERING) 
 
 DIFFUSE RADIATION DIRECT RADIATION EARTH 
 
 Figure 6-2. Atmospheric Effects on Solar Radiation Reaching Earth 
 
6-6 
 
 by the top of the atmosphere, much as light is reflected from a mirror. 
 Still more is reflected from the tops of clouds. 
 
 A portion of the radiation is absorbed by chemical constituents in 
 the atmosphere. The ozone layer absorbs much of the ultraviolet 
 radiation, and carbon dioxide, oxygen, and water vapor also absorb 
 radiation. Some of the radiation is scattered by dust and clouds. 
 
 Radiation that is received from the solar disc is called "direct 
 radiation", that is, the sun's rays have not been scattered in passing 
 through the atmosphere. Solar radiation received from other directions 
 is called "diffuse radiation" because it has been scattered by clouds or 
 other particles. On a "clear" day most of the energy reaches earth as 
 direct radiation, but on a cloudy overcast day, when the sun's disc 
 cannot be seen, a large portion or all of the solar radiation at a 
 particular location on earth may be diffuse. 
 
 MONTHLY VARIATIONS 
 
 Solar energy on a horizontal surface at any location on earth, 
 averaged over a month, shows a month-to-month variation. This variation 
 is due to earth's rotation about the sun and to seasonal changes in 
 weather which affect the cloud cover. In the winter the sun is lower in 
 the sky than in the summer, and the resultant larger incident angle 
 between the path of the sun rays and a line perpendicular to a hori- 
 zontal surface reduces the amount of radiation intercepted by the 
 earth's surface, as shown in Figure 6-3. Figure 6-3(A) shows the energy 
 intercepted by a unit width of horizontal surface when the sun is at a 
 low angle as it is in winter. In Figure 6-3(B), the sun is shown at a 
 higher angle, as in a summer month, and a larger amount of energy is 
 intercepted. 
 
6-7 
 
 SOLAR RADIATION 
 12 "UNITS" 
 
 SOLAR RADIATION 
 12 "UNITS" 
 
 (A) LOW SUN ANGLE, WINTER 
 4 "RADIATION UNITS" 
 INTERCEPTED 
 
 'B) HIGH ScK ANGLE, 
 SUMMER 
 
 6 "RADIAT'.CM JN! T 3" 
 INTERCEPT ID 
 
 Figure 6-3. Energy Intercepted by a Unit-Width Horizontal Surface 
 
 The monthly variation in solar radiation incident on a horizontal 
 surface in Boulder, Colorado, is shown in Figure 6-4. There is 
 approximately twice as much radiation during June and July as in 
 December and January. 
 
 2000 
 
 1000 
 
 CD 
 
 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 
 
 Figure 6-4. Monthly Variation of Average Daily Radiation on a 
 
 Horizontal Surface, Boulder, Colorado (From the Climatic 
 Atlas of the United States) 
 
6-8 
 
 Monthly variations for some other cities are listed in Table 6-3. 
 The variation in Chicago from December to June is about 6 times, and in 
 Washington it is about a factor of 3. Other cities in the U.S. exhibit 
 variations similar to those shown in Figure 6-4. 
 
 Table 6-3 
 
 Monthly Variations in Energy on a Horizontal Surface for 
 Selected Cities in the United States 
 Btu/(ft 2 -day) 
 
 City 
 
 December 
 
 March 
 
 June 
 
 September 
 
 Chicago, Illinois 
 
 280 
 
 835 
 
 1685 
 
 1152 
 
 Tucson, Arizona 
 
 1122 
 
 1987 
 
 2582 
 
 2098 
 
 Washington, D.C. 
 
 611 
 
 1266 
 
 1818 
 
 1380 
 
 Miami, Florida 
 
 1163 
 
 1800 
 
 1958 
 
 1619 
 
 Fairbanks, Alaska 
 
 22 
 
 784 
 
 1855 
 
 622 
 
 Los Angeles, California 
 
 887 
 
 1730 
 
 2193 
 
 1851 
 
 DAILY VARIATIONS 
 
 The total amount of solar radiation reaching a horizontal surface 
 on earth varies from day to day, primarily because of atmospheric 
 phenomena. Clouds, dust, and other particulate matter in the atmosphere 
 cause variations in radiation absorption and scatter. Daily variations 
 are large, and may range from zero useful heating energy to 2000 to 2500 
 Btu/(ft 2 -day). The values shown in Figure 6-4 are typical for the 
 Colorado Front Range region. 
 
6-9 
 
 HOURLY VARIATIONS 
 
 Hourly variations in available solar energy at a given location are 
 principally due to the earth's rotation although cloudiness can have 
 significant effects. Early morning sun is at a very low angle and the 
 solar rays must pass through a large thickness of atmosphere. The 
 intensity of the energy received is therefore low. The hourly peak in 
 radiation occurs at noon, when the sun is at the highest angle and is 
 passing through the minimum thickness of the atmosphere. Since winter 
 days are shorter than summer days, the period during which solar energy 
 can be collected varies with season. 
 
 The hourly variation in solar intensity on a horizontal surface, 
 measured in Fort Collins, Colorado, is shown in Figure 6-5. The smooth 
 curves indicate that these data were obtained on clear days. The 
 presence of clouds would result in breaks and irregularities in the 
 curves. Note the higher intensity and longer period of measurable 
 radiation during a summer month than in a winter month. 
 
 EFFECT OF SURFACE TILT 
 
 Discussion so far has concerned only the radiation on a horizontal 
 surface. In fact, when designing a solar collector, it is advantageous 
 to tilt the collector so that it is more nearly perpendicular to the 
 sun's rays. Figure 6-6 illustrates the increase in energy intercepted by 
 a collector when it is tilted with respect to a horizontal plane. The 
 maximum amount of energy that can be intercepted by a plane surface is 
 that which is received by the surface when perpendicular to the sun's 
 rays as shown in Figure 6-6(B). When the collector is tilted at any 
 
6-10 
 
 300 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6/ 
 
 /75 
 
 
 
 
 
 
 
 
 
 
 
 
 250 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4/26/75 
 
 
 
 
 
 
 
 
 ^ 200 
 
 x: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 M 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 150 
 
 m 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1/19/75 ^\ 
 
 
 
 
 
 
 
 100 
 50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <■ 
 
 » 5 6 7 8 9 10 II 12 
 
 2 3 4 5 6 7 
 
 Time of Day 
 
 Figure 6-5. Hourly Record of Clear Day Radiation on a Horizontal Surface 
 at Fort Collins, Colorado (Data from Solar House I) 
 
 (A) COLLECTOR TILT ANGLE 0° (B) COLLECTOR TILT ANGLE 45° (O COLLECTOR TILT ANGLE 75° 
 
 RADIATION INTERCEPTED BY A HORIZONTAL COLLECTOR 
 ADDITIONAL RADIATION INTERCEPTED BY TILTING COLLECTOR 
 
 Figure 6-6. Effect of Tilting the Collector on Energy Intercepted 
 
6-11 
 
 other angle the amount of energy intercepted is reduced as shown in 
 Figure 6-6(C). 
 
 Maximum energy would be intercepted by a collector if the plane 
 surface were to track the sun across the sky so that the rays would 
 always be perpendicular to the plane. Such a requirement would involve 
 continuous movement of the collector from east to west and in angle of 
 tilt, throughout the day. Tracking can be accomplished but is not 
 considered practical or economical for collectors in solar space heating 
 systems. 
 
 Since tracking is impractical, a compromise is to tilt the 
 collector so that it is roughly perpendicular to the sun's rays at solar 
 noon during the months when maximum heat collection is desired. The 
 best angle for a given location depends on the time of year most heat is 
 needed, since the sun moves across the sky at a lower angle in the 
 winter than in the summer. For space heating purposes, maximum 
 collection is desired during the coldest months. During this season, 
 from about October until March, the sun's angle varies from 5 degrees to 
 23 degrees below a line drawn at an angle from the perpendicular equal 
 to the latitude of the location as illustrated in Figure 6-7(A). To 
 maximize collection during the heating season a good compromise is to 
 tilt the collector at an angle of about latitude plus 15 degrees as 
 illustrated in Figure 6-7(B). 
 
 In the northern hemisphere the collector should be tilted to the 
 south; the opposite is true in the southern hemisphere. To maximize 
 summer collection the collector can be tilted to latitude minus 15 
 degrees. If both summer and winter collection are desired, a good 
 compromise is to tilt the collector to an angle equal to the latitude. 
 
6-12 
 
 SEPTEMBER 21 j Un e 21 
 MARCH 21 v \ 
 
 \ 
 \ 
 
 DECEMBER 21 
 
 HORIZONTAL 
 
 LATITUDE 
 ANGLE 
 
 (A) DECEMBER 21. SUN 23' BELOW LAT. ANGLE FROM 
 
 PERPENDICULAR 
 JUNE 21, SUN 23* ABOVE LAT. ANGLE FROM PERPENDICULAR. 
 SEPTEMBER 21 AND MARCH 21. SUN AT LAT. ANGLE FROM 
 
 PERPENDICULAR. 
 
 SEPTEMBER 21 
 
 MARCH 2K 
 
 
 DECEMBER 21 
 
 
 COLLECTOR 
 
 
 
 Vlatitude 
 
 HORIZONTAL // 
 
 \ +15" 
 
 -LATITUDE 
 ANGLE 
 
 (B) COLLECTOR TILTED AT LATITUDE +15* MAXIMIZES 
 WINTER COLLECTION. 
 
 Figure 6-7. (a) Variation of the Angle of Incoming Radiation 
 with Season 
 
 (b) Collector Tilt to Maximize Winter Collection 
 
 EFFECTS OF COLLECTOR ORIENTATION 
 
 Since the maximum intensity of direct radiation occurs at noon when 
 the sun is due south (northern hemisphere), the collectors should face 
 directly south. If this is not practical because of building 
 considerations, a variation of 15 degrees east or west of due south can 
 be tolerated without serious effect on the total energy collected. An 
 orientation 15 degrees east of south will advance the time of peak 
 collection one hour; an orientation 15 degrees west of south will delay 
 the peak one hour. In some cases a designer can take advantage of the 
 change in peak collection. If, for example, the collectors are 
 partially shaded in the later afternoon, facing the collectors east of 
 south would increase daily energy collection. 
 
6-13 
 
 SOLAR DATA FOR SYSTEM DESIGN 
 
 Solar heating and cooling systems can be sized on the basis of 
 monthly average daily radiation on a horizontal surface. Tabular values 
 are listed for each month in Table 6-4, for many cities in the United 
 States. The yearly average daily radiation for the cities is also 
 included in the table. Because the data for specific locations are 
 limited, and estimates for adjacent areas are desirable, it is 
 convenient to arrange a graphical presentation of the distributions of 
 the monthly average daily radiation as i so- intensity lines on a map of 
 the United States, as shown in Figures 6-8 through 6-19. 
 
 The sizing techniques used in this manual do not require detailed 
 knowledge of the quantities of solar radiation available. The 
 calculation method includes average available radiation intrinsically in 
 the procedure, and computer-generated tables are provided. 
 Nevertheless, it is instructive to examine the amount of solar radiation 
 available at a particular site in the tables or charts and compare the 
 differences in available solar energy in various parts of the United 
 States. 
 
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6-15 
 
 Figure 6-8. Mean Daily Solar Radiation (Langleys), January 
 
 Figure 6-9. Mean Daily Solar Radiation (Langleys), February 
 
6-16 
 
 Figure 6-10. Mean Daily Solar Radiation (Langleys), March 
 
 fi^Sr^? ~ ^MEAN DAILY SOLAR RADIATION (Langleys)' 
 
 —APRIL 
 
 Figure 6-11. Mean Daily Solar Radiation (Langleys), April 
 
6-17 
 
 Figure 6-12. Mean Daily Solar Radiation (Langleys), May 
 
 Figure 6-13. Mean Daily Solar Radiation (Langleys), June 
 
6-18 
 
 Figure 6-14. Mean Daily Solar Radiation (Langleys), July 
 
 Figure 6-15. Mean Daily Solar Radiation (Langleys), August 
 
6-19 
 
 Figure 6-16. Mean Daily Solar Radiation (Langleys), September 
 
 
 .. j^7~7~MEAN _DA I LY SOLAR RADIATION jLangleys) 
 
 Figure 6-17. Mean Daily Solar Radiation (Ungleys) , October 
 
6-20 
 
 h- .' )''■">" 'ft-*-' 
 
 Figure 6-18. Mean Daily Solar Radiation (Langleys), November 
 
 "(Mjjjfc;-- -L.TPBAN DAJLYSOLAR RADIATION (Langleys! 
 
 i M^t, W / /"'^y^fl iritl DECEMBER- 
 
 
 Figure 6-19. Mean Daily Solar Radiation (Langleys), December 
 
6-21 
 
 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-RA-N-74-062, NOAA, September 
 1974. 
 
 2. Liu, B.Y.H. and Jordan, R.C., "A Rational Procedure for Predicting 
 a Long-Term Average Performance of Flat-Plate Collectors", Solar 
 Energy , Vol. 17, No. 2, 1963. 
 
 3. Liu, B.Y.H. and Jordan, R.C., "The Interrelationship and 
 Characteristic Distribution of Direct, Diffuse, and Total Solar 
 Radiation", Solar Energy , Vol. 4, No. 3, pp. 1-19, 1960. 
 
 4. Duffie, J. A. and Beckman, W.A. , Solar Energy Thermal Processes , 
 John Wiley and Sons, New York, New York, 1974. 
 
 5. Liu, B.Y.H., and Jordan, R.C. , "Availability of Solar Energy for 
 Flat-Plate Solar Heat Collectors", Chapter V, Applications of Solar 
 Energy for Heating and Cooling of Buildings. ASHRAE GRP 170 edited 
 by Jordan and Liu, ASHRAE, Inc., N.Y., N.Y., 1977. 
 
 6. 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. 
 
 7. National Bureau of Standards, Intermediate Minimum Property 
 Standards for Solar Heating and Domestic Hot Water Systems. Report 
 No. NBSIR 77-1226, March 1977. 
 
 8. Beckman, W.A. , Klein, S.A. and Duffie, J. A., Solar Heating Design 
 by the f-chart Method , John Wiley and Sons, New York, N.Y., 1977. 
 
 9. Solar Energy Applications Laboratory, Colorado State University, 
 Solar Heating and Cooling of Residential Buildings, Design of 
 Systems, (Available from U.S. Government Printing Office). 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 7 
 
 SOLAR COLLECTORS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 7-ii 
 
 LIST OF TABLES 7-ii 
 
 INTRODUCTION 7-1 
 
 OBJECTIVE 7-1 
 
 BASIC PRINCIPLES 7-2 
 
 TYPES OF FLAT-PLATE COLLECTORS 7-3 
 
 TYPICAL LIQUID COLLECTOR 7-3 
 
 TYPICAL AIR COLLECTOR 7-6 
 
 DESIGN AND OPERATION OF FLAT-PLATE SOLAR COLLECTORS . . 7-6 
 
 GLAZING 7-9 
 
 Glass 7-9 
 
 Plastic 7-10 
 
 ABSORBER 7-11 
 
 INSULATION 7-12 
 
 FRAME 7-13 
 
 LIQUID COLLECTORS FOR SPACE HEATING AND HOT WATER . . . 7-14 
 
 AIR COLLECTORS FOR SPACE HEATING 7-16 
 
 LOW TEMPERATURE LIQUID COLLECTORS 7-19 
 
 HIGH TEMPERATURE COLLECTORS - EVACUATED TUBES . . . 7-20 
 
 COLLECTOR EFFICIENCY 7-24 
 
 INSTANTANEOUS COLLECTOR EFFICIENCY 7-24 
 
 DAILY COLLECTOR EFFICIENCY 7-28 
 
 REFERENCES 7-29 
 
7-ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 7-1 Typical Liquid-Heating Collector .... 7-4 
 
 7-2 Types of Flat-Plate Liquid Solar Collectors . . 7-5 
 
 7-3 Typical Air-Heating Collector ..... 7-7 
 
 7-4 Solar Air Heater with Internal Manifold - Two 
 
 Collectors in Series ...... 7-7 
 
 7-5 Types of Flat-Plate Air Solar Collectors . . 7-8 
 
 7-6 Typical Arrangement of Internally Manifolded 
 
 Collector Modules in an Array ..... 7-18 
 
 7-7 Types of Evacuated Tube Collectors .... 7-22 
 
 7-8 Measured Solar Collector Efficiencies of Several 
 
 Collectors 7-27 
 
 LIST OF TABLES 
 
 Table Page 
 
 7-1 Collector Performance Parameters .... 7-25 
 
7-1 
 
 INTRODUCTION 
 
 A solar collector is an energy exchange device which receives and 
 absorbs solar radiation and supplies a substantial portion of that 
 energy in the form of a heated stream of fluid. 
 
 The purpose of this module is to identify and explain those 
 principles which influence the installation, operation and design of the 
 principal commercial types of collectors and to indicate maintenance 
 requirements. 
 
 Solar collectors for space heating and hot water use are almost 
 exclusively factory-built. Construction of the collector itself is 
 therefore not the responsibility of the installer. Although a few 
 site-built solar collectors are in use, economy, quality and durability 
 "strongly depend on machine manufacture. Rather than explaining how 
 collectors are made, the purpose of this discussion is therefore to show 
 how they are selected, installed, used and serviced. 
 
 OBJECTIVE 
 
 At the end of this module, the trainee should be able to: 
 
 1. Identify and describe the functions of a solar collector and 
 its component parts. 
 
 2. Compare the performance of various types of collectors. 
 
 3. Describe methods for preventing corrosion and freezing of 
 collectors. 
 
 4. Describe the function of various fluids in collectors. 
 
 5. Recognize effect of system design changes on collector 
 performance. 
 
7-2 
 
 6. Explain the factors contributing to solar collector 
 durability. 
 
 BASIC PRINCIPLES 
 
 A solar collector receives solar radiation, converts the absorbed 
 energy to heat, and delivers a heated fluid to use. The collector 
 contains an absorber plate (commonly a black metal surface), the 
 temperature of which rises when solar energy is absorbed. A portion of 
 the absorbed energy is transferred to a fluid as heat and then trans- 
 ported to another part of the system. In the process of collecting 
 energy and transferring the heat, the absorber plate loses some of the 
 heat to its surroundings, so other components of the solar collector are 
 provided to reduce the heat losses. 
 
 Heat is lost from the absorber plate by radiation, convection, and 
 conduction. Insulation beneath the absorber reduces the heat loss 
 through the back of the collector, and one or more transparent covers 
 reduce the heat losses from the top or front of the collector. A glass 
 cover, which is opaque to the thermal radiation emitted by the plate, 
 also reduces convection losses to the outside air, because the air space 
 between the absorber plate and cover restricts convective air motion. 
 
 The useful energy from a solar collector is transferred to a fluid 
 and delivered directly to the building or to storage, where it can be 
 used at a later time. The two principal collector types are either 
 liquid (usually water) heaters or gas (always air) heaters. Water or a 
 solution of water and ethylene glycol (antifreeze) is normally used in 
 liquid collectors, but several other liquids can be used. 
 
7-3 
 
 TYPES OF FLAT-PLATE COLLECTORS 
 
 Solar collectors may be divided into two main classifications based 
 on the type of heat transfer fluid used. Liquid-heating collectors are 
 used for heating water and non-freezing aqueous solutions, and 
 occasionally for non-aqueous heat transfer liquids. Gas-heating 
 collectors are employed as air heaters. The principal difference 
 between the two types is the design of the passages for the heat 
 transfer fluid. 
 
 TYPICAL LIQUID COLLECTOR 
 
 Figure 7-1 is a partial sectional diagram of a typical flat-plate 
 liquid solar collector. The drawing shows a commercially manufactured 
 collector comprising a glass-covered metal box containing a blackened 
 absorber plate to which an array of tubes is attached and beneath which 
 insulation is provided. Typical collector dimensions are 6.5 ft by 3 ft 
 by 6 in. One or two glass covers may be used, depending on the 
 particular design and application. For swimming pool heating (see 
 below), glazing is usually omitted. If double covers are used, the 
 distance between them is about one-half inch and the inner glass cover 
 is usually about one inch above the absorber plate. Two to four inches 
 of insulation, such as heat resistant fibrous glass, fill the space 
 between the absorber plate and the bottom of the casing. Metal absorber 
 plates, usually copper, steel, or aluminum, with tubing of copper in 
 thermal contact with the plates, are the most commonly used materials. 
 
MOUNTING 
 BRACKET 
 
 7-4 
 
 SILICONE RUBBER PADS 
 TO ISOLATE ABSORBER PLATE 
 FROM FRAME 
 I 
 TWO COVER GLASSES 
 
 ABSORBER PLATE 
 WITH 
 SELECTIVE SURFACE 
 
 COPPER TUBES 
 
 GLASS SEAL 
 TO FRAME 
 
 STEEL FRAMING 
 
 INLET WATER 
 HEADER 
 
 SEMI-RIGID 
 INSULATION 
 
 PLUMBING FITTING 
 
 Figure 7-1. Typical Liquid-Heating Collector 
 
 Numerous variations on this design are illustrated in Figure 7-2. 
 Most of the design differences are in the fluid conduits. Designs A and 
 E show tubing and headers inside the plate itself. This absorber is 
 made by applying a tube pattern of stop-weld material to a copper or 
 aluminum sheet, cold welding another sheet to it, and forming the tubing 
 array by air "inflation". Another absorber, shown in Design F, 
 comprises two sheets of steel, welded together at the edges and at 1- to 
 2-inch intervals. Expansion of the unwelded space by hydraulic pressure 
 and attachment of inlet and outlet connections permits liquid flow 
 between the plates. 
 
 A composite absorber, shown in Design H, comprises copper tubes 
 clamped into extruded aluminum fins which form the absorber plate. 
 
7-5 
 
 (A) 
 
 GLAZING 
 
 INTEGRAL FLUID PASSAGES 
 'BLACKENED ABSORBER PLATE 
 
 INSULATION 
 
 (B) 
 
 GLAZING 
 
 ''TUBES BONDED TO BLACKENED 
 STRIPS 
 
 INSULATION 
 
 (C) 
 
 GLAZING 
 
 ,TUBES PRESSED INTO GROOVES 
 ROLLED IN PLATE 
 
 'INSULATION 
 
 GLAZING 
 
 'rectangular TUBES 
 
 'BONDED TO PLATE 
 
 INSULATION 
 
 (E 
 
 DOUBLE GLAZING 
 'TUBED SHEET WITH 
 'SELECTIVE SURFACE 
 
 'INSULATION 
 
 (F 
 
 ^LAZING 
 
 , FLAT PLATE EDGES WELDED 
 SPOT WELDS 
 
 INSULATION 
 
 GLAZING 
 'SEAM WELDS 
 
 INSULATION 
 
 (H) GLAZING 
 
 /COPPER TUBES IN 
 'ALUMINUM EXTRUSIONS 
 
 INSULATION 
 
 ( I 
 
 ^GLAZING 
 
 WATER FLOWS DOWNWARD 
 'lN TROUGHS 
 
 INSULATION 
 
 Figure 7-2. Types of Flat-Plate Liquid Solar Collectors 
 
7-6 
 
 Mechanical pressure between fins and tubes is required for good thermal 
 conduction from absorber surface to circulating liquid. 
 
 Several additional liquid collector designs are sketched in 
 Figure 7-2, all having essentially the same functional characteristics 
 achieved by various fabricating methods. 
 
 TYPICAL AIR COLLECTOR 
 
 Figure 7-3 is a cut-away sketch of a typical air- heating solar 
 collector, and Figure 7-4 shows a longitudinal cross-sectional view of 
 two air collectors joined in series flow. The principal difference 
 between air and liquid collectors is the size and configuration of the 
 fluid conduits. The figure shows three parallel air passages, each 
 about one-half inch high, beneath the absorber plate. For effective 
 heat transfer, air flows below, and in contact with, the entire absorber 
 surface. This design also has internal manifolds for air distribution 
 to all collector panels in a close-fitting array. 
 
 Numerous variations in the design of collectors for heating air by 
 solar energy are shown in Figure 7-5. Air can be passed in contact with 
 black solar-absorbing surfaces such as (A), finned plates or ducts (B), 
 several layers of metal screening (C), corrugated or roughened plates of 
 various metals (D), and overlapped glass plates (E). Flow may be 
 straight through, serpentine, above, below, or on both sides of the 
 absorber plate, or through a porous absorber material. 
 
 DESIGN AND OPERATION OF FLAT-PLATE SOLAR COLLECTORS 
 
 Several solar collector design features are not affected by the 
 type of fluid being heated. Whether used for heating air or liquid, 
 
7-7 
 
 METAL FRAME BOX 
 
 TRANSPARENT 
 COVERS 
 
 ABSORBER PLATE 
 
 INSULATION 
 AIR PASSAGES 
 
 INTERNAL MANIFOLD 
 
 Figure 7-3. Typical Air-Heating Collector 
 
 TEMPERED GLASS 
 COVER 
 
 SELECTIVE COATED 
 ABSORBER PLATE 
 
 AIR CHANNEL 
 
 COLD 
 AIR 
 
 Figure 7-4. Solar Air Heater with Internal Manifold 
 Two Collectors in Series 
 
7-8 
 
 (A 
 
 GLAZING 
 
 ABSORBER PLATE 
 
 AIR PASSAGE 
 
 INSULATION 
 
 ABSORBER PLATE 
 AIR PASSAGE 
 
 INS j[ 
 
 NSULATION 
 
 (C ) 
 
 -GLAZING 
 METAL MATRIX 
 
 INSULATION 
 
 (D 
 
 L 
 
 GLAZING 
 
 CORRUGATED SHEET METAL 
 WITH SELECTIVE SURFACE 
 
 INSULATION 
 
 (E 
 
 COLD 
 
 DOUBLE GLAZING 
 /: CLEAR GLASS 
 
 ■BLACK GLASS 
 
 3_ 
 
 AIR 
 
 — AIR 
 FLOW 
 
 HOT 
 AIR 
 
 "INSULATION 
 
 Figure 7-5. Types of Flat-Plate Air Solar Collectors 
 
7-9 
 
 glazing materials and design, absorber surface coating, insulation 
 beneath the heat transfer section, and the container or casing may be 
 the same. These components may therefore be discussed without reference 
 to fluid type. 
 
 GLAZING 
 
 A major component common to the two types of flat-plate collectors 
 is the glazing. Reduction of convection and radiation losses from the 
 absorber plate is its principal function. It also serves to protect the 
 absorbing surface from rain, snow, and atmospheric dust. The primary 
 requirements of a material for collector glazing are transparency to 
 solar radiation and opacity to radiation emitted by the absorber surface 
 at moderate temperature. Glass and various plastics have these 
 properties. Additional requirements are strength, hardness, and 
 resistance to damage by solar radiation, excessive temperature, wind, 
 and the components of the atmosphere. 
 
 Glass 
 
 The exceptional durability of glass, particularly if strengthened 
 by heat treatment (tempered), and its moderate cost, coupled with its 
 other desirable optical properties, make it by far the most widely used 
 solar collector glazing material. In sizes used in most standard glass 
 doors, 1/8 in. tempered glass is priced below one half dollar per square 
 foot when purchased in quantity. Framed in a durable gasket, supported 
 on four sides, and secured in place by some type of hold-down hardware, 
 a long-lived, maintenance-free, cost-effective glazing is obtained. A 
 
7-10 
 
 typical nominal size is 3 feet by 6.5 feet. The spacing between the 
 absorber plate and the lower (or single) glass cover is not critical, 
 typical values being one to two inches. 
 
 Small amounts of iron greatly reduce the transparency of glass, so 
 most commercial collectors have covers of low-iron glass. Common window 
 glass may absorb 5 percent to 8 percent of the solar energy per sheet, 
 which is an unacceptable loss. Low iron or "water-white" glass absorbs 
 only 1 percent to 2 percent, so is widely specified and used. 
 
 Commercially manufactured collectors may have single or double 
 transparent covers. Heat collection efficiency of a double-glazed 
 collector, especially in cold climates, is increased by virtue of the 
 additional barrier to heat loss. If a second glazing is used, it is 
 usually mounted half an inch above the first, either as a separate piece 
 or in an integral double-glazed assembly, the two pieces of glass being 
 bonded at their edges to a suitable spacer strip. The space between the 
 two layers of glass is usually sealed to prevent "breathing" and 
 resulting moisture condensation. Properties similar to those of double- 
 glazed windows ("insulated glass") provide greatest assurance of 
 long-term performance with minimum maintenance. The trend in the 
 industry is toward single-glazed collectors with selective absorber 
 coatings, described below. 
 
 Plastic 
 
 Glazings of transparent plastic have been used with varying degrees 
 of success, the uncertain property being durability. Rigid plastics 
 such as acrylics, polycarbonates, and fiberglass reinforced polyesters, 
 mounted in gasketed frames, can be employed as single and double covers. 
 
7-11 
 
 Several types of plastic film, usually a few thousandths of an inch 
 
 thick, have also been used as collector glazings. The materials 
 
 t a 
 ® 
 
 (B) (fh 
 
 receiving most attention have trade names such as Tedlar^ , Mylar w , 
 
 and Teflon FEP 
 
 Only a small fraction of commercially sold collectors are provided 
 with plastic covers, so a solar installer will seldom handle that type. 
 Lighter weight may be an advantage in some situations, but the large 
 effect of temperature change on sheet dimensions and loss of strength 
 and transparency of some types or prolonged exposure to sunlight call 
 for careful evaluation in collector selection. Collectors with plastic 
 covers, particularly of thin films, must be designed and installed so 
 that replacement of the covers can be made without major reconstruction 
 and expense. 
 
 ABSORBER 
 
 The surface of the absorber plate in a solar collector must absorb 
 a very high fraction of the solar radiation being received. Black 
 surfaces have high absorptivity for the visible portion of the solar 
 spectrum and are usually good absorbers for the infrared portion of the 
 solar radiation as well. Carbon black, numerous metal oxides, and most 
 black paints will absorb about 95 percent of the solar radiation 
 reaching the surface. The remainder of the solar radiation is reflected 
 upwards through the glazing. Collector efficiency is strongly dependent 
 on the absorptivity of this surface. 
 
7-12 
 
 A common type of absorber surface is a heat-resistant black paint, 
 usually applied by spraying, followed by curing with heat to vaporize 
 all solvents and to secure permanence. These surfaces must be able to 
 withstand temperatures of 300°F to 400°F in double-glazed collectors 
 without appreciable deterioration or outgassing. Black porcelain 
 enamel, applied to steel as a frit and fused to the surface in a 
 furnace, is also commercially used. 
 
 An efficient type of absorber coating is known as a selective 
 surface. If a bright metal, such as nickel-plated steel, copper, or 
 aluminum, is coated with a very thin layer of a black metal oxide, such 
 as chromium oxide, in an electroplating tank, it can absorb up to 95% of 
 the solar radiation being received. The underlying bright nickel is a 
 poor heat radiator, however, so the loss of heat from the metal surface 
 by radiation is much lower than from an ordinary black painted surface. 
 There are other types of selective surfaces, but this black chrome 
 combination has been found to have the greatest durability and very good 
 efficiency. As a result, most commercial collectors now being made in 
 the U.S. are provided with black chrome absorbers. The reduced 
 radiation loss from these surfaces permits the use of single rather than 
 double glass covers, without serious loss in solar collection efficiency 
 under most operating conditions. 
 
 INSULATION 
 
 Another material used in most collectors, whether of liquid or air 
 type, is insulation beneath the absorber. Typical designs involve 
 retaining two to four inches of flexible or rigid insulation in the 
 metal box or frame which encloses the absorber-glazing assembly. 
 
7-13 
 
 Fibrous glass is probably the most common material, but foam insulation 
 is also used. In addition to insulating properties, the material must 
 not shrink, expand, outgas, or deteriorate when exposed to stagnation 
 temperatures approaching 350°F. Fibrous glass must therefore be free of 
 bonding agents which decompose at these temperatures. Similarly, foam 
 type insulations must be overlaid with an adequate thickness of a 
 temperature-resistant insulation or a special type must be used. 
 Polystyrene foams and most urethane foams are not acceptable for these 
 applications, but an isocyanurate foam has been satisfactorily used by 
 some collector manufacturers. 
 
 The problem of outgassing is not limited exclusively to the 
 insulating material. Any substance in the collector which can vaporize 
 or decompose into vapors at temperatures encountered under stagnant 
 conditions will not only deteriorate, but will also cause the deposition 
 of films or coatings on the underside of glazings. Reduction in solar 
 transmission then results. Wood must be completely avoided, and paints, 
 insulating and gasketing materials, sealants, and all materials other 
 than glass and metal must be carefully screened for these potentially 
 damaging effects. 
 
 FRAME 
 
 Most factory-built collectors are protected in a steel or aluminum 
 frame or box forming the side edges and usually the bottom of the unit. 
 This structure provides the strength and integrity needed for damage- 
 free shipment and, more important, for installation in the final system. 
 The side rails or edges of the box are often formed with supports and 
 
7-14 
 
 fastenings for the absorber plate and for the glazings. Protection of 
 the insulation during construction and use is also provided. 
 
 LIQUID COLLECTORS FOR SPACE HEATING AND HOT WATER 
 
 The design features in a liquid-heating solar collector which 
 distinguish it from the air-heating type are associated with the 
 material and form of the absorber plate and the fluid conduits in 
 contact with it. The primary design considerations are heat transfer 
 effectiveness, pressure drop, fouling and corrosion in the liquid 
 passages, maintenance and durability, and cost. More than 100 different 
 solar liquid collectors are commercially available, the characteristics 
 of which cover wide ranges of these factors. 
 
 The materials of construction and the form of the fluid passages 
 can be divided into four main categories: 
 
 1. A tube and header array, brazed or soldered, usually copper, 
 with fins, usually aluminum or copper, clamped or bonded to 
 the tubes and spanning the distance between them, (Figure 7-2, 
 B and H). 
 
 2. A continuous thin sheet of metal, usually copper, soldered or 
 brazed to a tube and header assembly which is also soldered or 
 brazed together, (Figures 7-1 and 7-2, C, D, and G). 
 
 3. Continuous metal sheet, usually of copper but occasionally of 
 aluminum, with tubular passages within the sheet, the tubes 
 formed by expansion of unbonded areas defined by coatings on 
 one of two sheets and cold-welded areas formed by high 
 pressure rolls, Figures 7-2, A and E. 
 
7-15 
 
 4. Two metal plates, usually steel, electrically welded together 
 at their edges and at closely spaced intervals over the 
 surface, with the unbonded areas separated by expansion to 
 form a single wide liquid passage, (Figure 7-2, F). 
 
 Although there are other varieties and combinations of absorber 
 plate designs, the above categories cover nearly all commercially 
 manufactured collectors. 
 
 Of the commonly used metals for fluid passages in the collector, 
 copper is generally the most resistant to corrosion, followed by steel 
 and aluminum in that order. Limited use has also been made of stainless 
 steel, certain types being comparable with copper in resistance to 
 aqueous corrosion. Corrosion rates can be reduced by limiting access of 
 oxygen to the system and by the use of soluble inhibitors in the circu- 
 lating liquid. Air cannot be completely excluded, but a collector that 
 is continuously filled with liquid should have a substantially longer 
 life than one which is periodically drained and refilled. [Phosphates, 
 chromates, and a range of organic compounds, in low concentrations 
 (usually less than one percent) can provide a high degree of corrosion 
 protection, assuming proper maintenance and periodic checking and 
 adjustment.] Glycol solutions commonly used to protect the collector 
 from freezing (automobile radiator antifreeze) usually contain a 
 corrosion inhibitor suitable for protection of copper and steel. The 
 manufacturer's recommendations must be closely followed in using these 
 materials. System maintenance must include periodic checking for 
 acidity in the circulating liquid, because glycols have the property of 
 decomposing into corrosive organic acids. Corrective additives may be 
 
7-16 
 
 employed to counteract acidity, and periodic replacement of the 
 circulating liquid (typically every one or two years) is strongly 
 advisable. 
 
 Freezing is another collector problem which influences design. In 
 a draindown system, all of the liquid passages in the collector must be 
 vertical or downward sloping, and of sufficient diameter to drain freely 
 whenever desired. Return bends in the tubing, traps, and even 
 horizontal runs of tubing must be avoided. Admission and discharge of 
 air at the top of the collector, as mounted, are necessary. 
 
 Pressure requirements, friction loss, and pumping power are 
 important considerations in collector design. The pressure drop through 
 an individual panel at a satisfactory flow rate should be sufficient for 
 good distribution of flow in parallel channels, but should not be so 
 high that excessive pumping power is required. Typical commercial 
 liquid solar collectors are commonly operated with a pressure 
 difference, inlet to outlet, of about five pounds per square inch, 
 although higher and lower values are not unusual. 
 
 Although there are no fundamental limits to flow rates through 
 liquid collectors, practical considerations of heat transfer effective- 
 ness balanced against pumping power requirements generally result in 
 flow rates of 0.01 to 0.03 gallon per minute per square foot of 
 collector. At a nominal 0.02 gallon rate, water is heated 15°F to 20°F 
 in a single pass through a collector operating in full sun 
 (300 Btu/hr«ft 2 ) at about 50 percent collection efficiency. 
 
7-17 
 
 AIR COLLECTORS FOR SPACE HEATING 
 
 In its simplest form, a solar air heater has a continuous passage 
 beneath the absorber plate through which air is passed from one end of 
 the collector to the other, (Figures 7-3 and 7-4). Air comes in contact 
 with the entire absorber surface so that the heat transfer area is 
 maximized. A space below the absorber plate and above the insulation, 
 usually about one half inch high, forms the duct through which the air 
 passes. 
 
 To achieve satisfactory heat transfer, an air velocity of about 
 10 feet per second is a good compromise between pressure loss and heat 
 transfer effectiveness. With a flow path of about 12 feet and a 
 volumetric flow rate of about 2 cubic feet per minute per square foot of 
 collector, a pressure difference of 1/4- to 1/3- inch water column is 
 accompanied by satisfactory collector heat delivery. 
 
 Materials used in an air collector must withstand stagnation 
 temperatures without decomposition, melting, outgassing, or other 
 deterioration. There is no corrosion hazard, so mild steel or aluminum 
 can be used throughout an air collector. Freezing and boiling problems 
 do not occur. Stagnation temperatures are approximately the same as 
 those in liquid collectors provided that materials and design are 
 equivalent from the absorber surface upward. 
 
 As with liquid collectors, air collector panels require suitable 
 interconnections in parallel and series flow arrangements. The flow 
 between panels may be through interconnecting ducts, or between the 
 edges of collector panels (Figure 7-4), or in and out of the bottom of 
 the collector boxes. Manifolds with air inlets and outlets can be 
 
7-18 
 
 Arrows Indicate 
 Direction of 
 Air Flow. 
 
 Connections 
 
 To Collector 
 
 Manifold Ducts 
 
 Solar Heated Air ! ij| , 
 From the Collectors/ 
 Air to the Collectoi 
 
 irs/ 
 
 Figure 7-6. Typical Arrangement of Internally Manifolded Collector 
 Modules in an Array 
 
 designed into the collector panels so that their placement side-by-side 
 and end-to-end will form continuous passages (Figure 7-6). 
 
 Another type of absorber is composed of one or more porous screens 
 of woven wire or sheets of si it-and-expanded metal foil, which absorb 
 solar radiation and which are arranged for air to flow through the 
 screens from above to below (Figure 7-5, C). This "matrix" collector has 
 been tested in several forms, and in one commercially manufactured type, 
 air flow direction is largely longitudinal, the screens serving as the 
 equivalent of a continuous absorber plate. Concern must be given in 
 these matrix designs to eliminating dust and lint from the air stream to 
 avoid plugging of the porous absorber layers. 
 
7-19 
 
 LOW TEMPERATURE LIQUID COLLECTORS 
 
 Although single-glazed and double-glazed flat-plate collectors can 
 be used to supply heated air and water at temperatures only a few 
 degrees above ambient, lower cost alternatives may be used for such 
 applications. Solar heating of swimming pools, for example, can be 
 effectively accomplished with two types of special collectors; one is an 
 absorber with no glazing and the other is a glazing with no absorber. 
 Because swimming pool temperatures and ambient temperatures usually do 
 not differ by more than a few degrees, there is practically no heat loss 
 from the absorber to the atmosphere even if a transparent cover is 
 absent. An unglazed collector can therefore operate at satisfactory 
 efficiency and, because of its lower cost, can deliver heat more 
 economically than a higher priced glazed collector. 
 
 The low operating temperatures, 75°F to 85°F, also permit the use 
 of black plastics as absorber surfaces through which (or on the surface 
 of which) water is circulated. The absence of glazing makes it 
 impossible for the black plastic to reach damaging temperatures even 
 under no-flow conditions. For these low temperature applications, such 
 collectors may be the most cost-effective of the flat-plate types if 
 their durability is adequate. 
 
 The other type of solar pool heater is even simpler and less 
 costly, since the water itself is the absorber of solar energy, and only 
 a transparent plastic film, i.e., glazing, is required. The infrared 
 portion, about half of the radiation, is absorbed in the water near the 
 surface, and most of the visible portion is absorbed throughout the 
 water and on the pool bottom. Whenever the pool is not in use, the film 
 floats on the water, transmitting solar energy into the water and 
 
7-20 
 
 preventing evaporation, the primary heat loss. Pool temperatures 
 averaging 10°F to 20°F above ambient, corresponding to about 80°F to 
 90°F in summer use, are commonly attained. Films suitable for this 
 application, such as polyethylene (with ultraviolet protection), are 
 effective, low-priced, and replaceable in two to three years. 
 
 Another type of low temperature liquid collector involves open 
 channel water flow downward on blackened corrugated absorber plates, 
 sometimes beneath a transparent cover, Figure 7-2, I. Collection 
 efficiency is substantially decreased by evaporation of water from the 
 absorber plate and the operating temperature is not high enough for 
 conventional space heating applications. Use of this type of collector 
 for space heating would therefore require substantially larger heat 
 exchange surfaces for heat distribution to the living space in the 
 building than normally provided. Costs of larger storage and heat 
 exchange facilities must therefore be balanced against possible 
 economies in collector construction. Used as a swimming pool heater, 
 this type of collector must be protected from corrosion by water and 
 pool chemicals. This requirement and the lower efficiency than the 
 closed channel types limit practical application. 
 
 HIGH TEMPERATURE COLLECTORS - EVACUATED TUBES 
 
 Convective heat loss from the absorber plate can be eliminated by 
 removing most of the air in the space between the absorber plate and the 
 glazing. Unless supports were provided in the typical flat-plate 
 collector, a flat-glass surface would collapse with this pressure 
 difference, and the maintenance of a vacuum seal would also be 
 
7-21 
 
 difficult. Evacuated collectors have therefore involved tubular designs 
 which have higher strength to withstand external pressure. Some of the 
 designs involve flat absorbers inside the tubes and others employ 
 cylindrical absorbing surfaces. 
 
 In one U.S. type, sketched in Figure 7-7, A, the absorber is a 
 thin, blackened flat metal sheet supported across the diameter of a 
 single evacuated glass tube, with pipe connections for liquid circula- 
 tion sealed into one end of the tube. Liquid is circulated through the 
 pipe which is in close thermal contact with the absorber plate. A 
 selective black absorbing surface suppresses thermal radiation, so all 
 forms of heat loss are small at ordinary space heating temperatures. 
 Operation at temperatures approaching 300°F is possible at satisfactory 
 efficiency. 
 
 In another type, the conventional "vacuum bottle" principle is 
 used, there being a double glass wall with an evacuated space between. 
 Liquid (and in one experiment, air) is circulated through the hollow 
 interior of the inside tube (Figure 7-7, B) so the energy absorbed by a 
 black coating deposited on the outer surface of the inner glass tube is 
 transferred to the fluid. The open ends of individual tubes are 
 inserted into insulated manifolds which provide the proper fluid flow 
 pattern through tube multiples. 
 
 A third U.S. type is also a double-walled tube with a vacuum 
 between the two glass surfaces, Figure 7-7, C. The inner glass tube is 
 black-coated and contains a thin cylindrical copper "sleeve" to which a 
 copper pipe in the form of a long, narrow U is attached. Liquid is 
 circulated through the copper pipe in series flow with adjacent tubes. 
 
7-22 
 U-Bend in Copper Tube 
 
 Copper Plate with Selective 
 Black Coating 
 
 Evacuated Glass Tube 
 Glass to Metal Seal 
 Copper Tube Bonded to Plate 
 
 Double-Walled Glass Tube 
 
 Evacuated Space 
 
 Selective Black Coating 
 Outside Inner Tube 
 
 Glass Tube for Liquid 
 Supply or Withdrawal 
 
 Evacuated Space 
 Double-Walled Glass Tube 
 Selective Black Coating 
 
 •Copper Sleeve 
 "Copper Tubes Bonded to Sleeve 
 
 (D) 
 
 Cover Glass 
 
 -^ _^^_. .-^: — Evacuated Glass Tubes 
 JCyCA^yvT" Selective Black Coating 
 Aluminum Extrusion 
 
 Liquid Passages 
 Insulation 
 Cross Section 
 
 (E) /Glass Tube 
 
 Sealant 
 
 Evacuated 
 Space 
 
 Metal End- Cap Sealed 
 Ljj-T to Glass Tube 
 
 Expansion Bellows 
 
 Aluminum Fin with 
 Selective Coating 
 
 Copper Tube Pressed into Aluminum Fin 
 
 Figure 7-7. Types of Evacuated Tube Collectors 
 
7-23 
 
 An experimental evacuated tube collector from Germany comprises a 
 corrugated aluminum heat transfer surface, with internal liquid 
 passages, tightly fitting a closely packed array of evacuated glass 
 tubes which are internally coated with a selective black absorber, as 
 shown in Figure 7-7, D. A flat-glass cover is used primarily for 
 weather protection. 
 
 A Japanese design involves straight-through flow of liquid in a 
 small copper pipe bonded to a flat metal absorber plate inside a single 
 evacuated glass tube, Figure 7-7, E. Expansion differences are handled 
 by use of metal bellows bonded to the ends of the glass tube and to the 
 metal pipe. 
 
 The principle involved is similar in all types. A selective 
 surface and a high vacuum result in suppression of both radiative and 
 convective losses. With a glass-to-metal permanent seal or an all-glass 
 seal, loss of vacuum is only a rare occurrence. Even if vacuum is lost, 
 in a few of many tubes, performance of the entire collector array 
 decreases only slightly. Since the black coating is inside the 
 evacuated space in nearly all designs, it is fully protected from 
 oxidization, moisture, or any other form of attack. 
 
 Although the glass tubes do not involve costly materials and their 
 designs are simple, manifolding can be expensive. Distribution of 
 liquid flow in series and parallel channels requires extensive plumbing 
 assemblies, with accompanying requirements for insulation and weather 
 protection. Freezing of water inside the tubes is unlikely because of 
 the excellent insulating properties of a vacuum, but the danger of 
 freezing in the manifolds makes the use of non-freezing fluids advisable 
 in severe climates. 
 
7-24 
 
 COLLECTOR EFFICIENCY 
 
 INSTANTANEOUS COLLECTOR EFFICIENCY 
 
 Solar collector efficiency is the fraction of the solar energy 
 intercepted by the collector that is converted to heat and delivered to 
 the building. Factors which influence solar collector efficiency 
 include absorber surface coating, number and type of transparent covers, 
 fluid flow rate through the collector, fluid temperature, outdoor air 
 temperature, and the intensity of solar radiation on the collector glass 
 area. 
 
 The efficiency of a solar collector depends mainly on inlet fluid 
 temperature, ambient air temperature and solar radiation intensity. 
 Efficiencies of several representative solar collectors are shown in 
 Figure 7-8 and the selected collectors are described in Table 7-1. 
 
 It is seen that the lower the value of -^ a , the higher is the 
 
 Y T a 
 efficiency. Factors which decrease — ? — , and therefore raise effi- 
 ciency, are increase in solar intensity S, rise in ambient temperature 
 T , and decrease in temperature of fluid supplied to the collector, T. . 
 
 Maximum efficiency is realized when inlet temperature equals ambient 
 
 T.-T 
 temperature, so ^ is then zero. 
 
 The formula which conveniently correlates efficiency with the 
 
 principal characteristics of the collector and the operating conditions 
 
 can be written 
 
 Eff = A - B (-3-^), where 
 A and B are constants, the values of which depend on the collector 
 design and the operating conditions. The term A is equal to F R xof , and B 
 is equal to F R U. , where F R is a heat recovery factor dependent mainly on 
 the type of fluid (air or liquid) and its flow rate through the 
 
7-25 
 
 Table 7-1 
 Collector Performance Parameters 
 
 Ref. 
 No. 
 
 Manufacturer 
 
 F R (ta) 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. See also Figure 7-8. 
 
 ** 
 
 Numerical values apply to liquid collectors. 
 
7-26 
 
 collector, x is the fraction of solar radiation transmitted through the 
 
 glass cover(s), a is the fraction of solar radiation absorbed by the 
 
 black absorber surface, and U. is the overall coefficient of heat 
 
 transfer (heat loss) from the absorber plate to the atmosphere. Nearly 
 
 all collector manufacturers provide an efficiency graph, such as in 
 
 Figure 7-8, or they report the two factors A and B, usually designated 
 
 F R ta and F R U. , respectively. Knowing these two factors, the solar 
 
 radiation, and the two temperatures, the efficiency can be calculated by 
 
 the formula or it can be read from the graph at the calculated ratio 
 
 T.-T 
 
 — <^ — . Thus, if a particular collector corresponding to number 4 in 
 
 Figure 7-8 is supplied with water at 130°F, when the atmospheric temper- 
 ature is 30°F and when the solar intensity is 250 Btu per hour per 
 square foot of collector surface, "*<. a = — j^r- = 0.40, the efficiency 
 read from the graph is about 50 percent. Hence, solar heat delivery is 
 50 percent of 250 Btu, or 125 Btu per hour per square foot of collector. 
 If the collector manufacturer publishes values of F R Ta and F R U. , or 
 
 if he provides two or more efficiency levels at stated values of _i a, 
 
 S 
 
 the system designer can draw a graph similar to Figure 7-8, which can 
 then be used for reading efficiencies at any values of the operating 
 temperature and solar input. Table 7-1 contains data in this form, for 
 several well-known solar collectors. 
 
 In a liquid collector, the values of A and B are not significantly 
 affected by change in flow rate, but there is a sizeable influence of 
 flow rate in air collectors. Therefore, the efficiency graph or the 
 values of A and B for an air collector apply to a particular air 
 velocity through the collector. The collector manufacturer usually 
 provides data at several air rates. 
 
7-27 
 
 .0 
 
 0.9 
 
 0.2- 
 
 T ; - Fluid Temperature at Inlet, °F 
 
 Outdoor Air Temperature, 
 
 S -Solar Radiation on Tilted Col lector, rrrr-r^ 
 
 \\\ • hr; 
 
 0.8 1.0 
 (hr-ft 2 -°F) 
 
 BTU 
 
 Figure 7-8. Measured Solar Collector Efficiencies of Several Collectors 
 (Number labels on graph refer to Reference No. in Table 7-1) 
 
7-28 
 
 DAILY COLLECTOR EFFICIENCY 
 
 The graphs shown in Figure 7-8 are not convenient for obtaining or 
 predicting daily or monthly solar heat deliveries because the fluid and 
 ambient temperatures as well as the solar radiation are continually 
 changing. The efficiencies shown in Figure 7-8 are for steady-state 
 conditions and, while they are useful for comparing different 
 collectors, they are not directly useful in determining the quantity of 
 energy collected by a system throughout one or more days. For rough 
 estimates, average daily efficiency of collectors in a system is more 
 useful for that purpose. Reliable design requires use of analytical 
 methods, one of which is detailed in Module 14. 
 
 Careful monitoring of system efficiencies in Solar House I at 
 Colorado State University for five years has shown that conventional 
 flat-plate collectors in systems supplying about three-fourths of the 
 annual space heating requirements in a cold sunny climate operate at 
 average daily efficiencies of 15 to 25 percent depending on the solar 
 and climatic conditions and the operation of the system. Although 
 collector efficiency depends on many design factors of the system, an 
 average daily efficiency of 25 to 35 percent can be expected with most 
 collectors now available commercially. For rough estimates, one-fourth 
 to one-third of mean daily radiation on the collector surface may be 
 assumed recoverable as heat. Thus, if the average January daily 
 radiation on a tilted collector is 1200 Btu per day per square foot, a 
 500-square-foot collector could be expected to provide an average 
 January heat supply of 150,000 Btu to 200,000 Btu per day. Collector 
 sizing by more reliable methods is presented in Module 14. 
 
7-29 
 
 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. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 8 
 COMPONENTS OF LIQUID SYSTEMS 
 
 HEAT STORAGE 
 CONTROLS 
 HEAT EXCHANGERS 
 PUMPS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
8-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 
 Page 
 8- i i i 
 
 INTRODUCTION 
 
 OBJECTIVE 
 
 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 . 
 INSTALLATION OF CONTROL HARDWARE 
 
 Control Panels . 
 
 ng 
 
 8-1 
 
 8-1 
 
 8-1 
 
 8-2 
 
 8-2 
 
 8-4 
 
 8-6 
 
 8-7 
 
 8-8 
 
 8-10 
 
 8-12 
 
 8-12 
 
 8-13 
 
 8-13 
 
 8-17 
 
 8-18 
 
 8-19 
 
 8-19 
 
 8-20 
 
 8-21 
 
 8-21 
 
 8-21 
 
8-ii 
 
 
 Page 
 
 Locations of Temperature Sensors 
 
 8-21 
 
 AUXILIARY HEAT CONTROL .... 
 
 8-22 
 
 CONTROL SYSTEM CHECK-OUT .... 
 
 8-22 
 
 HEAT EXCHANGERS 
 
 8-23 
 
 COLLECTOR TO STORAGE HEAT EXCHANGER 
 
 8-23 
 
 Shell -and-Tube Type .... 
 
 8-23 
 
 Selection ...... 
 
 8-25 
 
 Installation ..... 
 
 8-26 
 
 SPACE HEATING 
 
 8-26 
 
 DOUBLE-WALL HEAT EXCHANGER 
 
 8-27 
 
 PUMPS 
 
 8-28 
 
 REFERENCES 
 
 8-33 
 
8-iii 
 LIST OF FIGURES 
 
 Figure Page 
 
 8-1 Effect of Storage Size on Solar Heat Contribution 
 
 to Total Load 8-3 
 
 8-2 Cylindrical Tanks 8-5 
 
 8-3 Reinforced Concrete Block Tank .... 8-5 
 
 8-4 A Prefabricated Water Tank for Thermal Energy 
 
 Storage ......... 8-6 
 
 8-5 Bottom Insulation and Support Scheme for Flat- 
 Bottom Water Storage Tanks ..... 8-8 
 
 8-6 Heat Storage in Phase-Change Materials . . . 8-11 
 
 8-7 Basic Components of Controls 8-12 
 
 8-8 Sensor Locations in a Typical Liquid-Heating 
 
 System 8-14 
 
 8-9 Typical Temperature Profiles of Collector 
 
 and Storage Liquids in a Liquid-Heating System . 8-15 
 
 8-10 Typical Circuitry for a Differential Thermostat . 8-19 
 
 8-11 Pictorial Representation of Hysteresis in the 
 
 Differential Thermostat . 8-19 
 
 8-12 Single-Pass Counterflow Shell-and-Tube Heat 
 
 Exchanger ......... 8-23 
 
 8-13 Multiple-Tube Heat Exchanger 8-24 
 
 8-14 Typical Performance Curves for a Centrifugal Pump . 8-29 
 
 8-15 Friction Losses in Copper Tubing .... 8-30 
 
 8-16 Pressure Loss in Various Elements .... 8-32 
 
8-1 
 
 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. 
 Collectors were described in a previous module and specific attention is 
 devoted here to other components of the solar system. 
 
 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. 
 
 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. 
 
8-2 
 
 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 
 storage 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 tempera- 
 ture 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 
 temperature 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 tempera- 
 ture 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 
 
8-3 
 
 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 8-1. 
 
 o 
 o 
 
 o 
 
 c 
 c 
 
 < 
 
 No 
 Storage 
 
 of Storage Volumes 
 
 Large 
 Volumes of 
 Storage 
 
 Figure 8-1. 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. 
 
8-4 
 
 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 8-2 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 8-3. 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 8-4, is commercially available and is suitable for storage of 
 water. The tank is made of flat sections with foam insulation 
 sandwiched between two thin galvanized steel plates. Special 
 connectors, corner sections, and steel channel whalers are used to form 
 a structurally 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 waterproof liner is required. 
 
8-5 
 
 UNDERGROUND STORAGE TANK 
 
 ; 
 
 © 
 
 1 1 
 1 
 
 \ 
 
 
 ABOVE-GROUND STORAGE TANK 
 
 Figure 8-2. Cylindrical Tanks 
 
 HYPALON LINING 
 ALTERNATIVES: 
 
 1 BUTYL RUBBER 
 
 2 MORTAR a COAL 
 TAR MEMBRANE 
 
 REINFORCED 
 CONCRETE BASE 
 
 TOP a BOTTOM 
 COURSE OF BOND 
 BEAM BLOCK 
 
 VERTICAL a HORIZONTAL 
 REINFORCING 
 
 Figure 8-3. Reinforced Concrete Block Tank 
 
8-6 
 
 URETHANE FOAM 
 
 STEEL STRAPS 
 
 GALVANIZED STEEL 
 PLASTIC LINER 
 
 REINFORCEMENT KIT 
 
 SPEED-LOK OPERATOR 
 TONGUE & GROOVE 
 CAM ACTION SPEED-LOK 
 
 Figure 8-4. 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 
 installation 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 
 
8-7 
 
 requirements of the building. To avoid overheating in summer, heat 
 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 8-5. 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 8-4 
 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 
 
8-8 
 
 HEAT STORAGE 
 WATER TANK 
 
 FOUNDATION! 
 
 Figure 8-5. 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 commer- 
 cial 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. 
 
8-9 
 
 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 
 pressurized. 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. 
 
8-10 
 
 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 
 collectors. 
 
 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 8-6. 
 
 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. 
 
8-11 
 
 SENSIBLE HEAT 
 IN LIQUID 
 
 SOLID PHASE 
 
 PHASE CHANGE 
 
 ~H TEMPERATURE 
 DIFFERENCE 
 
 TEMPERATURE 
 
 Figure 8-6. 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 signif- 
 icant improvements are being made. The melting temperatures of suitable 
 materials, like Glaubers salt, are too low for effective use in space 
 heating. (Glauber's salt melts at about 90°F.) Currently PCM materials 
 are expensive when compared to water storage units and containerizing is 
 costly also. Lastly, a current handicap is limited practical experience 
 with PCM materials in solar heating systems. 
 
8-12 
 
 SYSTEM CONTROLS 
 
 Controls in solar systems must: (1) regulate the automatic 
 collection and distribution of solar heat, and (2) operate the conven- 
 tional 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 
 functions 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 8-7. The sensors are generally temperature-measuring 
 
 SENSORS 
 
 COMPARATORS 
 
 OUTPUT 
 DEVICES 
 
 Figure 8-7. 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 
 the system, which in liquid systems are pumps, motorized valves, 
 circulating fans or fan-coil units and auxiliary heaters. 
 
8-13 
 
 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 8-8. 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. 
 
 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. 
 
8-14 
 
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 There are three temperature sensors identified in Figure 8-8. 
 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 the preheat 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 in Figure 8-9. The solid curve shows the 
 
 o 
 
 O 
 
 Q. 
 
 E 
 
 Collector — 
 Temperature 
 at SI 
 
 s 
 
 y 
 
 Storage 
 
 Temperature 
 
 at S2 
 
 j 
 
 \ 
 
 -► 
 
 12 
 Time (hours) 
 
 18 
 
 24 
 
 Figure 8-9. Typical Temperature Profiles of Collector and Storage 
 Liquids in a Liquid-Heating System 
 
 storage temperature as sensed by S2 and the dashed line is the collector 
 temperature at SI. The collector fluid temperature is low in the 
 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, 
 
8-16 
 
 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 (f) • If 
 the temperature 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 (3) , 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 circulation commences. The number of on-off cycles at system 
 start-up in the morning depends on solar intensity, setting of the 
 differential thermostats, fluid flow rate, and volume of water in the 
 collector loop. Generally, 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 
 between SI and S2 again reaches 20°F and the pumps are activated at 
 point (5) . However, the intensity of solar energy is not sufficient to 
 maintain high temperature at SI and the pumps shut off at point © . 
 
8-17 
 
 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. 
 
 To minimize the temperature swing the thermostat can be adjusted so 
 that the temperature differences between stages and set point are 
 reduced to 1°F to 2°F. However, when the temperature differences are 
 too small, frequent cycling may occur in the load loop. An alternative 
 
8-18 
 
 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 
 preheating 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 
 temperature 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 
 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. 
 
8-19 
 
 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 8-10. Temperature sensors are connected to a comparator 
 and to an output device. Hysteresis is the range in temperature between 
 the start and stop set points. Hysteresis (a pictorial representation 
 of which is shown in Figure 8-11) is achieved electrically by the 
 
 Collector 
 Sensor Sj 
 
 Storage 
 Sensor s 2 
 
 Vref 
 
 X 
 
 Hysteresis 
 
 Output 
 Device 
 
 Figure 8-10. Typical Circuitry for a Differential Thermostat 
 
 On 
 Off 
 
 Hysteresis \ 
 
 
 J t r 
 
 
 k 
 
 I L 
 
 AT, 
 
 Off 
 
 AT 
 
 On 
 
 Temperature 
 Difference 
 
 Figure 8-11. Pictorial Representation of Hysteresis in the Differential 
 Thermostat 
 
8-20 
 
 feedback loop shown in Figure 8-10. As the temperature difference 
 increases and eventually reaches an upper set point, AT« N , the 
 electrical circuit to the output device is completed and the device is 
 turned on. When the temperature difference decreases to the point where 
 it is equal to AT Q p F , 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 satisfactory. 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 
 cooling 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 
 functions. Usually the thermostat is the only control with which the 
 occupant needs to be concerned. Once set to winter or summer comfort 
 levels 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. 
 
8-21 
 
 Temperature Sensors 
 
 There are many types of temperature sensors that can be used in the 
 control subsystem, such as thermocouples, thermistors, silicon 
 transistors, 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 
 sensors, 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. 
 
 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 
 
8-22 
 
 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 preheat 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 temperatures to 
 start a heat collection mode or domestic water preheating mode. A 
 pre-operational check-out will assure that the system will "work" when 
 
8-23 
 
 it is put into operation. Adjustments to the control system may 
 sometimes 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 8-12, is the 
 simplest. 
 
 HOT COLLECTOR FLUID 
 
 COOL 
 
 STORAGE 
 
 FLUID 
 
 Figure 8-12. Single-Pass Counterflow Shell-and-Tube Heat Exchanger 
 
8-24 
 
 A tube which passes either the cold or hot fluid, shown as cold fluid in 
 Figure 8-12, is placed concentrically inside a larger tube which forms 
 the shell. 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. The hot and cold fluids 
 may flow in the same direction (parallel flow) or in opposite directions 
 (counterflow) as shown. 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 
 counterflow 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 8-13. 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 
 be used as compared to single tube design. There are also multiple-pass 
 
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 Figure 8-13. Multiple-Tube Heat Exchanger 
 
8-25 
 
 heat exchanger designs which cause flow in the tubes to reverse 
 directions within the shell. 
 
 Selection 
 
 Shell -and-tube heat exchangers are available from many 
 manufacturers as they have long been used in many industrial 
 applications. Manufacturer's representatives can provide advice in the 
 selection of a heat exchanger for the system. The information necessary 
 for selection are flow rates and temperatures desired for both the tube 
 and shell sides, and types of fluid in the collector and storage loops. 
 
 The flow rate through the tubes of the heat exchanger is normally 
 twice the flow rate through the shell. Since the flow rate through the 
 collectors is normally the flow rate through the shell, once collector 
 area is determined the flow rates through the heat exchanger can be 
 decided. For example, if a collector of 400 ft 2 is desired, the flow 
 rate in the collector loop should be about 8 gpm (0.02 gpm per square 
 foot of collector) and the flow rate of the storage liquid should be 
 about 16 gpm. 
 
 A temperature drop in the hot fluid from inlet to outlet of the 
 exchanger equal to the temperature rise in the collector is desired. 
 However, since the temperature rise in the collector varies with the 
 intensity of solar radiation while the temperature drop in a given heat 
 exchanger is dependent on flow rates and storage temperature, selection 
 of "design temperatures" based on typical noon-time collector operation 
 will generally be satisfactory. Specifying a temperature drop of 10°F 
 to 15°F for the hot fluid in the heat exchanger and temperature rise of 
 
8-26 
 
 5°F to 10°F for the storage fluid, with a temperature difference of 5°F 
 to 10°F between the entering storage fluid and the exiting collector 
 fluid, is suggested. Selecting a design temperature for storage to be 
 120°F, the fluid temperature entering the tubes of the heat exchanger 
 should be 120°F and exiting temperature should be 125°F or 130°F. The 
 hot collector fluid entering the heat exchanger shell is selected to be 
 140°F and exit temperature should be between 125°F and 130°F. With 
 these temperature specifications along with fluid flow rates through the 
 shell and tubes, an appropriate heat exchanger can be selected. 
 
 Installation 
 
 Heat exchangers should be installed as close to the storage tank as 
 possible. Pressure drops in heat exchangers are relatively large, and 
 minimizing pipe lengths in the fluid loops will minimize overall 
 pressure drops and requirements for pumping power. 
 
 Supports for heat exchangers are generally necessary because of 
 their size and weight. The entire outside surface of the heat exchanger 
 should be well insulated, including insulation between the shell and the 
 support frame. Pipe connections should be tested for leaks before 
 insulation is applied. 
 
 SPACE HEATING 
 
 There are several types of heat exchangers for heating room air. 
 Solar or auxiliary heated water may be circulated through water-to-air 
 cross-flow heat exchangers placed in an air circulation duct, separate 
 
8-27 
 
 fan-coil units placed in the rooms, baseboard hydronic systems or 
 radiant heating panels. The rate of heat transfer to room air (Btuh) 
 depends upon the surface area provided, temperature of the circulating 
 water and rate of water flow through the heat exchanger. Generally 
 water temperature of 100°F to 120°F is satisfactory for radiant heating 
 systems with piping networks in floors, walls, or ceilings. Hydronic 
 systems heat efficiently with water temperatures of 160°F to 190°F, and 
 cross-flow heat exchangers (fan coils) are satisfactory with 
 temperatures between 120°F and 150°F. 
 
 The type of load heat exchanger selected may depend substantially 
 on the type of existing heating system. For new buildings, selection is 
 arbitrary, although a central air distribution system with a duct heat 
 exchanger is preferred. It is advantageous to the solar system to be 
 able to lower the temperature in storage as much as possible and the 
 type of heat exchanger used and the arrangement for heat delivery can 
 bear importantly on the minimum water temperature achieved in storage at 
 the beginning of the collector day. 
 
 In selecting the load heat exchanger size (or length), normal HVAC 
 practices can be followed. For advice in choosing a cross-flow heat 
 exchanger, a manufacturer's representative can be sought. Information 
 needed to size a load heat exchanger (room heating system) are building 
 heating load (Btuh), water flow rates and temperatures. For cross-flow 
 heat exchangers it is also necessary to specify the air flow rate. 
 
 DOUBLE-WALL HEAT EXCHANGER 
 
 To prevent contamination of household water and water mains, 
 double-walled heat exchangers should be used for transfer of heat from 
 
8-28 
 
 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 v - / sheet is 
 particularly 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-wall heat exchangers is not well 
 established but, fortunately, sizing is not critical for domestic water 
 preheating. Typical flow rates for both sides of the heat exchanger are 
 2 gpm to 3 gpm. Temperature drops of 5°F to 10°F across the heat 
 exchanger are satisfactory and temperature difference of about 20°F 
 between the hot and cold fluids is tolerable. Since the water circula- 
 tion rate is small, pressure drop is low and only fractional horsepower 
 circulation pumps (1/10 to 1/30) are needed. 
 
 PUMPS 
 
 Centrifugal pumps are best suited for liquid-heating solar systems. 
 Typical performance curves for a centrifugal pump are shown in Figure 
 8-14. 
 
8-29 
 
 Desirable Operating 
 Region 
 
 Discharge 
 Figure 8-14. 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 8-14 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. 
 
 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 8-15. Similar charts are available for other 
 
8-30 
 
 10 
 
 10 10 
 
 FRICTION LOSS ( feet of water per 100 ft ) 
 
 Figure 8-15. Friction Losses in Copper Tubing 
 
8-31 
 
 types of piping from suppliers. A nomograph for estimating head losses 
 across valves and fittings is shown in Figure 8-16. 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 7ft/sec. With discharges 
 selected and pressure losses calculated for each circulation loop, pump 
 selections can be made from manufacturers' catalogs. 
 
8-32 
 
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 Standard Elbow. 
 
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8-33 
 
 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. 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. 
 
 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, 
 Charlottesville, 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 NODULE 9 
 
 COMPONENTS OF AIR SYSTEMS 
 
 HEAT STORAGE 
 CONTROLS 
 HEAT EXCHANGERS 
 BLOWERS, AIR HANDLERS 
 
 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 
 
 INTRODUCTION 
 
 9-1 
 
 OBJECTIVE 
 
 9-1 
 
 HEAT STORAGE 
 
 9-1 
 
 PEBBLE BEDS 
 
 9-1 
 
 Pebble-Bed Containers . 
 
 9-2 
 
 Sizing the Pebble Bed . 
 
 9-3 
 
 Rocks for the Pebble Bed . 
 
 9-5 
 
 Pressure Loss through Pebble Bed 
 
 9-5 
 
 PHASE-CHANGE STORAGE 
 
 9-6 
 
 SYSTEM CONTROLS 
 
 9-7 
 
 PRINCIPLES OF OPERATION 
 
 9-7 
 
 Collecting Solar Heat .... 
 
 9-7 
 
 Delivering Beat to Storage 
 
 9-9 
 
 Delivering Beat to Rooms. 
 
 9-11 
 
 Heating from Storage .... 
 
 9-11 
 
 Domestic Water Preheating 
 
 9-12 
 
 TEMPERATURE SENSORS 
 
 9-12 
 
 INSTALLATION OF CONTROL HARDWARE . 
 
 9-13 
 
 Control Panels ...... 
 
 9-13 
 
 Location of Temperature Sensors 
 
 9-13 
 
 AUXILIARY FURNACE CONTROL .... 
 
 9-14 
 
 CONTROL SYSTEM CHECK-OUT 
 
 9-14 
 
9-i i 
 
 HEAT EXCHANGER FOR SERVICE HOT WATER 
 BLOWERS, AIR HANDLERS 
 
 PERFORMANCE CURVES . 
 
 BLOWER SELECTION 
 REFERENCES 
 
 Page 
 9-15 
 9-16 
 9-16 
 9-17 
 9-20 
 
9—1 i i 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 9-1 Pebble-Bed Heat Storage Unit 9-3 
 
 9-2 Horizontal-Flow Pebble Bed 9-5 
 
 9-3 Sensor Locations in Typical Air-Heating System . 9-8 
 
 9-4 Typical Temperature Variations at SI and S2 . . 9-10 
 
 9-5 Typical Efficiency Curves for Blowers . . . 9-16 
 
 9-6 Friction Loss in a Straight Duct .... 9-18 
 
 LIST OF TABLES 
 
 Table Page 
 
 9-1 Pressure Loss in Pebble Beds ..... 9-6 
 
9-1 
 
 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 for the entire system. Module 8 contains general 
 discussion of system components as well as comments on specific items 
 applicable for liquid systems. This module is limited to discussion of 
 components appropriate for air systems. 
 
 OBJECTIVE 
 
 The objective is to present information on components of air 
 systems so that participants will be able to: 
 
 1. Establish an appropriate-size heat storage unit. 
 
 2. Select blowers. 
 
 3. Install components properly to operate air systems. 
 
 HEAT STORAGE 
 
 PEBBLE BEDS 
 
 Pebbles are commonly used in air-heating solar systems to store 
 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 temperature nearly 
 equal to the temperature of the rocks at the exit. The entrance to the 
 pebble bed is therefore warmer than the exit and the bed is said to 
 
9-2 
 
 be stratified. Temperature stratification is advantageous to collector 
 operation as well as for heat delivery to the rooms. During collection, 
 cool air is returned to the collectors from the bottom of storage and 
 collector operation is always at highest efficiency. When stored heat 
 is delivered to the rooms, air flow direction through storage is 
 reversed so that room air enters the cool end of the pebble bed and 
 exits at the warm end. 
 
 Heated air from collectors should generally 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. By this arrangement 
 stratification is naturally maintained in the pebble bed. 
 
 Pebble-Bed Containers 
 
 Pebble-bed containers can be wood frame boxes, concrete enclosures 
 or steel bins. Wood frame boxes are generally easiest to construct even 
 in places where access is limited. All containers must be structurally 
 adequate to prevent joints from cracking either from the force of 
 pebbles inside the container or by settlement of the foundation. 
 
 Air leaks from containers must be prevented as much as possible. A 
 pebble bed in a wooden box container is illustrated in Figure 9-1, with 
 plenums at the top and bottom. The bottom plenum is created by 
 supporting the pebble bed on a screen resting on steel frames or on 
 spaced concrete blocks. 
 
 Concrete or masonry blocks may also be used to construct the walls 
 of pebble beds. Walls should be reinforced and insulated and the 
 interior should be lined or sealed to prevent air leakage. Insulating 
 to achieve R-10 to R-13 rating is generally satisfactory. 
 
9-3 
 
 HOT AIR 
 CONNECTION 
 
 COLD AIR 
 CONNECTION 
 
 I in. CONCRETE 
 AGGREGATE 
 
 RIGID INSULATION 
 
 Figure 9-1. Pebble-Bed Heat Storage Unit 
 
 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 
 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 
 
9-4 
 
 container (perpendicular to flow direction) should be sized to achieve a 
 superficial flow velocity of about 20 ft per minute. In 5 ft to 8 ft of 
 path length, the pressure drop will be about 0.08- to 0.15-inch water 
 gauge through a pebble bed containing 3/4-in- to 1.5-in-diameter 
 pebbles. 
 
 The volume of pebbles 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 ft 3 to 400 ft 3 of rocks are desired. Because 
 
 the air flow rate through a collector of this size is about 800 cfm, 
 
 2 
 this container should have a cross-sectional area of about 40 ft which 
 
 will result in a superficial velocity of 20 ft/mi n. With a cross- 
 
 2 3 
 
 sectional area of 40 ft and volume of 200 ft the depth will be about 
 
 3 
 5 ft. For 400 ft volume, the depth will be about 10 ft, but since 8 ft 
 
 is a recommended maximum depth, the cross-sectional area should be 
 
 increased to about 50 ft . 
 
 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 if settlement of the rocks occurs in the 
 
 container. Barriers along the top placed perpendicular to the flow will 
 
 be useful to prevent channeling, but concentration of air flow along the 
 
 top could persist. A pebble-bed design which utilizes horizontal 
 
 separators (such as sheets of metal or plastic) placed about 12 inches 
 
 apart as shown in Figure 9-2 will be helpful in obtaining uniform flow 
 
 through the pebble bed. Because of space restrictions it is usually 
 
 difficult to maintain large cross-sectional areas and short path lengths 
 
 in horizontal pebble beds. Superficial flow velocities greater than 
 
 20 ft/mi n and path lengths longer than 8 ft may be necessary. Both 
 
9-5 
 
 Screen 
 
 Screen 
 
 ?"-;"•■'. 
 
 Figure 9-2. Horizontal-Flow Pebble Bed 
 
 higher velocities and longer flow paths will add substantially to 
 electrical power requirements for air circulation. 
 
 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 
 gravel should be screened for sizes usually from 0.75 inch to 1.5 inches 
 and washed before placement. 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. 
 
 Pressure Loss through Pebble Bed 
 
 The effect of pebble size and air velocity on the pressure loss 
 through the bed is indicated in Table 9-1. At a typical face velocity 
 
9-6 
 
 Table 9-1 
 Pressure Loss in Pebble Beds 
 
 Air Face Velocity 
 Feet per Minute 
 
 Pressure Loss 
 Inches Water Gauge/foot of length 
 
 3/4-inch pebbles 
 
 1^-inch pebbles 
 
 10 
 15 
 20 
 25 
 
 0.008 
 0.017 
 0.028 
 0.046 
 
 0.0025 
 0.008 
 0.015 
 0.023 
 
 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 
 prevailing with the smallest size, i.e., the 3/4-inch material. 
 
 PHASE-CHANGE STORAGE 
 
 Some phase -change storage materials for use with air-heating 
 systems are commercially available. Salt hydrates are packaged in 
 tubular or capsule form and heat is transferred by blowing air across 
 the encapsulated materials. Although technically a large amount of heat 
 can be stored in a small volume of material, with the types of materials 
 currently available, the freezing or melting temperatures are relatively 
 low (about 90°F) and not well suited for space heating. Costs for PCM 
 are also high, but through continued research, appropriate PCM devices 
 for space-heating systems may become practical in the future. 
 
9-7 
 
 SYSTEM CONTROLS 
 
 Components of a basic control subsystem for a solar air-heating 
 system consist of sensors, differential thermostats, and relays or 
 switches to activate the mechanical devices. The components are 
 substantially the same as for liquid-heating solar systems explained in 
 Module 8. 
 
 PRINCIPLES OF OPERATION 
 Collecting Solar Heat 
 
 A schematic diagram of a one-blower solar air-heating system is 
 shown in Figure 9-3. 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, 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 
 preheat 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. 
 
9-8 
 
 CD 
 -P 
 </) 
 >> 
 
 <•> 
 
 c 
 
 •I— 
 
 -M 
 
 03 
 <V 
 
 s- 
 
 •r- 
 
 03 
 
 u 
 
 •I— 
 
 Q. 
 .>> 
 
 10 
 
 c 
 o 
 
 •r— 
 ■!-> 
 03 
 U 
 O 
 
 S- 
 
 o 
 w> 
 
 c 
 
 0) 
 CO 
 
 CO 
 
 I 
 
 at 
 
 s- 
 
9-9 
 
 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. 
 
 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. Since air pressure at the 
 back draft damper (bottom of storage in Figure 9-3) is greater than 
 atmospheric (positive), the damper closes and air is directed to the 
 collectors. The pebbles at the bottom of storage will be at room 
 temperature at the start of a collection day and S2 will remain at 
 constant temperature until the thermal front advances through the pebble 
 bed. With proper sizing of storage, S2 will remain at room temperature 
 all through a typical winter collection day. 
 
 Temperature variations at sensors SI and S2 are shown for a typical 
 winter day in Figure 9-4. The blower is activated at point (Vs when the 
 temperature difference is, for example, about 15°F. As soon as the 
 blower is activated, 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 
 temperature difference setting for shutting off the blower may be as low 
 as 2°F or 3°F. As the intensity of solar energy increases, air 
 temperature at SI increases and reaches a maximum at midday. In the 
 afternoon, air temperature at SI continually decreases and the blower 
 
9-10 
 
 1 1 
 
 
 
 Collector Air /^ 
 
 
 
 
 Temperature Sl^/ 
 
 
 0) 
 
 a 
 
 0) 
 
 
 \ Air Temperature 
 
 Q. 
 
 <D / 
 
 \ at Bottom of 
 
 a> 
 
 
 \ @ Storages 2 
 
 
 _y ® 
 
 ® V 
 
 
 i i i i 3- 
 
 18 
 
 24 
 
 6 12 
 
 Time (hours) 
 
 Figure 9-4. Typical Temperature Variations at SI and S2 
 
 stops at point (3) when the temperature difference reaches the minimum 
 set point. The collector temperature then rises slightly (to point 
 (D ) after the blower stops because of additional solar radiation on 
 the absorber and heat retained in the collector. The temperature then 
 decreases fairly rapidly in the evening. 
 
 With a start set point of 15°F difference between SI and S2 and a 
 stop set point at 2°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 of 5 to 7, 
 normally there will not be any cycling of the blower 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 
 
9-11 
 
 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 
 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 are 
 positioned to direct the air stream to the rooms. Since the pressure in 
 the duct leading to the collectors is now under subatmospheric pressure 
 (negative) the air flows through the backdraft damper. 
 
 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 to the set point on the 
 thermostat; the auxiliary furnace is deactivated, dampers in the air 
 handler are repositioned, and solar heat is 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 
 
9-12 
 
 circulated through storage whether auxiliary heating is required or not; 
 thus all stored heat, regardless of its temperature, is utilized for 
 space heating. 
 
 Domestic Water Preheating 
 
 The control for preheating domestic water is a differential 
 thermostat for sensors SI and S4. The temperature difference setting to 
 start preheating may be about 15°F, and to stop preheating, the set 
 point may be as low as 3°F. There is considerable variation in 
 practice, 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 
 collector and water coil. A temperature limit switch in the preheat 
 tank may be advisable to prevent boiling. With the system shown in 
 Figure 9-3, where attic air is drawn through the collector and hot air 
 is discharged outdoors, it is not necessary to include a temperature 
 limiter. When air is recirculated through the collector during the 
 summer in a closed loop, 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 
 controller, and the signal is nearly linear. Matched sensors will 
 
9-13 
 
 provide consistent control for solar energy collection or water heating 
 because the temperature difference setting will be independent of 
 absolute temperatures. However, exactly matching sensors are seldom 
 available and variations of about 2°F from set temperature differences 
 should be expected. 
 
 INSTALLATION OF CONTROL HARDWARE 
 Control Panels 
 
 Control panels are usually compactly packaged for easy mounting. 
 Connection lugs for sensors and output devices are usually labeled and 
 wires are easy to attach. Some manufacturers include the control 
 assembly with the air handler, and connections to dampers and 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 with air flow from the bottom toward the top in the array. 
 If the air flow is from top to bottom in an array (not recommended) the 
 control becomes complicated. While the temperature is highest at the 
 exit regardless of location, when air is being circulated, the highest 
 temperature is in the top collector in the array if there is no air 
 flow. Thus if down-flow is used, a collector sensor is required at the 
 top to control system start-up, and a sensor is required at the exit 
 (bottom) to control system shut-down. 
 
9-14 
 
 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. 
 
 A sensor in the return duct to the collectors rather than at the 
 
 bottom of storage can create an occasional difficulty if located too 
 
 close to the collector. Without a damper between the sensor and the 
 
 collector, cold air from the idle collector may settle downward in the 
 
 duct and initiate system start-up even when storage is warmer than the 
 
 air at the collector outlet. The system could then operate a few 
 minutes until warm air from storage heats the sensor. 
 
 The sensor in the domestic water preheat 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 contribu- 
 tion to the seasonal heating load but will increase comfort. 
 
 CONTROL SYSTEM CHECK-OUT 
 
 To assure reliable performance, all operating modes of the system 
 should be checked out after installation. To initiate heat collection, 
 the terminals of sensor SI at the controller can be short-circuited to 
 simulate a high collector temperature. The blower should start and 
 
9-15 
 
 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 collection 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 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, is 
 required in a solar air- heating system in which service hot water is 
 provided. Water circulation rate of 2 gpm to 3 gpm is usually satis- 
 factory for most domestic systems. Temperature rise of water 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 exchanger is established 
 by the area of collectors. With information on temperatures and fluid 
 flow rates, 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 
 
9-16 
 
 reasonable 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 heating 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 in Figure 9-3. 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 9-5. The pressure-discharge curve has a dip at 
 
 o 
 
 c 
 
 o 
 
 UJ 
 
 £L 
 
 X 
 CD 
 
 * 
 
 if) 
 
 </> 
 
 Pressure - Discharge 
 
 Volume Flow Rate 
 
 Figure 9-5. Typical Efficiency Curves for Blowers 
 
9-17 
 
 20 to 30 percent of peak capacity and a maximum at mid range. The 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, N 2 , 
 being less than N-.. 
 
 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. Pressure drops 
 through the collector will be provided by the manufacturer but duct 
 losses must be estimated. A rough layout of the ducts is made and 
 approximate duct sizes are selected with air flow velocity not exceeding 
 about 600 feet per minute in the main circulation ducts. 
 
 Friction losses in ducts are shown in Figure 9-6 with duct sizes 
 shown as equivalent diameters. 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 in the calculations. 
 
 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. Normally, if a system is sized to provide 
 about 50 percent of the heating load, the air flow rate for the solar 
 
9-18 
 
 a> 
 
 c 
 
 a. 
 
 I0 & - 
 
 10 
 
 O 
 
 _J 
 
 10 
 
 i / 
 
 10 
 
 -2 
 
 <j> -i cp 
 
 o o O Of O 
 
 Y°\\ ft l \ <i \ ?\ft °i 
 
 ° o o o 
 o o o o 
 
 n ni i\i im 
 
 10 
 
 -i 
 
 10' 
 
 10' 
 
 FRICTION LOSS ( inches of water per 100 ft) 
 
 Figure 9-6. Friction Loss in a Straight Duct 
 
9-19 
 
 system will match the requirements for air circulation through the 
 rooms. 
 
 Many residential and commercial solar air-heating 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 
 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 12. 
 
9-20 
 
 REFERENCES 
 
 1. Dickinson, W.S., Neifert, R.D. , LSf , 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. 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. 
 
 3. Duffie, J. A. and Beckman, W.A., (1974). Solar Energy Thermal 
 Processes , John Wiley and Sons, New York, 1974. 
 
 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 10 
 
 DOMESTIC HOT WATER SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
10-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 10-i i i 
 
 INTRODUCTION 10-1 
 
 OBJECTIVES 10-1 
 
 TYPES AND CHARACTERISTICS OF SOLAR HOT WATER HEATERS . . 10-2 
 
 NON-CIRCULATING TYPE 10-2 
 
 DIRECT HEATING, THERMOSIPHON CIRCULATING TYPE . . 10-3 
 
 DIRECT HEATING, PUMP CIRCULATION TYPES .... 10 5 
 
 DIRECT HEATING, PUMP CIRCULATION, DRAINABLE TYPES . 10 7 
 
 CIRCULATING TYPE, INDIRECT HEATING 10-8 
 
 Liquid Transfer Media . . . . . 10-9 
 
 Air Transfer ........ 10-10 
 
 AUXILIARY HEATING 10-11 
 
 TWO-TANK ARRANGEMENT 10-11 
 
 ONE-TANK ARRANGEMENT 10-12 
 
 OIL OR GAS HEATERS 10-13 
 
 TEMPERATURE AND PRESSURE CONTROL 10-13 
 
 LOCATION OF COLLECTORS 10-16 
 
 ORIENTATION AND TILT OF COLLECTORS 10-16 
 
 INSTALLATION 10-17 
 
 COLLECTORS 10-17 
 
 PIPING 10-19 
 
 CONTROL SENSORS 10-20 
 
 VALVES AND DRAINS 10-20 
 
 FILLING AND LEAK TEST 10-21 
 
 INSULATION 10-21 
 
10-ii 
 
 MAINTENANCE 
 
 COLLECTORS 
 
 ANTIFREEZE LIQUID 
 
 VALVES AND AIR VENTS 
 
 PUMPS 
 SIZING OF TYPICAL SYSTEMS 
 
 GENERAL REQUIREMENTS 
 
 PROCEDURE . 
 
 SIZING EXAMPLES 
 Example 10-1 
 Example 10-2 
 REFERENCES 
 
 Page 
 
 10-22 
 
 10-22 
 
 10-23 
 
 10-23 
 
 10-23 
 
 10-24 
 
 10-24 
 
 10-25 
 
 10-28 
 
 10-28 
 
 10-28 
 
 10-29 
 
10-iii 
 LIST OF FIGURES 
 
 Figure Page 
 
 10-1 Direct Heating, Thermosiphon Circulating Solar Water 
 
 Heater 10-4 
 
 10-2 Direct Heating, Pump Circulation Solar Water Heater with 
 
 Automatic Drain-Down ....... 10-6 
 
 10-3 Indirect Heating, Pump Circulation Solar Water Heater with 
 
 Liquid Heat Transfer Media ...... 10-9 
 
 10-4 Solar Water Heater with Air Collectors .... 10-11 
 
 10-5 Fraction of Annual Load Supplied by Solar as a Function 
 
 of January Conditions for Hot Water Heaters . . . 10-26 
 
 10-6 Average Daily Solar Radiation (Btu/ft 2 ), Month of January 10-27 
 
10-1 
 
 INTRODUCTION 
 
 The oldest and simplest domestic use of solar energy is for heating 
 water. Solar water heaters have been in use for over 75 years in 
 various types and designs. They differ from space heating units 
 principally in size of collector area and volume of water storage. Hot 
 water systems can be assembled from components purchased separately, but 
 there are many prepackaged systems on the market with 2 to 4 collector 
 modules, preheat tank, pumps, valves, controls and sensors that are 
 preselected and sometimes preassembled. Installation instructions are 
 also provided by many manufacturers. 
 
 Whether the systems are assembled by the installer or prepackaged 
 by the manufacturer, basic principles of operation must be understood by 
 all installers and designers. Those principles are explained in this 
 module. 
 
 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 number of collector modules and tank size 
 for a specific application. 
 
 4. Install and put into operation a domestic hot water system. 
 
10-2 
 
 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 where stored water in containers is 
 heated by solar energy directly in the tank. 
 
 2. Circulating types where circulating fluid in solar collectors 
 is heated by solar energy and the heated fluid is used to heat 
 domestic or service water in a storage tank. 
 
 The circulating types may be subdivided as follows: 
 
 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 and domestic water 
 is heated in a heat exchanger when: 
 
 (a) Fluid in the collector is a non-freezing liquid. 
 
 (b) Fluid in the collector is air. 
 
 NON-CIRCULATING TYPE 
 
 A common type of non-circulating water heater used extensively in 
 Japan consists of a set of black plastic tubes about six inches in 
 diameter and several feet long in a box covered with glass 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. 
 
10-3 
 
 The filling can be accomplished by a float-controlled valve and a small 
 supply tank. Late in the day, heated water is drained from the tubes 
 for household use. 
 
 Another type that can be used in non-freezing climates consists of 
 a storage tank located inside a glazed and insulated box 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 required. Tanks 
 can be supported at a tilted angle to maximize exposure of the blackened 
 sides to sunshine, or the tank may be placed horizontally and an 
 insulated lid added to expose more of the tank wall to direct sunlight. 
 
 DIRECT HEATING, THERMQSIPHON CIRCULATING TYPE 
 
 A typical thermosiphon water heater is shown in Figure 10-1. The 
 number of collector modules used may vary from 1 to 6 depending upon 
 size of each unit; the storage tank capacity is commonly 40 to 
 80 gallons. Collectors are usually single glazed and the storage tank 
 must be well insulated. Systems are manufactured in Japan and Australia 
 where the collector and storage units are preassembled. The insulated 
 storage tank in such units is horizontal rather than vertical as shown 
 in Figure 10-1 and located above the collector. 
 
 The thermosiphon system may be pressurized, or it may be operated 
 at atmospheric pressure by installing a float valve to maintain a free 
 water surface in the tank. The incoming cold water is controlled by the 
 float valve, and the hot water supply line is connected to the tank 
 below the free surface and near the top. 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 
 
10-4 
 
 Collec 
 Varie 
 30 to 
 
 Vn^il 
 
 Drain 
 
 Hot Water 
 
 40 to 80 gallon Capacity 
 Insulated Storage Tank 
 
 Tank must be Elevated 
 above Collector by 
 about 18" 
 
 Figure 10-1. Direct Heating, Thermosiphon Circulating Solar Water 
 Heater 
 
 have to be accepted, although an automatic pump could be installed to 
 provide pressure in the hot water supply line. Plumbing systems and 
 fixtures in the United States normally require a pressurized system. 
 When solar energy heats the water in the collectors, warm water 
 rises by convection to the top of the collector and flows through the 
 upper pipeline to the storage tank. Locating the tank higher than the 
 top of the collector permits the colder water from the bottom of the 
 tank to flow to the collector where it is heated and circulated back to 
 the top of the tank. The density difference between cold and hot water 
 produces the circulating flow. Hot water from the collector accumulates 
 
10-5 
 
 near the top of the storage tank, and mixing is minimized if the hot 
 water from the collector enters the tank somewhat below the top as shown 
 in Figure 10-1. A vertical tank has an advantage over a horizontal tank 
 because of thermal stratification, and the hottest water available can 
 be drawn into use. Horizontal tanks of normal sizes tend to be well 
 mixed. 
 
 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 
 collector. To avoid draining the storage tank also, thermostatically 
 actuated valves in both 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. When freezing is no longer a 
 possibility, the drain and vent valves close, the valves in the circula- 
 ting line open, and operation resumes. The possibility of control 
 failure or valve malfunction makes this complex system unattractive in 
 freezing climates. 
 
 DIRECT HEATING, PUMP CIRCULATION TYPES 
 
 When thermosiphon systems are inconvenient or impossible, even in 
 favorable climates, direct heating of domestic water can still be 
 arranges by placing the tank in a utility room or in the basement and a 
 
10-6 
 
 small pump used to circulate water from the tank through the collector 
 as shown in Figure 10-2. To control water circulation, temperature 
 differences between a temperature sensor at the top of the collector and 
 a sensor at the bottom of the tank are used to start and stop the pump. 
 The sensor at the collector outlet must be located close enough to the 
 collector so that it is affected by collector temperature even when the 
 pump is not running, and the sensor in the storage tank should be 
 located in or near the bottom outlet from which the collector is 
 supplied. Usually a temperature difference of 10°F is set to actuate 
 pump circulation. 
 
 Drain 
 
 Normally Open 
 Solenoid Valve 
 
 Temp, 8 Pres. 
 Valve 
 
 jf Relief 
 
 Sensor 
 
 Collectors 
 
 Solenoid 
 
 XS£ 
 
 Gate Valve 
 
 ^ 
 
 ^ '\AA, 
 
 Differential 
 Thermostat 
 
 O 
 
 1 1 fi volt AC 
 
 Gate Valve 
 
 -] Auxiliary 
 J Elements 
 
 ^ 
 
 Pump 
 
 Gate Valve Normally Closed 
 Strainer bale valve Solenoid Valve 
 
 Cold Water 
 
 Hot Water 
 Mixing Valve 
 
 Figure 10-2. Direct Heating, Pump Circulation Solar Water Heater with 
 Automatic Drain-Down (Applicable also to a Two-Tank 
 System) 
 
10-7 
 
 When the temperature difference is less than about 2°F, the pump is shut 
 off and circulation ceases. A check valve is needed in the circulation 
 line to prevent reverse thermosiphon circulation and cooling of water in 
 the tank when no solar energy is being received. 
 
 If hot water is not drawn from the tank (for example when occupants 
 are on vacation, or there is below-normal use), boiling may occur in the 
 collector. The best procedure to prevent frequent boiling is proper 
 sizing of collectors and storage, but a pressure and temperature relief 
 valve must always be provided to allow steam to escape. 
 
 DIRECT HEATING, PUMP CIRCULATION, DRAINABLE TYPES 
 
 For direct heating solar water heaters installed in cold climates, 
 freeze protection must be provided. One arrangement, shown in 
 Figure 10-2, allows the collector to drain automatically when freezing 
 weather threatens. 
 
 When the temperature sensor at the bottom of the collector 
 indicates about 40°F, the drain and vent valves open and water in the 
 collector and connecting pipes drains into the sewer. Simultaneously, a 
 motorized valve between the storage tank and pump inlet closes and a 
 check valve in the line between collector and storage tank closes, 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 as shown in 
 Figure 10-2 where the valves are held closed by electrical means, 
 automatically opening when either electrical failure occurs or when 
 freeze threatens. The control system can also be arranged so that 
 whenever the circulating pump is not in operation the drain and vent 
 valves are open. 
 
10-8 
 
 Start-up of a vented collector system must allow air to escape from 
 the collector and connecting pipelines. In either the line-pressure 
 system or the unpressurized system, water flowing into the collector 
 will force 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 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 actuators, 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 
 used. Considerable simplification, cost reduction, and reliability 
 improvement may then be achieved. 
 
 CIRCULATING TYPE, INDIRECT HEATING 
 
 Freeze protection of direct heating systems involves 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. A heat exchanger is used to transfer 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. Also, 
 the corrosion rate in liquid collectors is decreased because the tubes 
 are always full and not exposed to free oxygen as in the drain-down 
 systems. 
 
10-9 
 
 Liquid Transfer Media 
 
 A method for solar water heating using a non-freezing liquid in the 
 solar collector is illustrated in Figure 10-3. The most commonly used 
 liquid is a solution of ethylene glycol (automobile radiator antifreeze) 
 in water, but propylene glycol solution is also used. A pump circulates 
 the solution through the collector and delivers the heated liquid to and 
 through a liquid-to-liquid double-wall heat exchanger. Simultaneously 
 another pump circulates domestic water from the storage tank through the 
 exchanger and back to storage. The control system is essentially the 
 same as that in Figure 10-2. 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. 
 
 Expansion 
 Tank 
 
 Temp. 8 Pres. 
 
 Relief Valve \ Gate Valve 
 
 n,.,L W Strainer K 
 
 Pump 
 
 Storage Tank 
 
 Auxiliary Heater 
 
 Boiler Drains 
 (or Filling System 
 
 Figure 10-3. Indirect Heating, Pump Circulation Solar Water Heater 
 with Liquid Heat Transfer Media 
 
10-10 
 
 A small expansion tank needs to be provided in the collector loop, 
 preferably near the high point of the system. This tank must have a 
 vent to the atmosphere or a diaphragm and pressurized air. 
 
 To meet most code requirements, the heat exchanger must be of a 
 design such that rupture or corrosion failure will not permit contamina- 
 tion of the potable water. A conventional single-wall tube-and-shell 
 exchanger is not usually acceptable. Similarly, a single pipe coil 
 inside the storage tank through which the collector fluid is circulated 
 would not be satisfactory. A suitable design would consist of parallel 
 tubes with metal bonds between them so that there would be no 
 possibility of contamination even if both tubes were perforated. A 
 double-row finned tube air-to-liquid heat exchanger can also be used by 
 circulating the two liquids through alternate rows of tubes. Heat is 
 transferred by conduction through the fins. Another type involves a 
 tube within a tube, with considerable contact of the two but enough 
 space for escape of liquid if perforation of one tube occurs. This type 
 is sometimes used in coils inside the tanks, thereby eliminating the use 
 of a second pump and external exchanger. 
 
 Although aqueous solutions of ethylene glycol and propylene glycol 
 
 appear to be most practical for solar energy collection, organic liquids 
 
 (R) fR) 
 
 such as silicone oil, Dowtherm J , and Therminol 55 ^ may be used. 
 
 Price and viscosity of organic liquids are drawbacks, but chemical 
 
 stability and assurance against boiling are advantages over aqueous 
 
 antifreeze mixtures. 
 
 Air Transfer 
 
 An air-heating collector can be used to heat domestic water with an 
 air-to-water heat exchanger as illustrated in Figure 10-4. Air is solar 
 
Motor 
 Damper 
 
 Duct 
 
 10-11 
 
 -VW- 
 
 Sensor 
 
 Collectors 
 
 Motor 
 Damper 
 
 U5voltAC 
 
 • Tan i — K -^ 
 
 •inm 
 "Diai'i 
 
 ''.1LQLC 
 
 icaoi 
 
 o 
 
 Air-To-Water 
 Heat Exchanger 
 
 XJ3= 
 
 jSMH 
 
 Sensor 
 
 Drain 
 
 Cold 
 Water 
 
 Mixing Valve 
 
 Hot Water 
 
 c;r;:irr: 
 
 "[Auxiliary 
 J Element 
 
 Auxiliary 
 Element 
 
 Drain 
 
 Storage Tank 
 
 Auxiliary Heater 
 
 Blower 
 
 Figure 10-4. Solar Water Heater with Air Collectors 
 
 heated in the collector, and the hot air then heats the domestic water 
 in the exchanger. Differential temperature (between collector and 
 storage) controls both air and liquid circulation. Use of air as a heat 
 transfer medium eliminates risks of corrosion, contamination, freezing 
 and boiling. However, larger conduits are needed for circulating the 
 heat transfer medium through the collector, and the collector area is 
 larger than that with required liquid-heating collectors. 
 
 AUXILIARY HEATING 
 
 TWO-TANK ARRANGEMENT 
 
 A dependable supply of hot water requires the use of a conventional 
 water heater to supplement the solar source. A common method of 
 
10-12 
 
 auxiliary heating in solar DHW systems is the use of a conventional 
 water heater in addition to the solar storage tank. Solar heating of 
 water can be maximized by avoiding direct or indirect auxiliary heating 
 of the fluid that circulates to the solar collector. If auxiliary heat 
 is added to the solar hot water storage tank so as to increase the fluid 
 temperature entering the collector, heat losses from the collector will 
 rise. Auxiliary heat should therefore be added where it cannot 
 influence the temperature in the solar collection circuit. Use of a 
 conventional hot water heater (tank), in a two-tank system, can result, 
 however, in excessive auxiliary use in the booster heater if the tanks 
 are not well insulated. 
 
 A conventional electric hot water heater is shown in Figures 10-3 
 and 10-4 with preheated water supplied to it 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. 
 Auxiliary heating in these designs cannot adversely affect the operation 
 of the solar system. 
 
 ONE-TANK ARRANGEMENT 
 
 A one-tank system with the electric resistance heaters only in the 
 upper portion of the solar storage tank, as shown in Figure 10-2, is 
 cheaper than the two-tank type, and should have nearly the same solar 
 collection efficiency. Temperature stratification in 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 
 
10-13 
 
 effect, the two tanks shown in Figures 10-3 and 10-4 are combined into 
 one, with temperature stratification providing a separation. 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. 
 
 OIL OR GAS HEATERS 
 
 If auxiliary heating is by oil or gas water heaters, a two-tank 
 system must be used. Since water is heated at the bottom of an oil or 
 gas water heater, thermal mixing will take place inside the tank. 
 Therefore, auxiliary heating of the fluid circulating to the collector 
 could not be avoided in a one- tank system. When hot water is used, cold 
 water entering the tank near the bottom may activate the thermostatted 
 burner even if solar heat is being collected. However, with a two-tank 
 system, solar heated water would enter the conventional tank and, 
 regardless of temperature, there could not be auxiliary heating of the 
 solar storage tank. 
 
 TEMPERATURE AND PRESSURE CONTROL 
 
 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 
 controlled mixing valve (tempering valve) can be used to provide hot 
 
10-14 
 
 water at constant temperature for household use as shown in Figures 10-3 
 and 10-4. 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- 
 1 i qui d design, with heat exchanger, should normally be through a 
 temperature-actuated valve in the hot water loop. Loss of collector 
 fluid by boiling and vaporization is thereby avoided. It is necessary, 
 however, 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 w 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. 
 
10-15 
 
 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 
 dissipated in the form of collector heat loss. The collector tempera- 
 ture 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 
 capability 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 
 
10-16 
 
 steam to avoid overheating service water when useage is small. A 
 
 temperature-actuated relief valve, set at a temperature of 210°F or 
 
 less, 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 
 structure 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, 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. 
 
 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 
 at the latitude angle, roof mounting may still be satisfactory. While 
 collectors should be oriented to face due south whenever possible, 
 
10-17 
 
 variations as much as 15 degrees east or west of due south will have 
 only slight effect on system performance. Off-south orientation could 
 be beneficial in situations where the collectors are subject to shading 
 in the early morning or late afternoon. Orienting the collectors 
 15 degrees to the east or west will generally reduce the amount of solar 
 heat collected by less than 5 percent. 
 
 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. 
 
 INSTALLATION 
 
 COLLECTORS 
 
 Mounting collectors on building roofs can be hazardous, and use of 
 safe methods and safety devices is strongly recommended. A scaffold 
 should be used whenever possible to provide access to the level of the 
 roof. 
 
 Plan the installation procedure before the first collector unit is 
 hoisted to the roof. Some collector manufacturers have considered the 
 problems of anchoring the collectors to mounting surfaces, and their 
 collector units are generally designed for easy mounting, hooks are 
 provided for lifting collectors, and installation instructions are often 
 included with purchase of the solar DHW system. Many other collector 
 manufacturers have made no provision for lifting or mounting, and 
 installation of such collectors can be time consuming and expensive. 
 
10-18 
 
 Collector modules may weigh between 50 and 200 pounds depending 
 upon the size of the module and its manufacturer. Mechanical equipment 
 can be used to facilitate the lifting of collectors from ground level to 
 the building roof, but the smaller-weight collectors may be readily 
 lifted manually. For the few collector modules usually needed with 
 domestic hot water systems, acquiring special lifting equipment may add 
 significantly to the overall installation cost. 
 
 On new buildings, collectors can be mounted on the roof sheathing 
 after the felt layer has been nailed down over the sheathing. It is 
 recommended that at least 60- lb felt be used between the collectors and 
 the roof, not only for weatherproof ing but also to withstand the foot 
 traffic during installation. Use of a 2 x 2 or 2 x 4 wooden guide strip 
 nailed to the roof is useful for positioning the collectors. After 
 attaching the collectors to the sheathing, the array should be 
 adequately flashed to prevent moisture accumulation and consequent 
 damage to the roof beneath the collectors. 
 
 On existing buildings it may be easier to mount the collector above 
 the existing roof rather than to incur additional expenses for removing 
 the roofing. Standoffs may be used to position the collectors at a 
 prescribed distance above the finished roof. Some collectors may 
 require frame supports which can be secured to the standoffs. 
 
 An advantage of mounting collectors on standoffs is that they may 
 be tilted to any desired angle. However, collectors extending above the 
 roof are susceptible to wind loads, and in some climates also to snow 
 and ice loads. 
 
10-19 
 
 There are many other possible arrangements for mounting and 
 installing collectors. Manufacturer's suggestions should be considered 
 whenever they are provided, but every installation should conform to 
 general and local building codes. 
 
 PIPING 
 
 Copper pipes are commonly used in domestic hot water systems. 
 However, if there are aluminum absorber tubes in the collector, it may 
 be advisable to consider CPVC or polybutylene pipes in the collector 
 loop. If dissimilar metals are used in an aqueous liquid loop, it is 
 necessary to use dielectric connectors. 
 
 Piping runs should be as short as possible to minimize cost for 
 materials, heat losses, and pumping head losses. Vertical copper pipe 
 runs should be anchored at about 10-ft intervals and plastic pipe at 
 5-ft intervals. On horizontal runs, copper pipe should be supported at 
 about 6-ft intervals, but plastic pipe may require hangers every 1 to 
 2 feet to prevent sagging. CPCV pipe will begin to yield noticeably at 
 a temperature of 160°F and polybutylene pipe will yield at 200°F. Allow 
 space at the ends of pipe runs for expansion and contraction due to 
 changes in temperature. 
 
 Connections to some collectors may require use of flexible hoses. 
 Silicone coupling hoses are often recommended by collector 
 manufacturers. Automotive grade rubber hoses are not suitable for 
 installations that are exposed to sunlight because of degradation under 
 exposure to ultraviolet light. If hose clamps are used, they should be 
 of a type which provides continuous pressure, even if the hose squeezes 
 or shrinks to small diameter. Whether silicone or rubber hoses are 
 
10-20 
 
 used, flexible couplings will probably require eventual replacement, and 
 installations should be made so that they are easily accessible for 
 maintenance purposes. In general, all-metal piping and connections are 
 most dependable and durable. 
 
 CONTROL SENSORS 
 
 Instructions for installing the controller are generally provided 
 with the system. Normally, controls require a difference between the 
 water temperature in storage and water temperature at the outlet of the 
 collector. The sensor at the collector outlet should be installed in 
 one leg of a tee placed as close to the collector as possible. If there 
 are multiple collector modules in the array, any collector outlet may be 
 chosen to install the sensor. However, if the collectors are connected 
 in series, the sensor should be located in the last (flow wise) 
 collector. The storage temperature sensor may be inserted into the 
 bottom of the tank through a tee connection in the circulation line. 
 
 VALVES AND DRAINS 
 
 It is recommended that isolation valves be installed in pipelines 
 on both sides of pumps and filters to facilitate removal for inspection 
 and maintenance. Drain valves should be placed in the line as shown in 
 Figures 10-2 and 10-3 to enable draining of pipelines and collectors. 
 
 For indirect heating types, as shown in Figure 10-3, provisions for 
 filling the collector loop with antifreeze liquid must be provided. The 
 fill system can also be used for drainage. Drains will normally be 
 provided with the storage (preheat) tank. 
 
10-21 
 
 FILLING AND LEAK TEST 
 
 To fill a direct-heating type system, simply open the cold water 
 line valve and fill the system slowly, allowing the vent to bleed air 
 from the line. Cycle the pump several times after filling to be sure 
 the system is not air locked. If a flow meter is not provided with the 
 system, determine that fluid is circulating by reading temperature 
 gauges or "feeling" the delivery line from the collectors during a 
 collection period to be sure that water is being heated by the solar 
 collectors. 
 
 Filling an indirect- heating system of the type shown in Figure 10-3 
 with antifreeze liquid is most easily accomplished by using a separate 
 pump. Collectors should be filled with liquid flowing from the bottom 
 towards the top. Alternatively, the circulation pump can be used to 
 pump the antifreeze liquid from a supply container. The gate valve (in 
 Figure 10-3) between the two fill/drain valves should first be closed 
 and short hoses should be attached to the drain valves. The other end 
 of each hose can then be immersed in a vessel containing the antifreeze 
 mixture. Once the system is filled, the gate valve can be opened and 
 the drain valves can then be closed. 
 
 All systems should be leak- tested before insulating the pipes. 
 Indirect heating systems may be pressurized to mains pressure by 
 connecting a hose to one of the fill/drain valves. 
 
 INSULATION 
 
 All exposed piping, except the cold water supply line, should be 
 insulated with closed-cell type insulation. Preformed, split fiberglass 
 
10-22 
 
 or urethane insulation is suitable. Insulation over outdoor piping must 
 be protected from weather by watertight plastic or foil jacket. 
 Prejacketed insulation is also available. The insulation must fit 
 tightly around the pipes to be effective. Loose-fitting insulation will 
 allow air circulation around the pipes and is only marginally effective. 
 Ells, wyes, tees, values and drains are the most difficult to insulate 
 but care in applying insulation will be rewarded with low heat losses. 
 
 In addition to fiberglass and urethane insulation, elastomers and 
 isocyanurates are used. Unprotected elastomers will degrade when 
 exposed to ultraviolet light and protective coatings must be used. 
 Different types are available and whenever possible manufacturer's 
 recommendations should be followed. 
 
 If conventional hot water tanks are used, either in a one-tank or 
 two-tank system, they may be provided with additional insulation if 
 desired. Special insulation jackets are being made to fit many 
 commercially available tanks. 
 
 Circulation ducts for air type domestic water heaters should be 
 insulated to about R-4 rating. Fiberglass, glass wool and urethane 
 insulating material are appropriate. 
 
 MAINTENANCE 
 
 COLLECTORS 
 
 Collectors will be relatively maintenance- free if quality units are 
 installed. However, periodic inspection to check for fluid leaks is 
 advisable. Unless collector glazings are damaged by unusual conditions, 
 
10-23 
 
 such as sandstorms, hail, windstorms, flying objects, etc., little 
 maintenance should be required. Normal dust accumulation does not 
 affect performance significantly, and periodic rain or snow should keep 
 the glazing relatively clear. In some locations, however, the glazing 
 may become coated with an oily film which will not be washed off by rain 
 or snow, so occasional cleaning may be advisable. 
 
 ANTIFREEZE LIQUID 
 
 In indirect heating systems, the antifreeze liquid may require 
 periodic replacement. The supplier's suggestions should be followed in 
 considering the replacement time interval. If none is suggested, the pH 
 of the solution should be tested and if the solution is becoming acidic, 
 it should be replaced. 
 
 VALVES AND AIR VENTS 
 
 Periodic inspection of valves and air vents is recommended. Air 
 bleed valves can be checked to see that they are functional, and packing 
 around valve stems may need to be tightened occasionally. 
 
 PUMPS 
 
 Pump bearings that require lubrication should be serviced 
 semi-annually. Instructions as to quantity and frequency of lubrication 
 are generally provided by the manufacturer. Seals should be inspected 
 for leaks periodically and tightened if possible. 
 
10-24 
 
 SIZING 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, the 
 amount of heat required is about 55,000 Btu per day. 
 
 Choosing a collector area for a system is made difficult because 
 solar availability varies widely from region to region and from season 
 to season. There are also the short-term radiation fluctuations due to 
 cloudiness and the day-night cycle. As a result of seasonal variations 
 in solar availability the variation in the solar heat supply to a hot 
 water system may be 200 to 400 percent. 
 
 To illustrate the effect of solar variation, assume that 50 ft 2 of 
 collectors could supply the major part, perhaps nearly all, of the 
 summer hot water requirements. The same system would supply less than 
 half the winter needs. If the collector area is increased to 100 ft 2 to 
 better meet winter needs, the system would be oversized for summer 
 operation and excess solar heat would have to be wasted. 
 
 An important disadvantage of oversizing a collector 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, and nearly all of 
 the solar heat would be used beneficially. But if heat is wasted, there 
 is a lower economic return per unit of investment. Stated another way, 
 
10-25 
 
 more Btu per dollar of investment (hence cheaper solar heat) can be 
 delivered by the smaller system. Therefore, practical designs of solar 
 water heaters should be based on desired hot water output in the 
 sunniest summer months rather than winter months. Normally, selecting a 
 collector area to supply 50 to 60 percent of the annual water heating 
 needs is a good criterion. 
 
 PROCEDURE 
 
 The curve shown in Figure 10-5 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 from 6:00 a.m. until midnight. A collector of good quality (but 
 not with the highest efficiency available, 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 represents results of computer calcula- 
 tions 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, 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 200 gpd. The sizing curves are approximate and should 
 not be expected to yield results closer than 10 percent of actual value. 
 
10-26 
 
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 .ATITUDE 
 
 
 
 
 
 
 
 S = MEAN JANUARY SOLAR 
 
 RADIATION ON A HORIZONTAL 
 
 
 
 
 
 SURFACE, Btu/(ft 2 )(day) 
 = AVERAGE nAMY hot 
 
 
 
 
 
 WATER 
 
 LOAD, Bt 
 
 li /day 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 0.2 0.4 0.6 0.8 1.0 1.2 
 
 SA/L 
 
 1.6 !.8 2.0 
 
 Figure 10-5. Fraction of Annual Load Supplied by Solar as a Function of 
 January Conditions for Hot Water Heaters 
 
 The vertical axis shows the fraction of the annual water heating 
 load supplied by solar. The horizontal axis shows values of the 
 parameter, SA/L, which involves the average daily January radiation on a 
 horizontal surface, S; the required collector area, A, and the average 
 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 10-6. Values on the map are given in Btu/(ft 2 -day). 
 
 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 
 
10-27 
 
10-28 
 
 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 10-1 
 
 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 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 10-6, is 
 680 Btu/(ft 2 *day). for a water system to provide 60 percent of the 
 annual load, from Figure 10-5, SA/L is about 0.8. Therefore: 
 
 A = 0.8 x L/S = (0.8 x 60048)/680 = 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. 
 
 Example 10-2 
 
 Determine the size of collector needed to provide hot water for a 
 family of four in Albuquerque, New Mexico. 
 
 SOLUTION: The average daily load will be approximately the same 
 as in Example 10-1: 
 L = 60,048 Btu/day 
 
10-29 
 
 From Figure 10-6, S = 1115 Btu/(ft 2 «day). For a system to provide 
 60 percent of the annual load, Figure 10-5 shows that SA/L is 
 approximately 0.8. The collector area required is: 
 
 A = (0.8 x 60048)/1115 = 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 11 
 
 INSTALLATION AND OPERATION OF 
 LIQUID SOLAR HEATING SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 

11-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 11- i i 
 
 LIST OF TABLES 11- ii 
 
 INTRODUCTION 11-1 
 
 OBJECTIVE 11-1 
 
 SYSTEM TYPES AND ARRANGEMENTS 11-2 
 
 DUAL-LIQUID COLLECTION SYSTEM 11-2 
 
 SINGLE-LIQUID (DRAIN-DOWN) SYSTEMS 11-5 
 
 SOLAR SUBSYSTEMS AND COMPONENTS 11-9 
 
 COLLECTORS AND STORAGE 11-9 
 
 COLLECTOR-STORAGE HEAT EXCHANGERS 11-10 
 
 SUBSYSTEMS FOR SUPPLY OF SOLAR HEAT TO USE . 11-11 
 
 AUXILIARY HEAT 11-14 
 
 AUXILIARY HEAT PUMP 11-15 
 
 SERVICE HOT WATER 11-21 
 
 PUMPS, PIPING AND ACCESSORIES 11-23 
 
 SYSTEM INTEGRATION AND CONTROL 11-26 
 
 SYSTEM CONTROL 11-28 
 
 PROTECTION AGAINST FREEZING AND BOILING .... 11-32 
 
 INSTALLATION GUIDELINES 11-34 
 
11-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 11-1 Schematic Diagram of Dual-Liquid Space 
 
 Heating and Hot Water System .... 11-3 
 
 11-2 Schematic Diagram of a Single Liquid (Drain- 
 Down) Space Heating and Water Heating System 
 (Gravity Return) 11-6 
 
 11-3 Schematic Diagram of a Single-Liquid (Drain- 
 Down) Space Heating and Water Heating System 
 (Siphon Return with Motorized Air Inlet 
 Valve) 11-7 
 
 11-4 Typical Temperature Profiles in a Single- Pass 
 
 Counterflow Heat Exchanger .... 11-11 
 
 11-5 Solar Heating with Auxiliary Furnace . . 11-13 
 
 11-6 Heat Pump in Heating Mode .... 11-17 
 
 11-7 Heat Pump in Cooling Mode .... 11-17 
 
 11-8 Solar Heating with Auxiliary Air- to- Air Heat 
 
 Pump 11-18 
 
 11-9 Solar Heating System with Auxiliary Heat 
 
 from Air-to-Water Heat Pump .... 11-19 
 
 11-10 Solar-Assisted Heat Pump (Liquid-to-Liquid) 
 
 Heat Pump in Series with Solar Storage . . 11-20 
 
 11-11 Collector Loop Fittings and Details . . 11-24 
 
 11-12 Typical Controls for Liquid Solar System . 11-29 
 
 LIST OF TABLES 
 
 Table Page 
 
 11-1 Recommended Pipe Diameters for Various Flow 
 
 Rates 11-26 
 
11-1 
 
 INTRODUCTION 
 
 Components of a solar heating system must be well selected, 
 compatibly sized, and carefully assembled in order to ensure that the 
 system will function properly. Collectors, heat storage units, pumps 
 and fans, controls, heat exchangers, and auxiliary heaters must be 
 combined into an effective system. In a liquid-heating system, heat 
 from the collector is usually delivered directly, or by heat-exchange, 
 to water storage, and the heating demands are met by supplying heat from 
 storage. An auxiliary fuel or electric heater is needed to provide heat 
 when stored solar energy is insufficient to meet the demand. Such 
 occasions can occur on excessively cold nights (or days) and after 
 successive cloudy days. A practical solar system must function 
 automatically, provide the desired comfort level in the building at all 
 times, require little maintenance, and operate reliably over a long 
 period of time. 
 
 After selection of a system type, collector area and storage volume 
 are determined, liquid circulation rate through the collector is 
 established and pumps can be selected. Heat exchanger size is based on 
 desired heat delivery rate. The auxiliary furnace is sized to meet the 
 design heating load of the building. If adequate attention is not given 
 to details of sizing, layout, and assembly, the system may not perform 
 as expected, even if the best available components are selected. 
 
 OBJECTIVE 
 
 The objective of this module is to describe the installation, 
 operation, and interdependence of the components in a liquid-heating 
 
11-2 
 
 solar system. The trainee should be able to: 
 
 1. Develop schematic and working plans of liquid solar systems. 
 
 2. Specify compatible system components. 
 
 3. Estimate the proper size of system components. 
 
 4. Identify all the system operating modes. 
 
 5. Install and service liquid solar heating systems. 
 
 SYSTEM TYPES AND ARRANGEMENTS 
 
 There are two types of liquid solar heating systems in common use, 
 the dual -liquid type and the drain-down type. 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. 
 
 DUAL-LIQUID COLLECTION SYSTEM 
 
 A widely used solar liquid heating system is shown in Figure 11-1. 
 The system is arranged to collect solar heat in a non-freezing liquid, 
 deliver the heat to water storage via a 1 i qui d-to- liquid heat exchanger, 
 and supply heat from storage to the space heating and service hot water 
 
11-3 
 
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11-4 
 
 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 the solar domestic hot water 
 system can be completely separate from the solar space heating system, 
 it is more convenient and economical to arrange an integrated system. 
 During the warm months of the year the collectors of an integrated 
 system, which would otherwise be unused can supply practically all of 
 the domestic water heating that is needed. 
 
 The most commonly used liquid in the collector loop is a mixture of 
 water and ethylene glycol (ordinary automobile radiator antifreeze), 
 although propylene glycol or alcohol and water mixtures 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 mixture through collectors 
 and heat exchanger, usually 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. The expansion tank is usually a convenient point 
 for charging the system with liquid. If liquid in the circulating loop 
 is depleted by leakage or boiling, the system can be recharged with 
 glycol and water through the expansion tank vent or other pipe 
 connection. 
 
 In a more limited number of systems, some type of oil is used as 
 the heat collection fluid. Silicones, diphenyl , Dowtherm w , 
 Therminol w are examples. In addition to providing complete 
 
11-5 
 
 protection from freezing, these liquids will not boil at temperatures 
 attainable in flat-plate collectors. They are more expensive than 
 antifreeze solutions, however, and their heat transfer properties 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 
 circulated 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, water 
 enters near the top of the tank. 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 
 the greater pressure loss through the coil results in more power usage 
 in the collector pump, and access to the heat exchange surface and 
 connections (coils) is more difficult. 
 
 SINGLE-LIQUID (DRAIN-DOWN) SYSTEMS 
 
 Alternative collection and storage arrangements are shown in 
 Figures 11-2 and 11-3. Heat is collected and stored in water, and 
 freezing is avoided by draining the collector when it is not in use 
 (Figure 11-2), or when freezing can occur (Figure 11-3). 
 
 A primary requirement of all types of drain-down liquid systems is 
 the design and positioning of collectors and exterior piping on at least 
 a slight slope. Any incidental upturns or lengthy horizontal passages 
 can prevent complete drainage. Freezing can then occur, with 
 consequential damage. 
 
11-6 
 
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11-8 
 
 Probably the most reliable drain-down type, shown in Figure 11-2, 
 requires no specific controls for collector drainage. When the pump 
 stops, water runs from the collector into the tank, mainly back through 
 the pump, 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 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 corrosion rates. 
 
 Pumping power can be minimized by use of the siphon return design 
 shown in Figure 11-3. Static head between storage and the top of the 
 collector is recovered in the water filled down-flow return line 
 (typically one-half to three-fourths inch). An automated air inlet 
 valve 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 into the storage tank 
 through the two connecting pipes while the collector fills with air. In 
 another design, a motorized drain valve in the return line to the top of 
 the tank is actuated by low temperature, and a siphon breaker air valve 
 at the top of the collector is opened by the suction pressure difference 
 which develops at that point. Water drains from the return line into 
 the tank through a separate pipe connected to the air space in the top 
 of the tank. Although this system requires less pumping power than the 
 non-siphoning type shown in Figure 11-2, dependence on a control sensor 
 
11-9 
 
 and automatic valve, even though opening without power, increases risks 
 of freeze-damage. 
 
 SOLAR SUBSYSTEMS AND COMPONENTS 
 
 COLLECTORS AND STORAGE 
 
 The efficiency of collectors in a solar system is influenced by all 
 other components in the system. For maximum efficiency, the collector 
 should be supplied with liquid at the lowest available temperature in 
 order that heat loss from the collector is minimized. A moderate amount 
 of temperature stratification in a water tank can be expected, with 
 warm, lower-density liquid near the surface and colder, heavier liquid 
 near the bottom of the tank. It follows, therefore, that liquid from 
 the bottom of the storage tank should be circulated directly or 
 indirectly to the collector. If a heat exchanger is used, as in Figure 
 11-1, 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 11-2 and 11-3, water from the bottom of storage is 
 pumped through the collector. Heated water is then returned to the top 
 of storage. Typical rise in temperature of water flowing through the 
 collector or through the heat exchanger is 10°F to 15°F during sunny 
 mid-day periods. 
 
 In addition to dependence on heat input from the collector, storage 
 temperatures are strongly affected by the rate of heat delivery to the 
 load, which, in turn, is dependent on the characteristics of the load 
 heat exchangers. Selection and sizing of heat exchangers are therefore 
 important in system design. While oversizing the heat exchangers 
 
11-10 
 
 has minor influence on system performance, undersizing can reduce the 
 quantity and efficiency of solar heat collection. 
 
 COLLECTOR-STORAGE HEAT EXCHANGERS 
 
 A heat exchanger must be provided to transfer heat from the 
 collector fluid to storage if the collector and storage fluids are in 
 different loops. Because of the limited temperatures available from 
 flat-plate solar collectors, the temperature difference across heat 
 exchangers 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-shell heat exchangers are simple, efficient, and readily 
 available. They usually consist of multiple tubes enclosed within an 
 outer jacket. One fluid passes through the tubes while the other fluid 
 passes outside the tubes. Large heat transfer surface can be achieved 
 in compact arrangements. 
 
 The performance characteristics of a single-pass counterflow heat 
 exchanger are illustrated in Figure 11-4. 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 can be followed in selecting the size of a 
 heat exchanger. If appropriate information is difficult to acquire, the 
 manufacturer's representative should be consulted for assistance and/or 
 advice. The information necessary for heat exchanger sizing and fluid 
 flow rate determination are the temperatures of the two fluids entering 
 the exchanger and the Btu per hour heat transfer rate desired or one of 
 the fluid exit temperatures. 
 
11-11 
 
 HOT COLLECTOR FLUID 
 
 COOL 
 
 STORAGE 
 
 FLUID 
 
 Figure 11-4. Typical Temperature Profiles in a Single-Pass 
 Counterflow Heat Exchanger 
 
 At high fluid velocities and flow rates good heat exchanger 
 
 efficiency can be achieved, but at the expense of pumping power. A 
 
 practical compromise in these two opposing objectives is sought in 
 system design. 
 
 SUBSYSTEMS FOR SUPPLY OF SOLAR HEAT TO USE 
 
 Heat from a solar hot water storage tank may be distributed to 
 living spaces either as hot water or as warm air. For water distribu- 
 tion, methods and equipment commonly used in conventional hydronic 
 
11-12 
 
 heating systems are employed. When activated by a room thermostat, a 
 pump draws solar-heated water from the top of the storage tank, through 
 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 11-1, 11-2 and 11-3 illustrate this application, and the 
 schematic heat exchanger in the building represents 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 
 
 temperatures of 160°F to 180°F. Their limited heat transfer surfaces 
 
 formed by a single water tube and 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 supplemented. A doubling of the usual baseboard heat transfer 
 
 surface permits reduction in design (maximum) temperature to 130°F-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 
 
 and flow rates are compatible with the requirements of most 
 
 fuel-operated systems. 
 
 ^ 
 
 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. 
 
11-13 
 
 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 11-5 ). Air is 
 circulated through the exchanger by a conventional fan or blower, and is 
 usually heated from about 70°F to a temperature within 10 to 
 15 degrees 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 temperature of air supplied from the solar coil can 
 be boosted by the auxiliary. 
 
 FROM 
 COLLECTOR 
 
 OR HEAT 4 VENT 
 EXCHANGER 
 
 TO 
 
 COLLECTOR 
 
 OR HEAT 
 
 EXCHANGER 
 
 THERMAL 
 STORAGE 
 
 ( WATER 
 TANK) 
 
 COLD 
 
 AIR 
 
 RETURN 
 
 WARM 
 
 AIR 
 SUPPLY 
 
 FINNED 
 
 COIL 
 
 EXCHANGER 
 
 AUXILIARY 
 
 WARM AIR 
 
 FURNACE 
 
 AND 
 
 BLOWER 
 
 Figure 11-5. Solar Heating with Auxiliary Furnace 
 
11-14 
 
 AUXILIARY HEAT 
 
 There are several methods for supplying auxiliary heat in a liquid 
 solar system for space heating. In virtually all practical solar 
 heating 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 11-1, 11-2, and 11-3. If a central heat exchanger 
 and ducted warm air are employed, 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. As shown in Figures 
 11-1, 11-2, and 11-3, a single pump and automatic valve provide hot 
 water 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. 
 
 Another possible arrangement would entail the auxiliary boiler in 
 series with the solar heat storage tank so that it could be used, when 
 necessary, to increase the temperature of water being supplied to the 
 heat distribution system. However, this design is seldom used, because 
 some of the heat supplied to the water stream, passing through an 
 auxiliary boiler which is thermostatted at a preset delivery 
 
11-15 
 
 temperature, 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. For example, if solar storage at 100°F is unable to 
 meet the demand, and the temperature is hence increased to 140°F in the 
 auxiliary boiler, water would return to solar storage at about 110°F to 
 115°F after delivering only a portion of its heat to the air coil. In 
 the dual source parallel system, either auxiliary or solar is used by 
 itself so there is no feedback of heat to the solar system from the 
 auxiliary. 
 
 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 11-5. There is no possibility that auxiliary heat can affect 
 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 
 
11-16 
 
 lower factor generally prevails. The process is identical to a 
 refrigeration 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 may be done inside the machine by 
 reversing the evaporator and condenser units, as shown in Figures 11-6 
 and 11-7, or externally by reversing the exchange circuits on the 
 evaporator and condenser side. 
 
 One method of heat pump use in an air distribution system, il- 
 lustrated in Figure 11-8, 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 system, 
 the flow of water through the solar exchanger can be interrupted so that 
 air is not supplied to the heat pump at excessive temperatures (e.g., 
 not above 100°F). As in conventional heat pump installations, electric 
 resistance coils are also included for use during severe cold weather 
 periods. 
 
 Another design (Figure 11-9) involves an air-to-water heat pump 
 rather than a hot water boiler for auxiliary heat supply. Replacement 
 of the auxiliary heater in Figure 11-1, 11-2, or 11-3 with the heat pump 
 condenser coil and back-up electric resistance heater permits a 
 reduction in electricity consumption by virtue of a Coefficient of 
 Performance greater than unity. Heat distribution 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 11-10. 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 
 
11-17 
 
 Heat 
 Exchanger 
 
 Evaporator 
 ( Heat from Aux, 
 Solor, Amb. Air, 
 or Ground H 2 0) 
 
 y- 
 
 -i Compressor 
 
 ft* 
 
 M 
 
 -Q- Closed Valve 
 -©- Open Valve 
 
 Figure 11-6. Heat Pump in Heating Mode 
 
 -c 
 
 Heat 
 Exchanger 
 
 -CD- 
 
 Evaporator 
 (Space Cooling) 
 
 ■e- 
 
 Receiver 
 
 Expansion 
 Valve 
 
 <D-i 
 
 Condenser 
 (Heat Rejection 
 to Ambient) 
 
 Compressor 
 
 i i 
 i i 
 
 Closed Valve 
 © Open Valve 
 
 Figure 11-7. Heat Pump in Cooling Mode 
 
11-18 
 
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11-20 
 
 FROM 
 
 COLLECTOR 
 OR HEAT 
 EXCHANGER 
 
 TO COLLECTOR 
 
 OR HEAT -« 
 
 EXCHANGER 
 
 VENT 
 A 
 
 THERMAL 
 
 STORAGE 
 
 (WATER TANK) 
 
 THREE-WAY VALVE 
 
 D 
 
 EVAPORATOR CONDENSER 
 COIL COIL 
 
 COMPRESSOR 
 
 HEAT TO 
 ROOMS 
 
 — C D — t%n 
 
 ■+ T TH( 
 
 HEAT PUMP 
 
 THREE-WAY 
 VALVE 
 
 Figure 11-10. Solar-Assisted Heat Pump (Liquid-to-Liquid) Heat Pump in 
 Series with Solar Storage 
 
 evaporator of the machine at a temperature higher than outdoor ambient 
 air. Higher COP and lower collector temperatures (with higher effi- 
 ciency) 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 an 
 individual water- to-air heat pump in each zone is supplied by 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 
 
11-21 
 
 temperature 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 
 specifically for operation at lower temperatures. When solar storage 
 may approach the freezing point in midwinter, as a result of large 
 withdrawals of 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 domestic 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 11-2 to 11-7. 
 Simultaneously, potable water from the solar preheat tank is circulated 
 through the heat exchanger and back to the top of the preheat tank. 
 These pumps operate whenever the temperature in the storage tank is 
 greater than the water temperature in the preheat tank by a preset 
 amount. When useful heat cannot be delivered from storage to the 
 preheat tank or when the preheat tank temperature has reached a limiting 
 high temperature, say 175°F, the pumps do not operate. 
 
11-22 
 
 During the heating season, the temperature of water in the storage 
 tank will frequently be less than 140°F, so dependable delivery of hot 
 service water requires an auxiliary hot water heater. Solar heat is 
 therefore used to preheat cold water from the water main before it 
 enters the hot water heater. During the summer, the water temperature 
 in the storage tank will usually be greater than 180°F, thus the preheat 
 tank can be kept at high temperature with only occasional auxiliary 
 heating. 
 
 Suppose that an average daily 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 tempera- 
 ture 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. Delivery 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 the interim 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 
 
11-23 
 
 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 preheat 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 
 stratification can be maintained. This design accomplishes the same 
 purpose at somewhat lower cost than incurred with a separate electric 
 water heater as auxiliary. 
 
 PUMPS, PIPING AND ACCESSORIES 
 
 Centrifugal pumps are normally used for circulating liquids in the 
 several loops of a solar heating system. With centrifugal pumps, 
 pumping pressure is limited so if valves fail to open or if piping 
 becomes obstructed, excessive pressures and ruptured pipes can be 
 avoided. 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. Impellers of stock item pumps may be trimmed to meet 
 specifications. Centrifugal pumps should be located so that priming is 
 not necessary, which could be a particular problem in a vented system or 
 where a storage tank is located underground. Five feet of head on the 
 suction side is sufficient to keep most pumps primed. 
 
 A check valve, strainer or filter, and an expansion tank are 
 usually installed in the collector loop as shown in Figure 11-11. The 
 check valve prevents thermosiphon flow and heat loss in the collector 
 when the pump is off and the collectors are colder than the storage tank 
 
11-24 
 
 CONNECTIONS TO ALLOW 
 FOR THERMAL 
 EXPANSION AND CONTRACT!' 
 
 UPPER HEADER 
 
 SOLAR 
 COLLECTORS 
 
 SF 
 
 >£ 
 
 \F 
 
 VENT 
 
 EXPANSION 
 TANK 
 
 CONNECTIONS 
 TO ALLOW FOR 
 THERMAL EXPANSION 
 AND CONTRACTION 
 
 SOLAR 
 COLLECTORS 
 
 -fc-^^FOR FILLING 
 
 'TO HEAT EXCHANGER 
 
 * 
 
 LTER 
 
 ^HECK VALVE 
 
 \J 
 
 £- MANUAL VALVES 
 
 (NORMALLY CLOSED)^ 
 
 FROM COLLECTOR 
 PUMP 
 
 Figure 11-11. Collector Loop Fittings and Details 
 
11-25 
 
 and the building interior. A filter or strainer prevents entry into the 
 collector of any particulate matter in the collector fluid. Special 
 attention is required at initial start-up because foreign substances are 
 usually present in the piping during installation. The filter cartridge 
 should be changed immediately after initial operation, and cleaned or 
 replaced as required thereafter. 
 
 An expansion tank must be provided in the collector loop to 
 accommodate the increase in volume of the collector fluid when it is 
 heated. It is also useful for trapping part of the collector fluid and 
 its antifreeze content if and when boiling occurs. The volume of the 
 tank should be at least half the volume of the fluid in the collectors 
 and headers. An open vent or pressure-relief valve at the top of the 
 tank will prevent dangerous pressure increase in the collector loop when 
 boiling occurs. 
 
 Two connections in the collector loop on the suction side of the 
 pump are useful in filling the collector loop with fluid; one is 
 connected to a container from which liquid is being supplied, and the 
 other to the same source to detect when filling is complete. If the 
 filling connection is at least a few feet above the centrifugal pump, 
 the filling operation is facilitated. If readily accessible, the 
 expansion tank can be used in the filling operation simply by pouring 
 liquid into the tank through a top opening permitting displaced air to 
 escape through the vent. Drain and fill points should be suitably 
 labeled. 
 
11-26 
 
 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 
 thickness. 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 11-1, recommended pipe 
 diameters are indicated for various flow rates. 
 
 Table 11-1 
 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 and control of the several solar components into a 
 well-functioning system are requirements of exceptional importance. 
 Collector, storage, heat exchangers, auxiliary heater, pumps and piping, 
 and control system must be mutually compatible in size, function, 
 materials, reliability, and cost. Although a great variety of 
 
11-27 
 
 components may be assembled into functional systems, experience shows 
 that certain equipment combinations and control methods provide superior 
 performance. 
 
 Previous subsections of this chapter 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. Therefore, 1.5 to 2.5 
 
 2 
 gal/ft of collector are usually employed, with 2.0 a practical average. 
 
 Even though the storage tank is usually inside the building, it should 
 
 be well insulated with fiberglass or plastic foam having an insulating 
 
 value of at least R-20. 
 
 The relative merits of drain-down 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. Care should be exercised in 
 
 assembly of pipes, connections and valves, and thorough testing for 
 
 possible leaks should be made before insulation is applied. 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. 
 
11-28 
 
 Pumps, preferably of centrifugal type, should be mounted in 
 accordance with recommended procedures, located so that they are 
 self-primed and provided with sufficient suction head to prevent vapor 
 lock. All pipes should be well insulated, typically with at least 
 1 inch of fiberglass or equivalent. Excessive pipe lengths and 
 unnecessary fittings should be avoided so that pumping power and heat 
 losses can be minimized. If a heat-exchanger is used (dual-liquid type) 
 it should be piped for counterflow of the two liquids, and it should 
 also be insulated. 
 
 Selection of collector size (which also results in storage size 
 determination) is a matter of balancing numerous design factors. 
 Climate (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 
 characteristics, and the control and configuration of the complete solar 
 system, all affect the required collector/storage size. There are 
 several procedures of various complexity and accuracy for collector 
 sizing, one of which is explained in detail in Module 14. 
 
 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 11-12. 
 
 A practical method for controlling the solar collection process 
 involves use of temperature sensors which actuate the collector pump 
 
11-29 
 
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11-30 
 
 (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. A sensor, 
 SI, placed in the flow passage as close as possible to the collector 
 exit, and a sensor, S2, near the bottom of the storage tank where 
 storage water is likely to be coldest, are compared electronically to 
 preset temperatures to start and stop the 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 starts the pumps, and the 
 hysteresis in the temperature difference between on and off set points 
 prevents cycling of the pumps at the beginning of the collection day and 
 also at the end of the day. 
 
 When the liquid first circulates through the collectors at the 
 beginning of the collection day, the temperature rise from inlet to the 
 exit is only a few degrees because of the low solar intensity. 
 Typically the temperature rise is 4°F or 5°F. As the solar intensity 
 increases, the temperature rise in the circulating liquid increases 
 until by mid-day 15°F to 20°F temperature rise occurs. During the 
 circulation period, the storage water temperature increases gradually 
 and by midafternoon when the solar intensity decreases, the collectors 
 can no longer provide useful heat to storage and circulation stops. 
 
 The best control strategy to deliver heat to the building space is 
 to use a room thermostat, S3, with dual set points. Whenever the rooms 
 require heat, the first stage contact of the thermostat is completed and 
 water from the storage tank is circulated to the load heat exchanger. 
 If the storage water is warm enough, the room temperature rises, and the 
 
11-31 
 
 circulation system stops. This contact in the thermostat regulates the 
 circulation pump No. 3 and air blower, if used. 
 
 If the storage water is not warm enough to deliver heat at a rate 
 that is greater than the rate of heat loss from the building, the room 
 temperature continues to fall until the second contact is made in the 
 thermostat. The auxiliary water boiler or the auxiliary warm air 
 furnace is then activated to restore the rooms to the comfort tempera- 
 ture set at the thermostat. If an auxiliary water boiler is used, an 
 automatic 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 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. 
 
 The control of a warm air furnace auxiliary is also by a second 
 (lower temperature) contact in the room thermostat. When it is 
 actuated, energy (fuel or electricity) is simply 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 the 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. 
 
11-32 
 
 Solar preheating of domestic water is best regulated by a 
 temperature 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 preheater loop control, and a 
 typical difference in temperature between the bottom and top of the 
 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 preheater circulation pumps. The difference in 
 temperature between sensors S2 and S4 controls pumps 4 and 5, as shown 
 in Figure 11-12. 
 
 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 circula- 
 ting 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. 
 
 
11-33 
 
 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 
 additives, as needed, can reduce the frequency of solution replacement, 
 but careful monitoring is essential. 
 
 In drain-down 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 also 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 
 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 
 subfreezing temperatures are rarely encountered. Another option in such 
 climates is the use of a low- temperature sensor to open a valve 
 (requiring power to close) that allows 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 systems, boiling can be permitted, 
 the vented steam being made up by automatic or manual addition of 
 
11-34 
 
 water to the storage tank. The collector may, alternatively, 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 
 discharge 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 antifreeze solution 
 must then be promptly added to the collector loop. 
 
 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. 
 
 INSTALLATION GUIDELINES 
 
 In the foregoing sections, system types and characteristics have 
 been described, and operation of the principal subsystems has been 
 
11-35 
 
 explained. But information on the installation and adjustment of 
 components has been included only where essential to the understanding 
 of operation. In this section are presented some additional installa- 
 tion guidelines. Information on similar equipment and integrated 
 systems for solar water heating is in Module 10. 
 
 With the exception of collectors, storage tanks, and controllers, 
 conventional HVAC components are used in most solar heating systems. 
 The installation of pumps, heat exchangers, manual and motorized valves, 
 auxiliary heaters, blowers and piping requires the skills normally used 
 by installers of conventional HVAC equipment. As with conventional 
 heating systems, the installers of these components should closely 
 follow manufacturer's instructions and standard practice. 
 
 The design of a heating system in which a liquid is heated by solar 
 energy is usually provided by a mechanical engineer or HVAC design 
 specialist. The collector manufacturer or supplier does not normally 
 offer complete designs of solar heating systems in which his collector 
 may be used. So the installation and integration of the various solar 
 and conventional components require first a complete system design and 
 secondly a faithful and competent installation of components in 
 conformity with the design. 
 
 Several manufacturers of solar collectors have provided detailed 
 instructions and procedures for installing their own product. Manuals, 
 training programs, and field services are offered. Installers of solar 
 collectors should avail themselves of such information on the particular 
 components being used. Detailed instructions on roof surface prepara- 
 tion, collector assembly and attachment to the roof or other structure, 
 
11-36 
 
 flashing and weatherproof ing methods, control sensor placement, 
 manifolding design and installation, and all other collector installa- 
 tion requirements should be carefully followed. Although there are many 
 similarities among collector designs and installation procedures, 
 differences demand attention to specific recommended procedures. 
 
 Unless a collector manufacturer provides detailed assembly and 
 construction guidelines, the installer must either rely on his own 
 judgement and experience or follow plans and drawings furnished by the 
 system designer - often a mechanical engineer serving as consultant to 
 the architect of the building. Such plans may be lacking in specific 
 detail, so careful planning and attention by the installer are essential 
 to achieving a well -functioning system. Low efficiency, fluid leakage, 
 poor weatherability, damage from corrosion, freezing and boiling, 
 distortion and breakage, and short life may otherwise result. A solar 
 collector and its installation may appear to be extremely simple, but 
 good performance requires exceptional skill and care in installation. 
 
 The effectiveness of a solar heating system can be no better than 
 its control. Several commercial solar heating controllers are 
 available, each with detailed information on installation and 
 adjustment. Provided that the design of the entire heating system, 
 including solar and auxiliary/hot water supply and auxiliary space 
 heater, conforms to a design for which the controller is furnished, the 
 installation instructions supplied by the controller manufacturer should 
 be carefully followed. Location of the several temperature sensors, 
 settings (if not preset) of thermostats, and connections to all elements 
 should meet all specifications. After installation, proper functioning 
 
11-37 
 
 of all valves, dampers, pumps, and blowers, including safety elements 
 preventing freezing and overheating, must be verified by the test 
 procedure provided by the controller supplier. 
 
 If a control assembly is installed in a manner different from one 
 of those specified or in a heating system of special type or design, the 
 installer must set up and follow a test procedure by which efficient 
 collection, storage, and delivery of solar and auxiliary heat is 
 verified. A full range of practical solar and temperature conditions 
 should either be imposed or simulated so that proper thermostat settings 
 can be made and correct operation of motors, valves, and fuel supply can 
 be observed. 
 
 The other special component in a typical liquid solar heating 
 system is the heat storage tank. If in a building under construction, 
 the tank should be installed before walls and floors form an enclosure 
 without an adequate opening. The weight of the full tank, usually 
 several hundred pounds per square foot of bearing surface, usually 
 requires support on ground-level foundations. If the tank is insulated 
 prior to installation, careful handling is required for avoiding 
 insulation damage. Application of insulation after placement requires 
 sufficient clearance for access to all surfaces. If ttie tank is located 
 outdoors or in the ground, exceptional precautions must be taken to 
 avoid penetration of the insulation by moisture. Closed-cell insulating 
 materials must be used, and coatings or wrappings impervious to water 
 and water vapor are required. 
 
 Other precautions in storage tank installation include gravity 
 drainage capability, preferably with nearby floor drain to sewer, 
 adequate venting or pressure relief to the exterior of the building 
 
11-38 
 
 for overheat conditions, manual shut-off valves for piping maintenance 
 without tank drainage, and accessibility to all connecting piping and 
 fittings. 
 
 In addition to the requirements for proper installation of each 
 solar and conventional component, they must be assembled and integrated 
 into a well-functioning system. With few exceptions, solar heating 
 systems are designed by HVAC engineers and by experienced heating 
 contractors rather than by manufacturers or distributors of solar 
 collectors or other components. Installers should carefully follow such 
 plans if provided for a particular system. In situations where system 
 plans and specifications are not available or may require modification, 
 an installer should base the system design on prior experience with a 
 similar system or he should seek guidance and advice from an engineer or 
 other installer with such experience. Their assistance with final 
 testing and adjustment after completion of the installation can add 
 assurance of satisfactory operation and performance. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 12 
 
 INSTALLATION AND OPERATION OF 
 AIR SOLAR HEATING SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 12- i i 
 
 LIST OF TABLES 12- i i 
 
 INTRODUCTION 12-1 
 
 OBJECTIVE 12-2 
 
 SYSTEM ARRANGEMENTS 12-2 
 
 DOUBLE BLOWER DESIGN 12-3 
 
 Storing Solar Heat and Heating Hot Water . . 12-7 
 
 Daytime Space Heating ...... 12-9 
 
 Space Heating from Storage ..... 12-10 
 
 Summer Water Heating ...... 12-11 
 
 SINGLE-BLOWER DESIGN 12-11 
 
 STORAGE SYSTEM ..... 12-11 
 
 AIR FLOW RATES 12-15 
 
 AUXILIARY HEAT 12-16 
 
 COMPONENTS AND INSTALLATION 12-18 
 
 SYSTEM SIZING 12-23 
 
12-ii 
 LIST OF FIGURES 
 
 Figure Page 
 
 12-1 Storing Heat from Collectors ..... 12-4 
 
 12-2 Heating Building from Collectors .... 12-4 
 
 12-3 Heating Building from Storage Unit (Also heating 
 
 from auxiliary) ....... 12-5 
 
 12-4 Service Hot Water Heating (Summer Operation) . . 12-5 
 
 12-5 Single-Blower System 12-12 
 
 12-6 Solar Heating System with Air- to-Air Heat Pump 
 
 Auxiliary 12-17 
 
 12-7 General Layout of Typical Air Solar Heating 
 
 System 12-19 
 
 LIST OF TABLES 
 
 Table Page 
 
 12-1 Control Truth Table for a Two-Blower, Air-Heating 
 
 Solar System Operation ...... 12-6 
 
12-1 
 
 INTRODUCTION 
 
 As outlined in Module 11 on liquid systems for solar space heating, 
 the components of an air system must also be well selected and carefully 
 assembled in order to ensure that the system will function properly. 
 Collectors, pebble bed heat storage units, blowers, controls, heat 
 exchangers and auxiliary heaters must be compatible. Procurement of the 
 maximum practical number of components and materials from a single 
 supplier of well -coordinated equipment is usually advantageous. 
 
 In an air-heating system, heat from the collectors is supplied 
 either to a pebble bed for storage or to the rooms when heat is needed. 
 When the sun is not shining, the building is heated by circulating air 
 through the storage unit. An auxiliary heater provides heat when stored 
 solar energy is insufficient to meet the demand. Such occasions 
 commonly occur at night in mid-winter and after one or two successive 
 cloudy days. A practical solar system must function automatically, 
 provide the desired comfort level in the building at all times, require 
 little maintenance, and operate reliably over a long period of time. 
 
 After selection of system type and specific components, a collector 
 area is determined on which a storage volume is then based. The air 
 flow rate through the collector is established and blower size can then 
 be determined. Warm air delivery rate to the rooms is based on the size 
 of the house, and the auxiliary furnace is sized by conventional methods 
 based on the design heating load of the building. If adequate attention 
 is not given to details of sizing, layout, and assembly, the system may 
 not perform as expected, even if the best available components in the 
 market are selected. 
 
12-2 
 
 OBJECTIVE 
 
 The objective of this module is to describe the installation, 
 operation, and interdependence of the components in an air solar 
 heating system. The trainee should be able to: 
 
 1. Develop schematic and working plans of air solar systems. 
 
 2. Specify compatible system components. 
 
 3. Estimate the proper size of system components. 
 
 4. Identify all the system operating modes. 
 
 5. Install and service air solar heating systems. 
 
 SYSTEM ARRANGEMENTS 
 
 In addition to the obvious differences between heat collection 
 in liquids and in air, the following technical and operational 
 factors may be noted. 
 
 1. Air solar 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 
 
12-3 
 
 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°F to 90°F increase) than 
 in a liquid type. 
 
 DOUBLE-BLOWER DESIGN 
 
 As with liquid solar heating systems, there are numerous options 
 for integrating an air solar collector and a pebble-bed heat storage 
 unit into a complete building heating assembly. One of the most widely 
 used air solar systems involves two blowers for air circulation. A 
 schematic design of a two-blower air-heating solar system for both space 
 and domestic water heating is shown in Figure 12-1. There are six 
 principal components: solar collector, heat storage unit, air handler, 
 auxiliary heater, 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 12-1). The operating modes are shown in Figures 12-1 through 
 12-4. In the table and figures the abbreviation MD denotes a motorized 
 damper and BD a back-draft damper which swings shut except when air is 
 being forced against one of its faces. 
 
12-4 
 
 STORAGE 
 
 (PEBBLE 
 
 BED) 
 
 SUMMER 
 BY- PASS 
 
 BDI 
 
 4 
 
 FILTER 
 
 rr rrf-oMDi 
 
 COLLECTOR BLOWER 
 
 ^ BD2 J [n 
 
 ~~ IT 
 
 DISTRIBUTION- 
 BLOWER 
 
 LTER 
 
 ROOMS 
 
 Figure 12-1. Storing Heat from Collectors 
 
 FILTER 
 
 IMDI 
 
 COLLECTOR BLOWER 
 
 IMD2 
 
 AUXILIARY 
 
 FURNACE 
 
 DISTRIBUTION 
 BLOWER 
 
 ROOMS 
 
 Figure 12-2. Heating Building from Collectors 
 
12-5 
 
 - U 
 
 Figure 12-3. Heating Building from Storage Unit (Also Heating from 
 Auxiliary) 
 
 FILTER 
 
 hOMDI 
 
 COLLECTOR BLOWER 
 
 IMD2 
 
 AUXILIARY 
 
 FURNACE 
 
 DISTRIBUTION 
 BLOWER 
 
 ROOMS 
 
 Figure 12-4. Service Hot Water Heating (Summer Operation) 
 
12-6 
 
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12-7 
 
 Storing Solar Heat and Heating Hot Water 
 
 Solar collection and delivery of heat to storage are achieved by 
 circulation of 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 
 the collector. A temperature difference setting of 10°F to 20°F permits 
 operation whenever the value of collected heat exceeds the cost of 
 blower operation. The signal from the controller that actuates the 
 blower also positions dampers so that collector discharge air passes to 
 the hot end of the storage bed, through the pebbles, and from the cold 
 end back to the collector. Figure 12-1 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 5°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-distance 
 profile through the bed in the direction of air flow. 
 
 In most residential solar air heating systems, solar heated water 
 is also provided. A common finned coil is mounted usually at the 
 
12-8 
 
 air- handler outlet leading to the pebble bed. During typical operation 
 on sunny days, a small pump circulates water from the bottom of an 
 insulated 50 to 100 gallon "preheat" tank, through the coil, and back to 
 the top of the tank. If the air temperature is higher than the tank 
 bottom temperature by a preset amount, the pump is actuated. 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 tempera- 
 ture two or three degrees. The rise in water temperature per pass 
 depends on the temperature in the tank as well as on the air 
 temperature. Normally when heat is being stored in the pebble bed, 
 water is also being heated. 
 
 Experience has shown that the coil location shown in Figures 12-1 
 to 12-4 is more satisfactory than in the duct between the collector and 
 air handler, primarily because the possibility of freezing caused by 
 nighttime leakage of damper MD 1 is eliminated. 
 
 As shown in Figures 11-1 and 11-2 in the previous module, solar 
 heated water for domestic use is usually supplemented with auxiliary 
 heat in a conventional water heater. The same arrangement is used with 
 air type collection systems. The two-tank design is nearly always 
 employed if a fuel auxiliary is involved, but a single tank may be used 
 if electric boosting is provided. In that case, solar heated water from 
 the heat exchanger 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 immediately above that point. Electrically heated water is 
 therefore only in the upper third of the tank, and because of tempera- 
 ture stratification, the auxiliary heat does not adversely affect the 
 solar heat exchange. 
 
12-9 
 
 Daytime Space Heating 
 
 When heat is needed in the building at the same time the collectors 
 are on, a room thermostat signals the control unit to open damper MD 2 
 and direct the flow of heated air from the collector directly to the 
 zones requiring heat, bypassing storage, as shown in Figure 12-2. 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 from the rooms circulates 
 back to the collector through the 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 that increases 
 the temperature of the air in the distribution system. 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 
 the distribution ducts. In a typical all-air solar installation, the 
 furnace 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 to storage 
 or to distribution. 
 
12-10 
 
 Space Heating from Storage 
 
 The third mode of operation, illustrated in Figure 12-3, 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 
 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. Collector damper MD 1 is 
 closed and distribution damper MD 2 is open. Heat is thus supplied to 
 the room air by transfer from the heated pebbles. Air leaving the hot 
 end of the bed is only a few degrees below the rock temperature at that 
 level. 
 
 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 
 actuated by the lower thermostat set point, and auxiliary heat will also 
 be supplied. With most control systems, auxiliary operation continues 
 until the upper set point is regained and shut-off occurs. 
 
 It can be seen from the above description that the use of solar 
 heat is maximized by (1) collecting solar heat whenever moderate 
 temperature delivery of 80°F to 90°F is possible; (2) utilizing even 
 such low temperature heat, supplemented if necessary with auxiliary; 
 (3) providing, 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. 
 
12-11 
 
 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 12-4. When warm weather 
 commences, manual damper is opened in a by-pass duct so that air is 
 circulated in a closed 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 collector 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 needed. This 
 system type is shown in Figure 12-5, 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. 
 
 STORAGE SYSTEM 
 
 A pebble bed as a heat storage component has been discussed in 
 Module 9. There are, however, some additional features that affect the 
 use of a pebble bed in a complete solar heating system. 
 
12-12 
 
 AUXILIARY HEATER 
 
 ROOMS 
 
 AIR 
 
 HANDLING 
 
 UNIT 
 
 BACK- 
 DRAFT 
 DAMPERS 
 
 FROM 
 ROOMS 
 
 LTER 
 
 Figure 12-5. Single-Blower System 
 
 Heat flow in a pebble bed is almost negligible when there is no air 
 circulation, even in designs where the hot end is at the bottom and the 
 cold end is at the top. Convective heat transfer is minimized by the 
 limited space between pebbles for air movement, 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. 
 
 For similar reasons, heat loss from the pebble bed through the 
 container walls can be easily controlled. Thick insulation is not 
 
12-13 
 
 required, both because of low conduction between the pebbles and the 
 wall and also because the bed is usually in the building so that heat 
 transferred 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 are suitable wall materials. A typical design comprises top and 
 side panels of 2 by 4 studs and fiberglass insulation between plywood or 
 gypsum board facings. In all of these arrangements, an overnight heat 
 loss from a completely filled storage unit through the walls should not 
 exceed 1 percent of the thermal content. 
 
 The direction of air flow in the pebble bed is usually limited by 
 heating system design requirements rather than by thermal performance 
 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 with 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 otherwise, heated 
 air should be supplied to the top of the bed so that there is an 
 absolute minimum loss of temperature stratification. 
 
 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 upper part of the bed 
 and of cool air through the lower part may occur. If a horizontal 
 position cannot be avoided, vertical baffles may be provided to direct 
 the air in an up-and-down, zig-zag flow pattern. Another arrangement 
 
12-14 
 
 involves use of horizontal plastic sheets spaced 6 to 12 inches apart to 
 form several thin layers of rock through which air flows at more uniform 
 velocity. 
 
 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 
 storage, maximum mid-winter collection of about 800 Btu per square foot 
 of collector would result in heating the pebbles from a starting 
 temperature 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 
 
12-15 
 
 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 of water gauge. 
 
 AIR FLOW RATES 
 
 The designer of a solar air system has the decision as to air flow 
 rate through the collector. Delivery temperature, hence absorber plate 
 temperature, is strongly dependent on air circulation rate; in a 
 specific design, the rate of heat transfer between plate and fluid 
 depends on air velocity. But fan power requirement is also a function 
 of air flow, and there are practical limits to air circulation rates in 
 the occupied space of a building. The efficiency of a solar air heater 
 is dependent not only on volumetric air rate, but also on air velocity. 
 Velocity, in turn, is affected by manifolding and length of travel of 
 air in the collector, as well as on the width of the air passages. 
 
 At a practical level of 2 cfm/ft 2 of collector and a velocity of 
 about 10 ft/s, efficiency and pressure drop are at satisfactory levels. 
 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. 
 
12-16 
 
 AUXILIARY HEAT 
 
 Auxiliary heat is usually supplied in air solar systems by use of a 
 warm air furnace in series with the collector and storage units 
 (Figures 12-2 and 12-3). This design permits maximum use of solar 
 energy by utilizing the solar system as a preheater of the air when heat 
 requirements 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 
 electricity is usually provided through a dual-stage house thermostat, 
 the lower temperature contact actuating the fuel valve or electric 
 switch. 
 
 The motor and blower in commercial warm air furnaces are usually 
 sized for air flow rates commensurate with the heat supply rating of the 
 furnace and the duct resistances in typical installations. When used as 
 solar auxiliaries, the pressure requirements may be higher, so the 
 furnace fan speed may have to be increased by changing the pulleys on 
 the motor and fan. The standard motor may also have to be replaced with 
 one of moderately higher output, such as one horsepower instead of 
 3/4 horsepower. If the motor is in the circulating air stream, it is 
 advisable to substitute a type B motor, suitable for higher temperature 
 operation than the standard type A usually supplied. 
 
 An air-to-air heat pump may also be used for supplying auxiliary 
 heat, as shown in Figure 12-6. The condenser coil of the heat pump 
 provides heat to the house air as the outdoor evaporator coil utilizes 
 
12-17 
 
 TO AND FROM 
 STORAGE 
 
 COLD AIR RETURN 
 
 TO COLLECTOR 
 
 AND STORAGE 
 
 AIR HANDLER 
 
 FROM 
 COLLECTOR 
 
 HEAT PUMP 
 
 OUTDOOR UNIT 
 
 OUTDOOR 
 AIR 
 
 COLLECTOR 
 BLOWER 
 
 COMPRESSOR^ 
 
 ELECTRIC 
 
 RESISTANCE 
 
 COIL 
 
 CPI 
 
 INDOOR UNIT 
 
 ROOMS 
 
 — FROM 
 
 — ROOMS 
 
 Figure 12-6. Solar Heating System with Air-to-Air Heat Pump Auxiliary 
 
 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 
 conventional manner. 
 
 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 12-6 rather than from the solar system. 
 
12-18 
 
 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 
 thermostat, which simultaneously closes the damper at the air handler 
 outlet. The electric resistance back-up coil is usually controlled by a 
 temperature sensor in the heat pump system. 
 
 COMPONENTS AND INSTALLATION 
 
 An illustrative layout of a commercial solar air-heating system 
 (auxiliary heater and hot water tanks not shown) is presented in Figure 
 12-7. 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. 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 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 usually about one-half to three-fourths 
 horsepower. In a one-blower system, a one-horsepower motor will 
 
 
12-19 
 
 COLLECTOR 
 ARRAY 
 
 HOT AIR FROM 
 COLLECTORS — 
 
 BACK- DRAFT 
 DAMPERS 
 
 HOT WATER COIL 
 MOTORIZED DAMPER -I 
 
 AIR HANDLER 
 MOTORIZED DAMPER -2 
 
 COLD AIR TO 
 COLLECTORS 
 
 HEAT 
 
 STORAGE 
 
 UNIT 
 
 TOP PLENUM 
 
 -ROCK 
 
 %" TO 
 l'/ 2 " SIZE 
 
 BOTTOM PLENUM 
 
 SUPPLY AIR TO THE BLDG. a TO THE 
 AUXILIARY HEATING UNIT 
 
 Figure 12-7. General Layout of Typical Air Solar Heating System 
 
 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 in residential systems from the 
 standpoint of blower power cost, although the electricity requirement is 
 usually less than 10 percent of the solar heat supply. 
 
12-20 
 
 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 the 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. 
 Insulation may be either inside or outside sheet metal ducts. 
 
 It is especially important with an air solar 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. 
 Solar duct-work and component assembly can be done at the same time that 
 the distribution ducts and furnace are installed in a typical 
 construction schedule. 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 well 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. 
 
12-21 
 
 Blowers, dampers, and auxiliary heaters may be provided by a single 
 solar system supplier or they may be purchased separately. Factory 
 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 
 installation. Blowers should be forward-curved squirrel cage type and 
 preferably 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 
 recommended. 
 
 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 on opening and closing. 
 
 Back draft dampers, used in ducts to prevent reverse airflow, 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 
 
12-22 
 
 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. 
 
 Provision for supply of domestic hot water can be made in the air 
 system by use of an air-to-water heat exchanger in the hot air duct 
 between the blower and storage unit. The particular location is chosen 
 to prevent freezing during winter operation. The heat exchanger coil is 
 a finned type, with one or two rows of tubes. A small pump circulates 
 water from the bottom of an insulated tank (usually about 80-gallon 
 capacity), through the coil, and back to the top of the tank. Cold 
 water enters the solar-heated tank and warm water flows to a conven- 
 tional automatic water heater whenever a hot water faucet is opened in 
 the building. In summer, a duct by-pass, as shown in Figure 12-4, 
 permits operation of the service hot water coil without heating the 
 pebble bed. A thermostatic mixing valve can be installed in the line 
 connected to the service hot water tank from the cold water main to 
 prevent delivery of scalding hot water. 
 
 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 the 
 conventional system, 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 important requirement for obtaining good performance 
 of an air-heating solar system. 
 
12-23 
 
 SYSTEM SIZING 
 
 Solar heating systems are sized to provide the desired fraction of 
 the total annual heating load of the building. The desired fraction of 
 heating load can be chosen arbitrarily, or determined from economic 
 analysis, so that the annual heating cost of the solar-auxiliary system 
 is minimized. The collector area is the main component to be 
 determined, and from the collector area the storage size is selected. 
 The size of the auxiliary furnace is based upon the design heating load 
 and the desired heat delivery rate. The blowers and duct sizes depend 
 primarily upon collector area and heat delivery rate. Methods for 
 sizing the collector and storage are presented in Module 14. 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 13 
 
 HEATING LOAD CALCULATIONS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
13-i 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 GLOSSARY . 
 
 Page 
 13- ii 
 
 13- ii 
 13-i ii 
 
 INTRODUCTION 13-1 
 
 OBJECTIVES 13-1 
 
 HEAT LOSS MECHANISMS 13-2 
 
 CONDUCTION 13-2 
 
 CONVECTION 13-2 
 
 RADIATION 13-3 
 
 HEAT LOSS CALCULATIONS . 13-3 
 
 CONDUCTION HEAT LOSS 13-3 
 
 INFILTRATION HEAT LOSS 13-5 
 
 FLOOR HEAT LOSS 13-6 
 
 Floors Over Unheated Basements or Crawl Spaces . 13-6 
 
 Concrete Slabs on Grade ...... 13-7 
 
 Heated Basements ....... 13-7 
 
 DESIGN HEAT LOSS RATE AND ANNUAL HEAT LOSS CALCULATIONS. 13-7 
 
 SAMPLE HEAT LOSS CALCULATIONS 13-9 
 
 Heat Transmission Coefficients .... 13-9 
 
 Insulated Frame Wall (2x6 studs) .... 13-9 
 
 Insulated Ceiling, 12 inches ..... 13-10 
 
 Insulated Floor (Over Unheated Basement) . . 13-10 
 
 Domestic Hot Water Load ...... 13-11 
 
 WORKSHEET HL-1 13-13 
 
 REFERENCES 13-12 
 
13-ii 
 
 LIST OF FIGURES 
 
 Fi gure Page 
 
 13-1 Sample Building 13-12 
 
 13-2 Degree Day Maps 13-31 
 
 to thru 
 
 13-13 13-42 
 
 LIST OF TABLES 
 
 Table Page 
 
 13-1 Values of R and U for Some Structural and 
 
 Finish Materials, Glass, Doors, Insulation, 
 Air Spaces and Surface Air Films . . . 13-15 
 
 13-2 Heating Load Data 13-17 
 
13-iii 
 
 GLOSSARY 
 
 Average Heating Average heat loss rate from a building based upon 
 
 long-term average outdoor air temperature. 
 
 Btu British Thermal Unit. It is the amount of heat 
 
 required to raise the temperature of one pound of 
 water one degree Fahrenheit. 
 
 Degree Days (DD) The temperature difference between a reference 
 
 temperature, 65°F, and the average of the high and 
 low temperatures during a day (°F-days). 
 
 Example: 
 
 high temperature = 30°F 
 
 low temperature = -10°F 
 
 average temperature = [30 + (-10)]/2 = 10°F 
 
 Degree Days = 65 - 10 = 55°F-days . 
 
 Design Temperature The difference between the indoor design temperature 
 Difference and the outdoor design temperature used to calculate 
 
 heat losses from buildings. 
 
 Design Heat Loss The heat loss rate (Btu/hr) from a building based 
 Rate upon the Design Temperature Difference. 
 
 UA bldg Thermal property of a building which characterizes 
 
 (or building UA) the rate of heat loss from the building. 
 
 Outdoor Design A statistically determined low temperature in a 
 Temperature locality from weather records. 
 

13-1 
 
 INTRODUCTION 
 
 Heating loads, or heat losses from residential buildings, are 
 
 rarely calculated by HVAC contractors although procedures have been 
 
 * 
 prescribed by ASHRAE, SMACNA, NAHB and other organizations. The 
 
 ** 
 reasons are that sizes of furnaces (Btuh output ratings) available for 
 
 residential building use are limited in number, and rules of thumb based 
 on experience are adequate to select furnaces that will give satisfac- 
 tory service. Satisfactory service in many instances is judged to be 
 the capability of a furnace to maintain preset temperatures in the 
 building on the coldest winter nights. 
 
 It is important to determine the expected heat loss rates and 
 heating loads of solar buildings because technical procedures for sizing 
 solar systems require reasonable estimates of loads, and it is not 
 economical to choose undersized or oversized solar systems. Also, heat 
 loss calculations will help in the selection of an adequately sized 
 auxiliary heating unit for the building. 
 
 OBJECTIVES 
 
 The objective in this module is to explain the principles and 
 methods by which trainees should be able to: 
 
 1. Calculate a design heat loss rate for a selected building. 
 
 2. Calculate the average monthly and annual heating loads. 
 
 -* 
 
 ASHRAE - American Society of Heating, Refrigeration, and Air 
 
 Conditioning Engineers 
 
 SMACNA - Sheet Metal and Air Conditioning Contractors National 
 
 Association 
 
 NAHB - National Association of Home Builders 
 ** 
 
 Btuh - Btu per hour 
 
13-2 
 
 HEAT LOSS MECHANISMS 
 
 Heat that is transmitted out of a building is called "heat loss". 
 Heat is lost by conduction, convection, and radiation. The first two 
 are the most important for buildings, although radiation losses also 
 occur from the outside surface of a building to the surroundings. 
 
 CONDUCTION 
 
 Conduction is the process whereby heat is transferred through solid 
 materials from a region of high temperature to a region of low 
 temperature. Building materials are rated for their resistance to this 
 type of heat transfer by an "R-value". The best resistance to this type 
 of heat transfer is offered by a vacuum as utilized in the common 
 "Thermos" or vacuum bottle. Spaces containing stagnant air also have 
 high R values, and good insulating materials offer resistance to heat 
 loss by confining air in small pockets or bubbles. 
 
 CONVECTION 
 
 Convection is the process of heat transfer by movement of fluids 
 from areas of high temperature to areas of low temperature. Convection 
 is called "free" or "natural" when it occurs without the aid of fans or 
 pumps (as in baseboard convectors used in some home heating systems), or 
 "forced" when fans or pumps are used to move the fluid (as in hot air 
 heating systems). Convective heat transfer occurs at both inside and 
 outside surfaces of the building enclosure and also by a process called 
 infiltration, when cold outside air leaks into a house forcing warm air 
 
13-3 
 
 out of the house. These air leaks are due to poor construction, 
 inadequate weather stripping and caulking, non-sealing appliance vents, 
 and opening of doors and windows. Wind is the major driving force for 
 infiltration as cold air enters on the windward side of a house and warm 
 air is forced out on the leeward side. Infiltration is also caused by 
 natural convection, or the so-called chimney effect, due to a tempera- 
 ture difference between the inside and outside of a building which 
 produces a flow of cold air into the lower parts of a house and a 
 corresponding loss of warm air from the upper parts of a house. 
 
 RADIATION 
 
 Radiation is the heat transfer process which occurs when a high 
 temperature body radiates electromagnetic waves (infra-red or light). 
 It is the mechanism by which solar energy is transmitted through space 
 and is the only type of heat transfer which can occur through a vacuum. 
 Heat loss by radiation can be minimized through the use of reflective 
 surfaces. In a well-insulated house, radiation is not a major cause for 
 heat loss and the effect is usually included in the "R-values" for air 
 spaces and surface air films. 
 
 HEAT LOSS CALCULATIONS 
 
 CONDUCTION HEAT LOSS 
 
 Conduction heat loss occurs through all of the components of the 
 building envelope, i.e., walls, ceilings, floors, windows and doors. 
 The rate of heat loss (in Btu/hr) depends upon the area of a given 
 building component, the materials of which it is constructed (and their 
 
13-4 
 
 thickness), and the temperature differences between the inside and 
 outside air. The heat transfer rate for a given building component (for 
 instance, a wall) is given by: 
 
 h = UA (T R -T a ), (Btu/hr) (13-1) 
 
 where 
 
 h is the rate of heat loss, Btu/hr 
 
 U is the heat transfer coefficient of the wall, Btu/(hr«ft 2 *°F) 
 
 A is the area of the wall, ft 2 
 
 T R is the room temperature, °F 
 
 T is the outside air temperature, °F. 
 a 
 
 The heat transfer coefficient U depends upon the materials in the 
 building component and upon their thicknesses. It can be calculated 
 from the sum of thermal resistances or R-values of the elements in the 
 wall by: 
 
 U = 1/R T [Btu/(hr-ft 2 -°F)] (13-2) 
 
 where R-j- is the total thermal resistance in (hr«ft 2 '°F)/Btu and is the 
 sum of the thermal resistances of the wall elements (sheathing, 
 insulation, siding, etc.): 
 
 R T = R 1 + R 2 + R 3 + etc. [Btu/(hr-ft 2 -°F)] (13-3) 
 
 Thermal resistances (R-values) of common building materials and 
 heat transfer coefficients (U-values) of common building elements are 
 
13-5 
 
 given in Table 13-1 (located at the end of this module). Several 
 features of this table are worth noting. The thermal resistances of 
 common insulating materials are much larger than other building 
 materials and the thermal resistances of well-insulated walls and 
 ceilings are therefore primarily due to the insulation. Air layers and 
 surface air films have thermal resistances and R-values that depend upon 
 the direction of heat flow and whether or not adjoining surfaces are 
 reflective. Surface air films are thin layers of air which are made 
 immobile by the adjoining solid surface. These surface films exist on 
 the inside and outside of all surfaces exposed to air. Because their 
 thickness depends upon the speed of air movement, film resistances are 
 different for inside and outside surfaces. It should also be noted that 
 from Table 13-1, building materials which are available in various 
 thicknesses are specified by an R-value per inch of thickness. 
 
 INFILTRATION HEAT LOSS 
 
 Infiltration heat loss occurs when cold outside air leaks into a 
 building displacing warm, heated air. It can be minimized (often 
 inexpensively) by the use of caulking and weather-stripping, sealing of 
 appliance vents, and use of air locks (vestibules) on outside doors. It 
 is the most difficult heat loss to account for accurately. A simplified 
 technique involves an estimate of the number of times each hour that an 
 equivalent to the total volume of inside air is exchanged with outside 
 air. The rate of heat loss by infiltration is estimated by: 
 
 h = 0.018 NV (T D -T ), (Btu/hr) (13-4) 
 
 k a 
 
13-6 
 
 where 
 
 0.018 is the volumetric heat capacity of air, Btu/(ft 3 «°F) 
 
 N is the number of air changes per hour, hr 
 
 V is the volume of the heated space, ft 3 . 
 
 In an older poorly sealed house without storm windows or doors, N 
 may be as high as three air changes per hour. For a modern, well- 
 constructed house, N should be about one air change per hour and with 
 extra careful construction and the use of air locks (vestibules) N may 
 be as low as one-half air change per hour. Life-style of building 
 occupants has a large influence on N due to opening of doors and 
 windows. 
 
 FLOOR HEAT LOSS 
 
 Building floors are often exposed to ground temperature rather than 
 ambient air temperature and therefore require different calculation 
 techniques depending upon type of building foundation. 
 
 Floors Over Unheated Basements or Crawl Spaces 
 
 The U- value of the floor is calculated by summing the R- values of 
 the floor materials and using Equation (13-1). The design temperature 
 difference to be used in the equation is the inside temperature minus 
 the design ambient air temperature. If the floor is over an unheated 
 basement use one-third of design temperature difference in the heat loss 
 calculations. If the floor is over an unvented crawlspace with 
 insulated walls use one-half of the design temperature difference. If 
 the crawlspace is vented or otherwise open to the outside use the design 
 temperature difference. 
 
13-7 
 
 Concrete Slabs on Grade 
 
 The heat loss rate from a concrete slab on grade is calculated on 
 the basis of exposed edge length rather than on floor area. The heat 
 loss rate is: 
 
 h = U'L(T D -T ) — (Btu/hr) (13-5) 
 
 k a 
 
 where 
 
 u" is the heat transfer coefficient per lineal foot; Btu/(ft-hr-°F), 
 
 L is the perimeter length of the slab, (ft). 
 
 The U 1 -values for use in Equation (13-5) are listed in Table 13-1 in the 
 U column. 
 
 Heated Basements 
 
 To estimate heat loss rate from basement floors the ground 
 temperature for most areas may be assumed to be about 50°F in winter. 
 For heated basement walls extending above grade the heat loss is 
 calculated using the same procedure as an exposed wall. 
 
 DESIGN HEAT LOSS RATE AND ANNUAL HEAT LOSS CALCULATIONS 
 
 To calculate the design heat loss rate for a building it is 
 necessary to determine the heat transmission rate through all parts of 
 the building envelope and add the infiltration heat loss rate. 
 
 The design heat loss rate, h D , is the total building heat loss when 
 the inside temperature, T R , is at 70°F and the outside temperature is at 
 the design temperature, T . These design temperatures have been 
 calculated for many locations by the American Society of Heating, 
 Refrigeration and Air Conditioning Engineers (ASHRAE) and are given 
 
13-8 
 
 in the two columns on the right of Table 13-2. One column lists winter 
 
 design temperatures and the other lists summer design temperatures. 
 
 Also of interest is the heating load per degree day, h^. This can 
 
 be calculated from: 
 
 . _ Design heat los s rate x 2 4 , D , i/nn , , 10 c . 
 
 h DD a / 7Q _ T % (Btu/DD) (13-6) 
 
 o 
 
 If the heating load per degree day is divided by the heated floor area 
 of the house, a useful measure of the thermal effectiveness of the 
 building envelope is obtained: 
 
 Envelope Thermal Effectiveness = Seated Moo/area* [Btu/(ft 2 -DD)] 
 
 (13-7) 
 
 A low value indicates an effective thermal envelope. 
 
 The monthly heating load is calculated by multiplying the heat loss 
 rate per degree day by the number of degree days, DD, for the month. It 
 is usually expressed in millions of Btu (MMBtu): 
 
 Monthly Heating Load = Heating load per^DD^Monthly DD (MMBtu) (13 . 8) 
 The average monthly degree days are listed for various cities in 
 Table 13-2, and are shown in degree-day maps in Figure 13-2 through 
 Figure 13-13 (at the end of this module). 
 
 The annual heating load is calculated in similar manner to the 
 monthly heating load except that the annual average degree days is used 
 instead of the monthly degree days. 
 Annual Heating Load = Heating load per DD^x Annual DD (mUu) (13 _ g) 
 
 Average annual degree days for various cities in the United States are 
 also listed in Table 13-2. 
 
13-9 
 
 SAMPLE HEAT LOSS CALCULATIONS 
 
 Heat loss calculations for a sample house are illustrated in this 
 section. A simple floor plan of a one-story house with an unheated full 
 basement located in Denver is shown in Figure 13-1. Energy 
 conservation measures in the building are: 
 
 (a) Insulation - 6 inches in walls, 12 inches above ceiling, 
 
 9 inches under a wooden floor. 
 
 (b) Windows - Triple glazed, 1/2 inch air space, weatherstripped. 
 
 (c) Doors - Storm doors, weatherstripped, and vestibule. 
 
 (d) Infiltration - One-half air change per hour. 
 
 (e) Floors - carpeted. 
 
 The heat loss calculations are on worksheets (HL-1). (Extra 
 worksheets are provided at the end of this module.) The calculations of 
 heat transmission coefficients (U- factors) are given below. 
 
 Heat Transmission Coefficients 
 
 Calculations of U-factors for walls, ceiling, and floor are shown 
 below. U-factors for windows and doors can be found directly from Table 
 13-1. 
 
 Insulated Frame Wall (2x6 studs) 
 
 ITEM R 
 
 1. Outside film (15 mph wind, winter) 0.17 
 
 2. Siding, wood (1/2 x 8 lapped) 0.81 
 
 3. Sheathing (1/2 inch regular) 1.32 
 
 4. Insulation batt (6-inch) 19.00 
 
 5. Gypsum wall board (1/2 inch) 0.45 
 
 6. Inside surface (winter) 0.68 
 
 Total Resistance, R-j- 22.43 
 
 U = 1/R T 0.045 
 
13-10 
 
 The calculated U-f actor for the wall applies to the area between 
 studs. Although the resistance to heat flow through the 2x6 studs 
 is different from the insulated section, the effective correction to R T 
 is small and considered unnecessary. 
 
 Insulated Ceiling, 12 inches 
 
 ITEM 
 1. 
 2. 
 3. 
 4. 
 
 Total Resistance, Rj 
 
 U = 1/R, 
 
 Inside surface 
 
 0.68 
 
 Insulation batts (2, 6-inch) 
 
 38.00 
 
 Gypsum board (1/2 inch) 
 
 0.45 
 
 Inside surface 
 
 0.68 
 
 39.81 
 0.025 
 
 Insulated Floor (Over Unheated Basement) 
 
 
 ITEM 
 Surface (heat flow down) 
 
 R 
 
 1. 
 
 0.92 
 
 2. 
 
 Carpet and fibrous pad 
 
 2.08 
 
 3. 
 
 Plywood (3/4 inch) 
 
 0.93 
 
 4. 
 
 Insulation (9 inch) 
 
 28.00 
 
 5. 
 
 Surface (still air) 
 
 0.61 
 
 
 Total Resistance, R T 
 
 32.54 
 
 
 U = 1/R T 
 
 0.031 
 
13-11 
 
 Domestic Hot Water Load 
 
 Domestic hot water load is based on household use of hot water 
 which may vary from 40 to 120 gallons per day depending upon the family. 
 Assuming an annual average residential use of 70 gallons per day, with a 
 set delivery temperature of 140° F and cold water main temperature of 
 50 degrees, the annual heating load for domestic hot water is: 
 
 70 gal x 8.3 ~y x 1 yjjjSp x (140-50)°F = 52,290 Btu/day 
 
 Since 70 gallons per day and temperature difference of 90 degrees 
 
 (140-50) are averages, the annual domestic hot water load can be 
 
 determined by multiplying the average daily load by the number of days 
 in a year. In this case, the annual load is 19.09 MMBtu. 
 
13-12 
 
 (2) 4'x5'„ 
 Windows 
 
 (2) 3'x7' 
 
 Doors 
 
 S 
 
 28' 
 
 One Floor 
 
 Over Unheated 
 Basement 
 
 (2) 2'x3' 
 Windows 
 
 \. 
 
 [] 50' 
 
 Living Space 
 Windows 
 
 Doors 
 
 o 
 
 i 
 
 Scale 
 
 1400 ft 
 160 ft' 
 
 42 ft 
 
 10 ft 
 
 — f 3 — 
 
 (9) 3' x 4' Windows 
 
 Figure 13-1. Sample Building 
 
 REFERENCES 
 
 1. Load Calculation Guide (1 and 2 Family Dwellings) for Heating and 
 Air Conditioning , Better Heating and Cooling Bureau, Sheet Metal 
 and Air Conditioning Contractor's National Association, Inc. 
 
 (SMACNA), 8224 
 Virginia, 1975. 
 
 Old Courthouse Road, Tyson's Corner, Vienna, 
 
 Load Calculation for Residential Winter and Summer Air Conditioning 
 Manual J, National Environmental Systems Contractors Association 
 (NESCA), 1501 Wilson Boulevard, Arlington, Virginia, Fourth 
 Edition, Second Printing, 1975. 
 
 Insulation Manual , NAHB (National Association of Home Builders) 
 Research Foundation, Inc., P.O. Box 1627, Rockville, Maryland, 
 September 1971. 
 
 Handbook of Fundamentals , ASHRAE (American Society of Heating, 
 Refrigeration, and Air Conditioning Engineers) New York, 1974. 
 
13-13 
 
 Worksheet HL-1 
 Sheet 1 of 2 
 
 Building Heat Load Calculations 
 
 Job (Sample. clQjASjL, Number of Occupants jj 
 
 Computed by Date Ai/a(7^ ; Ml 6 ! 
 
 Location D(?At)^r f Cq1i1D3ucL Latitude ^.^ 
 
 Indoor temperature, T R 70 ° F 
 
 Design winter outdoor temperature, T ~2 ° F 
 
 Design temperature difference 1£ ° F 
 
 Building Dimensions: 
 Above Grade: Length 50 f t Width J% f t Ceiling Ht. % f t 
 
 Below Grade: Length 5q ft Width ^g ft Depth 2Jl f t 
 
 Concrete Floor Slab: Exposed perimeter ft 
 
 Exterior Wall Area: % X CSo+JLK^ X P - /3Mft -Pf J 
 
 Wi ndow Area : 3 XM Y3 + LlXSX.3 ± ^X^Xa - /£,n£ + a 
 
 Door Area : 2 X 3 X 7 ~ M3^4 - * 
 
 Net Exterior Wall UMS - ICoO ~t/3l - fOM^ -Pf- 
 
 Area: 
 
 Ceiling Area: 5o X 2% = IHPO f f 
 
 Floor Area: ^£) X P% I MOO ti- 
 
 Basement Wall Area: f\|,s+ fWfllfcf f.Uhlwrt-M) 
 
 Heating Degree-Days*: Annual 6>^ % 3 °F-days 
 *From Table 13-2 
 
13-14 
 
 Worksheet HL-1 
 Sheet 2 of 2 
 
 
 U 
 Btu 
 
 A 
 
 AT °F 
 
 h = UAAT 
 Btu/hr 
 
 
 (hr)(ft')( 6 F) 
 
 Exterior Walls (net) 
 
 0-0^5 
 
 /cW6 
 
 7,2 
 
 33*** 
 
 Basement 
 Walls 
 
 Above grade 
 
 
 
 
 
 Below grade 
 
 Unh^-htc/ 
 
 
 * 
 
 
 Windows 
 
 and 
 
 Sliding 
 
 Patio 
 
 Doors 
 
 Single 
 
 
 
 
 
 Double 
 
 
 
 
 
 Triple (1/4" air spaces) 
 
 0. 41 
 
 /60 
 
 11 
 
 5^/4 
 
 Storm 
 
 
 
 
 
 Exterior Slab Doors (1.5 in thick) 
 
 o.aT 
 
 « 
 
 12 
 
 8/6 
 
 Floors 
 
 Over Crawl space 
 
 
 
 
 
 Concrete Slab on Grade 
 
 
 
 
 
 Basement (Heat loss to 
 basement) 
 
 0-03/ 
 
 MOO 
 
 ^ 
 
 io<ja 
 
 Ceiling 
 
 o oas 
 
 Moo 
 
 1* 
 
 *?sao 
 
 Infiltration: (0.018) x/tj ojr£ft 3 x 
 
 #j* o F n ,- Air changes 
 — £2- r i^>_ hour 
 
 7^5 g 
 
 Design Heating Load: Btu/hr 
 
 «?OW39 
 
 Design Heating Load: Btu/DD 
 Design Heating Load (Btu/hr) x (24 hr/Design TD) 
 
 6*73 
 
 Annual Heating Load: MMBtu 
 (Btu/DD) x (Annual DD) 
 
 Va.g/ 
 
 *AT = T R - 45° 
 
 DOMESTIC HOT WATER LOAD 
 
 Average Use of 70 gal /day 
 
 52,210 
 
 Sfci/a&i 
 
 Annual Load (MMBtu) ( 
 
 iifll 
 
 TOTAL ANNUAL SPACE AND WATER HEATING LOAD 
 
 6/.* 
 
13-15 
 
 Table 13-1 
 
 Values of R and U for Some Structural and Finish Materials, 
 Glass, Doors, Insulation, Air Spaces and Surface Air Films* 
 
 Materials 
 
 R/in 
 
 R 
 
 U 
 
 Wood bevel siding, .5 x 8, lapped 
 
 
 
 0.81 
 
 
 Wood siding shingles, 16" x 7.5" exposure 
 
 
 
 0.87 
 
 
 Asbestos-cement shingles 
 
 
 
 0.21 
 
 
 Stucco 
 
 
 0.20 
 
 
 
 Building paper 
 
 
 
 0.06 
 
 
 Nail -base insulation board sheathing 
 
 1/2 in. 
 
 
 1.14 
 
 
 Insulation board sheathing, regular 
 
 
 
 
 
 density 
 
 1/2 in. 
 
 
 1.32 
 
 i 
 
 Plywood 
 
 1/2 in. 
 
 
 0.62 
 
 
 Hardboard (medium density) 
 
 7/16 in. 
 
 
 0.67 
 
 
 Softwood board 
 
 
 1.25 
 
 
 
 Concrete blocks, 3 oval cores 
 
 
 
 
 1 
 
 Cinder, 4" thick 
 
 
 
 1.11 
 
 
 Aggregate, 12" thick 
 
 
 
 1.89 
 
 
 8" thick 
 
 
 
 1.72 
 
 
 Sand and gravel aggregate, 8" thick 
 
 
 
 1.11 
 
 
 Lightweight aggregate, 8" thick 
 
 
 
 2.00 
 
 
 Concrete blocks, 2 rectangular cores 
 
 
 
 
 
 Sand and gravel aggregate, 8" thick 
 
 
 
 1.04 
 
 
 Lightweight aggregate, 8" thick 
 
 
 
 2.18 
 
 
 Common brick 
 
 
 0.20 
 
 
 
 Face brick 
 
 
 0.11 
 
 
 
 Sand-and-gravel concrete 
 
 
 0.08 
 
 
 
 Gypsumboard (plasterboard) 
 
 
 0.90 
 
 
 
 Lightweight-aggregate gypsum plaster 
 
 1/2 in. 
 
 
 0.32 
 
 
 Hardwood finish flooring 
 
 3/4 in. 
 
 
 0.68 
 
 
 Asphalt, linoleum, vinyl, or rubber 
 
 
 
 
 
 floor tile 
 
 
 
 0.05 
 
 
 Carpet and fibrous pad 
 
 
 
 2.08 
 
 
 Carpet and foam rubber pad 
 
 
 
 1.23 
 
 
 Asphalt roof shingles 
 
 
 
 0.44 
 
 
 Wood roof shingles 
 
 
 
 0.94 
 
 
 Built-up roof 
 
 3/8 in. 
 
 
 0.33 
 
 
 Glass 
 
 
 
 
 
 Single, winter 
 
 
 
 
 1.13 
 
 Double, 1/4" air space 
 
 
 
 
 0.65 
 
 1/2" air space 
 
 
 
 
 0.58 
 
 Triple, 1/4" air spaces 
 
 
 
 
 0.47 
 
 1/2" air spaces 
 
 
 
 
 0.36 
 
 Storm Windows, l"-4" air space 
 
 
 
 
 0.56 
 
 * From ASHRAE Handbook of Fundamentals 
 
13-16 
 
 Table 13-1 (continued) 
 
 Solid Wood Slab Door U-Values: 
 
 1.00" thick 
 1.25" thick 
 1.50" thick 
 2.20" thick 
 
 No 
 
 Storm 
 
 Storm Door 
 
 Door 
 
 Wood Metal 
 
 0.64 
 0.55 
 0.49 
 0.43 
 
 0.30 
 0.28 
 0.27 
 0.24 
 
 0.39 
 0.34 
 0.33 
 0.29 
 
 
 Materials 
 
 R/in 
 
 R 
 
 U 
 
 Insulation 
 
 Fiberglass (approximately) 
 Styrofoam 
 Urethane foam 
 Fiberglass, 3"-3V' 
 5V-6V 
 
 3.14 
 5.50 
 6.00 
 
 11.0 
 19.0 
 
 
 Concrete Slab Floors: Use linear feet of exposed 
 length of slab edge in place of A:h=U (Tin. ft) AT 
 
 1" x 24" insulation 
 1" x 12" insulation 
 No insulation 
 
 
 
 0.21 
 0.46 
 0.81 
 
 AIR SPACES, 3-4 inches 
 
 Heat Flow Up, Non-reflective 
 
 Reflective, 1 surface** 
 
 Heat Flow Down or Horizontal, 
 Non reflective 
 Reflective, 1 surface** 
 
 
 0.87 
 2.23 
 
 1.01 
 3.50 
 
 
 SURFACE AIR FILMS 
 
 Heat Flow Up, Non-reflective 
 
 Reflective (c * 0.20) 
 
 Heat Flow Down, Non-Reflective 
 
 Reflective (e n 0.2Q) 
 
 Heat Flow Horizontal 
 
 Through vertical surface, non-reflective 
 
 Outside (15 mph wind) 
 
 
 0.61 
 1.10 
 
 0.92 
 2.70 
 
 0.68 
 0.17 
 
 
 ** The addition of a second reflective surface facing the first 
 reflective surface increases the thermal resistance values of 
 
 an air space only 4 to 7 percent. 
 
13-17 
 
 Table 13-2 
 Heating Load Data* 
 
 o 
 
 K 
 
 r^ r-~ lo 
 
 00 
 
 CO 00 CM 
 
 LO UD 
 
 
 h- 
 
 ST 
 
 ID 
 C/) 
 
 Gl CTl CTi 
 
 <Tv 
 
 r^ lo 00 
 
 r^ ud 
 
 
 c: 
 coll. 
 
 
 
 
 
 
 
 
 
 
 
 
 •I— 
 
 4— 
 
 CT> CO CO 
 
 CM 
 
 LO LO CO 
 
 r-~ cm 
 
 
 co 
 
 21 
 
 »— 1 r-H CXJ 
 
 CM 
 
 CM "=3- LO 
 
 1 CO 
 
 
 CU 
 
 1 — 1 
 
 
 
 1 1 1 
 
 1 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 _J 
 
 HOO 
 
 r— 1 
 
 ■^-a^«^-CMVOO^J-CT> 
 
 LO CO LO CO <— 1 
 
 cr> r-. cm 
 
 
 <: 
 
 LO |-~. CO 
 
 cn 
 
 cocor^.cocncocor^ 
 
 o^j-ocon 
 
 en co en 
 
 
 ZD 
 
 LO O ID 
 
 CM 
 
 MO HcOHCorv w 
 
 r~~ co 1— 1 cm <— 1 
 
 i-H UD 
 
 
 21 
 
 CM CO t— 1 
 
 CM 
 
 or-^ocncocncn«3- 
 
 CTi r-HD «d-<^ 
 
 t— 1 en cr> 
 
 
 21 
 
 
 
 r-H CM 1— 1 1 — 1 1 — 1 
 
 1— 1 1— 1 r— 1 t— 1 
 
 r-H 
 
 
 < 
 
 
 
 
 
 
 LxJ 
 
 000 
 
 O 
 
 IDrHN^CMH^W 
 
 t— 1 CO VO 00 CO 
 
 <JD CO LO 
 
 
 s^ 
 
 
 
 «— ICMLOCMOCn^CM 
 
 COOCOLON 
 
 cm en co 
 
 
 ID 
 
 
 
 roroaicn^i-LO^-oj 
 
 CO "vf UD CM LO 
 
 r-. vo >^- 
 
 
 aioio 
 
 O 
 
 CMOLOCOCOCMOIO 
 
 HOONCOO 
 
 «x> r^ cm 
 
 
 >- 
 
 1 — 1 
 
 
 cncn^-r--ocncOLO 
 
 ON UT^-CO 
 
 CO CO CO 
 
 
 <C 
 
 
 
 Ln^^rocors^DLO 
 
 <£> UD O UD CTl 
 
 en co co 
 
 
 2: 
 
 
 
 t— 1 r— 1 
 
 1— » 
 
 
 . 
 
 CO 00 CM 
 
 O 
 
 cnco*d-coco<— i-vj-co 
 
 oio^toj^- 
 
 CO LO CD 
 
 
 a: 
 
 om<- 
 
 cn 
 
 r^^-^tMNLOy3lO 
 
 1— H U3 LO CM t— 1 
 
 en 00 -3- 
 
 
 Q_ 
 
 1— i 1— 1 
 
 
 cococncnt-Hcncoo 
 
 00 O^ LO 1— 1 CO 
 
 O CO CO 
 
 
 <: 
 
 
 
 1 — 1 1 — 1 < — 1 1 — 1 
 
 r— 1 1— t 1— 1 
 
 1—1 
 
 . 
 
 CO «=i- 1— 1 
 
 co 
 
 cocooor-^t-ocMcocr> 
 
 CO «— 1 00 
 
 LO t— 1 CM 
 
 o 
 
 a; 
 
 CO CO r-H 
 
 r-H 
 
 o^j-iDNinwHn 
 
 NHCOlflN 
 
 CO <— 1 t ^- 
 
 lo 
 
 ■=c 
 
 co <^t- cm 
 
 CO 
 
 CMCO^^lflHHIS 
 
 *3- r^. n 
 
 CM O O 
 
 co 
 at 
 
 2: 
 
 
 
 
 
 
 . 
 
 CJNO 
 
 f-«. 
 
 IDNMOlOlO^OH 
 
 OCOMNU3 
 
 00 00 en 
 
 CO 
 
 03 
 
 CO LO O 
 
 r- 1 
 
 r-icocococnoocoor^cocor-Hco 
 
 CO LO 1— 1 
 
 fO 
 
 CO 
 
 UJ 
 
 «3- LO CO 
 
 "3" 
 
 cooococoLOOOcn 
 
 co cr> 00 vo 
 
 1— 1 <T> 
 
 
 
 
 
 . 
 
 CM *H- LO 
 
 co 
 
 i—icnr^cocococmcn 
 
 r->- cm <3- cr> 
 
 co lo en 
 
 co 
 
 21 
 
 CT> CJ> 1— 1 
 
 ^J- 
 
 OO^r-HCOOLOCnLO 
 
 toooiaiN 
 
 CM ^- CO 
 
 >- 
 
 •=X. 
 
 LO CO ^ 
 
 LO 
 
 CO CT> LO LO Cn i— ICMCO 
 
 CM UD i-H CM CO 
 
 CM O i— 1 
 
 
 •~3 
 
 
 
 1— 1 CM CM t— t 1— t 1— I CM 
 
 1—1 1— 1 CM CM 1— 1 
 
 . — i H 1 — 1 
 
 . 
 
 IflOON 
 
 r^. 
 
 <MmMNU5(MH^ 
 
 U1U5NMO 
 
 r^ cm >=j- 
 
 Ul 
 
 C_> 
 
 LO lO LO 
 
 CM 
 
 NCncOCOCDCMCMLO 
 
 CO O CM CO CM 
 
 cn -vi- ^h- 
 
 UJ 
 
 UJ 
 
 LO CO CO 
 
 LO 
 
 LOCOCOCOCO'-HCMCM 
 
 r-H CO i-H CM 00 
 
 1— 1 «— 1 
 
 DC 
 CD 
 Ul 
 
 Q 
 
 
 
 r-H CM CM r-H r-H r-H CM 
 
 HHMMH 
 
 r— 1 f— 1 r— 1 
 
 . 
 
 CO CO CO O 
 
 «3-co<-H<3-*ct-cor^co 
 
 1— 1 O CO >— • LO 
 
 CO CO CD 
 
 O. 
 
 > 
 
 CO CM r-H 
 
 CO 
 
 COnN^OOHHCO 
 
 cm cr> cm cr> lo 
 
 u)Nn 
 
 
 O 
 
 CO «3" CM 
 
 CO 
 
 <Mr-^cncn>=d-cnooo 
 
 cr> cm r^. r^ >^- 
 
 en co en 
 
 
 21 
 
 
 
 1— 1 t— 1 t— 1 r— 1 r-H i—l 
 
 1— 4 r- 1 1— 1 1— 1 
 
 
 . 
 
 co r>- cm 
 
 00 
 
 ONOCJCJCjHn 
 
 LO CO C7> «^- =d" 
 
 CM >^- CO 
 
 I— 
 
 \— 
 
 Cn CM OJ 
 
 CO 
 
 fO^OCO'd-NOOOOJO^COO^OCOH 
 
 < 
 
 O 
 
 t— I 
 
 
 cnLOLO^-or^.r^cM 
 
 NOlCJr- 1 Ol 00 NN 
 
 ZC 
 
 O 
 
 
 
 1— 1 1— 1 1— 1 1— i 
 
 I— 1 I— 1 »— 1 
 
 
 I— 
 
 CD CM 
 
 O 
 
 COr-^LOr-^CMLOCMCM 
 
 CO CO CO CO CO 
 
 CM i-H <=d- 
 
 _J 
 
 O- 
 
 t— 1 
 
 
 r-HCMCOCOr-HCMCM^r 
 
 CO «-H CM CO CTl 
 
 T-t O l^« 
 
 <£ 
 
 Ul 
 
 
 
 LOOOOCTiCOLOLDCO 
 
 >^- LO r^- U3 UD 
 
 CO LO •>!- 
 
 o 
 
 CO 
 
 
 
 i-H 
 
 
 
 . 
 
 000 
 
 O 
 
 1— 1 CO CD LO "vf LO «— ICM 
 
 O0 CM CO CO VO 
 
 cti lo r^. 
 
 
 O 
 
 
 
 cno>3-r^cncMcnco 
 
 CO CM ^J- CO CT> 
 
 roi^<- 
 
 _l 
 
 rz> 
 
 f 
 
 
 CMCMCOr^co-vrroco 
 
 CO CO 'd- CO ■* 
 
 LO «H" CO 
 
 <C 
 
 <C 
 
 
 
 
 
 
 2: 
 
 
 
 
 
 
 
 2- 
 
 000 
 
 O 
 
 LOCMCOLOCy>«H-COr-H 
 
 HfOHODH 
 
 lo r^ 00 
 
 o 
 
 _J 
 
 
 
 «t^OrOr- IISION 
 
 OHCOOCO 
 
 cd r^ co 
 
 21 
 
 ZD 
 
 
 
 csJCMoor-^co«=j-cor-H 
 
 CO CO CO CM <3" 
 
 CO LO CO 
 
 
 ■21 
 O 
 1 — 1 
 1— 
 
 < 
 
 
 
 
 
 
 
 1— 
 
 
 
 -0 
 
 
 
 
 CO 
 
 
 
 ra 
 
 c 
 
 
 
 Q 
 
 E CU 
 
 >> 
 
 1 — 
 
 
 
 1 — 
 
 
 21 
 
 ra r— 
 
 s_ 
 
 d) co to 
 
 E 
 
 3 
 
 
 <c 
 
 JC 1 — 
 
 a) 
 
 cn 1— 1 >j -m 
 
 1— a> 
 
 rO 
 
 
 
 <C 
 
 OVr- 
 
 E 
 
 <o cu ro ro cz 
 
 ro 3r 
 
 o_ +■> 
 
 
 UJ 
 
 2: 
 
 c > a> 
 
 O <C 
 CO i2 
 
 S-+JSS-1— CO. > ro 
 
 31/JXl+J 
 
 ro ro 
 
 
 1— 
 
 <=t 
 
 •f- co 1 — 
 
 O 4-> O CU CU O -Q 
 
 03 CU OJ 
 
 +-> >,+-> 
 
 
 <: 
 
 CO 
 
 s +-> •«- 
 
 +-> CO 
 
 JZ (U t+lrTJ-D i- 
 
 CJJ CD N S- CD 
 
 c E ^ 
 
 
 1— 
 
 <c 
 
 J- C -Q 
 
 C ■=£ 
 
 <_>CS-S-+->r— S-T- 
 
 C C 4-> CD E 
 
 •1- CU -^ 
 
 
 CO 
 
 _J 
 
 •r D O 
 
 O — 1 
 
 ccrarocuoora 
 
 ZJ -r- 
 
 ro -C ro 
 
 
 
 < 
 
 CQIS 
 
 SI < 
 
 <<CQD3caUULl. 
 
 >-3 ^ ^ 2: ^ 
 
 CO CO >- 
 
 
 
 0) 
 
 
 
 s- 
 
 
 
 3 
 
 • 
 
 CO 
 
 4-> 
 
 E 
 
 •r— 
 
 ro 
 
 -a 
 
 -C 
 
 S- 
 
 <C 
 
 +-> 
 
 cu 
 
 Q. 
 
 • 
 
 c 
 
 E 
 
 > 
 
 ro 
 
 0) 
 
 i- 
 
 ^: 
 
 -M 
 
 <D 
 
 -M 
 
 
 co 
 
 
 JD 
 
 
 S- 
 
 ■ — 
 
 • 
 
 CU 
 
 Z3 
 
 ■1 — 
 
 E 
 
 JD 
 
 
 
 5- 
 
 
 CO 
 
 ro 
 
 >> 
 
 
 £ 
 
 S- 
 
 • 
 
 
 -O 
 
 > 
 
 CU 
 
 
 cz 
 
 E 
 
 CU 
 
 LxJ 
 
 •1— 
 
 E 
 
 
 +-> 
 
 •r— 
 
 ft 
 
 
 +-> 
 
 a> 
 
 M- 
 
 
 
 
 O 
 
 4- 
 
 S- 
 
 
 O 
 
 cu 
 
 ^S 
 
 
 E 
 
 en 
 
 &S 
 
 E 
 
 CTl 
 
 i-H 
 
 O 
 
 *■«** 
 
 v_ ** 
 
 CD 
 
 
 
 
 CM 
 
 CM 
 
 H- 
 
 r*s 
 
 r^ 
 
 O 
 
 en 
 
 en 
 
 
 .—1 
 
 r-H 
 
 +-> 
 
 
 
 C 
 
 to 
 
 CO 
 
 aj 
 
 1 — 
 
 |— 
 
 E 
 
 ro 
 
 ra 
 
 +J 
 
 4-> 
 
 4-> 
 
 5- 
 
 C 
 
 c 
 
 ra 
 
 CU 
 
 CU 
 
 Q. 
 
 E 
 
 E 
 
 CU 
 
 ro 
 
 ro 
 
 Q 
 
 X> 
 
 TD 
 
 
 C 
 
 £Z 
 
 • 
 
 Z3 
 
 Z3 
 
 CO 
 
 U_ 
 
 U_ 
 
 . 
 
 4- 
 
 <+- 
 
 ID 
 
 O 
 
 O 
 
 #\ 
 
 -x: 
 
 ^<i 
 
 CO 
 
 O 
 
 O 
 
 a> 
 
 O 
 
 O 
 
 +j 
 
 JD 
 
 JD 
 
 ro 
 
 "O 
 
 -O 
 
 +-> 
 
 cz 
 
 £Z 
 
 CO 
 
 ra 
 
 ra 
 
 
 zrz 
 
 zc 
 
 -a 
 
 
 
 <u 
 
 Ul 
 
 Ul 
 
 +j 
 
 <C 
 
 < 
 
 •1 — 
 
 c2 
 
 o; 
 
 c 
 
 zc 
 
 zc 
 
 ZD 
 
 CO 
 
 CO 
 
 
 ■3; 
 
 <C 
 
 CU 
 
 
 
 JC 
 
 #* 
 
 
 
 +-> 
 
 CO 
 
 ro 
 
 
 CO 
 
 CO 
 
 M- 
 
 
 
 O 
 
 5- 
 
 i_ 
 
 
 cu 
 
 CU 
 
 CO 
 
 +-> 
 
 4-> 
 
 ra 
 
 O- 
 
 CL 
 
 1 — 
 
 ro 
 
 rO 
 
 +-> 
 
 ^Z 
 
 x: 
 
 < 
 
 
 
 CD 
 
 •I— T-H^-^!— I 
 
 +j a> — 
 
 ro CO rjj S_ CU $_ 
 
 E UD 1— Z3i— CU 
 
 •1- rzn XI 4-> JD +-> 
 
 r— \ — I rO ro rO ro 
 
 o 1 — s- 1 — a> 
 
 •> cu s- 
 
 E CU E Q. E en 
 
 O C O E o 
 
 S- Z3 S- CU i. CO 
 
 U. •"D U. +-> U. •!— 
 
13-18 
 
 Table 13-2 (Continued) 
 
 o 
 
 t=; 
 
 ^t- 
 
 co lo 
 
 lo n 
 
 r-H 
 
 < — 1 
 
 CT) CTl 
 
 CO 
 
 N-. N- r-H N <^" LO 
 
 O LO 
 
 
 
 LO 
 
 I— 
 
 2: 
 
 00 
 
 O CTl 
 
 O CTl 
 
 r-H 
 
 
 
 cri cr> 
 
 
 
 CTi LO O CO CTi 00 
 
 O CO 
 
 CO 
 
 CO 
 
 
 ZD 
 
 
 i-H 
 
 1—1 
 
 r-H 
 
 i—l 
 
 
 r-H 
 
 r-H 
 
 i-H 
 
 
 
 CDU- 
 •l— 
 
 co 
 
 
 
 
 
 
 
 
 
 
 
 
 4- 
 
 
 
 1— 1 LO 
 
 CTl CTi 
 
 n 
 
 LO 
 
 CTl CM 
 
 r-H 
 
 LO CM CO LO CM LO 
 
 O CM 
 
 CM 
 
 CM 
 
 to 
 
 
 
 OO i—l 
 
 CM 
 
 CO 
 
 1— 1 
 
 r-H CM 
 
 CO 
 
 CO CO CM CO -^1- CO 
 
 CO «3" 
 
 <vt- 
 
 CO 
 
 CD 
 
 zs. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _1 
 
 CM 
 
 LO CM 
 
 O CM 
 
 n 
 
 CM 
 
 CTl CO 
 
 CMixrv 
 
 LOCOCMi— li— ICMCDLOLO 
 
 CO CTi CTi 
 
 LO 
 
 CM N 
 
 
 «ac 
 
 LO 
 
 LO LO 
 
 O CO 
 
 r-H 
 
 ex. 
 
 r-H CO 
 
 CM CM O 
 
 ■^■^•OiiHLOCMNCnr-l 
 
 Non 
 
 1 — 1 
 
 LO LO 
 
 
 Z3 
 
 t— 1 
 
 1 — CO 
 
 00 r-». 
 
 CM 
 
 CM 
 
 CM LO 
 
 r-H CM LO 
 
 LOLO>3-NONC0LOLO 
 
 NCM<t 
 
 O 
 
 O cn 
 
 
 2: 
 
 N 
 
 r-H *H/ 
 
 r-H «^- 
 
 r-H 
 
 CO 
 
 CO CM 
 
 CM «3" LO 
 
 HrJ-OJr- ICMLOCMCOCM 
 
 CM -^t- r-H 
 
 co 
 
 CM CM 
 
 
 LU 
 
 O 
 
 O LO 
 
 O O 
 
 O 
 
 
 
 O O 
 
 O LO LO 
 
 COLOOOOr-HCTiOCOCDLOINLO 
 
 LO 
 
 LO LO 
 
 
 2; 
 
 CO 
 
 i-H 
 
 
 
 
 
 co cn 
 
 1— 1 CO r— 1 00 LO CTi "^f 
 
 LO CO 
 
 CM 
 
 O LO 
 
 
 Z3 
 
 1—1 
 
 
 
 
 
 
 1 — 1 
 
 CM i-H CM 
 
 
 r-H 
 
 i-H 1— 1 
 
 
 n 
 
 O CO 
 
 LO LO 
 
 O 
 
 CM 
 
 CTl CD 
 
 CTl CO 1-^ 
 
 r-HCMLOOCONOCON 
 
 CM <3" "=J- 
 
 ■=3" 
 
 CM CO 
 
 
 >- 
 
 CO 
 
 LO 
 
 CTl 
 
 
 CM 
 
 
 r-H -^t CTl 
 
 cor^.LOCTiLO'^-cocri"^- 
 
 O LO CO 
 
 . — 1 
 
 cn co 
 
 
 < 
 
 "5j- 
 
 i—l 
 
 
 
 
 
 r-H CO 
 
 CO r-H CO r-H CM 
 
 1— 1 CM 
 
 CM 
 
 1— 1 CM 
 
 . 
 
 I— 1 
 
 LO O 
 
 LO H 
 
 CTl 
 
 =3- 
 
 LO LO 
 
 LO LO CM 
 
 COCOOCOCTiLOLOCTiOO 
 
 LO LO CO 
 
 CTl 
 
 cn cm 
 
 
 o; 
 
 LO 
 
 r-» lo 
 
 n en 
 
 CM 
 
 sd- 
 
 CM CD 
 
 O O CO 
 
 COCOLOLOi-HCMLOCOLO 
 
 1— 1 CM CM 
 
 N» ^1- 00 
 
 
 
 lo 
 
 CO 
 
 CM 
 
 
 rH 
 
 r-H r-H 
 
 r-H CO LO 
 
 r-l«^-i— li-HCMLOCMCOr- 1 
 
 CM «3" r-H 
 
 CM 
 
 CM CM 
 
 . 
 
 1 — 1 
 
 n lo 
 
 CM r-H 
 
 O 
 
 to 
 
 >=d- O 
 
 NQH 
 
 CTiLOCTiNCOCOCOCOr-H 
 
 O O CM 
 
 00 
 
 LO CO 
 
 o 
 
 C£ 
 
 1 — 1 
 
 r-4 
 
 *3" O 
 
 CO 
 
 LO 
 
 CO LO 
 
 LO CO CTl 
 
 COOi-HLOOOCOLOO"^!- 
 
 LO CM O LO CM LO 
 
 lo 
 
 <=C 
 
 CTi 
 
 CM LO 
 
 CM LO 
 
 r-H 
 
 ■=3" 
 
 ■^- CO 
 
 WLON 
 
 CMLOCOCMCMN-CO'^t-CO 
 
 CO LO CM 
 
 CO 
 
 CO CO 
 
 vo 
 
 s: 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 i— 1 
 
 CO >— 1 
 
 *d- 
 
 CO 
 
 c— ! 
 
 r^ 00 
 
 rJ-UDH 
 
 NOLONCM<^OCMCO 
 
 CM r-H CTi 
 
 LO 
 
 00 
 
 to 
 
 DQ 
 
 CXi 
 
 CM r-1 
 
 *d- n. 
 
 CM 
 
 cn 
 
 r-^ lo 
 
 LO LO CO 
 
 NNOCTlOCOOCTlCM 
 
 ■3" LO "^1- 
 
 CTi 
 
 O N 
 
 03 
 
 LU 
 
 CTi 
 
 00 n 
 
 co n 
 
 CM 
 
 LO 
 
 LO ^3- 
 
 COLON 
 
 cM«t^-c\jroN^ro^-^-LOC\J 
 
 co 
 
 CO CO 
 
 CO 
 
 U_ 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 . 
 
 cn *3- lo 
 
 r-H <^- 
 
 CO 
 
 .— 
 
 LO LO 
 
 LO «3" LO 
 
 LOLOLOLOCMCON-'d-LO 
 
 <3- CO CO 
 
 CO 
 
 co cn 
 
 CO 
 
 :s 
 
 LO 
 
 n lo 
 
 n lo 
 
 LO 
 
 CO 
 
 LO CM 
 
 ^t- r^ lo 
 
 lO«tCONNCOCMNO 
 
 i— 1 N» t— 1 
 
 
 
 LO LO 
 
 >- 
 
 -=C 
 
 r-H 
 
 "3- CO 
 
 «3" CD CO 
 
 r-^ 
 
 r^. lo 
 
 LO CO CO 
 
 COLOLOCOCOCTiLO^-LO 
 
 LONfO 
 
 LO 
 
 CO «3" 
 
 
 <~3 
 
 1—1 
 
 
 i— 1 
 
 
 
 
 
 
 
 
 
 . 
 
 CO 
 
 lo n 
 
 LO 03 Ol 
 
 ** 
 
 VO r-H 
 
 cm r^ lo 
 
 r-HCTlC0C0r-HCMr-HOLO 
 
 NHH 
 
 CM 
 
 CTi i—l 
 
 LU 
 
 CD 
 
 n 
 
 1— I CTi 
 
 O O 
 
 1— 1 
 
 O 
 
 l—l LO 
 
 O CTi LO 
 
 OCTiLOCOCTiOOOOLO 
 
 N» CTl LO 
 
 LO 
 
 N CTi 
 
 LU 
 
 LU 
 
 CD 
 
 <d" n 
 
 <3" O 
 
 CO 
 
 r-^ 
 
 r-^ lo 
 
 LONN 
 
 CO^tLOCMCMCTl'^-^LO 
 
 LO LO CM 
 
 «* 
 
 CM CO 
 
 o 
 
 LU 
 
 O 
 
 «— 1 
 
 
 r-H 
 
 
 
 
 
 
 
 
 
 . 
 
 n *3- cn 
 
 r-H r-H 
 
 co 
 
 O LO LO 
 
 CM LO CTi 
 
 N^OHOOUDOlHCO 
 
 CO O CO 
 
 LO 
 
 LO O 
 
 Q 
 
 > 
 
 LQ 
 
 co n 
 
 CO r-H 
 
 >=3- 
 
 LO 
 
 LO "=3" 
 
 CONN 
 
 NrHCOLOCOCTlOCBr-l 
 
 LO CO CM 
 
 O 
 
 LO N 
 
 
 o 
 
 CO 
 
 CM LO 
 
 cm n 
 
 1— 1 
 
 "=d- "^ 
 
 CM LO LO 
 
 1— l-^-COr-Hi— ILOCOCMCO 
 
 CO «3" i-H 
 
 CO 
 
 i-H CM 
 
 CD 
 i — i 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO CM LO 
 
 LO LO 
 
 
 
 r^ 1^. co 
 
 NCON 
 
 COCTiCOOCQLONLOCO 
 
 HMN 
 
 CO 
 
 O LO 
 
 1— 
 
 1— 
 
 LO 
 
 CM «^j- 
 
 CM "=3- 
 
 
 CM 
 
 cm r^. 
 
 CO <3r <=H- 
 
 ^CON^NOMOW 
 
 CO O CO 
 
 <vl- 
 
 LO >vj- 
 
 <c 
 
 <_) 
 
 LO 
 
 CM 
 
 CM 
 
 
 t— * 
 
 i — 1 
 
 CM CO 
 
 CO ^HC\J 
 
 CM 
 
 r— 1 
 
 r— 1 
 
 LU 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 t— 1 
 
 ONOlO 
 
 
 
 CM 
 
 CTl O 
 
 O CM O 
 
 LOCOOCMCMCOLOCMO 
 
 CM O LO 
 
 O 
 
 CTi LO 
 
 _u 
 
 Q_ 
 
 O 
 
 CM 
 
 
 
 r-H 
 
 
 "=i- CM 
 
 LO 1— 1 «d- CM >?1- LO 
 
 i-H CO 1— 1 
 
 LO 
 
 CT. 
 
 <c 
 
 LU 
 
 C\J 
 
 
 
 
 
 
 i-H 
 
 CM r-H r-H 
 
 
 
 
 O 
 
 1— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO 
 
 
 
 O O 
 
 
 
 O 
 
 O O 
 
 OOO 
 
 ON-OOCM^f-CDLOO 
 
 O CD O 
 
 CO 
 
 O CO 
 
 
 cd 
 
 LO 
 
 
 
 
 
 
 LO 
 
 LO CM CO LO 00 
 
 
 N 
 
 CTi 
 
 _l 
 
 rs 
 
 
 
 
 
 
 
 
 CM r-H 
 
 
 
 
 
 <c 
 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 LO 
 
 
 
 O O 
 
 
 
 O 
 
 O O 
 
 O O >^- 
 
 OOOOCOLOCOCMO 
 
 O O LO 
 
 1 — 1 
 
 LO CTi 
 
 o 
 
 _J 
 
 <3- 
 
 
 
 
 
 
 co 
 
 r^. CM CM LO 
 
 
 co 
 
 i-H CTl 
 
 s: 
 
 
 
 
 
 
 
 
 
 CM CM 
 
 
 
 
 2: 
 
 1 — 1 
 I— 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 
 
 
 
 
 
 
 O 
 
 
 
 fO 
 
 
 h- 
 
 
 
 
 
 
 
 
 r— 
 
 
 
 
 C 
 
 
 CO 
 
 
 
 
 
 
 -^ 
 
 x> c 
 
 to 0) 
 
 
 
 
 •1 — 
 r— ra 
 
 
 Q 
 
 
 
 
 
 -C 
 
 O <E 
 
 r— O 
 
 x: cd as zs 
 
 O 
 
 •r— 
 
 ra v- 
 
 
 SZ 
 
 <+- 
 
 
 
 
 +-> 
 
 O 03 >—i 
 
 CD >, 
 
 a r— +-> ctjM- 
 
 +J O 
 
 O 
 
 +-> 1- 
 
 
 «=C 
 
 <4- 
 
 +-> 
 
 
 00 
 
 •1 — 
 
 a: c ^ 
 
 •r- C 
 
 f0 CD to S- L|_ 
 
 c cn cn 
 
 E 
 
 ra ta 
 
 
 
 <: 
 
 f0 
 
 X +-> 
 
 3 
 
 =c 
 
 E 
 
 re ct: 
 
 Lt- fO 
 
 -i<i tU CO fOTD< 3 
 
 CD i- CD 
 
 13 
 
 02: 
 
 
 LU 
 
 Z^" 
 
 +J 
 
 •r- O 
 
 c 
 
 00 
 
 00 
 
 CD -^ 
 
 to o_c_> 
 
 Cfoocac-cc: i — 
 
 E CD •>- 
 
 S- 
 
 
 
 1— 
 
 
 
 CO 
 
 c 
 
 O r— 
 
 z: 
 
 
 r— S_ Ll_ 
 
 S- O 
 
 (O^ c =a:GO<a-t->ca 
 
 (Oi3D 
 
 u_ 
 
 fO ra 
 
 
 <c 
 
 M 
 
 cr 
 
 CD LO 
 
 to 
 
 (O =C 
 
 +-> 
 
 4-> ra 1— 1 
 
 CD -C CD 
 
 -Q CD to CTl 1 — C 
 
 s- -0 
 
 
 +-> +j 
 
 
 r- 
 
 1 — < 
 
 ra 
 
 O CD 
 
 to C 
 
 s ^ 
 
 s_ 
 
 4-> X _J 
 
 -i<: to zs 
 
 s-s-CDCto .^«iT--a 
 
 c c 
 
 C 
 
 c: c 
 
 
 CO 
 
 cc 
 
 1 — 
 
 -C i- 
 
 =3 -r- 
 
 =3 cc 
 
 
 
 •r- aj .< 
 
 (TJ T- r— 
 
 33S-00+->fOOCD 
 
 ra ra ra 
 
 ro 
 
 ra ra 
 
 
 
 < 
 
 u_ 
 
 o_ o_ 
 
 1— 3 
 
 >- =ar 
 
 u_ 
 
 —II— 
 
 CQ CQ CO 
 
 CQLULl 1 jsoo-o: 
 
 co 00 t/) 
 
 LO 
 
 <J~) CO 
 
13-19 
 
 Table 13-2 (Continued) 
 
 o 
 
 t=; 
 
 "vT O CNJ CD CO 
 
 O O CO 
 
 CO 
 
 ^1-^1-COOLOrHCOCNJCOCNJCNI 
 
 I— 
 
 2: 
 00 
 
 CO CT> CT> Ol CT> 
 
 en en 00 
 
 en 
 
 encncncncTicricncncncTvcn 
 
 c 
 cnu_ 
 
 
 
 
 
 
 
 
 
 
 •r- o 
 
 +- 
 
 IN 1— 1 CNJ CO LO 
 
 ■*Hlfl 
 
 CNJ 
 
 CNJCOCnLOLOLOCOCnLOCOO 
 
 to 
 
 z: 
 
 « — f I 1 1 
 
 
 rH 
 
 COCOCNJLOCO«=i-COCNICNJC0^1- 
 
 en 
 
 1 — 1 
 
 1 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 _j 
 
 Cn CO CO rH CNJ 
 
 IN CNI IN 
 
 
 
 oocncNjcnoOrHrHcocoLococo 
 
 
 < 
 
 CNJ CNJ CO ^" CO 
 
 r-i in en 
 
 CO 
 
 OIN^J-COC3CO«^-COCOCOCOLO 
 
 
 o 
 
 LO >* CNJ CO «3" 
 
 CO rH CO 
 
 en 
 
 COC0"^-CNJ<— ICOt— IIN>^-«^-COCNJ 
 
 
 2: 
 
 CO CO CO LO LO 
 
 LO CO LO 
 
 «3- 
 
 rH rH rH rH 
 
 
 LU 
 
 CO ^J- CO 1— 1 LO 
 
 IN «3- LO 
 
 co 
 
 OOOOOOOOOOOO 
 
 
 ZT 
 
 CO 00 CO CNI rH 
 
 CNJ CNJ <3" 
 
 
 
 
 o 
 
 1— 1 
 
 
 
 
 
 ■"D 
 
 
 
 
 , 
 
 
 cn 00 co ^1- 
 
 00 rN lo 
 
 CNJ 
 
 OOOOOOOOOOOO 
 
 
 >- 
 
 <d- rH CO <^ IN 
 
 Oist 
 
 1— 1 
 
 
 
 21 
 
 "v|- CO CNJ 1— 1 r-l 
 
 CNJ rH CNJ 
 
 rH 
 
 
 . 
 
 CO CNJ CO l>» CT» 
 
 O LO CO 
 
 IN 
 
 COLOOrHOOOCOCOCOOO 
 
 
 or 
 
 Cn CO LO CO CNJ 
 
 r-i en «=j- 
 
 CO 
 
 CO rH CNI CO CO 
 
 
 D_ 
 
 CO LO LO CO "=3- 
 
 LO "3- LO 
 
 CO 
 
 
 
 ■cC 
 
 
 
 
 
 . 
 
 co in cn cnj 
 
 co en r-i 
 
 LO 
 
 oocNj<3-cncncnLOcocNJCNjrH 
 
 o 
 
 q: 
 
 cnj cn co cni in 
 
 lo en in 
 
 CO 
 
 oo <d- co in cn oooooco 
 
 LO 
 
 ■=c 
 
 OCOCONN 
 
 CO CO 00 
 
 IN 
 
 rH rH rH rH i— 1 CNI rH 
 
 
 2: 
 
 t— \ 
 
 
 
 
 . 
 
 cnj co 00 r^ f-n 
 
 CO rH rH 
 
 "5J- 
 
 OOi— «COrHCOCOLOJNCOCO«^- 
 
 co 
 
 CO 
 
 CO CO CO O IN 
 
 co co en 
 
 IN 
 
 cocno«^-co«d-cocoiNco^-co 
 
 (O 
 
 LU 
 
 rH cn cn cn co 
 
 en en 
 
 CO 
 
 CNJrHrHCAJ rH rHCNJCNJrH 
 
 CO 
 
 u_ 
 
 rH 
 
 f—t 
 
 
 
 
 . 
 
 CO CO CNJ <J\ LO 
 
 en en in 
 
 
 
 INCOCOCNIOLOCOOOLOCNIIN 
 
 CO 
 
 ■21 
 
 IN CNJ CO O CO 
 
 in en 
 
 CO 
 
 *3-«3-*j-co<3-cnLocNjoiNooo 
 
 >- 
 
 <C 
 
 «3" t-» t— I CNJ O 
 
 CNJ 
 
 en 
 
 COCNJrHCO rH CNJ^fCOCNJ 
 
 <£ 
 
 ^D 
 
 rH i— 1 T-H r-l 1— 1 
 
 rH rH rH 
 
 
 
 Q 
 
 
 
 
 
 
 . 
 
 O CNJ LO CO CO 
 
 co en t— 1 
 
 IN 
 
 cnrHcnooO"^-ooocoOrHLO 
 
 LU 
 
 C_> 
 
 CNJ CO CO rH CO 
 
 CO rH rH 
 
 CNJ 
 
 rHrHOrHCNJCO"^-CnLOCO|NCO 
 
 LU 
 
 LU 
 
 "^OOHOl 
 
 en rH 
 
 en 
 
 COCNJrHCO rH rHCOCOrH 
 
 cc: 
 
 CD 
 LU 
 
 Q 
 
 rH rH rH i— 1 
 
 rH 1— 1 
 
 
 
 . 
 
 LO LO Cn CO O 
 
 LO rH CO 
 
 CO 
 
 COLO"vi-"v]-OtNOCNJLOCOOCO 
 
 Q 
 
 > 
 
 CO CNJ rH CO LO 
 
 HH^J- 
 
 CO 
 
 loincni"^- lo iNcncnco 
 
 
 O 
 
 O CO 00 IN IN 
 
 CO IN CO 
 
 LO 
 
 rH rH rH rH 
 
 O 
 
 ►— i 
 
 •ZL 
 
 rH 
 
 
 
 
 . 
 
 CT> CO CO CO CO 
 
 rN CNJ IN 
 
 O 
 
 CQOOCNJOOOOCnCQOO 
 
 I— 
 
 \— 
 
 CO LO CNJ t-H CNI 
 
 ON-i- 
 
 IN 
 
 rH rH rH CNJ 
 
 «=c 
 
 <_) 
 
 CO >3- *3" CO CO 
 
 CO CO CO 
 
 CNI 
 
 
 LU 
 
 O 
 
 
 
 
 
 IE 
 
 H- 
 
 cn cni in o ^j- 
 
 co en in 
 
 rH 
 
 OOOOOOOOOOOO 
 
 _1 
 
 Q. 
 
 IN CO r-l CO LO 
 
 co en 00 
 
 LO 
 
 
 <c 
 
 LU 
 
 CNJ r-l r-l 
 
 
 
 
 O 
 
 J— 
 
 I/) 
 
 
 
 
 
 . 
 
 CT» LO CI O O 
 
 O CO CNI 
 
 O 
 
 OOOOOOOOOOOO 
 
 
 O 
 
 cn cnj 
 
 rH 
 
 
 
 _J 
 
 O 
 
 
 
 
 
 < 
 
 <c 
 
 
 
 
 
 2: 
 cc 
 
 
 
 
 
 
 >- 
 
 lo en co 
 
 OOO 
 
 O 
 
 OOOOOOOOOOOO 
 
 o 
 
 _J 
 
 CO 
 
 
 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 l-H 
 
 CO 
 
 
 
 
 
 1— 
 
 o> 
 
 
 
 -C 
 
 
 <=c 
 
 c c 
 
 
 
 o 
 
 
 \— 
 
 •r- O 
 
 
 
 J=. fO 
 
 
 CO 
 
 Q. +J 1— 
 
 
 
 ro u (L) <u 
 
 r— (0 r— .C (U CO 
 
 
 Q 
 
 co rj 
 
 4-> 
 
 c 
 
 o a; to i — o a» 
 
 
 z: 
 
 
 c 
 
 S- C 
 
 
 
 UCQS-.r- fO as to E 
 
 
 «=C 
 
 
 
 O 3 i—i 
 
 OT5 d) LU 
 
 4-> 
 
 •i- (U >P"D d) i — CO i — 
 
 
 
 Q 
 
 «"0 n l— 
 
 o_ s- > cc 
 
 cn <C 
 
 JZf0>»Ct0C0QOO(0 f0 
 
 
 LU 
 
 ■=t 
 
 CO 03 i- O O 
 
 <u (O <c 
 
 c: q 
 
 O C 2! O CD fl3 TJ or Q_ 
 
 
 1— 
 
 cc 
 
 O S- CjJ -0 r— LU 
 
 am- zc :s 
 
 •1 — 1— 1 
 
 (O O CO 3 i — -r C (O IB fl 
 
 
 < 
 
 
 
 E O > £= JO 2: 
 
 ■0 +■> -<c 
 
 E cc 
 
 i — +j+jj*: cuEnatoi — q.-i-> 
 
 
 1— 
 
 _] 
 
 101 — c ro <u 2: 
 
 •r- S- 3S _l 
 
 1— O 
 
 aj >> s- o >>-*: <a r— c i— E co 
 
 
 CO 
 
 
 
 r-O (US- 3 O 
 
 s- <a cjj lu 
 
 •1- _i 
 
 Q.(oofl(U<OT-c.aj(0<o(u 
 
 
 
 C_) 
 
 <OQCDO. O 
 
 caiz 
 
 3 LL. 
 
 cCQU.'-^i.i—ISIOQ.l— 1— 3 
 
13-20 
 
 Table 13-2 (Continued) 
 
 o 
 
 « 
 
 CO 
 
 LO 00 CO 
 
 00 r^. 
 
 CO 
 
 
 co CO «=d- 
 
 ^■■^■■^•CvJ LO 
 
 CO 
 
 CO CO CM 
 
 I— 
 
 CO 
 
 CTi 
 
 CT> CT> CTi 
 
 en en 
 
 cn 
 
 
 cn cn en 
 
 cn en cn cn cn 
 
 cn 
 
 cn cn cn 
 
 c 
 
 
 
 
 
 
 
 
 
 
 cr> U_ 
 
 
 
 
 
 
 
 
 
 
 
 •r— O 
 
 +- 
 
 r^» a 
 
 CO CO 
 
 <3- 
 
 
 ■=d- co 00 
 
 CONCMPs i-l 
 
 CO 
 
 O O CM 
 
 CO 
 
 ^ 
 
 1—1 
 
 rHPJW 
 
 CM i-H 
 
 CM 
 
 
 1 
 
 1 1 1 1 1 
 
 
 1 
 
 <U 
 
 ►— 1 
 
 
 
 
 
 
 
 
 
 
 O 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 _J 
 
 cn 
 
 co r» co 
 
 CD CO 
 
 cn 
 
 en 
 
 cn LO O CM CO 
 
 1— • lo co lo cn 
 
 LO 
 
 lo cn cn 
 
 
 < 
 
 CM 
 
 CO Cn CO 
 
 CO CM 
 
 rH 
 
 CM 
 
 cd r~^ co «* co 
 
 CM LO O CM CO CM 
 
 CO 
 
 cn co 
 
 
 ZD 
 
 CT> 
 
 en co co 
 
 .— 1 CO 
 
 co 
 
 LO 
 
 co^t-NLno 
 
 CO rH rj- O CO <sf 
 
 ^t- 
 
 CMCO^f 
 
 
 <: 
 
 CM 
 
 CM C\J CM 
 
 CM CO 
 
 t— 1 
 
 i-H 
 
 LOCOCOLON 
 
 CO CO CO CO CO LO 
 
 <d- 
 
 CO LO CO 
 
 
 UJ 
 
 
 
 
 
 
 
 
 
 CD 
 
 i-H CM CM O <— 1 
 
 00 cn co co 
 
 
 
 cn cn CD 
 
 
 2: 
 
 
 
 
 
 
 00 cn cn cn >^- 
 
 «3- CO CO CO r-l 
 
 
 CO CO CO 
 
 
 ID 
 ■"3 
 
 
 
 
 
 
 1— 1 r— 1 H 
 
 
 
 
 
 00 
 
 LO O O 
 
 <3- 
 
 
 
 O 
 
 lo 1— i co cn cn 
 
 r>» r-H cn co co co 
 
 co 
 
 cn r^ cn 
 
 
 >- 
 
 00 
 
 CM 
 
 co 
 
 
 
 ■vt- cn co co 1— 1 
 
 «3" rH 00 00 CO CO 
 
 CO 
 
 00 r^ co 
 
 
 21 
 
 
 
 
 
 
 CM CO CO CM CO 
 
 CM «— 1 1— 1 CM rH 
 
 
 1— 1 rH CM 
 
 . 
 
 I— 1 
 
 00 O CO 
 
 co r^ 
 
 LO 
 
 CO 
 
 CO HNCOLO 
 
 U)OOCOCO<t 
 
 r^. 
 
 1— 1 CM LO 
 
 
 CC 
 
 «* 
 
 CD CT> CTi 
 
 co r-~ 
 
 "* 
 
 CO 
 
 CO LO LO CM LO 
 
 Cn 00 LO CM i-H LO 
 
 CO 
 
 r-N. co cm 
 
 
 
 r— 1 
 
 t— 1 
 
 rH 
 
 
 
 <d" CO CO >^- LO 
 
 i-H ^" ">j- "^- LO CO 
 
 CM 
 
 <3" "vt" LO 
 
 . 
 
 i-H 
 
 NOCO 
 
 LO CO 
 
 ■^f- 
 
 CO 
 
 CM LO r^ "vl- LO 
 
 cn 00 cn 1— i cn 
 
 
 
 cn co 
 
 o 
 
 CC 
 
 CO 
 
 CO LO CO 
 
 en co 
 
 LO 
 
 
 
 cm co cn 
 
 co cn i-h «3- co co 
 
 CM 
 
 cn co 
 
 lo 
 
 =£ 
 
 ^3- 
 
 ■=3- co co 
 
 CM *3" 
 
 CM 
 
 CM 
 
 r-^ 1— 1 co cn 
 
 lo 00 cn 00 cn r-^ 
 
 CD 
 
 00 co cn 
 
 co 
 
 CU 
 
 S 
 
 
 
 
 
 
 t-H i-H 
 
 
 
 
 . 
 
 CT> 
 
 en lo >vr 
 
 CO hx 
 
 CO 
 
 LO 
 
 «5f- cn 1— 1 lo co 
 
 0<tOLONLO 
 
 r--» 
 
 00 cn 
 
 I/) 
 
 CO 
 
 CM 
 
 CM «3" CO 
 
 r-^ 
 
 LO 
 
 O 
 
 LO "^" Cn r- 1 LO 
 
 CO <3" CD CM CO CO 
 
 CO 
 
 cm <=j- r-^ 
 
 03 
 
 UJ 
 
 LO 
 
 LO «5}" <H- 
 
 "vt" LO 
 
 CO 
 
 CO 
 
 00 CM CM CO O 
 
 co t—i i-h cn 
 
 r-^ 
 
 cn 
 
 cn 
 
 U_ 
 
 
 
 
 
 
 1— 1 t—H 1— 1 
 
 t-H rH i-H rH 
 
 
 t-H t-H 
 
 . 
 
 CJ 
 
 cn en cm 
 
 LO O 
 
 r>» **• 
 
 CO CO CD CO "=3- 
 
 co cn *3- 00 co lo 
 
 LO 
 
 CO CO rH 
 
 co 
 
 ■ZL 
 
 «3- 
 
 CO <^f LO 
 
 O i-H 
 
 CO 
 
 en 
 
 1—1 CO O CO CM 
 
 LO O t-H i-H CO CO 
 
 LO 
 
 r-~ 1— i cm 
 
 >- 
 
 <c 
 
 co 
 
 CO LO LO 
 
 lo r-~ 
 
 ^t- 
 
 CO 
 
 t-H LO CO O CO 
 
 CO CM CO CM CO i-H 
 
 cn 
 
 rH i-H CM 
 
 Q 
 
 *"D 
 
 
 
 
 
 
 «— 1 i— 1 t— < r-H r— 1 
 
 I-H i-H 1 — 1 rH 1 — 1 
 
 
 rH rH rH 
 
 . 
 
 CM 
 
 CO CM CO 
 
 CM rH 
 
 r^» 
 
 CO 
 
 r^ cm co co 
 
 1— 1 CO t-H CO rH CO 
 
 CO 
 
 LO 1— 1 LO 
 
 UJ 
 
 O 
 
 co 
 
 CM LO «sf 
 
 O O 
 
 CO CO 
 
 HNCOP1CO 
 
 cn rH CO rH CM CM 
 
 cn 
 
 CO LO CM 
 
 UJ 
 
 UJ 
 
 CO 
 
 CO LO LO 
 
 lo r-» 
 
 ■vt" 
 
 CO 
 
 OCO^OlH 
 
 r^ i-H t-H i-H CM O 
 
 CO 
 
 i-H O rH 
 
 CD 
 
 O 
 
 
 
 
 
 
 l—l «— 4 t-H .—1 
 
 i — 1 1— 1 . — 1 rH t-H 
 
 
 i-H i-H i-H 
 
 . 
 
 LO 
 
 "^ CO CO 
 
 r^ *3- 
 
 ■^f 
 
 CO 
 
 MCONCOO 
 
 co co «tf- cn r->. co 
 
 CO 
 
 co co r^ 
 
 Q 
 
 > 
 
 
 
 1— 1 CO CO 
 
 cn r^» cm 
 
 en 
 
 cn lo lo cz> 
 
 1— 1 lo r^. lo co cn 
 
 CD 
 
 COCJN 
 
 
 O 
 
 ■*<tfOCO 
 
 CM <3- 
 
 
 I— 1 
 
 n r-ir — cn 
 
 LONr^rvco co 
 
 CO 
 
 r^ r^. i->» 
 
 CD 
 
 ^ 
 
 
 
 
 
 
 i-H r-l 
 
 
 
 
 . 
 
 LO 
 
 rvcors 
 
 1—1 i-H 
 
 r^ 
 
 LO 
 
 LO CO 00 CO CO 
 
 «3" CO LO CO O 1— 1 
 
 
 
 CO CO CM 
 
 I— 
 
 1— 
 
 I— 1 
 
 cm r^ 00 
 
 r~» co 
 
 ■=3- 
 
 CM 
 
 t-n cm «=j- cn 
 
 co cm co cm cn 
 
 CM 
 
 r^ 1— 1 !■>•» 
 
 < 
 
 c_> 
 
 I— 1 
 
 1— 1 
 
 T— 1 
 
 
 
 *d- co CO *3- ^d" 
 
 rH CO CO CO -^J" CM 
 
 CM 
 
 CO CO CO 
 
 re 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 CNJ 
 
 CO O O 
 
 ^1- 
 
 
 
 O 
 
 CM O CM CO CM 
 
 COHOTNtCM 
 
 CO 
 
 LO 1— 1 
 
 _J 
 
 Q_ 
 
 T— 1 
 
 1— 1 
 
 CM 
 
 
 
 COrvCOCM N 
 
 co co cn 00 i-h r^ 
 
 CO 
 
 cn 1— 1 
 
 < 
 
 UJ 
 
 
 
 
 
 
 «— i CM CM «— « i— 1 
 
 i-H 
 
 
 r-H t-H 
 
 1— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 o 
 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 000 
 
 
 
 
 
 O 
 
 0^000 
 
 cn co cn 
 
 cn co 
 
 
 CD 
 
 
 
 
 
 
 co , ^- 
 
 
 
 
 _l 
 
 ZD 
 
 
 
 
 
 
 
 
 
 
 «=c 
 
 <c 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 
 
 000 
 
 O CD 
 
 
 
 O 
 
 O CO CO O CD 
 
 CO 
 
 
 
 000 
 
 o 
 
 _l 
 
 
 
 
 
 
 .—1 r-l 
 
 
 
 
 -ZL 
 
 "-3 
 
 
 
 
 
 
 
 
 
 
 
 sz 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 — 1 
 
 
 
 
 
 
 rs 
 
 
 
 
 
 I— 
 
 
 
 
 
 
 rs ^ 
 
 
 
 
 
 <c 
 
 
 
 
 
 
 CO CM 
 
 
 
 
 
 t— 
 
 
 
 
 
 
 'd- -=d- 
 
 
 
 
 
 co 
 
 
 
 
 
 CU 
 
 10 CO 
 
 -0 
 
 
 to 
 
 "r— 
 
 
 Q 
 
 
 
 
 
 r— 
 
 r— p— 
 
 1— « 
 
 cu 
 
 a> r— -a 
 
 
 ^ 
 
 
 
 
 
 r— 
 
 r— r— O 
 
 cu 
 
 1 — 
 
 c c 
 
 
 «=E 
 
 
 
 </) 
 
 
 .c: 
 
 •r— 
 
 lO ffl Ei — CO 
 
 "O T- 
 
 1 — 
 
 >> a. cu 
 
 
 
 ■=c 
 
 
 (O (0 3 
 
 
 03 
 
 > 
 
 u_ u_ • — •— < 
 
 O i- <4- <C 
 
 •r- 
 
 03 03 CQ 
 
 
 UJ 
 
 1— 1 
 
 CO 
 
 ■P-PJ2 
 
 
 c 
 
 co 
 
 +-> cu 
 
 cn cu 03 cn ^ 
 
 > 13 C 
 
 
 I— 
 
 CD 
 
 C 
 
 c co E 
 
 c 
 
 c 
 
 <a 
 
 a> to 4-> 2: 
 
 03 c: -r- <4- c <a: 
 
 CO 
 
 03 -C 
 
 
 < 
 
 CC 
 
 CD 
 
 (O 3 J 
 
 cu 
 
 03 
 
 E zc 
 
 co jz: -C •!— o3 ' — 1 
 
 S- O T- S- -*C "1- t-H 
 
 c 
 
 +->•■- +-> 
 
 
 h~ 
 
 
 
 -£Z 
 
 1— enr— 
 
 u E 
 
 > 
 
 «=c 
 
 •r- 03 03 3 O _J 
 
 •r- -r- 1 O U S- O 
 
 03 
 
 C-TI 3 
 
 
 CO 
 
 LU 
 
 4-> 
 
 •M 3 O 
 
 TCI O 
 
 03 
 
 -C C2i 
 
 O T3 TD O) O _J 
 
 03 -E O CU O Q. 7Z. 
 
 > 
 
 O E O 
 
 
 
 
 
 <=C <X. <C C_) 
 
 21 CtL 
 
 CO 
 
 h- 1— 
 
 CQ I-H I-H 1 Cl_ I-H 
 
 OOS: O-Qi I/) i-h 
 
 LU 
 
 U_ 1— 1 to 
 
13-21 
 
 Table 13-2 (Continued) 
 
 o 
 
 1=; 
 
 mincvuDH 
 
 CT1CT1 CTiCM 
 
 co st LO 
 
 r^- 
 
 LO LO CO 
 
 en 
 
 LO CO 
 
 1— 
 
 2: 
 zd 
 
 CTl CTl CTl CT> CJ1 
 
 Cn CT> CTl O 
 r— 1 
 
 CTl CTl CTl 
 
 en 
 
 CTl CTl CTl 
 
 en 
 
 CO CO 
 
 c 
 cnix. 
 
 •I— O 
 
 00 
 
 
 
 
 
 
 
 
 +- 
 
 <* rv H OtM 
 
 CO CM CO LO 
 
 CO LO CO 
 
 LO 
 
 LO CTl CM 
 
 CM 
 
 00 lo 
 
 lo 
 
 21 
 
 1 1 I— 1 1— 1 1— 1 
 
 1 
 
 
 CM 
 
 CM CM CO 
 
 CM 
 
 t—l 1 
 
 CD 
 
 1— 1 
 
 1 1 1 
 
 
 
 
 
 
 1 
 
 Q 
 
 3: 
 
 
 
 
 
 
 
 
 
 _i 
 
 Sf 00 LO r-4 O 
 
 CT» 00 «— 1 CM O 
 
 ^■roo 
 
 r-H 
 
 «sj- en lo 
 
 «=3- 
 
 r-» t—i 
 
 
 ■=c 
 
 <* ONinoa 
 
 r-* <o st co cm 
 
 LO CO LO 
 
 CM 
 
 LO CM LO CO 
 
 co 
 
 LO t—l 
 
 
 zd 
 
 1— 1 00 co cti ro 
 
 St CT» t— 1 r-H LO 
 
 CM LO LO 
 
 en 
 
 LO O ^ CO 
 
 t—i 
 
 r--. lo 
 
 
 21 
 21 
 
 vo ^Dhsvor^ 
 
 LO st LO LO «^}- 
 
 LO St St 
 
 r-H 
 
 i-H r-H i-H r-l 
 
 CM 
 
 en r-^ 
 
 
 
 
 
 
 
 
 
 Ixl 
 
 CO CTl CO CTl «3" 
 
 00 CT» CM CM LO 
 
 St O CT> 
 
 
 
 O CD CD O 
 
 CD 
 
 CO t—l 
 
 
 21 
 
 co co r-^ co lo 
 
 r-H st 1— 1 
 
 CM 
 
 
 
 
 00 l-H 
 
 
 ZD 
 
 
 
 
 
 
 
 1— 1 t—l 
 
 
 «Z> 
 
 
 
 
 
 
 
 
 
 r-* 1— 1 O st en 
 
 en st lo st r-^ 
 
 CTl LO LO 
 
 
 
 O O CD CD 
 
 CD 
 
 CO CM 
 
 
 >- 
 
 NtH«3rHCM 
 
 St CM CO CM CO 
 
 sl- O O 
 
 
 
 
 lo r^- 
 
 
 
 t—l CM CM CM CM 
 
 HHCMH 
 
 1— 1 1— 1 1— 1 
 
 
 
 
 sj- CO 
 
 . 
 
 iDcrnDroH 
 
 CM^-NOO 
 
 O LO LO 
 
 CTl 
 
 CONCTiCn 
 
 i-H 
 
 co lo 
 
 
 a; 
 
 CM 00 st 00 CO 
 
 MflOfOS 
 
 CTl CM <—l 
 
 LO 
 
 CO CM CO CO 
 
 CO 
 
 lo r^. 
 
 
 Q. 
 
 St «=t LO St LO 
 
 CO CO LO CO CM 
 
 CO CO CO 
 
 
 
 
 CO LO 
 
 
 <: 
 
 
 
 
 
 
 
 
 . 
 
 en r^ lo en co 
 
 1— 1 CTl St CM LO 
 
 LO LO CM 
 
 O 
 
 00 r-l LO CM 
 
 *3" 
 
 CO CM 
 
 
 
 a: 
 
 LO LO CM 00 CM 
 
 00 r-H CO CM st 
 
 LO CO CO 
 
 LO 
 
 ONCT1CT1 
 
 O 
 
 sl- 
 
 lo 
 
 ■=t 
 
 CO CTl O CTl O 
 
 r- r-» co f*. lo 
 
 r^ LO LO 
 
 CM 
 
 CM i-H r-H t—l 
 
 CO 
 
 co 
 
 LO 
 01 
 
 2: 
 
 t— 1 t— 1 
 
 
 
 
 
 
 t—l t-H 
 
 . 
 
 CM CO st CO «— 1 
 
 LO O LO CO St 
 
 CO CO CO 
 
 t—l 
 
 •3- CO "=3- CO 
 
 LO 
 
 O CM 
 
 </) 
 
 en 
 
 St LO O CTl CM 
 
 CO St LO CTl O 
 
 CTl r-l r-H 
 
 LO 
 
 oiHNin 
 
 CM 
 
 r-^ co 
 
 rO 
 
 Ixl 
 
 OHWHCV1 
 
 CTl 00 CTl CO 00 
 
 00 CO CO 
 
 CO CM CM CM CM 
 
 "3" 
 
 S^ r-l 
 
 QQ 
 
 u_ 
 
 
 
 
 
 
 
 t-H t—l 
 
 
 . 
 
 en co o lo o 
 
 CO <— 1 LO CM CO 
 
 LO LO O 
 
 t—l 
 
 CTl CO rH CO 
 
 CM 
 
 en 
 
 co 
 
 21 
 
 LO CTl CM CO LO 
 
 LO LO LO CM CM 
 
 CO ^- CO 
 
 r»« 
 
 O CTl CO LO 
 
 LO 
 
 en co 
 
 I 5- 
 
 <: 
 
 cm ro>^->*<a- 
 
 r-H O 1— 1 t— • O 
 
 O CTl CTl 
 
 St 
 
 ^J- CM CO CO 
 
 LO 
 
 LO CO 
 
 
 •"D 
 
 I— 1 t-H t— 1 . — 1 t— 1 
 
 r-l i—l r-l 1— 1 1— 1 
 
 r-l 
 
 
 
 
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 IflHSOU) 
 
 CO CTl CO O LO 
 
 CO CM O 
 
 «—) 
 
 CTl sf" «— 1 CM 
 
 r^. 
 
 LO LO 
 
 UJ 
 
 O 
 
 co co co st en 
 
 (MCONCOO 
 
 CO CD CTl 
 
 CO 
 
 LOrHrJ-(M 
 
 r^ 
 
 CO t—l 
 
 1x1 
 
 Ixl 
 
 1— 1 CM CM CM CM 
 
 O CTl O CTl CTl 
 
 CTl CTl CO 
 
 St 
 
 CO CM CO CO *3- 
 
 LO CM 
 
 cc 
 
 O 
 
 i-H I— 1 1— 1 <— 1 1— 1 
 
 r-l i-H 
 
 
 
 
 
 t—l t—l 
 
 CD 
 
 Ixl 
 
 
 
 
 
 
 
 
 
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 co r-» co r-» en 
 
 LO LO O CM CO 
 
 CTl CTl CTl 
 
 CO 
 
 LO LO O CM 
 
 r^ 
 
 st r^ 
 
 Q 
 
 > 
 
 lOCOOlOO 
 
 OtOHNH 
 
 LO O O 
 
 r»% 
 
 i-H CTl r-H CTl 
 
 en 
 
 st O 
 
 
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 rv co a>co cti 
 
 r^. lo 00 lo lo 
 
 LO LO LO 
 
 CM 
 
 CM CM r-l 
 
 CM 
 
 CD CO 
 
 O 
 
 21 
 i— i 
 
 21 
 
 
 
 
 
 
 
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 CM CO O Cn CO 
 
 LO r-l 1— « O Ol 
 
 r-l CTl CO 
 
 LO 
 
 t—l O CTl CTl 
 
 r^ 
 
 CM CO 
 
 1— 
 
 1— 
 
 CM LO LO LO CM 
 
 I^LOCO NCVI 
 
 CTl CO sf 
 
 LO 
 
 CO i-H r-H 
 
 ■=3- 
 
 CO 
 
 «=t 
 
 C_) 
 
 CO CO St CO ^J" 
 
 CM CM CO CM CM 
 
 CM CM CM 
 
 
 
 
 LO LO 
 
 UJ 
 
 3: 
 
 CD 
 
 
 
 
 
 
 
 
 J— 
 
 co en lo co co 
 
 NCOHNfO 
 
 LO St *3" 
 
 
 
 0000 
 
 
 
 LO LO 
 
 _i 
 
 D_ 
 
 CTiCTllOOfO 
 
 LO CO CO LO CO 
 
 r-~ LO LO 
 
 
 
 
 co en 
 
 <c 
 
 Ixl 
 
 I— 1 «— 1 t— 1 
 
 
 
 
 
 
 CO t-H 
 
 I— 
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 CO 
 
 
 
 
 
 
 
 
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 O CTl i-HCTl CTl 
 
 O O LO O O 
 
 O CD CD 
 
 
 
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 LO CO 
 
 
 O 
 
 CO i-H 
 
 
 
 
 
 
 r-H LO 
 
 _i 
 
 ID 
 
 
 
 
 
 
 
 t—l 
 
 
 <C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a; 
 
 >- 
 
 O O CM O CM 
 
 OOOOO 
 
 CD O O 
 
 
 
 0000 
 
 
 
 CO CM 
 
 o 
 
 _1 
 
 r-H t— 1 
 
 
 
 
 
 
 r- t-H 
 
 21 
 
 zd 
 •~3 
 
 
 
 
 
 
 
 
 21 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 H- 1 
 
 
 
 
 
 
 
 
 
 1— 
 
 
 
 
 
 
 
 
 
 <=c 
 
 
 
 
 
 
 
 
 
 1— 
 
 
 
 
 
 
 
 
 
 00 
 
 
 
 
 
 LO 
 
 CU CU LO 
 
 
 
 
 
 
 SZ CO >> 
 
 >> 
 
 CD 
 
 as 
 
 CTl r— C 
 
 +-> 
 
 
 
 21 
 
 a> +-> 
 
 ro +-> 
 
 E C r- < 
 
 -1 — 
 
 3 S- ro 
 
 S- 
 
 
 
 <c 
 
 4-> C 'i- O 
 
 •1- •!- -O >- 
 
 O O ■— 21 
 
 L- 
 
 O "O (O CU 
 
 
 
 -a 
 
 
 
 OVr- CU O O 
 
 T3UC fO ^ 
 
 +-> -i-> -r- <; 
 
 Hd 
 
 or O -£= f— 
 
 a. 
 
 3 c 
 
 
 Ixl 
 
 E O 3 1— CO 
 
 i- 03 fO +■> O 
 
 CTl CJ> > l-H 
 
 c 
 
 O CD S- 
 
 cu 
 
 O ro 
 
 
 t— 
 
 •r- 2: cr x s- <; 
 
 O d) r- ^ -r O 
 
 C E L0 CO 
 
 ro 
 
 C S O 
 
 > Ixl 
 
 -Q r— 
 
 
 ■=c 
 
 «=C 
 
 r— zj zj a> co 
 
 u cj>-o a> -c i— 
 
 •r— •!— -r— l-H 
 
 X 
 
 O s- CU 
 
 CU 21 
 
 •r- +-> 
 
 
 I— 
 
 3 
 
 i- to .a +-> s 
 
 c -a o_ 21 
 
 > X 3 O 
 
 a> 
 
 4-> i- .*: 2 
 
 S_ >-* 
 
 s- $- 
 
 
 CO 
 
 O 
 
 zj cu n -i- A3 <C 
 
 O O -i- Ixl 
 
 O CU O O 
 
 
 ro 3 ro CU 
 
 -c < 
 
 ro O 
 
 
 
 I-H 
 
 CQQQ(/)3 ^Z 
 
 o o o h- 3: ^ 
 
 CJ> 1 1 _l 
 
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 cacQ_iz 
 
 LO 21 
 
 o_ 
 
13-22 
 
 Table 13-2 (Continued) 
 
 o 
 
 t=: 
 
 «^- «3- 
 
 t-H 
 
 CO CTl 
 
 r^-CMCMCTit— icnoor^co 
 
 LO 
 
 CO CM O O 
 
 co h^ r^ 
 
 I— 
 
 2: 
 
 ZO 
 OO 
 
 cn en 
 
 en 
 
 CO CO 
 
 ooencococncocooooo 
 
 CO 
 
 CO en en CTl 
 
 en cti cti 
 
 E 
 
 cnu_ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •I— O 
 
 +- 
 
 co r~- 
 
 CO 
 
 r-l t-H 
 
 LO^r^rHCMNOO^IM 
 
 CT. 
 
 en *3- r^ o 
 
 t-H O CO 
 
 co 
 
 2! 
 
 1—1 
 
 
 1 
 
 III 1 i-H 
 
 t-H 
 
 CM t-H t-H CM 
 
 CM CM CM 
 
 CD 
 
 1 — 1 
 
 
 
 
 1 
 
 1 
 
 1 1 1 1 
 
 
 o 
 
 3 
 
 
 
 
 
 
 
 
 
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 ■=* r-^ 
 
 CO *3" r-H 
 
 co en 
 
 COCMr-ir-^>^-CTiCOCOCO 
 
 
 
 CO CM LO CTl 
 
 en en i-H 
 
 
 ■a: 
 
 LO CO 
 
 co co en 
 
 r-^ co 
 
 Ococor^cTiOcncn«^- 
 
 
 
 ooocTirx 
 
 OO CO ^3" 
 
 
 ID 
 
 CO CD 
 
 CO CO CO 
 
 co en 
 
 LOCM<^t-0-)COCTlCOCOO 
 
 
 
 CO CO CM 00 
 
 CM CM O 
 
 
 s: 
 
 *d- lo 
 
 CO CO LO 
 
 r^ co 
 
 oococor--.cococococn 
 
 CD 
 
 CD CO CO CO 
 
 CM CM CM 
 
 
 7ZC 
 
 < 
 
 
 
 
 
 t — 1 
 
 t-H 
 
 
 UJ 
 
 O C\J 
 
 CT) CO CTl 
 
 LO CO 
 
 UDWCnOLOWNCOH 
 
 CO 
 
 >^1- 1— 1 CO LO 
 
 000 
 
 
 ^r: 
 
 t— 1 
 
 CO CO CM 
 
 r^~ 
 
 LO^LOCTlNCONNO 
 
 CTl 
 
 Ncocno 
 
 
 
 rD 
 
 
 I-H 
 
 t— 1 
 
 r— 1 1— 1 I-H CM 
 
 i-H 
 
 i-H t-H 
 
 
 
 r^ 
 
 r-«. co >=d- 
 
 co ^ 
 
 coococTiCTicooocnr^ 
 
 
 
 CO CO i-H CO 
 
 000 
 
 
 >- 
 
 Cn CM 
 
 UD CD CO 
 
 CM O 
 
 ^■(MLOHNNlflHN 
 
 CTl 
 
 ^1- CO O CM 
 
 
 
 2: 
 
 t-H 
 
 CM CM CO 
 
 CO CO 
 
 ^t-CM"=j-COCMCM*3-CO"^- 
 
 «3" 
 
 -=J- CM CO CO 
 
 
 . 
 
 r^ *h- 
 
 CTl CO r-H 
 
 O CM 
 
 r-~CMr^.cTiCTiCTii— i«^-o 
 
 
 
 CO t-H O CO 
 
 r^ i-H en 
 
 
 ct: 
 
 CM CO 
 
 NH CM 
 
 CO 1— 1 
 
 rvojrvco^Txrscri'H 
 
 «=J- 
 
 CM CM CO CO 
 
 CO CO CO 
 
 
 a. 
 
 CO 00 
 
 LO LO CO 
 
 CO CO 
 
 NLnNUjLncoNLOCo 
 
 00 
 
 CO CO CO CO 
 
 
 . 
 
 en 1— 1 
 
 CO CO CO 
 
 CO 00 
 
 OOCOCOCOt-Hi— INLON 
 
 LO 
 
 'H- CO CD t-H 
 
 O O CM 
 
 o 
 
 c£ 
 
 r-^ <h- 
 
 co ^j- en 
 
 co en 
 
 HfOOWHHCOWN 
 
 LO 
 
 1— 1 CO CO CM 
 
 r-H t-H CO 
 
 LO 
 
 <=C 
 
 co r~- 
 
 en co 00 
 
 en 
 
 CMCTiCMOOCDi— iCTiCM 
 
 CO 
 
 *HHM 
 
 CO CO CM 
 
 CO 
 <D 
 
 2: 
 
 
 
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 K 1 I 1 1 1 I 1 1 1 I— 1 1 1 
 
 r— 1 
 
 t— 1 1 — It — 1 r-H 
 
 
 . 
 
 O CO 
 
 CO CM i—l 
 
 CO CO 
 
 CncOCOCO^CMCOOO 
 
 co 
 
 i-H O CO LO 
 
 ^j- r-^ -^1- 
 
 Ml 
 
 CQ 
 
 CM f^- 
 
 LON>* 
 
 en cm 
 
 criLOcncricO"^-cooco 
 
 t-H 
 
 CM CO CO ^ 
 
 H t— 1 CO 
 
 <t> 
 
 UJ 
 
 CO CO 
 
 CD en en 
 
 t— 1 1—1 
 
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 LO 
 
 corona 
 
 <ht ^r co 
 
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 U_ 
 
 
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 1 — It — 1 I — 1 I — 1 1— 1 1 — 1 1 — 1 1 — 1 1 — 1 
 
 t-H 
 
 t-H t-H i-H t-H 
 
 
 . 
 
 CO LO 
 
 CO CO CM 
 
 CTt r-H 
 
 *3"r— (LOOCnCMt— ICTiLO 
 
 LO 
 
 CTi i-H CO CM 
 
 CO CO CM 
 
 00 
 
 2£ 
 
 CO CTl 
 
 r^. CO cti 
 
 CO r^. 
 
 OCO*d-OOLOCOr-HOCM 
 
 ■^t- 
 
 t-H CO CTi O 
 
 *3- «=1- t-H 
 
 >- 
 
 <C 
 
 en en 
 
 r-H CD <Ti 
 
 CO CM 
 
 *3- i— l^t-COCMCM-^-CMLO 
 
 r~^ 
 
 anoLor^ 
 
 LO LO LO 
 
 
 •"D 
 
 
 1— I 1— 1 
 
 r-H 1— 1 
 
 1 — 1 1 — 1 1 — 1 t — 1 <— 4 »— 1 r— IHt- 1 
 
 t— 1 
 
 i-H t-H r-H t-H 
 
 
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 LO LO 
 
 LO CO CO 
 
 1— I CM 
 
 cooDncviNfococorx 
 
 t-H 
 
 <d-«d-COO 
 
 CM CO CM 
 
 LjJ 
 
 O 
 
 O LO 
 
 co co en 
 
 co r^ 
 
 COCOCT11— i«^-cocococo 
 
 CO 
 
 CM LO CO CD 
 
 O i-H CO 
 
 LlJ 
 
 UJ 
 
 CT) CTl 
 
 O CT. CO 
 
 CM r-H 
 
 CMOCMCMr-H^HCMCDCO 
 
 LO 
 
 1^ «3" "H^ LO 
 
 LOLO<H- 
 
 CC 
 CJ3 
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 Q 
 
 
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 i-H i-H 
 
 1 — 1 1 — It— 1 1 — It— It— 1 1— It — It — 1 
 
 1 — 1 
 
 t-H t-H i-H t-H 
 
 
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 LO >=3- 
 
 O CO CO 
 
 r-l t^f- 
 
 CMCO<=J-CO*d-OOcaCM.-H 
 
 t-H 
 
 CD<* LO LO 
 
 lo en en 
 
 CD 
 
 > 
 
 00 CM 
 
 cnON 
 
 co r->. 
 
 i-HCOCM'3-CD'— ICOCOLO 
 
 CO 
 
 CO t-H O CO 
 
 HC1N 
 
 
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 LO CO 
 
 CO CO LO 
 
 co r^ 
 
 cnr^.cncocococTir^.cTi 
 
 t-H 
 
 CM CD O CD 
 
 CO CO CM 
 
 CD 
 i — i 
 
 2: 
 
 
 
 
 
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 i-H t-H t-H i-H 
 
 
 . 
 
 ^t r^ 
 
 <— 1 CO CM 
 
 ■=3- 
 
 ooaiLOtjHNOO 
 
 CM 
 
 t-H Lo >^r en 
 
 LO <— 1 CO 
 
 h- 
 
 H- 
 
 CO O 
 
 CO t-H CO 
 
 CM LO 
 
 COCOCOCOCOCOCMCDCO 
 
 CO 
 
 O O r^ <^- 
 
 CO CO LO 
 
 ■=£ 
 
 CD 
 
 CM CO 
 
 CO CO CO 
 
 LO <H/- 
 
 LOCOLO"=3-"^-<3-LO"=l-LO 
 
 CO 
 
 r^« 10 «3- lo 
 
 
 LU 
 
 DC 
 
 O 
 
 
 
 
 
 
 
 
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 CO CO 
 
 CO O CO 
 
 CTl I>^ 
 
 COr-^-COCTiLOCOOOCTi 
 
 
 
 co en co lo 
 
 CD O O 
 
 _l 
 
 a. 
 
 «=}• CO 
 
 CD co en 
 
 H ■=d- 
 
 r^cO'st-LOcocO'tojr^ 
 
 CO 
 
 CO 00 CO CM 
 
 
 ■=c 
 
 UJ 
 
 
 t-H 
 
 CM r-H 
 
 CM C^HHHCMHM 
 
 CO 
 
 CO t-H r-H CM 
 
 
 o 
 
 c/o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 • 
 
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 cm en cm 
 
 CTl >>1- 
 
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 CT) 
 
 CVIHrJ-N 
 
 000 
 
 
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 CM CM 
 
 LO CO 
 
 O CO^fCMCMCX)CMO 
 
 
 
 HfOfO^f 
 
 
 _J 
 
 =D 
 
 
 
 
 t-H t-H 
 
 i-H 
 
 t-H 
 
 
 2: 
 
 <C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o; 
 
 >- 
 
 O O 
 
 O CM 
 
 LO CO 
 
 coocTicocncQcncMco 
 
 t-H 
 
 t-H CM LO CO 
 
 000 
 
 CD 
 
 _i 
 
 
 1—1 
 
 CM 
 
 CO LO i-H LO t-H CTl 
 
 r^ 
 
 r^ CM CM CM 
 
 
 s: 
 
 ZD 
 •~3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 co 
 
 
 
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 r— 
 
 
 
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 1 — 
 
 
 
 1 — 1 
 
 
 
 
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 fO 
 
 
 
 h- 
 
 
 
 
 •r— 
 
 
 u_ 
 
 
 
 •< 
 
 
 >> 
 
 
 S- 
 
 
 
 
 
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 OO 
 
 CO 
 
 
 >> (O 
 
 
 r— 
 
 
 
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 JD 
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 4-> CO 21 
 
 •I- -0 
 
 
 e co -a 1— 1 
 
 
 
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 UJ 
 
 
 •a 
 
 CD t- 
 
 
 O T- ^ Q- 
 
 
 
 7Z^ 
 
 CD -^ CO 
 
 1— 4-> 
 
 r— S_ 
 
 Q. CD CD cC 
 
 
 •1- 1 — s- a. 
 
 CO 
 
 
 «=c 
 
 CD 
 
 $- O ZD 
 
 f— CD 
 
 CD CD ^ 
 
 (0 (0 +-> c +-> 1— 
 
 
 4-> O CD 1 — l-H 
 
 E S- 
 
 
 
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 O -i- DT 
 
 •r- -S^ 
 
 •1- +J <c 
 
 4-> JD CC CT<+-> O OO O 
 
 
 n3 Q.+J U 00 
 
 e ta zs 
 
 
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 <c 
 
 E S- 
 
 zn e 
 
 4- co CD 
 
 fO -r- f0 C CD CD OO 
 
 sz 
 
 E fO CO OO 
 
 O •«- JD 
 
 
 h- 
 
 _1 
 
 •r- a) car 
 
 =3 
 
 CO CD l-H 
 
 EOE4->T3T-rjCD4-> UJ 
 
 4-> 
 
 S- CD CD +-> 1— 1 
 
 CO "O CO 
 
 
 <t 
 
 >- 
 
 +-> "O CO 
 
 CD +-> +-> 
 
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 CD S- n3 E E CO CT-^ 1 — 21 
 
 ^ 
 
 CD E JZ E OO 
 
 JXi •!- JSli 
 
 
 r- 
 
 CC 
 
 1— CD CO 
 
 n co e 
 
 +•> S- CD 
 
 CL+JOT-fOES-CO^ Z 
 
 1 — 
 
 +-> E O •!- OO 
 
 O S- 
 
 
 00 
 
 <: 
 
 fO s- «=C 
 
 1 — O «3 
 
 •r— O *—* 
 
 1 — CDcOi — S. (O (O 3 O i-h 
 
 Z5 
 
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 fO CD •!- 
 
 
 
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 coll 2: 
 
 CQCQZQ.3 21 
 
 <qluu.cd_js:s:lo ~sl 
 
 CD 
 
 i-H 2: cc 00 2: 
 
 n 2: > 
 
13-23 
 
 Table 13-2 (Continued) 
 
 ! o 
 
 K 
 
 is 
 
 ONU3 N 
 
 <3" tO I— 1 T— 1 
 
 O CO 
 
 r^ cm 
 
 00 cd r^ h% r*. to 
 
 >^r 
 
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 CO <* rs 
 
 1— 
 
 2: 
 
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 cn en cn 
 
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 0~> Oi Cn CT> 
 
 en 00 
 
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 cn cd en cn cn cn 
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 cn 
 
 cn 
 
 o en cn 
 ■ — i 
 
 c 
 
 CT)U_ 
 •1— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
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 cm 
 
 <^- iHI^slf) 
 
 O LO O CM 
 
 is r~- 
 
 en r-» 
 
 tO >^- i—l to LO CO 
 
 rr> 
 
 to 
 
 CO CM r-H 
 
 10 
 
 SZ 
 
 
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 i—l CM CM CM 
 
 1— 1 1 
 
 1—1 1 
 
 1 1 i-H 1 1 1 
 
 I— 1 
 
 i 
 
 CM t-H 
 
 Co 
 
 ►— i 
 
 
 
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 1 
 
 1 
 
 1 
 
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 3 
 
 
 
 
 
 
 
 
 
 
 
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 to 
 
 HtJ-OH 
 
 C7HOOO 
 
 en 1—1 
 
 CO LO 
 
 O rj- CD ^ OJ CO LO 
 
 CO 
 
 CO 
 
 en cm r-i 
 
 
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 1— 1 CO O to 
 
 ^1" CT> LO O 
 
 cm en 
 
 CM CM 
 
 CO tD fv CO rH I-x CVJ 
 
 CO 
 
 CO 
 
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 ID 
 
 
 
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 i-H i—l 
 
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 lo co en to to to >^- 
 
 ■si- 
 
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 rs co is 
 
 
 sz 
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 LO 
 
 <3- LO ^ «3- 
 
 ts CO rs CO 
 
 00 co 
 
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 to lo to to to to r^ 
 
 rs 
 
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 CM tO LO 
 
 
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 CM 
 
 O LO LO tO 
 
 CM O tO CM 
 
 lo r-«. 
 
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 LO O CO N CVJ Lf) r| 
 
 CM 
 
 LO 
 
 o cn co 
 
 
 sz 
 
 1— 1 
 
 r-H i—l 
 
 O LO 00 to 
 
 en 
 
 en 1—1 
 
 ^j- co «^- lo <^- r~-- 00 
 
 en 
 
 CM 
 
 co lo 
 
 
 
 
 
 
 1— 1 1—1 1— I i—l 
 
 r-H CM 
 
 CM 
 
 
 i-H, CM 
 
 i-H, i-H 
 
 
 r— 1 
 
 Cn CO r— 1 LO 
 
 LO LO «3" CO 
 
 1— 1 r-^ 
 
 tO r-H 
 
 r-H r-H CO CO 00 LO CO 
 
 cn 
 
 to 
 
 to IS CO 
 
 
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 CM 
 
 O CO CM O 
 
 CO CO 00 CO 
 
 00 en 
 
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 o 
 
 LO 
 
 LO tO 
 
 
 < 
 
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 1— 1 T— 1 I— 1 I— t 
 
 CM CO CO CO 
 
 CO CO 
 
 CM CO 
 
 CM r-l CM CM CM CM CM 
 
 •^r 
 
 •^r 
 
 CO CO 
 
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 <*C0WH 
 
 OCOWN 
 
 i—i en 
 
 Cn r-H 
 
 cm cm 00 cn lo cm en 
 
 <— i 
 
 CM 
 
 r-H O CO 
 
 
 ct 
 
 CM 
 
 cn «=*■ i—t cn 
 
 rs ^- >vt- lo 
 
 LO CO 
 
 r-^ CM 
 
 to cn 1— i to lo r^ 
 
 CM 
 
 IS 
 
 r-H I-H IS 
 
 
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 CM CO CO CM 
 
 lo to to to 
 
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 LO tO 
 
 <3- <H- ^J- LO ^3" LO LO 
 
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 i— 1 LO LO 
 
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 to cm cn >^r- o 
 
 osnn 
 
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 lo cn is. 
 
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 or 
 
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 rs CO LO CO ^T CM 
 
 lo r^ 
 
 CO CO CO (O CO CM rj- 
 
 r-H 
 
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 CO CM CO 
 
 lo 
 
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 CO 
 
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 co cn oo rs 
 
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 CM CM tO OO 
 
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 CO 1— < 
 
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 CO CO CM 
 
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 CO 
 
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 1— 1 co r-i rs lo co cn 
 
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 lo cn to rs 
 
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 CM tO "3" LO LO CO IS 
 
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 i— i cm cn 
 
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 T-l«5* 
 
 CM r-H 
 
 t— i r-H rs o is cn co 
 
 t-H CM 
 
 CO o to 
 
 1— 
 
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 CM CO LO CM 
 
 COO^Cft 
 
 O LO 
 
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 co o cn >^t- lo lo cn 
 
 to 
 
 cn 
 
 rs en co 
 
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 CD 
 
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 CM CM CM CM 
 
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 CO CO CO «H- co «3- -=d- 
 
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 a* O O LO 
 
 to 00 to 
 
 -3" T-H 
 
 «d- CO 
 
 00 LO i-H CO LO CO LO 
 
 LO 
 
 ■stf- 
 
 o ^- o 
 
 _i 
 
 Q_ 
 
 LO 
 
 COVOU)^- 
 
 co is lo o 
 
 en cm 
 
 1^ O 
 
 CD IS i-H CM CD CO tO 
 
 CM 
 
 CO 
 
 CD i-h 
 
 <C 
 
 UJ 
 
 
 
 i—l CM CM CO 
 
 CM CO 
 
 i-H CO 
 
 r-H i— 1 i— • r— 1 i— 1 i-H 
 
 CXI 
 
 CO 
 
 CM CM 
 
 t— 
 o 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 • 
 
 CD 
 
 O LO O O 
 
 lo rs co oo 
 
 en en 
 
 to <3- 
 
 tO tO O tO CM O CM 
 
 «H- 
 
 CO 
 
 ONrt 
 
 
 
 
 
 
 I— 1 *H" LO LO 
 
 lo en 
 
 r-^ 
 
 r-H r-H 
 
 co «^ 
 
 CO CO 
 
 _l 
 
 rzj 
 
 
 
 
 
 
 
 
 
 
 2: 
 
 <C 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CtZ 
 
 >- 
 
 O 
 
 OOOO 
 
 tO i-H 00 00 
 
 i-H 
 
 to <^- 
 
 o o cn cd o cd cn 
 
 cn 
 
 CO 
 
 O CO CD 
 
 O 
 
 _i 
 
 
 
 CO CM CM 
 
 CO LO 
 
 co 
 
 
 
 CM 
 
 <3" 
 
 SZ 
 
 ZD 
 
 ■"3 
 
 
 
 
 
 
 
 
 
 
 SZ 
 O 
 1 — 1 
 
 I— 
 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 CO 
 
 
 -O 
 
 to 
 
 
 
 T3 CO 
 
 c: +-> q- 
 
 
 
 
 
 Q 
 
 
 JZ r — 
 
 1 — 
 
 
 >> 
 
 <a +J 4- 
 
 
 
 fO 
 
 
 SZ 
 
 
 
 Q. tO CO 
 
 r— 
 
 1 — 
 
 +-> 
 
 •— fO ZZ CO 
 
 
 
 CO O 
 
 
 •a: 
 
 r— i 
 
 fO 
 
 CO -i- T- 
 
 co ra 
 
 I— 
 
 •r- fO «=C 
 
 tO r— l— c 
 
 
 
 tO O 
 
 
 
 oi 
 
 •1 — 
 
 00 3 4- ct 
 
 CD 3 u_ 
 
 CO 
 
 Or— ^. 
 
 t— i C -^ Q_ JD •■- 
 
 
 
 co rs 
 
 
 UJ 
 
 i ID 
 
 -O 
 
 oo o o cn sz 
 
 c: 
 
 fO 0. 
 
 =3 CO 
 
 ■ — i — oo +-> <C 
 
 
 
 CO £ 
 
 
 h— 
 
 O 
 
 £ 
 
 1X3 r D —1 C CC 
 
 •1- CJ>+-> CO 
 
 c: to 
 
 00 <C 
 
 -OOO-£=r0+->C CD 
 
 
 
 >* CO 
 
 
 <c 
 
 CO 
 
 3 
 
 00 -i- 1— 
 
 1 — 00 ra S- 
 
 CO -r- 
 
 CO 00 CC 
 
 ccj*4-+->jz+->aj <c 
 
 o 
 
 
 o c 
 
 
 r— 
 
 CO 
 
 1 — 
 
 c . . s_ sz 
 
 r— CD CO > 
 
 1— r— 
 
 1 — tO CQ 
 
 fdcs_s-f0Or— >« 
 
 ^e 
 
 >> 
 
 00 c c 
 
 
 CO 
 
 1— 1 
 
 
 
 (0+J4J a 
 
 •1- 1 — S- ro 
 
 <D (O 
 
 •r- T- UJ 
 
 S- v- o O £ U fO LU 
 
 i — 
 
 
 re CO •!— 
 
 
 
 2: 
 
 
 
 ^i co co co 2: 
 
 on cd re 
 
 -C ^ 
 
 2! 21 2= 
 
 O-J^ZOCO^* SI 
 
 LU 
 
 LU 
 
 _J Cd zs. 
 
13-24 
 
 Table 13-2 (Continued) 
 
 o 
 
 G 
 
 I— 1 
 
 r-H 
 
 *3- CM 
 
 CO CM i-i LO 
 
 rH 1— 1 O ^f r-H CO <— 1 O O 
 
 I— 
 
 2: 
 
 ID 
 
 CT> 
 
 Cn 
 
 cn cn 
 
 o> cn 
 l-H 
 
 cncTt o>(Ticy>cncncncn 
 
 c 
 cnu_ 
 
 co 
 
 
 
 
 
 
 
 
 
 
 
 
 •l— o 
 
 4- 
 
 1—1 
 
 ■^f 
 
 i— 1 CM 
 
 «3" CM CD «3- 
 
 t-HCM U5 H N CVJ CJ in CM 
 
 co 
 
 21 
 
 r-H 
 
 1— 1 
 
 i— 1 1— i 
 
 r- 1 1 1 — 1 1 — 1 
 
 1 1 l-H r-H l-H II 
 
 QJ 
 
 M 
 
 1 
 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 _1 
 
 ro r^» 
 
 C\J 
 
 cn 
 
 00 CO CO CO LO 
 
 LOCO«— ICM«— ICT>«— ICOOCO 
 
 
 <=£ 
 
 00 «— 1 
 
 r-H 
 
 LO 00 
 
 •vf lo cm cn 
 
 NOOUHONHH^-Ulin 
 
 
 ZD 
 
 CO 00 
 
 CO 00 cn 
 
 fOHCMNN 
 
 COCVKJOOOPJOONlflN 
 
 
 21 
 
 i^n. co 
 
 *d- 
 
 «* «3- 
 
 «3" LO CO CO CO 
 
 coi s >«cor^'^-LO'=d-cococD 
 
 
 21 
 
 1— 1 
 
 
 
 
 
 LU 
 
 LO CO 
 
 LO 
 
 O CM 
 
 O i—l CO O 
 
 LOCnLOOOC7>CMCOOOOLO 
 
 
 21 
 
 r->. 
 
 i-H 
 
 i— 1 
 
 CM CD 
 
 «3-cn«3-r^ t— • "=^-co^- 
 
 
 •"3 
 
 CD 
 
 
 
 
 
 
 00 
 
 CO 
 
 00 «-• 
 
 nnHi-irs 
 
 cnncricncorv^-cnr- ico 
 
 
 >- 
 
 CT> CO 
 
 CO 
 
 t-H CM 
 
 00 00 O CO 00 
 
 nHwcMHiowisH^- 
 
 
 2: 
 
 CM C71 
 
 T-H 
 
 t— 1 t— 1 
 
 .-1 CO 
 
 CMCOCMCOi— 1 i— It- ICMCMCM 
 
 . 
 
 CD O 
 
 
 
 t— i cn 
 
 co cn co i-H «— 1 
 
 •=a-LncoLOooo«^-r^-coo 
 
 
 or 
 
 CO CO 
 
 C\J 
 
 00 en 
 
 CO CM <3" O CO 
 
 io«t«t<^oco<Hcn«tiN 
 
 
 O- 
 
 CD CM 
 
 «fr 
 
 CO CO 
 
 CM ^- LO CM CM 
 
 LOCOLOCO«^-«^-"5d-LOLOLO 
 
 
 < 
 
 t— 1 
 
 
 
 
 
 . 
 
 CM CM 
 
 t— 1 
 
 CT> CO 
 
 inrs^-HH 
 
 CMLOCnC3^0LOO'^-0«^- 
 
 o 
 
 o; 
 
 CO LO 
 
 «3- 
 
 CM LO 
 
 cn «3- co 00 co 
 
 Cn<^<T010iHinrHhvO 
 
 LO 
 
 <: 
 
 O CD 
 
 r-^ 
 
 r^ r-*. 
 
 lo r-. co ^ lo 
 
 cnocnor^cor^ocno 
 
 10 
 
 2: 
 
 l-H .—1 
 
 
 
 
 i—l i—l r— 1 i— 1 
 
 . 
 
 «^- CO 
 
 00 
 
 CO LO 
 
 CO CM «3- ■— 1 LO 
 
 VO«vl-i— ILOLOLOCTlCOi— IO 
 
 CO 
 
 CO 
 
 CO CD 
 
 «a- r>^ co 
 
 O i-H >^- 
 
 LOLO00«^-C0COr^CMCO«a- 
 
 (O 
 
 LU 
 
 1— 1 CO 
 
 CO 
 
 CO CO 
 
 r^» co cn co co 
 
 t— It— IOi— 1 CO CT> CO i- It— <T— 1 
 
 an 
 
 Ll_ 
 
 i—l l-H 
 
 
 
 
 t— 1 I—l I—l i—l i— 1 t— 1 i— 1 
 
 . 
 
 CO O 
 
 CD 
 
 co cn 
 
 O CD CO O »-H 
 
 HNOvoiocncotfOi-i 
 
 co 
 
 "^ 
 
 LO CM 
 
 CO 
 
 CO CO 
 
 cocOiH^tcn 
 
 iHNcnincocvjNcocoN 
 
 >- 
 
 < 
 
 CO CO 
 
 cn 
 
 en cn 
 
 cn cn 1— i co r>» 
 
 COCMi-HCMCftOCncMCMCM 
 
 Q 
 
 <r> 
 
 i— 1 t— 1 
 
 
 
 t— 1 
 
 i— It— It— It— 1 i— 1 i— 1 i— It— 1 
 
 . 
 
 O CM 
 
 
 
 r-H «3- 
 
 00 cn 00 co cn 
 
 ^■<*Nioc\jcoNincrtco 
 
 LlI 
 
 
 
 <3- *a- 
 
 CO 
 
 CM CM 
 
 CO CT» «3" O CM 
 
 CnCOOLOOCOCOCMLOLO 
 
 Ixl 
 
 LU 
 
 c\i r». 
 
 CO 
 
 cn cn 
 
 COCOOOON 
 
 i— It— It— It— iCnCnCOt— It— li—l 
 
 a: 
 
 CD 
 Ul 
 
 O 
 
 t— 1 r-H 
 
 
 
 1— 1 
 
 i— 1 1— 1 1— i i— i i— i r— i t— i 
 
 . 
 
 CM t-l 
 
 cn 
 
 CO CO 
 
 CM CT» LO CO LO 
 
 NOCVJNO^OOMO 1 * 
 
 Q 
 
 > 
 
 CM «^- 
 
 "* 
 
 r^ 1^. 
 
 <tO)WNCM 
 
 r^t— icor^^i-cocM«3-LO«3- 
 
 
 O 
 
 CO CO 
 
 LO 
 
 LO LO 
 
 CO CD 00 LO LO 
 
 NCONNLDiniONNN 
 
 CD 
 
 21 
 
 I— 1 
 
 
 
 
 
 i— • 
 
 . 
 
 lo r>- 
 
 i— 1 
 
 00 -53- 
 
 cn 1-1 cm co 
 
 Ot-ICOOCOCOCOLOCMLO 
 
 J— 
 
 \— 
 
 O LO 
 
 LO 
 
 «3- CO 
 
 CM .-1 CO O CO 
 
 i!l-NO'!tfO , *MHCMH 
 
 ■=t 
 
 O 
 
 LO O 
 
 C\J 
 
 CM CM 
 
 CM CO «3" CM iH 
 
 "=3-«^-<tf-«53-CMCMCM'3-«vt-«^- 
 
 Ul 
 
 3C 
 
 O 
 
 1— ( 
 
 
 
 
 
 1— 
 
 r^» 
 
 en 
 
 r^ 
 
 CM CO CO CO CO 
 
 COHHHOlOMOriM 
 
 _J 
 
 Q_ 
 
 r^ cm 
 
 CO 
 
 CO LO 
 
 1— 1 CO CM «— 1 
 
 COO«^-«^-COCOCMCMCMCO 
 
 <c 
 
 LU 
 
 f-n r^ 
 
 
 
 i—l 
 
 T-l CM i— 1 i—l i—l i-H i—l 
 
 b- 
 O 
 
 »— 
 
 CO 
 
 
 
 
 
 
 . 
 
 10 
 
 
 
 
 
 O CD 00 O O 
 
 cnincONOOOHCvjoo 
 
 
 CD 
 
 LO CO 
 
 
 
 CM 
 
 t— 1 CO CM CO CO CM CM 
 
 _J 
 
 rD 
 
 LO 
 
 
 
 
 
 21 
 
 err 
 
 < 
 
 
 
 
 
 
 >- 
 
 co co 
 
 
 
 
 
 O O D» O O 
 
 ocMOcnooocnoco 
 
 o 
 
 __i 
 
 a\ 
 
 
 
 
 CM t-l 
 
 
 ID 
 
 «3- 
 
 
 
 
 
 ■21 
 O 
 
 
 
 
 
 
 
 1— t 
 
 
 
 
 
 • 
 
 
 »— 
 
 • 
 
 
 
 
 ^ — ^^ — ^ r— 
 
 
 «t 
 
 >» 
 
 
 
 
 o_ o +-> 
 
 
 1— 
 
 LU 
 
 co 
 
 >> 
 
 
 
 <C o_ c 
 
 
 CO 
 
 CC 
 
 XI 
 
 +J 
 
 
 
 ' J^ l-H 
 
 
 
 1— 1 
 
 
 
 •r— 
 
 
 <U >> 
 
 s- >> 
 
 
 O 
 
 •X. 
 
 >- 
 
 O 
 
 
 
 3 ■(-> 
 
 c c as >, ea "o 
 
 
 21 
 
 CO 
 
 LU 
 
 
 
 
 cr •■- 
 
 O O O- ~o t- J- (0 
 
 
 <C 
 
 D_ 
 
 -C CO 
 
 O 
 
 l-H 
 
 i. :*£ 
 
 +■> +-» <u -a cu +-> <u 
 
 
 
 21 
 
 T3 W CC 
 
 •I— 
 
 C X 
 
 CO C r— CC 
 
 EEOr— C S.P U W 
 
 
 LU 
 
 < 
 
 S- f0 LU 
 
 +-> 
 
 -i<£ O LU 
 
 3 O 1— J- O 
 
 >,irj its. — ig c to in qi 3 
 
 
 1— 
 
 re 
 
 03 rs 
 
 c 
 
 s- +-> 2: 
 
 cr+J c cu >- 
 
 E^Z-C<OS-CU3CUCO 
 
 
 «=c 
 
 
 u 
 
 f0 
 
 to c 
 
 3 >> O 2 > 
 
 to cn a)4- ■»-> i^ CD -c: cu to 
 
 
 1— 
 
 3 
 
 C • IS 
 
 
 5 a> 3 
 
 X) fa -i-> co 1 — 3 
 
 -Ctc:c:4-c ox:s- 
 
 
 CO 
 
 LU 
 
 O 4-> LU 
 
 4J 
 
 CD i- LU 
 
 1 — r— (0 O t— LU 
 
 r— 1- 't- 3 CU U- (O O O >> 
 
 
 
 21 
 
 OS! 21 
 
 < 2: 1— z: 
 
 ca: c_) q: cm co 2: 
 
 <CCQCQ00C_> r -0_JC£:cOCO 
 
13-25 
 
 Table 13-2 (Continued) 
 
 o 
 
 e 
 
 t— 1 
 
 LO 
 
 ^f LO *H- "3" 
 
 LO CO CM «d" 
 
 CT> 
 
 ^H- i-H CM CM 
 
 i-H CM CM CT) 
 
 CD CM 
 
 1— 
 
 2: 
 
 cn 
 
 CT> 
 
 lti cr> cr> en 
 
 CTl CTl CTl CTl 
 
 CO 
 
 CTl CTl CTl CTi 
 
 CTl CT) CTl 00 
 
 O O 
 l-H r-H 
 
 E 
 
 cnu. 
 
 to 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •I— o 
 
 +- 
 
 00 
 
 00 
 
 •^•Loro'v)- 
 
 <jTOMH 
 
 1 — 1 
 
 CO CM CM O 
 
 1— 1 ^J" i-H 1— 1 
 
 r-H CM 
 
 to 
 
 -zr. 
 
 t— t 
 
 t— 1 
 
 r— 1 I— 1 CM i-H 
 
 CM CM CM CM 
 
 
 
 
 r-H r-H 
 
 CD 
 
 i— i 
 
 
 
 
 1 1 1 1 
 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 
 
 
 _I 
 
 CM 
 
 CM t-H 
 
 LO CO r-. LO 
 
 r— 1 1— 1 LO CO 
 
 I\ 
 
 LO i-H O CM 
 
 co lo ^j- r— 
 
 LO O 
 
 
 <: 
 
 «d- 
 
 r— 1 CT> 
 
 oa> ^|- en 
 
 LO O CM «3" 
 
 CO 
 
 O LO LO CM 
 
 O CTl CTl r-H 
 
 CM LO 
 
 
 rD 
 
 
 
 LO i—< 
 
 CO CO CO LO 
 
 CO CTl CM CM 
 
 
 
 CO CO LO LO 
 
 'd- r^ «=j- -vi- 
 
 r-- 00 
 
 
 2: 
 
 ■=3- 
 
 cm ro 
 
 CO CO CM CO 
 
 00 CTl CTl CTl 
 
 LO 
 
 ^H- LO LO LO 
 
 LO LO LO LO 
 
 CO CO 
 
 
 UJ 
 
 
 
 
 
 OOOO 
 
 t^ CO CTl i-H 
 
 CTi 
 
 CTi lo r^ O 
 
 O LO O O 
 
 
 
 
 ^ 
 
 
 
 
 i-H CO CTl «3" 
 
 CO 
 
 LO CM CO 
 
 LO CO LO LO 
 
 
 
 
 
 
 
 
 1— 1 r-H i-H 
 
 
 
 
 
 
 "-a 
 
 
 
 
 
 
 
 
 
 
 r-«. 
 
 LO C\J 
 
 r-^ ^d- r^. 
 
 CTl <— 1 CM r^ 
 
 CM 
 
 co 1—1 r*- 
 
 LO CO CM 00 
 
 «d- r-~ 
 
 
 >- 
 
 CO 
 
 C\J CM 
 
 "Zt CO CO 
 
 CM 00 CO LO 
 
 
 
 1 — 1 lo r**. lo 
 
 =Cf CTi «* ^ 
 
 CO "3" 
 
 
 2: 
 
 
 
 
 CO CO CO CO 
 
 CM 
 
 t-H CM i-H i-H 
 
 CM r-H CM CM 
 
 
 . 
 
 ro 
 
 r-» lo 
 
 ^O^DN 
 
 LO CO CD i-H 
 
 CT. 
 
 LO CM LO CTi 
 
 CO LO CO O 
 
 CTi CO 
 
 
 C£ 
 
 r-^ 
 
 h*. lo 
 
 co co en 
 
 ^3- LO CTl 00 
 
 00 
 
 CO LO CM CM 
 
 "=d" CTi «d" «d" 
 
 CO r-H 
 
 
 a. 
 
 C\J 
 
 t— 1 1— 1 
 
 CM r-H CM 
 
 lo r-> lo lo 
 
 «* 
 
 CO LO <3" "3- 
 
 LO rJ-LO LO 
 
 r-H CM 
 
 . 
 
 CM 
 
 r-H 
 
 CMNrv<t 
 
 CO LO CM CO 
 
 i-H 
 
 t— 1 co cn en 
 
 <*CO^rH 
 
 r-^ cti 
 
 o 
 
 cc 
 
 en 
 
 «=*• CO 
 
 LO CO LO CM 
 
 O ^J" LO LO 
 
 r^ 
 
 Oi-hOOCMLOCMCM 
 
 CM CO 
 
 lo 
 
 < 
 
 in 
 
 «^- «=d- 
 
 LO =3- CO LO 
 
 CM CO CM CM 
 
 00 
 
 r-> cti co co 
 
 CTi CO CTl CTl 
 
 LO LO 
 
 LO 
 
 2: 
 
 
 
 
 t— 1 1 1 1 1 T— 1 
 
 
 
 
 
 . 
 
 ro 
 
 00 C\J 
 
 CM LO CM CM 
 
 CM CTl O CO 
 
 LO 
 
 r^. r^» cn lo 
 
 CM r-H lo r^ 
 
 «d- CO 
 
 to 
 
 OQ 
 
 CO 
 
 r-H CO 
 
 NrHkOLO 
 
 <t NWN 
 
 i-H 
 
 co ^1- <3- 10 
 
 <3- CTl LO «H- 
 
 LO CO 
 
 rO 
 
 UJ 
 
 LO 
 
 LO LO 
 
 LO LO ^ LO 
 
 ^f LO LO «=J- 
 
 
 
 CO O CTi CTl 
 
 ocnoo 
 
 LO LO 
 
 CO 
 
 U_ 
 
 
 
 
 i—l i-H i-H «— 1 
 
 <— 1 
 
 i-H 
 
 r-H i-H r-H 
 
 
 . 
 
 «^- 
 
 O t-H 
 
 ^H- LO LO CO 
 
 00 CM CTi 00 
 
 co 
 
 CTi co r-^ 
 
 CTi r-^ cn 
 
 co co 
 
 co 
 
 2: 
 
 co 
 
 CO CTl 
 
 00 CM ^ LO 
 
 ONCOLO 
 
 CO 
 
 r^ 10 od cn 
 
 LO O O LO 
 
 lo cn 
 
 >- 
 
 •=c 
 
 r^. 
 
 LO LO 
 
 NNLDN 
 
 1^ cor^N 
 
 i-H 
 
 CTl i-H 
 
 r— 1 1— 1 CM r—t 
 
 CO CO 
 
 O 
 
 •"D 
 
 
 
 
 1 — 1 1 — 1 i-H 1 — 1 
 
 i-H 
 
 i-H i-H i-H 
 
 r-H i-H r-H t-H 
 
 
 . 
 
 to 
 
 l-H t-H 
 
 COLO rHN 
 
 CO ^ CTi CO 
 
 
 
 i-H CO CTi LO 
 
 ONCO<* 
 
 lo r^. 
 
 U4 
 
 C_) 
 
 r^ 
 
 CM CTi 
 
 r» 1-1 cm *3- 
 
 LO CO LO 1— 1 
 
 1^. 
 
 CM CO CO <3" 
 
 r-H CO CO 
 
 LO CO 
 
 LjJ 
 
 UJ 
 
 r->. 
 
 LO LO 
 
 NNinN 
 
 ^- LO LO LO 
 
 
 
 cn 
 
 i-H O r-H r-H 
 
 r-~ r^. 
 
 cc 
 o 
 
 UJ 
 
 O 
 
 
 
 
 1 — 1 i-H i-H 1 — 1 
 
 1— i 
 
 1 — 1 1— 1 1 — 1 
 
 i — 1 r-H i-H 1 — 1 
 
 
 . 
 
 LO 
 
 noononn 
 
 cohncj 
 
 LO CM 00 «^" LO 
 
 COrJ-CVJrH 
 
 CO CM 
 
 Q 
 
 > 
 
 LO 
 
 r^ ro 
 
 r-H LO CTl 00 
 
 CO CTl O CM 
 
 CM 
 
 i-H CO t-h CTl 
 
 lo 00 cn r^» 
 
 CTl CM 
 
 
 
 
 LO 
 
 CM «3" 
 
 LO "=3" CM *3- 
 
 O i-H i-H i-H 
 
 r^ 
 
 lo r^r^ lo 
 
 NIONN 
 
 <=J- LO 
 
 1 o 
 
 l-H 
 
 2: 
 
 
 
 
 i— 1 i — 1 1— 1 1 — 1 
 
 
 
 
 
 . 
 
 LO 
 
 00 "^" CM «3- "^J- i-H 
 
 r^ cm «^r i-H 
 
 1 — 1 
 
 00 «si- r^. 
 
 r~~ co lo cm 
 
 ■^- CO 
 
 1— 
 
 t— 
 
 *3" 
 
 r^. cm 
 
 cr» lo r-^ r*«. 
 
 r-^ ^- r^ 
 
 co 
 
 ■sl-OO^H 
 
 CTl r-H O r-H 
 
 LO LO 
 
 <: 
 
 CJ 
 
 OO 
 
 1— 1 
 
 r— 1 1— 1 »— 1 
 
 LO LO LO LO 
 
 CO 
 
 CM CO CO CO 
 
 nrorj-rj- 
 
 r-H 1— t 
 
 UJ 
 
 DC 
 
 
 
 
 
 
 
 
 
 
 
 r— 
 
 CO 
 
 O LO 
 
 CO t— 1 O r-H 
 
 CM CO CT> r-H 
 
 LO 
 
 «=3- LO «^J- CO 
 
 ^LONO 
 
 LO CO 
 
 _l 
 
 Q. 
 
 *3- 
 
 
 CO CM CM 
 
 CVlNrHlD 
 
 CTi 
 
 lo 00 r^ 
 
 r— 1 LO r-H CM 
 
 r-H r-H 
 
 <c 
 
 UJ 
 
 
 
 
 CM CM CM CM 
 
 
 i-H 
 
 r-H r-H i-H 
 
 
 t— 
 
 co 
 
 
 
 
 
 
 
 
 
 o 
 t— 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 O O 
 
 OOOO 
 
 CO co r^. CO 
 
 CTl 
 
 O LO LO LO 
 
 CM LO LO CTl 
 
 O O 
 
 
 to 
 
 
 
 
 MLoro^- 
 
 
 CM 
 
 CM r-H r-H 
 
 
 _i 
 
 ID 
 
 
 
 
 
 
 
 
 
 <c 
 
 <C 
 
 
 
 
 
 
 
 
 
 2: 
 ct: 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 
 
 O O 
 
 OOOO 
 
 "tOOOH 
 
 O 
 
 O CT. O O 
 
 CTl O O LO 
 
 O O 
 
 o 
 
 —i 
 
 
 
 
 CO <3r CM CO 
 
 
 
 
 
 z 
 
 :d 
 
 •"3 
 
 
 
 
 
 
 
 
 
 
 2T 
 
 
 
 
 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 
 
 I— 1 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 
 
 
 
 
 
 
 
 
 <; 
 
 «=C 
 
 
 
 
 
 
 
 
 
 
 t— 
 
 ^ 
 
 
 </) 
 
 E 
 
 
 
 
 
 >) 
 
 
 CO 
 
 1 — 1 
 
 _1 
 
 
 <T3 
 
 CD <C 
 
 1— J— 
 
 CD 
 
 
 
 
 -»-> 
 
 
 Q 
 
 
 
 
 O) 
 
 e to 
 
 jx: 
 
 
 •r— 
 
 c 
 
 O 
 
 
 2: 
 
 cc 
 
 a) 
 
 4-> 0) 
 
 s- CO ^ 
 
 (0 c 
 
 
 4-> "a 
 
 -a 3 
 
 
 
 <c 
 
 «=c 
 
 1 — 
 
 +-> +J 
 
 O +-> cC 
 
 -i<i _i 
 
 
 lO C l/l 
 
 r— >, O <C 
 
 re 
 
 
 
 
 
 1 — 
 
 CO +-> 
 
 XIX D)C O 
 
 O 4-> 
 
 
 E (O Z3 
 
 CD -^ +-> S 
 
 E 
 
 
 UJ 
 
 
 •r— 
 
 ac 
 
 W QIC O 
 
 i_ L0 LO 
 
 
 C r— JD C 
 
 •r— LO O LO O 
 
 
 
 
 1— 
 
 in 
 
 > 
 
 r— 
 
 E •.- •!- ■+-> DC 
 
 (Oi — ••- 
 
 sz 
 
 •r- CD E O 
 
 >r- 3tj 01 n: 
 
 -E ro 
 
 
 <=c 
 
 1— 
 
 CD 
 
 CD i- 
 
 0) <U E O r— 
 
 E -r- ct»i— 
 
 
 
 O > =3 +-> 
 
 to TD CD E <C 
 
 CO LO 
 
 
 1— 
 
 cc 
 
 -E 
 
 Q. 03 
 
 a) 1— 1— c c£ 
 
 LO > S- 1 l-H 
 
 S- 
 
 C CD r— >, 
 
 E £Z 1— 3 _J 
 
 r— r— 
 
 
 CO 
 
 
 
 LO 
 
 ro jt 
 
 S- 03 1- -r- O 
 
 •1- cd to •!- =n 
 
 jx: 
 
 •1- r— <a 
 
 n3 rrj O O ^ 
 
 -^ 3 
 
 
 
 *£Z 
 
 =3; 
 
 0000:33 s 
 
 □a u_ 3: 
 
 <C 
 
 C_> O <_) Q 
 
 s: CO H- >- O 
 
 O 1— 
 
13-26 
 
 Table 13-2 (Continued) 
 
 o 
 
 t=s 
 
 CT> 
 
 r-H CONH 
 
 CO 
 
 CM 
 
 CM CO 
 
 CM CO O 
 
 CM CTl r-i 
 
 CTi 
 
 LO 00 CO LO LO 
 
 h- 
 
 21 
 
 ZD 
 CO 
 
 r-^ 
 
 CT) CTl CTi CTl 
 
 en 
 
 en 
 
 CTi CO 
 
 CTl CTi CTl 
 
 CTi CO CTi 
 
 00 
 
 CTl CTl CTi CTi CTi 
 
 c 
 
 
 
 
 
 
 
 
 
 
 cnu_ 
 
 
 
 
 
 
 
 
 
 
 
 •«— o 
 
 +- 
 
 r^. 
 
 CM 1— 1 ro CO 
 
 LO 
 
 1— 1 
 
 co r-» 
 
 en r-i r-^ 
 
 CO CM r-« 
 
 CD 
 
 CO O r-t CTi CO 
 
 to 
 
 21 
 
 CM 
 
 CM CM CM 
 
 CM 
 
 CM 
 
 
 r-H 
 
 
 
 CM CM CM t-H r-H 
 
 CD 
 
 ►—I 
 
 
 
 
 
 
 
 
 
 
 O. 
 
 3: 
 
 
 
 
 
 
 
 
 
 
 
 _i 
 
 CD r-» 
 
 CD <^r CO r-» LO 
 
 1— 1 
 
 «3- «^- 
 
 CD r-H 
 
 r-H r-t r~v 
 
 LO «* -vj- 
 
 «d- ^1- 
 
 ro ^- r^ ^f ^h- 
 
 
 =3: 
 
 00 LO 
 
 cm r^ cm ro 
 
 CTi 
 
 LO CM 
 
 r-H LO 
 
 LO O 00 
 
 ■ct inn 
 
 O LO 
 
 co co 00 co r-* 
 
 
 o 
 
 r-H CTi 
 
 1^ CO O r-H CD 
 
 «rj- 
 
 N LO 
 
 CO ^3- CM r-H en 
 
 CTi CM CTi 
 
 CO CTi 
 
 O <=f CO CO 
 
 
 21 
 21 
 < 
 
 LO CD 
 
 <d-Ninmn 
 
 «* 
 
 ^ CO 
 
 LO CO 
 
 LO LO LO 
 
 «* CO LO 
 
 LO LO 
 
 CM CM CM CM CO 
 
 
 UJ 
 
 i— 1 r^ 
 
 LO CTl CO CO LO 
 
 ro ^1- en 
 
 «* O 
 
 CM CM CTi 
 
 CD CO "^1- 
 
 CTl r-H 
 
 00000 
 
 
 21 
 
 ro r^ 
 
 co co r^. co 
 
 CM 
 
 **■ r-« 
 
 CM CD 
 
 r-H r-H CO 
 
 CO CM 
 
 CTi LO 
 
 
 
 
 
 •"3 
 
 C\J T-H 
 
 «-h ro i—i 
 
 <— 1 
 
 r-H CM 
 
 
 
 
 
 
 
 CO CD 
 
 en r^ cm lo lo 
 
 hs 
 
 CO LO 
 
 P^ CO 
 
 ■^- LO LO 
 
 lo lo r^ 
 
 "3- CO 
 
 O O O CM LO 
 
 
 >- 
 
 CO CD 
 
 r^. cm *rj- >vt- 
 
 CO 
 
 K CD 
 
 CD CO 
 
 cm i-h en 
 
 OCTIN 
 
 «3- CO 
 
 r-H CM 
 
 
 
 CO CO 
 
 CM LO CM CM CM 
 
 CM 
 
 CM «3" 
 
 r-H CM 
 
 
 
 CO CM 
 
 
 . 
 
 
 
 CD CD CM CO CD 
 
 LO 
 
 r-. en 
 
 r-H LO 
 
 CO CD 
 
 CM OD CO 
 
 CM «=J- 
 
 «vf- r-H «^- O «3" 
 
 
 C£ 
 
 CO r^ cm c\J 00 en en 
 
 O 
 
 <— 1 CD 
 
 I-- CO 
 
 en en co 
 
 r^ en CD 
 
 i-H CO 
 
 LO CO CO CM >^- 
 
 
 
 <5l- LO 
 
 ^i-N«troco 
 
 ">»■ 
 
 ^J- CD 
 
 ^" LO 
 
 co ro 1^- 
 
 ro *d- "=d- 
 
 CO LO 
 
 1— 1 r-H 
 
 . 
 
 CO CD 
 
 CTl CO CM 1-^ CD 
 
 O 
 
 r-H CO 
 
 en co 
 
 CO ^j- *3- 
 
 lo ro co 
 
 1""-. 00 
 
 HNN^CO 
 
 o 
 
 cc 
 
 ro LO 
 
 COCOtHCON 
 
 I— 1 r-H 
 
 «3- r-^ 
 
 co «3- r^- 
 
 ro en LO 
 
 r^ co 
 
 CTi LO «3" CO LO 
 
 lo 
 
 < 
 
 CO CO 
 
 lo cr> co co lo 
 
 LO 
 
 CD CO 
 
 CO CTi 
 
 r-* r^ CO 
 
 r-^ co 00 
 
 00 00 
 
 CM CO CO «3* "=3" 
 
 CO 
 
 CD 
 
 2: 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CM CO 
 
 Kin tv.ro«^- 
 
 00 r->. en 
 
 CM r-H 
 
 NOW 
 
 LO CO CM 
 
 LO 00 
 
 cn en lo 
 
 </> 
 
 QQ 
 
 CM CO 
 
 NOO^Nt 
 
 
 
 •^- O 
 
 O CO 
 
 en 
 
 CO CM O 
 
 LO CO 
 
 CO K. LO CO CO 
 
 ro 
 
 UJ 
 
 to cr 
 
 CD O CD r-^ CO 
 
 CO 
 
 CD CO 
 
 O O 
 
 en co 
 
 CO 
 
 CTi CTi 
 
 CO «3" «d" LO LO 
 
 ca 
 
 U_ 
 
 
 t— 1 
 
 
 
 r-H r-H 
 
 r-H 
 
 r-H r-H 
 
 
 
 
 . 
 
 CO CD 
 
 co en co r-^ lo 
 
 CO 
 
 CM CO 
 
 CD CTl 
 
 LO «^- CTi 
 
 1— 1 CD CM 
 
 O O 
 
 NOCMCOOO 
 
 CO 
 
 21 
 
 LO «tf" 
 
 O O i— i r-H CM 
 
 CO 
 
 CM LO 
 
 r-H CD -=j- H r-l 
 
 O LO CM 
 
 CM 1—1 
 
 co r^. lo >^- to 
 
 >- 
 
 «c 
 
 r- cm 
 
 CO CM CTi CD CO 
 
 r-- 
 
 CO CTi 
 
 r-H r-H O O r-H 
 
 O r-H r-H 
 
 O r-H 
 
 «^J- LO LO CO CO 
 
 
 ■"D 
 
 1 — 1 
 
 r— 1 r— 1 
 
 
 
 r-H r-H 
 
 r-H r— 1 t—4 
 
 t— 1 r— 1 1— 1 
 
 1— 1 r-H 
 
 
 . 
 
 cr> ro 
 
 CTi t—1 r-l ^- LO 
 
 ro 
 
 en «rj- 
 
 LO CO 
 
 CM «=d" CO 
 
 CTi ^ CO 
 
 CM CO 
 
 HNOJION 
 
 LU 
 
 O 
 
 K r-H 
 
 1— 1 cti r^. co ro 
 
 ■ — 1 
 
 cm r^» 
 
 «3" CD 
 
 CTi VD CO 
 
 co r-» 
 
 O CM 
 
 Nrvinro to 
 
 UJ 
 
 UJ 
 
 VD 1—1 
 
 NOCOOON 
 
 h» 
 
 r-, co 
 
 O O 
 
 en en 
 
 Ol HO 
 
 CTi O 
 
 *H- LO LO tO CD 
 
 cc 
 
 o 
 
 o 
 
 1 — 1 
 
 r-t 
 
 
 
 r-H r-H 
 
 r-H 
 
 r-H r-H 
 
 r-H 
 
 
 . 
 
 i-H r-». 
 
 lococOi— ir-^r-»>rH-to 
 
 CO «3- 
 
 CO r-H tO 
 
 Nt\IN 
 
 "3" O 
 
 MLOIONN 
 
 Q 
 
 > 
 
 CO CO 
 
 00 t— 1 r^ t— 1 en 
 
 CO 
 
 en CD 
 
 CTi i-H 
 
 *3- CM CM 
 
 CTl tD r— 1 
 
 CTi CO 
 
 CO«*HC0H 
 
 
 O 
 
 LO CO 
 
 LO CTi co r^ LO 
 
 LO 
 
 LO CD 
 
 co r-» 
 
 to co r>> 
 
 mNN 
 
 LO CO 
 
 CM CO CO CO ■=d- 
 
 CD 
 
 ■21 
 
 
 
 
 
 
 
 
 
 
 i— i 
 
 . 
 
 LO LO 
 
 CO O CM O LO 
 
 en 
 
 00 ro 
 
 CO i-H 
 
 CO «-H LO 
 
 r-» *3- lo 
 
 r^ cm 
 
 CTi «3- CO CM O 
 
 I— 
 
 t— 
 
 r-^ i-» 
 
 lOCONlDfO 
 
 CM 
 
 ro >^- 
 
 LO CTi 
 
 en en r^ 
 
 lo co r-^ 
 
 O r-^ 
 
 LO CO r^. r-H CO 
 
 <: 
 
 O 
 
 ro LO 
 
 CO LO CO CO CO 
 
 ro 
 
 co «3- 
 
 ro ro 
 
 CM CM ro 
 
 cm ^3- ro 
 
 CO CO 
 
 r-H r-H 
 
 UJ 
 
 O 
 
 
 
 
 
 
 
 
 
 
 DZ 
 
 h- 
 
 O CD en CO CO H «rj- 
 
 LO 
 
 r-H r-H 
 
 CD CM 
 
 ro lo 
 
 «=1- CM r-l 
 
 00 CD 
 
 O O O O LO 
 
 _I 
 
 o_ 
 
 T-H <— 1 
 
 MODNHH 
 
 O 
 
 r-H r^. 
 
 CTi O CO CD CD 
 
 LO CO r-H 
 
 (->. en 
 
 r-H 
 
 <c 
 
 UJ 
 
 CM CM 
 
 r— i CM r- 1 i— t 
 
 1 — 1 
 
 1— 1 r-H 
 
 r-H 
 
 1—1 
 
 r-H r-H 
 
 
 
 1— 
 
 CD 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CD r-- >h- *rj- CD CD CO 
 
 co 
 
 r-H r-H 
 
 O LO 
 
 O CD CTi 
 
 en en 
 
 CO CD 
 
 OOOOO 
 
 
 CD 
 
 CO CO 
 
 CO CM CM 
 
 r-H 
 
 CO CO 
 
 CM 
 
 
 r-H 
 
 l—l r-H 
 
 
 —I 
 
 ZD 
 
 I-H 
 
 1— 1 
 
 
 
 
 
 
 
 
 CC 
 
 ■=£ 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 CO CM 
 
 •=H- «rj- O O LO 
 
 CM 
 
 1^ r-H 
 
 CD O 
 
 000 
 
 OOO 
 
 O O 
 
 OOOOO 
 
 o 
 
 _1 
 
 "^J- T-H 
 
 CO CO CM 
 
 CM 
 
 CO CO 
 
 
 
 
 
 
 21 
 
 "-D 
 
 t— 1 
 
 
 
 
 
 
 
 
 
 ■21 
 
 1— 1 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 «c 
 
 
 
 
 
 
 
 
 < 
 
 
 
 1— 
 
 
 
 
 +-> 
 
 
 
 
 21 
 
 
 
 CO 
 
 
 
 
 •r- <C 
 E *" H 
 
 
 ro 
 
 •1 — 
 
 4-> O. 
 
 i. 21 
 
 T3 r-H 
 
 en 
 
 
 Q 
 
 
 
 
 E 21 
 
 
 cn-c .c: 
 
 O < 
 
 ro a> 
 
 c ai s_ 
 
 
 21 
 
 
 E 
 
 
 =J <C 
 
 c 
 
 s- a. en 
 
 o_ _1 
 
 1 — U CC 
 
 O r— Z3 
 
 
 <X. 
 
 
 ~a 
 
 en 
 
 CO > 
 
 2 
 
 3 r— S_ 
 
 C </) CO 
 
 V) C <C 
 
 +-> ro CU 1 — JD 
 
 
 
 rO 
 
 E -a 4-> c 
 
 s_ 
 
 _J 
 
 O 
 
 J3 Q) 3 
 
 CD O (O 1 — • 
 
 r- 1 <D O 
 
 to -i- •!- c: 
 
 
 UJ 
 
 21 
 
 •!■" 
 
 a> ro i- a> ro 
 
 =3 
 
 c >- 
 
 +-> 
 
 to TD -Q 
 
 C 4-> E 
 
 "O 
 
 CU JD C > ro 
 
 
 1— 
 
 O 
 
 s- to 
 
 C -C O r— r— 
 
 -Q 
 
 E O co 
 
 c 
 
 •1— ro to 
 
 •r- C -r- UJ 
 
 .*: •■- =n 
 
 p- E <u c+> 
 
 
 «=t 
 
 CD 
 
 c 
 
 cu <+- -0 +-> 
 
 CD 
 
 CU +-> 21 
 
 cu a> 
 
 S- r— 4-> 
 
 XI ro r— O 
 
 CJ > 1— 
 
 i. D i. Q) i. 
 
 
 h- 
 
 UJ 
 
 +-> s- 
 
 D1IOT3 C C. 
 
 CO 
 
 r— X 21 
 
 1 — *r™ 
 
 S_ •(- 4-> 
 
 ro i- r— O 
 
 OO ZD 
 
 ro 1 — O CD ro 
 
 
 CO 
 
 CC 
 
 tn 3 
 
 zs a> <u a> 
 
 O 
 
 (t) (U LU 
 
 1— s- 
 
 hjj:t- 
 
 tl) O •■- HZ 
 
 1— S- CD 
 
 SZ O r— i_ Q. 
 
 
 
 O 
 
 <01UJ22Q.D. 
 
 CC 
 
 CO CO o_ 
 
 <X. UJ 
 
 IQ.Q. 
 
 CC CO 3 cc 
 
 CO Q. CO 
 
 O O U_ CD CO 
 
 
13-27 
 
 Table 13-2 (Continued) 
 
 o 
 
 t=! 
 
 r-» to to 
 
 CVJ 
 
 nlo con 
 
 <— i CO 
 
 t— 1 
 
 «^- LO i— I O 
 
 CM i-H tO CO 
 
 CD 
 
 o 
 
 >* r-H 
 
 CD CO 
 
 i-H CO 
 
 1— 
 
 s 
 
 cd cd CT> 
 
 CD 
 
 CTl CTl CTl CTl 
 
 o en 
 
 o 
 
 CD CD O O 
 
 O CD CD O 
 
 CD 
 
 o 
 
 CD O 
 
 CD CD 
 
 o o 
 
 
 O 
 
 
 
 
 I—l 
 
 r— 1 
 
 1—1 1— 1 
 
 I— 1 1—1 
 
 
 1—1 
 
 I— 1 
 
 
 1—1 1—1 
 
 E 
 
 cnu_ 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •l— o 
 
 +- 
 
 CO CD <3" 
 
 1 — 1 
 
 LO CO N CM 
 
 r^ co 
 
 LO 
 
 tO CM CD i— 1 
 
 O CM CD CM 
 
 i-H 
 
 CD 
 
 CD O 
 
 lo co 
 
 i—l LO 
 
 CO 
 
 CD 
 
 Q 
 
 21 
 
 l—l 1 i— 1 
 
 T— 1 
 
 I — 1 1 — 1 1 — 1 1 — 1 
 
 1—1 
 
 CM 
 
 CO CO r-H CM 
 
 CM CO CM CO 
 
 I—l 
 
 I—l 
 
 CM CM 
 
 CM CM 
 
 CM i-H 
 
 rs 
 
 1 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _j 
 
 co lo cd 
 
 CO 
 
 tt^tOJCON 
 
 «^f- to 
 
 1— 1 
 
 o^-no 
 
 lo lo to r^ co 
 
 1 — 1 
 
 r^ io 
 
 CD CO 
 
 O CM 
 
 
 < 
 
 c\j >^t- n 
 
 «* 
 
 to CTi co r^ i—i 
 
 CM CO 
 
 <— 1 
 
 O i— I to o 
 
 CD CO CD CD 
 
 r^. 
 
 CD 
 
 >^J- LO 
 
 ■3- N 
 
 CO CO 
 
 
 ZD 
 
 C\J CO 00 
 
 r— 1 
 
 CM >^- CM tO 00 
 
 tO CT 
 
 r«<. 
 
 to cd co r^ 
 
 <d-wroN 
 
 LO 
 
 LT) 
 
 «^- CM 
 
 LO i-H 
 
 O CO 
 
 
 21 
 21 
 
 cor^rN 
 
 >* 
 
 CO CO CO CO CO 
 
 CM CO 
 
 1—1 
 
 CM CM 
 
 CM i-H i-H 
 
 co 
 
 CM 
 
 i-H CM 
 
 1— 1 1— 1 
 
 CM CM 
 
 
 UJ 
 
 r^ to co 
 
 o 
 
 ooooo 
 
 o o 
 
 o 
 
 o o o o 
 
 o o o o 
 
 o 
 
 o 
 
 O CD 
 
 o o 
 
 CD CD 
 
 
 21 
 
 co cvj r~- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ZD 
 
 i— i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 co to o 
 
 00 
 
 to CO CM o to 
 
 O to 
 
 o 
 
 o o to o 
 
 o o o o 
 
 1 — 1 
 
 o 
 
 o o 
 
 o o 
 
 o to 
 
 
 >- 
 
 co cm r-^ 
 
 to 
 
 CM ^d- CM ^1- to 
 
 to 
 
 
 
 
 CO 
 
 
 
 
 
 
 
 CM CO Cxi 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 o to CO 
 
 I — 1 
 
 OCO NCTiCO 
 
 «3" CM 
 
 r-H 
 
 o o o lo 
 
 CD O to O 
 
 <— 1 
 
 o 
 
 CD tO 
 
 CD i—l 
 
 tO CD 
 
 
 cd 
 
 o i— i r^ 
 
 to 
 
 to CTi ^r CO CM 
 
 i-H LO 
 
 LO 
 
 CD O 
 
 CD CO CO 
 
 o 
 
 CD 
 
 CO to 
 
 CO CM 
 
 CO CM 
 
 
 
 to to to 
 
 CM 
 
 i— 1 i— 1 i— 1 i-H CM 
 
 i— 1 CM 
 
 
 1— 1 
 
 
 CM 
 
 
 
 
 i—l 
 
 . 
 
 tO ■— t C\J 
 
 CO 
 
 CO CO tO CM CM 
 
 r^ to 
 
 CO ^j- CTi CTi CD 
 
 CD CD CM <3" 
 
 ■vT CM 
 
 CM 00 
 
 LO CM 
 
 O CO 
 
 o 
 
 cc 
 
 CM CO CO 
 
 CTl 
 
 LO CTi LO i-H tO 
 
 ■=3- "=3- 
 
 CM 
 
 1^. O i— i i— i 
 
 rHCOC^N 
 
 00 
 
 CM 
 
 CD CO 
 
 CD LO 
 
 r^. r->. 
 
 to 
 
 < 
 
 i-i o o 
 
 to 
 
 ^j- <3- ^j- to to 
 
 CO LO 
 
 CM 
 
 i-H CO CO 
 
 CO i-H i-H 
 
 "=^- 
 
 CO 
 
 i-H CM 
 
 i—l i—l 
 
 CM CO 
 
 CO 
 CD 
 
 si 
 
 1— 1 I— 1 1— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 to to to 
 
 o 
 
 r-» co to «^r en 
 
 O «3" 
 
 LO 
 
 ta^-OLo 
 
 CO CO CO «3" CO 
 
 CO 
 
 <* CM 
 
 to O 
 
 CD CO 
 
 to 
 
 OQ 
 
 to «3" CO 
 
 o 
 
 r-» i-i co "^ to 
 
 r-» to 
 
 CM 
 
 ON^-^1- 
 
 ^d- LO CO CO 
 
 . — 1 
 
 to 
 
 r^ i-H 
 
 CO CO 
 
 00 i—l 
 
 ro 
 
 UJ 
 
 CO i— 1 CM 
 
 h*. 
 
 to to to to to 
 
 ■vt- to 
 
 CO 
 
 t— 1 I— 1 <^" "vj" 
 
 «3- CM CM r-l 
 
 to 
 
 ■3- 
 
 CM ■^- 
 
 CM CM 
 
 CO LO 
 
 CQ 
 
 U. 
 
 1— 1 1 — 1 1— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO CO <3" 
 
 CO 
 
 CM CM CTi CO 00 
 
 cm r«» 
 
 CO 
 
 LO i— 1 i— 1 LO 
 
 <tO"*N 
 
 o 
 
 ^-1 
 
 •^- r-- 
 
 co -=^- 
 
 to CO 
 
 co 
 
 21 
 
 oj ro>* 
 
 CM 
 
 CM0OC0NN 
 
 ■^1- N 
 
 to 
 
 O CD O 00 
 
 •— 1 LO CO tO 
 
 o 
 
 LO 
 
 CO to 
 
 CM «3- 
 
 CO CD 
 
 >- 
 
 <t 
 
 to CO to 
 
 co 
 
 r-^ n n r^ r->. 
 
 to CO 
 
 <3- 
 
 CM CM tO CO 
 
 tO CO CO CM 
 
 CO 
 
 to 
 
 CO LO 
 
 «^" CO 
 
 LO to 
 
 < 
 
 •"3 
 
 I— 1 I— 1 T— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CM CM i— 1 
 
 CO 
 
 CO tO CO CM CM 
 
 to r^ 
 
 CO 
 
 CD O *3- CO 
 
 aONSit 
 
 CM 
 
 CD tO 
 
 CO O 
 
 tO CM 
 
 UJ 
 
 CD 
 
 co r^ to 
 
 CM 
 
 CTi CM CTi co r^ 
 
 CO CTi 
 
 CO ^" CM CM >=3- 
 
 ONOH 
 
 ■^1- 
 
 CD 
 
 CM CO 
 
 to r^ 
 
 LO CO 
 
 Ul 
 
 UJ 
 
 *d- i—i co 
 
 CO 
 
 l£)N(£)NN 
 
 LO r^. 
 
 co 
 
 i—l CM LO tO 
 
 LO CM CO CM 
 
 r-~ 
 
 LO 
 
 CO LO 
 
 CO CM 
 
 <^- to 
 
 o 
 
 Q 
 
 1—1 1—1 1—1 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 <3- r^ cm 
 
 CO 
 
 oo CTi r^ to i— • 
 
 to o 
 
 LO 
 
 tOOi-H«vl-«3-COCOtO 
 
 CO 
 
 r-H 
 
 1-^ CO 
 
 N o 
 
 O i-H 
 
 Q 
 
 > 
 
 rHCTllv. 
 
 r*. 
 
 to co ^r en co 
 
 to 1^. 
 
 CM 
 
 tO CM CM i—l 
 
 CM CO CO O 
 
 1 — 1 
 
 co 
 
 O i-H 
 
 O LO 
 
 N CO 
 
 
 O 
 
 o co cd 
 
 LO 
 
 «3- ^- •* ^J- to 
 
 CO LO 
 
 CM 
 
 i— 1 CO >^T 
 
 CO i—l r-H r-H 
 
 LO 
 
 CO 
 
 CM CO 
 
 CM i-H 
 
 CM CO 
 
 21 
 i— i 
 
 21 
 
 i— 1 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CO r-l CM 
 
 to 
 
 CO i-H O CO CM 
 
 CTi LO 
 
 i-H 
 
 OOCM^LOOtQO 
 
 <3- 
 
 r^ 
 
 CM CO 
 
 i-H tO 
 
 CO CD 
 
 1— 
 
 I— 
 
 O CO to 
 
 CO 
 
 >vt- r^» co to CTi 
 
 CTi CD 
 
 CO 
 
 to CO 
 
 to 
 
 r^ co 
 
 CM tO 
 
 CO 
 
 ■=3- CD 
 
 <c 
 
 O 
 
 to «=j- ^r 
 
 CM 
 
 i—l i-H »—l i— 1 i—l 
 
 CM 
 
 
 
 
 1—1 
 
 
 
 
 
 UJ 
 
 re 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1— 
 
 LO to CO 
 
 1 — 1 
 
 CO O CO O CTi 
 
 O CO 
 
 o 
 
 o o o o 
 
 o o o o 
 
 co 
 
 o 
 
 o o 
 
 o o 
 
 O O 
 
 _i 
 
 o_ 
 
 to to to 
 
 en 
 
 r— I CO i-H CO CO 
 
 1—1 
 
 
 
 
 r— 1 
 
 
 
 
 
 <c 
 
 UJ 
 
 i— 1 i-H i-H 
 
 
 
 
 
 
 
 
 
 
 
 
 i— 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 CM CM LO 
 i-H i—l CM 
 
 o 
 
 ooooo 
 
 O CD 
 
 o 
 
 o o o o 
 
 o o o o 
 
 o 
 
 o 
 
 o o 
 
 o o 
 
 O O 
 
 _J 
 
 ID 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 < 
 
 
 
 
 
 
 
 
 
 
 
 
 
 >- 
 
 tr> cm cd 
 
 o 
 
 o o o o o 
 
 o o 
 
 o 
 
 o o o o 
 
 o o o o 
 
 o 
 
 o 
 
 o o 
 
 o o 
 
 O O 
 
 o 
 
 _l 
 
 CM i-H 
 
 
 
 
 
 
 
 
 
 
 
 
 21 
 
 ZD 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■21 
 O 
 i— i 
 
 1— 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 
 
 . — » 
 
 
 
 •!— 
 
 
 
 
 
 
 
 
 1— 
 
 
 
 o 
 
 
 
 +-> 
 
 
 
 
 
 
 to 
 
 
 CO 
 
 < 
 1— 
 
 to 
 
 
 o 
 
 fO 
 
 
 
 co 
 
 CD •<- 
 
 
 
 
 S- 
 
 o 
 
 ^ 
 
 
 o 
 
 O 
 
 >><— 
 
 
 CT/ 
 
 
 
 i— S- 
 
 JZ. 
 
 
 
 3 O 
 
 
 CO 
 
 
 21 
 
 ^. 
 
 +-> i — UJ 
 
 
 O CD CD CD 
 
 
 
 l JC 
 
 +J E 
 
 
 
 -E , — 
 
 E 
 
 u. 
 
 
 <c 
 
 =a: 
 
 •i- CO UJ 
 
 
 O ■— r— CD 
 
 o 
 
 
 •r- O 
 
 i- o 
 
 
 
 4-> CD 
 
 O CO 
 
 
 
 
 Q 
 
 O U_ CO 
 
 r— 
 
 E i — tO i — "O 
 
 CD i— 
 
 
 > o 
 
 o +-> c: 
 
 -^. 
 
 -o 
 
 S_ CTl+J -r- 
 
 CO 
 
 
 UJ 
 
 
 CO 
 
 o 
 
 CO T— *r— •!■■ •!"■ 
 
 e i — 
 
 c 
 
 to to to CO 
 
 3 to O o 
 
 u 
 
 E <C 
 
 E i- 
 
 +-> 
 
 
 I— 
 
 zc 
 
 e -o x uj 
 
 4-> 
 
 +-> > JE > CC CO 
 
 CD t- 
 
 •1 — 
 
 a zi ro ro 
 
 CD +-> "O 
 
 o 
 
 fO 
 
 <<o 
 
 •r" 
 
 
 «=c 
 
 1— 
 
 O •!- ZJ 21 
 
 to 
 
 +J x Q..E «a: 
 
 1— $- 
 
 +-> 
 
 3 O-r— 0_ 
 
 -M > to CD 
 
 JD 
 
 , — 
 
 4-> 
 
 +J 
 
 O -E 
 
 
 1— 
 
 =5 
 
 i- D_ O 21 
 
 •r— 
 
 co O E to ^L X 
 
 •r- A3 
 
 to 
 
 O S- i— 
 
 S- i— Z3 S- 
 
 JD 
 
 T3 
 
 J_ E 
 
 E O 
 
 U O 
 
 
 CO 
 
 o 
 
 =3 fO •■- Ul 
 
 i~ 
 
 .e E QJ CO CO Ul 
 
 -Q E 
 
 Z3 
 
 S- O CO i— 
 
 O co O CO 
 
 13 
 
 • 1 — 
 
 O rtJ 
 
 CO -i- 
 
 CO •«- 
 
 
 
 CO 
 
 re ca co h- 
 
 ca <^> ^i si2i o t— 
 
 <<<CQOQLU 
 
 U.OI-J 
 
 - J 
 
 s 
 
 Q- CO 
 
 co > 
 
 3 3 
 
13-28 
 
 Table 13-2 (Continued) 
 
 o 
 
 K 
 
 
 r^ 
 
 CO 
 
 «3" "3" CO ^ 
 
 lo cm lo ro 
 
 00 *s- 
 
 cm r-^ lo ro 
 
 I— 
 
 ZD 
 CO 
 
 
 en 
 
 CO 
 
 cn en en en 
 
 co co co en 
 
 cn en 
 
 en co en en 
 
 enLi_ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •i— o 
 
 +- 
 
 
 LO 
 
 CM 
 
 LO «* LO 
 
 1— 1 ro cm 
 
 CM CO 
 
 en t—i 00 
 
 CO 
 
 21 
 
 
 
 1—1 
 
 r-H CM T-H i— 1 
 
 CM CM CM 1 
 
 1—1 
 
 i-H 
 
 <u 
 
 *— i 
 
 
 
 1 
 
 
 
 
 
 Q 
 
 3 
 
 
 
 
 
 
 
 
 
 _1 
 
 r>. 
 
 CNJ CO 
 
 en 
 
 0>U)HlflO^ 
 
 co *d- 00 lo lo ro en 
 
 LO t-H 
 
 CO LO CO <3- 
 
 
 >=C 
 
 CT> 
 
 10 r^ 
 
 CO 
 
 r^. CO CM CO LO CM 
 
 cm cm ro «3- LO CO i-l 
 
 O <3" 
 
 (--. 1-^ «^- LO 
 
 
 CD 
 
 *3- 
 
 r^ 
 
 CM 
 
 CM 1— 1 «3" CO ■—! CM 
 
 ro -vj- co i— 1 co cm r~» 
 
 co en 
 
 «=t co «vT r-^ 
 
 
 21 
 21 
 
 CO 
 
 CO *H- 
 
 CO 
 
 ro ^- ro ro «^t- «=t- 
 
 lo «j- >^- lo co en lo 
 
 «=t LO 
 
 ^d- lo «^- ^f 
 
 LU 
 
 r-^ 
 
 «* r-i 
 
 
 
 000000 
 
 r-^ r-^ en en 10 ro ro 
 
 lo en 
 
 cn 00 cm co 
 
 
 21 
 
 00 
 
 CO CO 
 
 en 
 
 
 r^ r^ en 10 ro co co 
 
 «3" CO 
 
 «^- I-H 
 
 
 zd 
 
 
 
 
 
 
 1— 1 1— 1 1— 1 1— « >vj- ro 
 
 
 
 
 en 
 
 ro r-» 
 
 CO 
 
 ro co r^ ro lo <* 
 
 r*» cm cm lo 00 ^- t-H 
 
 r^ 
 
 co 00 en lo 
 
 
 >- 
 
 r-^ 
 
 co r^ 
 
 LO 
 
 LO r-^ ro lo co r-~. 
 
 ^3- sj- en co lo ro 
 
 r^ cm 
 
 en en en t-h 
 
 
 1? 
 
 CM 
 
 CM t-H 
 
 ro 
 
 
 ro CM CM CM CM CO *d" 
 
 i-H CM 
 
 i-H i-H 
 
 . 
 
 CTl 
 
 en co 
 
 «=* 
 
 co r-^ co en 1— t 00 
 
 O CO 1— 1 Sj" •— 1 LO LO 
 
 CM LO 
 
 cd <3- ^- en 
 
 
 ct: 
 
 i— t 
 
 LO 
 
 t— 1 
 
 «^- CO i—l i—l CO CO 
 
 lo en 1— i r^ ro lo cm 
 
 *d- ro 
 
 ro ^ en ro 
 
 
 
 Lf) ^t ^t- 
 
 r-^ 
 
 CM CM CM CM CM CM 
 
 ^t- ro «tf- i* 10 00 10 
 
 ro «=j- 
 
 ro ^- cm ro 
 
 . 
 
 C\J 
 
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Worksheet HL-1 
 Sheet 1 of 2 
 
 Building Heat Load Calculations 
 
 Job 
 
 Computed by 
 Location 
 
 meter 
 
 Number 
 
 Date 
 
 Latituc 
 
 °F 
 
 op 
 
 °F 
 
 Width 
 Width 
 ft 
 
 of Occupants 
 le 
 
 Indoor temperature, T R 
 
 Design winter outdoor temperature, 
 
 Design temperature difference 
 
 Building Dimensions: 
 Above Grade: Length ft 
 Below Grade: Length ft 
 
 Concrete Floor Slab: Exposed peri 
 
 Exterior Wall Area: 
 
 ft 
 ft 
 
 Ceiling Ht. 1 
 Depth ft 
 
 
 Window Area: 
 
 
 Door Area: 
 
 
 Net Exterior Wall 
 
 Area: 
 
 Ceiling Area: 
 
 
 Floor Area: 
 
 
 Basement Wall Area: 
 
 
 Heating Degree-Days*: Annual 
 
 
 °F-days 
 
 
 
 ft 
 
 *From Table 13-2 
 
Worksheet HL-1 
 Sheet 2 of 2 
 
 
 U 
 Btu 
 
 A 
 
 AT °F 
 
 <V T o> 
 
 h = UAAT 
 Btu/hr 
 
 
 (hr)(ft')(°F) 
 
 Exterior Walls (net) 
 
 
 
 
 
 Basement 
 Walls 
 
 Above grade 
 
 
 
 
 
 Below grade 
 
 
 
 * 
 
 
 Windows 
 
 and 
 
 Sliding 
 
 Patio 
 
 Doors 
 
 Single 
 
 
 
 
 
 Double 
 
 
 
 
 
 Triple (1/4" air spaces) 
 
 
 
 
 
 Storm 
 
 
 
 
 
 Exterior Slab Doors (1.5 in thick) 
 
 
 
 
 
 Floors 
 
 Over Crawl space 
 
 
 
 
 
 Concrete Slab on Grade 
 
 
 
 
 
 Basement (Heat loss to 
 basement) 
 
 
 
 
 
 Ceiling 
 
 
 
 
 
 Infiltration: (0.018) x ft 3 x °F Air changes 
 
 
 Design Heating Load: Btu/hr 
 
 
 Design Heating Load: Btu/DD 
 Design Heating Load (Btu/hr) x (24 hr/Design TD) 
 
 
 Annual Heating Load: MMBtu 
 (Btu/DD) x (Annual DD) 
 
 
 *AT = T R - 45° 
 
 DOMESTIC HOT WATER LOAD 
 
 Average Use of 70 gal /day 
 
 
 
 Annual Load (MMBtu) ( ) 
 
 
 
 
 TOTAL ANNUAL SPACE AND WATER HEATING LOAD 
 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 NODULE M 
 
 SOLAR SYSTEM SIZING 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
14-1 
 
 TABLE OF CONTENTS 
 
 
 
 
 
 
 Page 
 
 LIST OF FIGURES 14- ii 
 
 LIST OF TABLES 14- i i 
 
 INTRODUCTION .... 
 
 
 . 
 
 
 
 14-1 
 
 OBJECTIVE 
 
 
 • 
 
 
 
 14-1 
 
 RULES OF THUMB 
 
 
 • 
 
 
 
 14-2 
 
 THE RELATIVE AREAS METHOD 
 
 
 • 
 
 
 
 14-2 
 
 EXAMPLE 14-1 . 
 
 
 • 
 
 
 
 14-7 
 
 EXAMPLE 14-2 . 
 
 
 • 
 
 
 
 14-11 
 
 EXAMPLE 14-3 . 
 
 
 • 
 
 
 
 14-11 
 
 EFFECT OF COLLECTOR TILT . 
 
 
 • 
 
 
 
 14-15 
 
 EFFECT OF ORIENTATION 
 
 
 • 
 
 
 
 14-15 
 
 REFERENCES .... 
 
 
 
 
 
 14-17 
 
14-ii 
 
 LIST OF FIGURES 
 
 Figure 
 
 
 14-1 
 
 Annual Solar Fraction as a Function of 
 
 
 log e (A/A Q ) 
 
 14-2 
 
 Effect of Collector Tilt . 
 
 14-3 
 
 Effect of Collector Orientation 
 
 Page 
 
 14-6 
 
 14-15 
 
 14-16 
 
 LIST OF TABLES 
 
 Table Page 
 
 14-1 Rules of Thumb for Sizing Components of 
 
 Solar Systems ........ 14-3 
 
 14-2 F Values for Different Collector Areas (for 
 
 a given building and location) .... 14-4 
 
 14-3 Constants for Relative Areas Method . . . 14-18 
 
 Table of Natural Logarithms ..... 14-21 
 
14-1 
 
 INTRODUCTION 
 
 Solar heating systems are generally sized to provide between 30 and 
 70 percent of the total space and water heating load of the building. 
 The desired solar fraction can be chosen arbitrarily, and system size 
 determined from performance and economic analysis so that the annual 
 cost of the solar plus auxiliary system is minimized. Usually, however, 
 the collector area is selected and the solar fraction is estimated from 
 performance calculations. After selecting the collector area, storage 
 volume and fluid flow rates are established and sizes of the appurtenant 
 pumps, blowers, and heat exchangers can be decided. The size of the 
 auxiliary furnace in the heating system is based upon the design heat 
 loss rate from the building. 
 
 There are various methods for estimating the fraction of annual 
 heating load supplied by solar systems which range from simplified 
 estimates using charts and tables to detailed analysis by computer 
 programs. The method described in this module requires only simple 
 calculations but allows a choice in the type of system, air or liquid, a 
 specific collector, and the size of the building. 
 
 OBJECTIVE 
 
 The objectives of this module are to describe a method to: 
 
 1. Estimate the fraction of annual heating load supplied by solar 
 air-heating systems, liquid-heating systems, or indirect 
 heating domestic hot water system. 
 
 2. Size the system components relative to collector area. 
 
14-2 
 
 RULES OF THUMB 
 
 Rules of thumb for sizing components of air- and liquid-heating 
 solar systems are presented in Table 14-1. Collector area can be 
 decided on the basis of solar fraction, F, economic evaluation as 
 described in Module 15, or chosen arbitrarily. Component sizes may be 
 determined from the selected collector area. 
 
 THE RELATIVE AREAS METHOD 
 
 The solar fraction, F, of the annual heating load is the ratio of 
 the quantity of solar heat expected from the solar system divided by the 
 total annual heating requirements for the building. The relative areas 
 method described in this module is a method to determine F by direct 
 computation and was developed by Barley and Winn at Colorado State 
 University. It is a simple method suited for hand computation and is 
 based on observations that a unique relationship exists between F and 
 collector area, A, for a particular collector type, building size and 
 location. The relative areas method enables the designer to change 
 collector area, collector type and building size, but the collector 
 slope and orientation are fixed at latitude plus 15 degrees for combined 
 space and water heating systems and at latitude for domestic water 
 systems. Collector orientation is assumed to be due south. 
 
 A particular set of F values for various areas, A, computed for a 
 specific collector and system type, at a given location are listed in 
 Table 14-2. If the set of points F and A were plotted on a graph, 
 
14-3 
 
 Table 14-1 
 Rules of Thumb for Sizing Components of Solar Systems 
 
 SOLAR AIR HEATING SYSTEMS FOR SPACE AND WATER HEATING 
 
 Collector slope 
 
 Latitude + 15° 
 
 Collector air flow rate 
 
 1.5 to 2 cfm/ft 2 of collector 
 
 ' Pebble-bed storage size 
 
 1/2 to 1 ft 3 of rock/ft 2 of collector 
 
 Rock depth 
 
 4 to 8 feet in air flow direction 
 
 Pebble size 
 
 3/4" to IV concrete aggregate 
 
 Duct insulation 
 
 1" fiberglass minimum 
 
 Pressure drops: 
 
 
 Pebble-bed 
 
 0.1 to 0.3" W.G. 
 
 Collector (12-14 ft lengths) 
 
 0.2 to 0.3" W.G. 
 
 Collector (18-20 ft lengths) 
 
 0.3 to 0.5" W.G. 
 
 Ductwork 
 
 -0.08" W.G./100' duct length 
 
 SOLAR LIQUID SYSTEMS FOR SPACE AND 
 
 WATER HEATING 
 
 Collector slope 
 
 Latitude + 15° 
 
 Collector flow rate 
 
 -0.02 gpm/ft 2 of collector 
 
 Water storage size 
 
 1.5 to 2.5 gallons/ft 2 of collector 
 
 Pressure drop across 
 collector 
 
 0.5 to 5 psi/collector module 
 
 SOLAR DOMESTIC HOT WATER HEATING S 
 
 YSTEMS, INDIRECT HEATING LIQUID TYPE 
 
 Collector slope 
 
 Latitude 
 
 Collector flow rate 
 
 -0.02 gpm/ft 2 of collector 
 
 Preheat tank size 
 
 1.5 to 2.0 times DHW auxiliary tank 
 
 
 size 
 
 Pressure drop across 
 collector 
 
 0.5 to 5 psi/collector module 
 
14-4 
 
 Table 14-2 
 
 F Values for Different Collector Areas 
 (for a given building and location) 
 
 A(ft 2 ) 
 
 F 
 
 A/A Q 
 
 Log e (A/A ) 
 
 500 
 
 0.68 
 
 1.61 
 
 0.48 
 
 400 
 
 0.59 
 
 1.29 
 
 0.25 
 
 310* 
 
 0.50 
 
 1.00 
 
 0.00 
 
 300 
 
 0.49 
 
 0.97 
 
 -0.03 
 
 200 
 
 0.33 
 
 0.65 
 
 -0.43 
 
 150 
 
 0.22 
 
 0.48 
 
 -0.73 
 
 a curve could be drawn through the points. However, the relationship 
 would apply only to one building size. It would be desirable to 
 establish a generalized curve that would be applicable for many 
 different collectors and a variety of building sizes. 
 
 To accomplish the generalization, let us first define a parameter 
 Aq such that a collector area of that size will carry approximately 
 50 percent of the load. 
 
 A = 
 
 A S (UA) L 
 
 (F R ior)-(F R U L )(Z) 
 
 (14-1) 
 
14-5 
 
 where 
 
 A<. is a location dependent constant [(°F*ft 2 «hr)/Btu] 
 
 (UA). is the thermal conductance for the building but it also 
 may include the water heating load in a combined system 
 [Btu/(hr-°F)] 
 
 F R xa is the maximum efficiency of a specific collector which 
 
 is derated for angular effects of the solar beam and also 
 for the heat exchanger in the collector loop if one is 
 used (no dimension). 
 i 
 
 F R U, is the rate at which the efficiency of a specific 
 collector reduces because of temperature rise in the 
 collector. [Btu/(hr»ft 2 «°F)] 
 
 Z is a location dependent constant [(°F«ft 2 'hr)/Btu] 
 
 By dividing the chosen collector area, A, by A« and plotting the annual 
 solar fraction, F, against log (A/A Q ) , a straight line results as shown 
 by the solid line in Figure 14-1. Values of A/A Q and log A/A Q are also 
 listed in Table 14-2. For other geographical locations, the solar 
 fractions for the same system would be slightly different, and are 
 represented by broken lines in Figure 14-1. All lines on Figure 14-1 
 can be represented by an equation of the form: 
 
 F = C;L + c 2 log e (A/A ) (14-2) 
 
 where the values of c-. and c« depend upon geographical location. In 
 Equation (14-2), 
 
 F is the annual solar fraction, 
 
 A/A is the ratio of the chosen collector area to A Q which is 
 determined from Equation (14-1), 
 
 c-. and c« are site-dependent constants 
 
 log is a notation for natural logarithm. Natural logarithm function 
 
 is available on many hand-held calculators, and for convenience, tables 
 
 of natural logarithms for a useful range of A/A Q values are included at 
 the end of this module. 
 
14-6 
 
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14-7 
 
 Values of c,, c 2 , A<- and Z for specific sites are listed in 
 Table 14-3 for 170 cities in the United States and Canada. There are 
 three sets of numbers, one for integrated liquid- type space and domestic 
 water heating systems, one for integrated air- type space and domestic 
 water heating systems and one for stand-alone domestic hot water 
 systems. Included in the tables also are the latitudes and heating 
 "degree-days" expressed in (°F'hr)/yr (divide the numbers in the table 
 by 24 to get degree-days expressed in the usual units, °F-days/yr). 
 
 Equation (14-2) also applies to domestic hot water systems. 
 However, A Q is determined by Equation (14-3) instead of Equation (14-1). 
 For solar domestic hot water systems: 
 
 A n D AT x 10" 3 
 A n = -r~ 1 (14-3) 
 
 F R Ia " F R U L (Z) 
 
 where 
 
 A n and Z are location dependent constants that are listed in 
 u Table 14-3 
 
 D is the daily hot water demand, gal /day 
 
 AT is the difference between the temperature of water 
 
 in the mains and set temperature of water in the 
 conventional hot water tank; °F 
 
 EXAMPLE 14-1 
 
 Determine the annual solar fraction for a liquid heating solar 
 system with 150 ft 2 , 200 ft 2 and 300 ft 2 of American Heliothermal 
 (Miromit) collectors for a building with a UA of 400 Btu/(hr«°F) in 
 Denver, Colorado. 
 
 Solution: See worksheets on pages 9 to 10. 
 
14-8 
 
 Worksheets are provided for convenience; items on the worksheets 
 are explained below along with the solution to Example 14-1. 
 The top four lines are self-explanatory. 
 Line Explanation 
 
 1 The nearest city identifies the line to select 
 
 on Table 14-3. 
 
 2 Building UA is determined from heat loss 
 
 calculations. 
 
 3 Hot water use per day is used as part of UA 
 
 determination for integrated systems and for 
 determining the load in DHW systems. 
 
 6 Collector performance data will normally be 
 
 provided by the manufacturer along with results 
 
 of collector tests performed in accordance with 
 ASHRAE 93-77 guidelines. 
 
 7-9 The collector efficiency is derated if there is 
 
 a heat exchanger in the collector loop and the 
 sun angle varies with respect to the collector 
 glazing and absorber. 
 
 10 Calculate the new collector parameters. 
 
 11 Read appropriate values from Table 14-3. 
 12-15 Perform the indicated calculations. 
 
 Answers 
 
 F = 0.53 for A„ = 150 ft 2 
 c 
 
 F = 0.62 for A„ = 200 ft 2 
 c 
 
 F = 0.74 for A = 300 ft 2 
 c » 
 
14-9 
 
 Worksheet 
 
 SOLAR SYSTEM DATA 
 RELATIVE AREAS METHOD 
 
 Building Owner_ 
 Address 
 
 b 
 
 tlX^v^pl^ [ 
 
 cv\^ t y 
 
 Ph. 
 
 Contractor 
 
 Ph. 
 
 Type of System (liquid, air, H/DHW, DWH) L±dJLiA j !j / flJlil/ 
 Site and Building Data 
 
 1. Location: Nearest City Qcywcr Latitude 3^,5 ' N 
 
 2. Building UA 
 
 \0O 
 
 3. DHW volume per day_ 
 Collector Data 
 
 10 
 
 _Btu/(hr-°F) 
 gallons/ day 
 
 4. 
 5. 
 6. 
 
 Collector manufacturer^ 
 Collector Area, A = 
 
 v\\ lroyv\\ \ 
 
 6-0 
 
 ft' 
 
 Collector efficiency data from manufacturer's information: 
 
 (a) F R (xa) 0.1 
 
 (b) F R U L OAI^ B tu/(hr-ft 2 -°F) 
 
 F R /F R = 1.0 
 
 F R /F R =1.0 
 
 Derating Factors for Heat Exchanger in Collector Loop 
 
 7. For air collectors 
 
 8. For liquid collectors: 
 
 (a) No heat exchangers 
 
 (b) With heat exchanger F R /F R = 0.95 
 Corrections to Collector Parameters 
 
 9. Derating factors for solar angular effect on collector: 
 
 (a) For double glazing, 0.91 
 
 (b) For single glazing, 0.93 
 
14-10 
 
 10. Derated collector efficiency parameters 
 
 la; r R xa - ling 6a x linfi 7> 8a Qr 8b x line 9a Qr gb - ;_» 
 
 ^ F R U L = Twi x Hne 7 f 'JoTsb = Mi Btu/(hr^F) 
 
 List c, s Cp, A s , A D , Z from Table 14-3 
 
 11. A s orA D = ^l15; z . ^H| c 1 -._^S' c. . ■ g 1^ 
 
 For Integrated Solar Heating and DHW Systems: 
 
 12. A rt = 
 
 A S (UA) L 
 
 where fUA) = Design Heating Load + HW Load 
 wnere [Uf\) L Design Temp. Diff. 
 
 F r to- F R U L (Z) L 
 
 (- 115 ) ( *00 ) - \«l **2 
 
 A = riZ) " U7 )(.!«?) = -^- f t 
 
 TRIAL 1 TRIAL 2 TRIAL 3 
 
 13. A/A 1 60 J \% ~.U J?cO/lS£> = US' 3QO/IS 6 - 1^2- 
 
 14. log e (A/A Q ) 
 
 (see Tables) - ,0 4 "! .«M7 ■ (£ 5" 2- 
 
 15. F = c x + c 2 log e (A/A Q ) 
 
 ,i T3g + (3U)(«mj = jA 2 " 
 
14-11 
 
 EXAMPLE 14-2 
 
 Calculate the area of air-heating collectors required to supply 60 
 percent of the space and hot water needs for a residential building. 
 The UA of the building, which is located in Twin Falls, Idaho, is 
 400 Btu/(hr«°F). Collectors are Solaron Series 3000 collectors with 
 F R ia = 0,62, F R U L = 1.00 Btu/(hr-ft 2 -°F). 
 
 Solution: (no worksheets were used in this example) From 
 Table 14-3, C-, = 0.529 c 2 = 0.296 
 
 A $ = 0.247 Z = 0.233 
 
 . = 0.247(400) = 255 f 2 
 rt 0.62 - (1)(.233) ^ DD TX 
 
 F = c 1 + c 2 log e (A/A Q ) 
 
 0.6 = 0.529 + 0.296 log e (A/A Q ) 
 
 inn fn/n \ - 0-6 - 0.529 .. n 0ACi 
 log e (A/A Q ) ^gg 0.240 
 
 A/A Q = 1.271 (See Table of Natural Logarithms) 
 
 Answer 
 
 A = 1.271 x 255 = 324 ft 2 
 
 EXAMPLE 14-3 
 
 Determine the area of collector needed to provide 60 percent of the 
 hot water needs for a family of four in a residential building in Kansas 
 City, Missouri. 
 
 Solution: See Worksheets on pages 13 and 14 
 
 Since the worksheets are arranged for calculating F for selected 
 collector area A, the problem must be worked "backwards" to calculate A 
 from a selected value of F. 
 
14-12 
 
 1. After calculating line 16, go to line 19 and calculate 
 log e A/A (= 0.178). 
 
 2. Enter the value on line 18. 
 
 3. Look in table of natural logarithms and find the number whose 
 natural logarithm is the value on line 18. Enter the number 
 on line 17 (1.195). 
 
 4. Multiply the number (1.195) by A Q (= 53) to get A = 63 ft 2 . 
 
 5. Refer to Module 10 (Example 10-1) where the same problem was 
 solved using the approximate curves. The solution was 
 A = 70 ft 2 and the difference is about 10 percent. However, 
 since collector modules are 24 ft 2 each, three modules would 
 be selected by both procedures, and the practical answers are 
 therefore the same. 
 
14-13 
 
 Relative Areas 
 Method Worksheet 
 
 SOLAR SYSTEM DATA 
 
 Building Owner__ '-— X <& v*\ p 
 
 ±- Y^wn a L_ I4~\3 
 
 \\<\\\^^t> C ij~y 
 
 Address l\au^6 Li'h/ Ph. 
 
 Contractor Ph. 
 
 Type of System (liquid, air, H/DHW, DWH) 
 
 Site and Building Data 
 
 1. Location: Nearest City lCins«A Cj fv r)o Latitude 31 - 2 a J\j 
 
 2. Building UA Btu/(hr«°F) 
 
 3. DHW volume per day ^ gallons/day 
 
 Collector Data 
 
 4. Collector manufacturer L<? yvvto X 
 
 5. Collector Area, A = ft 2 
 
 6. Collector efficiency data from manufacturer's information: 
 
 (a) F R (ia) 0, 75" 
 
 (b) F R U L ,C \0 B tu/(hr-ft 2 -°F) 
 
 Derating Factors for Heat Exchanger in Collector Loop 
 
 7. For air collectors Fr/^r B 1-0 
 
 8. For liquid collectors: 
 
 i 
 
 (a) no heat exchangers ^r/^r = 1*0 
 
 (b) with heat exchangers Fr/Fr = °-95 
 Corrections to Collector Parameters 
 
 9. Derating factors for solar angular effect on collector: 
 
 (a) for double glazing, 0.91 
 
 (b) for single glazing, 0.93 
 
14-14 
 
 10. Derated collector efficiency parameters 
 
 fa) r ~- °> 1S x 0AS x °^ 3 - H U 
 
 \*) r R Ta line 6a x line 7j 8a Qr 8b x line 9a op gb jj_ L (c_( (f 
 
 (b) F 'u = °'1° L x O'l* = 0_^Btu/(hr-°F) 
 
 K) h R u L line 6b x line 7, 8a, 8b 
 
 List c,, c 2 » A s , A D , Z from Table 14-3 
 
 11. A $ or A D = 3,35 7 Z = .A34 - C]L = , f&l c 2 = 1 ^ 2 - 
 
 For Integrated Solar Heating and DHW Systems: 
 
 I? A = A S (UA) L wh e r e (UA} = Des1gn Heatin 3 Load + HW Load 
 u ' A c — _ ., f7 , wnere m) L Design Temp. Diff. 
 
 F R xa - F R U L (Z) 3 K 
 
 A - ( ) ( ) - ft 2 
 
 A o - 1 rn n ) " — f t 
 
 13. A/A Q = = 
 
 14. log e (A/A Q ) = 
 
 15. F = cj + c 2 log e (A/A Q ) 
 
 = + ( )( ) 
 
 For DHW Systems: 
 
 A n DATxlO" 3 
 
 16. A n = 
 
 F R xa - F R U L (Z) 
 
 A m (3-35? )( 1Q ){ 1Q )xlQ- 3 = 5J 
 
 17. A/A = I . h 5 : T^«y«. fo>r^ A^ ^ 
 
 18. Log e (A/A ) = Q.H g _Av^s . 
 
 19. F = c x + c 2 Log e (A/A Q ) (YW 3 ^v^U£^ c^ 
 F = .54| + (33^)(U r A//) o ) = 0,6 ^* g -f^ 
 
14-15 
 
 EFFECT OF COLLECTOR TILT 
 
 The assumed optimum angle between the plane of solar collectors and 
 the horizontal in Table 14-3 is latitude plus 15 degrees. The effect of 
 solar collectors mounted at tilt angles other than optimum angle is 
 shown in Figure 14-2. The curve applies only to south-facing 
 collectors. 
 
 I. Or 
 
 -60 -50 -40 -30 -20 -10 10 20 30 40 50 
 
 Off-Optimum Tilt 
 
 Figure 14-2. Effect of Collector Tilt 
 
 EFFECT OF ORIENTATION 
 
 The effect of solar collector orientation on annual system 
 performance is shown in Figure 14-3 and is dependent upon tilt angle. 
 In Figure 14-3, s is the optimum tilt angle. To determine the effect 
 of both tilt and orientation on seasonal solar fraction, F, multiply F, 
 determined by Equation (14-2), by both tilt and orientation factors 
 
14-16 
 
 o 1.0 
 
 o 
 o 
 u. 
 
 c 
 o 
 
 c 
 
 CD 
 
 0.9 
 0.8 
 0.7 
 
 a6 o 
 
 South 
 
 
 
 
 
 
 
 
 
 
 -loriz. 
 
 
 
 
 
 
 
 
 
 
 
 *-S - 
 
 - 45° 
 
 
 
 
 
 
 
 
 
 
 — So- 
 
 - 30° 
 
 
 
 
 
 
 
 
 ert-"^ 
 
 f^^N 
 
 — S - 
 *-S 
 
 - 15° 
 
 
 
 
 
 
 
 V 
 
 
 ~-S + 15° 
 ^S + 30° 
 
 1 
 
 20 
 
 70 
 
 30 40 50 60 
 Azimuth Angle 
 Figure 14-3. Effect of Collector Orientation 
 
 80 90 100 110 
 East, West 
 
 determined in Figures 14-2 and 14-3. If the collectors in Example 14-1 
 are installed at a tilt angle of 30 degrees, and face 30 degrees east of 
 south, the expected seasonal solar fraction F with 150 ft 2 of collectors 
 would be: 
 
 F (corrected) = F (uncorrected) x (tilt factor) x (orientation factor) 
 or 
 
 F = 0.53 x 0.93 x .97 = 0.48 
 
 Since a value for F of 0.53 was determined for a collector tilted 
 at latitude plus 15 degrees, the collector tilt angle is assumed to be 
 55 degrees. For Denver, the optimum angle is latitude plus 15 degrees; 
 thus, if the collectors are at 30 degrees, the off-optimum tilt angle is 
 minus 25 degrees. The tilt factor, from Figure 14-2, is thus 0.93 and 
 the orientation factor, from Figure 14-3, is 0.97. 
 
14-17 
 
 REFERENCES 
 
 1. Klein, S. A., Beckman, W.A. , and Duffie, J. A., "Design Procedure 
 for Solar Heating Systems," Solar Energy, Vol. 18, pp. 113-127, 
 1976. 
 
 2. ASHRAE Handbook of Fundamentals, American Society of Heating, 
 Refrigeration, and Air Conditioning Engineers, Inc., 345 East 
 47th Street, New York, N.Y. 10017, 1972. 
 
 3. ASHRAE Systems Handbook, Chapter 43, American Society of Heating, 
 Refrigeration, and Air Conditioning Engineers, Inc., 345 East 47th 
 Street, New York, N.Y. 10017, 1976. 
 
 4. Climatic Atlas of the United States, U.S. Department of Commerce, 
 NOAA, National Climatic Center, Federal Building, Asheville, N.C. 
 28801. 
 
 5. Load Calculation for Residential Winter and Summer Air 
 Conditioning, Manual J, National Environmental Systems Contractors 
 Association, 1501 Wilson Blvd., Arlington, Va. 22209. 
 
 6. Heat Loss Calculation Guide, No. H-21, The Hydronics Institute, 
 35 Russo Place, Berkeley Heights, N.J. 07922. 
 
 7. ASHRAE Applications of Solar Energy for Heating and Cooling of 
 Buildings, American Society of Heating, Refrigeration, and Air 
 Conditioning Engineers, Inc., 345 East 47th Street, New York, N.Y. 
 10017, 1977. 
 
 8. Klein, S. A., Beckman, W. A., and Duffie, J. A., "A Design 
 Procedure for Solar Air Heating Systems," Proceedings of American 
 Section ISES Meeting, Winnipeg, Canada, Vol. 4, August, 1976. 
 
 9. "f-chart Computer Program," Solar Engineering Laboratory, 
 University of Wisconsin, Madison, Wisconsin. 
 
 10. Solar Heating and Cooling of Residential Buildings, Training 
 Manuals, Sizing, Installation, and Operation of Systems, Design of 
 Systems, Solar Energy Applications Laboratory, Colorado State 
 University, Fort Collins, 1977. 
 
 11. Barley, C. D. and Winn, C. B. , "The Relative Areas Method for 
 Optimal Collector Sizing of Solar Systems," Solar Energy 
 Applications Laboratory, Colorado State University, Fort Collins, 
 Colorado, 1978. 
 
14-18 
 Table 14-3 
 Constants for Relative Areas Method 
 
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14-19 
 
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 ;>>>>->-: 
 
 0>i— C 4J 
 
 O r- 
 Q.4-> -r- 
 
 . -C ZJ VI 
 
 : E— o 
 
 ) < CQ CO 
 
 r— O 
 
 ■* O E 
 O CL*r- 
 
 5S5 
 
 S- O t) ■ 
 CD -O •— O 
 
 ■— S- t- +J 
 
 C £ 
 *p» t 
 
 V) V 
 
 C +J fCJ t 
 
 •r- -!-> 
 C3 
 
 ffii/ioai 
 
 §1; 
 
 c +j 
 
 ■r- 3 
 1- r- 
 
 > o c 
 »— o 
 
 ^ Oi 4J 0) £ ' 
 
 </> fO r— +J 4-> O ( 
 
 C7I S U- r- n3 -P .O 
 
 CO -P 'r- I O </> 
 
 ■r- a» +j •<- > i— c f 
 
 <— vi re E QJ at i- ai 
 
 p- « 0) E-c O-fO ai 
 
 -E -C 
 
 O 
 
 
 c 
 
 
 .,_ 
 
 C 
 
 
 
 
 
 
 F 
 
 
 en o> i- 
 
 
 
 
 +-> 
 
 3 
 
 3 
 
 
 a> 
 
 
 >> TO 
 
 *1 
 
 
 3 
 
 O 
 
 O £ 
 
 c 
 
 cr 
 
 
 >• 
 
 
 C 
 
 X. 
 
 I) 
 
 
 D> U 4-> 
 
 
 C 
 
 3 
 
 
 
 
 ffi 
 
 rr 
 
 
 
 
 i- 
 
 c 
 
 L- 
 
 
 a> -o 
 
 >> 
 
 VI 
 
 c .o 
 
 c 
 
 C 
 
 £3 
 
 •r- (0 
 CO U_ 
 
 13 
 
 £ 
 
 +J U r- t— 
 < 1— < LU 
 
 *3 
 
 £ 
 
 3 
 
 CQ 
 
 £ 
 
 t «"« 
 
 -^ OJ 4-J CD C vi 
 
 i. P O VI aj 3 
 
 v> ai 3 i— .a c 
 >- ai B u cu b p 
 
 -C ai to > 3 -m 
 
 1 o j= u. oi-— >» 
 aiou >>r— q - 
 z cc i/i i/i c_> o 
 
14-20 
 
 Table 14-3 (Continued) 
 
 O^^^Crtooocr>cvjcsjrHCMirtcocopoc\ic\jini^u^ii^in^^OLn^iri^irtCMCMCOPO«^ 
 
 CO CO CO CO C\J C\J CO CvJ CO CO CO CO CO CO CO CO CO PO CO CO CO CO CO CO CO CO CO PO CO CO CO PO PO CO CO PO PO CSJ CO PO PO PO PO PO PO PO PO CM CO CO CO CO PO CO CO PO 
 
 ^o\in^H<»»nwoii«o^i/)0^mc\i^cof^Nc\jO(\irHcqrviHO\rtrNrHeON^c>JNO^«)NNiHncsjr^ 
 CM^^^csj^csiCAJcococ\iro^^«*^cocou^iriininu^^ir>in^ui^i^coco^^ 
 
 a3a^o^coOLncotfi^o^o^CNjevj^Po^r^r^r^^or^co^r^oor^cnr^co^c\)coco^^cors.oco 
 
 CM^CMCMPOCOCSICOC\JCMPOC\Jr^CMCAjCslC^C>Jf^^H^Hi^i^i^^^^Hf^t^t^C\JCSJC^ 
 CCOrsCvlNCOO^^OO^^^Hps^NOlOrt^OO^rHnNVOW^9^fOWO^m^lfiO(B^CgO\VOOnH^(n*COi-<'-i^fvJVO 
 
 OTro^co^OinuD^i^or^csjo%^co^r^OT^OTO'^'^c\jcoaic\jr^^oc\j^co 
 
 POCMCOCO^^CO^COPO^COCOCMCOPO^POCSJCSICMCOCOPOCVJCMP^ 
 
 < INI —* 
 
 cococvic>jr^in»r^*HOChc\jcococsj^©OPO^po^copOPOPOCMPocNjco©CMC\]^^co^^cocn 
 
 CMCOCOCOC\lCMCMCNjCOmCSJPOPOPOCOPOPO«COPOCOCOCOCOCOCOCOC 
 
 c^jc\j^cocoPor^i^o%iocvjo^Por^^cMi^roo^csJooino^r^o^c\j«^incMO«^^CAjin^«^0\oo^-c\j 
 
 potn^^^Hi^i^csjcococo^u^^^^^^u^^ir>^co^in^^u^^-uico^^^«^c\jrHf^c\iPocococo^^csj 
 
 a^LOuTiu^LOLni^. u^'j^LOuou^Lnu^LOuiu^iX)u^LOunLnLnij^LOLn^ 
 
 co^^^t^c\i^^cMcsjcoo^i^cMi^cocooicooco^rHco^csjco^p^coco^Lncftc\i^^ 
 ovoa^oo\o^CMcoLr>aiPocococ\jf^^^voLni^r^o^^c\ji^^uiOr^i^c\i©iMco^cocoLnr^ 
 
 COrH^HCAjCMCOCNJCOC\JCAJC\JC\Jr^^CsJCMCSICMl^'^r^rHi^^H^Hi^r^^HC\Jr^CNJCSJCMCM 
 
 ^rt0^coooornc\jcsjcvinincoinNWrHfo^^forN<-w(si\ocoMOiHC\i^inaiui^uirN.^o^rH^coOiflnn 
 inir>r^cooc\jcsju^covoco^o.^cor^r^c\i«^coi^^Lnc\jmr^opocnr^co^^<Tii^^^co 
 
 PO<-*r-ir-«C>jr\(eSICsaC\JCMCOC\Ji-tCMr-*rHCMCM «-Hi-ii-<OOi-t©i-lOi-iOOPsJC\J «^i^C\IC\ICsJCMC\JCOCOCOCNJr*C\lCOC\ICOir>CO«3"«d-incOCO^- 
 
 ^^OHN^oimo\eONiHuiooio^ii)?^nwrxrHcovoniJioOHO>oiina>oofvj^^wooHa)no\NMNvovDi^cON 
 inoww*NN*rsiSifleooosiatowOHOOO»HOwowo«cococo'twf>jc\j^ i «)Nii3inHO<flNirtNsin<3vooiflv 
 
 CJCOCslCJCMC>JCsJCNJCsJCsJCMC^COPOCMCgCUC\lPOPOCOCOCOe>JPOCOC\JPO 
 i^COCMC\lOOO^C\Ji^t^OJCOCOC\JC\JCsJC\JCOCOCOCOC\JCO^COCOCOPOCO^CAlC^CM 
 
 w\ONOwo3HHnwNinHi^>.inHOQ3npoioinwo>inotnHHO*NHnoicoowoiflNnrtQ*sN«WNvoioc4co 
 ^onini/)snocooiJio>cg(\;^^oo(7icoOHitfoinofl , c>iflHNeoin<oo>o< , HHfOHOjif)o>NOrsscsjcooo^NHCoot 
 cocMr\ic\i<^coco^cMcopocMc>jp\jrsjevjcopOf^T^e>Jc\iesjc^ 
 
 \ocT>©^ocMC\iino^r^OTc\ioocsicoLf)cocsiPOOPOi^io^CM^^cvjiiiCft^^or^ir>^in 
 ^^u^cocJ»c^J^PO'^^r^u^Ln^Hroo^cOPOPOCsl^CM^^cool1^0l^^CJ^oo^l^^^oco^O^Ol/ , )a^oo<, _ 
 
 fOMrHrH(\JW(\JNC\IC\jnNi^C>JrHMC\JWrH I Hr^OOiHO^OpHOONrg-HCv|(\|NCNJ(NJNnrOfOMN 
 
 X >- 
 
 O^Miflcor^o^rHuii/)cn^rNjo^r>.ronoo^wc\iooDc\icoocNJCNj(»miH^rvO(»^vDcoo^*jooirHO>NOiflpNMtDr^w 
 ns^Hrsc^HOifl\ou)o>ONiHtfOirtncocoo^inoiNrH03(s)ooi<^OMrsrsONci^csj^OsrtciifliflNo^^cONn'*r^ 
 
 c\JCO^oor^^ocoi^vo^or^ovoo^^r^co^c\jOCAiine\i^^r^^<Ni^Of^co^ro^^cor^io^^ 
 
 ,-t ,-4,-H,-Hr-4,-lf-lf4t-4 -H _< t-t r-l ^*^^H-Hi^^H^HT^^Ht^CNJCVJOJ»-'^-eSJC\JC>JC\JCSJi-li-H 
 
 *tcvjrHrHrtrnw«tinoinnwiHOOiHoniHcsivDinini/»uivo^«3coinouiinN^NM^coiHU)c^uiN 
 
 n:^^^ci:Q:a:a:«a:<:<c» 
 
 >> 
 
 
 QJ 
 
 
 
 fO o> 
 
 
 
 
 >,o i- 
 
 
 j: .c i— c 
 
 T3 1) 
 
 
 V) D. o>r- q 
 
 •r- -O t— J- O -M 
 
 m g+J 
 
 
 1 E "3 
 
 
 fli-TJ CflJ 3LJ-M t/l 
 
 COS 
 
 
 •r- r- t. (O "O -Q S- a> 
 
 •r- -C 1— 
 
 ns 
 
 t-fOOi— q V) U Oi- 
 
 1 fl »— 
 
 ul 
 
 •P i- TJ t--r-4-»(0 JrtJ 
 
 4-> 1— -^ 
 
 
 3 -* +J 
 
 -J 
 
 I/) OttJ O -C ■»- +-> QJ -C 
 <tO£o_0_G_LOZO 
 
 Q_ O l/> 
 
 >— 
 
 >> 
 
 CD 
 
 
 
 
 
 
 
 pS 
 
 i. 
 
 
 
 
 
 
 
 •r- 
 
 
 a; 
 
 
 
 +-> 
 
 o 
 
 
 a; 
 
 0) 
 
 
 
 B 
 
 
 -C 
 
 
 
 4-> 
 
 
 
 f 
 
 c 
 
 <u £ 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 l_ 
 
 
 
 +J 
 
 s 
 
 _* 
 
 
 
 ■o 
 
 ( ) 
 
 c 
 
 1/) 
 
 
 -a 
 
 U 
 
 
 u 
 
 > 
 
 
 
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 o 
 
 c -o 
 
 u 
 
 re 
 
 re -* 
 
 c 
 
 
 
 
 
 
 c 
 
 
 
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 1/1 
 
 1/1 
 
 ^c 
 
 o 
 
 c < 
 
 c 
 
 
 (U 
 
 
 
 
 4-> 
 
 -C 
 
 >a: 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 <r 
 
 
 -* 
 
 a 
 
 
 
 4-> 
 
 C3.SZ 
 
 
 
 t_ 
 
 
 O. 
 
 
 Q- 
 
 -t-> 
 
 
 
 +J 
 
 
 4-) 
 
 
 M- 
 
 
 a. to 
 
 F 
 
 i/) _*: 
 
 
 ra 
 
 Ol o 
 
 s- 
 
 
 
 1- 
 
 3 -o 
 
 i- 
 
 c 
 
 
 
 
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 <s 
 
 J= OJ ra m 
 OE ZO 
 
 %$ 
 
 ■r- t O fl i— 
 
 CQCQOQLil 
 
 o 
 
 o 'i- o re re ■*-> 
 
 o ■»- 
 
 Z OS 
 
 •o re a> .o c-a aip- o> cm f- 
 
 u c c ai ojcoc^ vi o;o*«->-'-a>ej=re ore 
 
 0) « re r— C 03S-J-'*--Pl-=I.C0,Q0J*re-t-><U 
 
 i/)»— -C-M-^ai-r-XJC-OfOQ-COi-CU 3IOO+J 
 
 Or- UWOQJT3r-J-CJ-E+JC3CC •O.-MI-C 
 
 s- 3-f- <u o-i-jg-r- re re re "O <u re .c -f- o ■*-> re -m o _b 
 
14-21 
 
 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 
 
 0.668 
 
 0.668 
 
 0.669 
 
 0.669 
 
 0.670 
 
 0.670 
 
 0.671 
 
 0.671 
 
 0.672 
 
 0.672 
 
 1.96 
 
 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 
 
 0.728 
 
 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 
 
 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 
 
14-22 
 
 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 
 
 0.454 
 
 0.454 
 
 0.455 
 
 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 
 
 .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 
 
 0.552 
 
 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 
 
 0.572 
 
 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 
 
 0.605 
 
 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 
 
 0.632 
 
 0.632 
 
 0.633 
 
 0.633 
 
 0.634 
 
 0.634 
 
 0.63 5 
 
 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 
 
14-23 
 
 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 
 
 0.19 2 
 
 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 
 
 1.30 
 
 0.262 
 
 0.263 
 
 0.264 
 
 0.265 
 
 0.265 
 
 0.266 
 
 0.267 
 
 0.268 
 
 0.268 
 
 0.269 
 
 1.31 
 
 0.270 
 
 0.271 
 
 0.27 2 
 
 0.272 
 
 0.273 
 
 0.274 
 
 0.27 5 
 
 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 
 
 0.324 
 
 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 i 
 
 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 
 
14-24 
 
 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 
 
 -0.226 
 
 -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 
 
 -0.172 
 
 -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 
 
 -0.13 6 
 
 -0.13 5 
 
 -0.134 
 
 -0.13 2 
 
 -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 
 
 -0.066 
 
 -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 
 
 -0.039 
 
 -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 
 
 0.042 
 
 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 
 
14-25 
 
 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 
 
 -0.87 2 
 
 -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 
 
 -0.64 2 
 
 -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 
 
 -0.528 
 
 -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 
 
 r-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 
 
 -0.459 
 
 -0.4 57 
 
 -0.456 
 
 -0.454 
 
 -0.453 
 
 -0.4 51 
 
 -0.449 
 
 -0.448 
 
 0.64 
 
 -0.446 
 
 -0.445 
 
 -0.443 
 
 -0.442 
 
 -0.4A0 
 
 -0.439 
 
 -0.437 
 
 -0.435 
 
 -0.434 
 
 -0.43 2 
 
 0.65 
 
 -0.431 
 
 -0.4 29 
 
 -0.428 
 
 -0.426 
 
 -0.425 
 
 -0.423 
 
 -0.422 
 
 -0.420 
 
 -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 
 
 -0.383 
 
 -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 
 
 -0.361 
 
 -0.360 
 
 -0.3 58 
 
14-26 
 
 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 
 
 0.89A 
 
 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 
 
 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 
 
 I 
 
 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 
 
 0.9 20 
 
 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 
 
 0.982 
 
 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 
 
14-27 
 
 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 
 
 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 
 
 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 
 
 l o 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 
 
 1.042 
 
 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 
 
 2.88 
 
 1.058 
 
 1.058 
 
 1.058 
 
 1.059 
 
 1.059 
 
 1.060 
 
 1.060 
 
 1.060 
 
 1.061 
 
 1.061 
 
 2.89 
 
 1.061 
 
 1.062 
 
 1.062 
 
 1.062 
 
 1.063 
 
 1.063 
 
 1.063 
 
 1.064 
 
 1.064 
 
 1.064 j 
 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 
 
 2.92 
 
 1.072 
 
 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 
 
 1.076 
 
 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 
 
 1.08 2 
 
 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 
 
 1.111 
 
 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 
 
 1.118 
 
 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 
 

Relative Areas 
 Method Worksheet 
 
 SOLAR SYSTEM DATA 
 
 Building Owner 
 
 Address Ph. 
 
 Contractor Ph. 
 
 Type of System (liquid, air, H/DHW, DWH) 
 
 Site and Building Data 
 
 1. Location: Nearest City Latitude 
 
 2. Building UA Btu/(hr-°F) 
 
 3. DHW volume per day gallons/day 
 
 Collector Data 
 
 4. Collector manufacturer 
 
 5. Collector Area, A = ft 
 
 6. Collector efficiency data from manufacturer's information: 
 
 (a) F R (xa) 
 
 (b) F R U L Btu/(hr-ft 2 -°F) 
 
 Derating Factors for Heat Exchanger in Collector Loop 
 
 7. For air collectors f r/^r = l m ® 
 
 8. For liquid collectors: 
 
 (a) no heat exchangers ^r/^r = l-° 
 
 (b) with heat exchangers Fr/Fr = 0-95 
 Corrections to Collector Parameters 
 
 9. Derating factors for solar angular effect on collector: 
 
 (a) for double glazing, 0.91 
 
 (b) for single glazing, 0.93 
 
10. Derated collector efficiency parameters 
 
 ( a ) F R Ta = line 6a x line 7, 8a or 8b x line 9a or 9b = - 
 
 t b) f 'm = x = Btu/(hr.°F) 
 
 {D) h R u L line 6b x line 7, 8a, 8b 
 
 List c,, c 2> A s , A D , Z from Table 14-3 
 
 11. A s or A D = Z = c, = c 2 = 
 
 For Integrated Solar Heating and DHW Systems: 
 
 A $ (UA) 
 
 12. A n = 
 
 F R™ " F R U L< Z > 
 
 L whprp /, IA x _ Design Heating Load + HW Load 
 
 wnere [ui\) l - Desi T Diff _ 
 
 c ^r _ f n (7\ L Design Temp, 
 
 2 
 
 V I j-1 )( < ■ ft 
 
 13. A/A Q = 
 
 14. log p (A/A ) = 
 
 15. F = Cj + c 2 log e (A/A Q ) 
 
 = + 1 )( ) = 
 
 For DHW Systems: 
 
 A n DATxlO" 3 
 
 16. A n = -r^z i 
 
 F R Ta " F R U L (Z) 
 
 A - ( )( )( )xl0" 3 
 ° ( ) - ( )( ) 
 
 17. A/A Q 
 
 18. Log e (A/A ) = 
 
 19. F = c x + c 2 Log e (A/A ) 
 
 F = + ( )( ) = 
 
TRAINING COURSE IN 
 THE PRACTICAL ASPECTS OF 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 15 
 
 ECONOMIC CONSIDERATIONS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 

15-i 
 TABLE OF CONTENTS 
 
 Page 
 
 LIST OF FIGURES 15- i i i 
 
 LIST OF TABLES 15-iv 
 
 INTRODUCTION . 15-1 
 
 OBJECTIVES 15-2 
 
 FACTORS IN ECONOMIC ANALYSES 15-2 
 
 COSTS FOR EQUIPMENT AND INSTALLATION 15-3 
 
 EQUIPMENT AND INSTALLATION TIME ESTIMATES . . . 15-4 
 
 Liquid-Heating Systems ...... 15-4 
 
 Air-Heating Systems ....... 15-5 
 
 Domestic Water Heaters ...... 15-6 
 
 TYPICAL INSTALLED COSTS OF SYSTEMS 15-8 
 
 Space Heating System - Liquid Collectors . . 15-8 
 
 Space Heating System - Air Collectors . . . 15-8 
 
 Domestic Water Heaters ...... 15-9 
 
 MORTGAGE PAYMENTS 15-11 
 
 OPERATING COSTS 15-11 
 
 FUEL COSTS 15-11 
 
 ELECTRICAL ENERGY COSTS FOR OPERATION .... 15-15 
 
 PROPERTY TAXES 15-16 
 
 INSURANCE 15-16 
 
 MAINTENANCE COSTS 15-17 
 
 INFLATION 15-17 
 
 TAX CREDITS 15-19 
 
 INITIAL INVESTMENT 15-19 
 
15-ii 
 
 INTEREST AND PROPERTY TAX 
 INDIVIDUAL INCOME TAX RATE 
 METHODS OF ECONOMIC ANALYSIS . 
 BREAKEVEN COST . 
 
 Example 15-1 
 
 Solution . 
 PAYBACK . 
 
 Example 15-2 
 
 Solution . 
 LIFE-CYCLE COST ANALYSIS 
 
 Example 15-3 
 
 Example 15-4 
 
 Example 15-5 
 ECONOMIC ANALYSIS WORKSHEETS 
 WORKSHEET LCA-1 
 WORKSHEET LCA-2 
 WORKSHEET LCA-3 
 WORKSHEET LCA-4 
 EXAMPLE 15-6 . 
 EXAMPLE 15-7 . 
 APPENDIX - State Solar Legislation 
 
 Page 
 
 15-19 
 
 15-20 
 
 15-26 
 
 15-26 
 
 15-26 
 
 15-27 
 
 15-27 
 
 15-28 
 
 15-28 
 
 15-30 
 
 15-40 
 
 15-40 
 
 15-41 
 
 15-43 
 
 15-43 
 
 15-43 
 
 15-49 
 
 15-52 
 
 15-54 
 
 15-59 
 
15-iii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 15-1 Repayment on Loan ....... 15-12 
 
 15-2 Energy Cost per Million Btu for Natural Gas, 
 
 Propane, and No. 2 Fuel Oil 15-13 
 
 15-3 Energy Cost per Million Btu for Electricity . . 15-14 
 
 15-4 Inflation Factors 15-18 
 
 15-5 Nomograph for Determining SPB and DPB . . . 15-29 
 
15-iv 
 LIST OF TABLES 
 
 Table Page 
 
 Typical Equipment and Material Prices (in 1978) 
 
 for Liquid-Heating Systems ..... 15-4 
 
 Installation Time Estimates for Typical Liquid- 
 Heating Systems ....... 15-5 
 
 Typical Equipment and Material Prices (in 1978) 
 
 for Air-Heating Systems ...... 15-5 
 
 Installation Time Estimates for Typical Air- 
 Heating Systems ....... 15-6 
 
 Equipment Costs for Components of Domestic Water 
 
 Heaters (1978 prices) ...... 15-7 
 
 Estimates of Installation Times for Domestic Water 
 
 Heaters ......... 15-7 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 10 years . 15-21 
 
 15-8 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-d+i)- 3 "" 1 " 1 Mortgage Term (m) = 15 years . 15-22 
 
 15-9 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 20 years . 15-23 
 
 15-10 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+i) J " m_1 Mortgage Term (m) = 25 years . 15-24 
 
 15-11 Fraction of Mortgage Payment (A) Which is Interest 
 
 I/A = l-(l+1)^" m ' 1 Mortgage Term (m) = 30 years . 15-25 
 
 15-12 Values of P/X (d,r,n) for Discount Rate of 
 
 Percent 15-34 
 
 15-13 Values of P/X(d,r,n) for Discount Rate of 
 
 4 Percent 15-35 
 
 15-14 Values of P/X(d,r,n) for Discount Rate of 
 
 6 Percent 15-36 
 
 15-15 Values of P/X(d,r,n) for Discount Rate of 
 
 8 Percent 15-37 
 
 15- 
 
 -1 
 
 15- 
 
 -2 
 
 15- 
 
 ■3 
 
 15- 
 
 •4 
 
 15- 
 
 ■5 
 
 15- 
 
 ■6 
 
 15- 
 
 ■7 
 
15-v 
 
 Table Page 
 
 15-16 Values of P/X(d,r,n) for Discount Rate of 10 
 
 Percent 15-38 
 
 15-17 Values of P/X(d,r,n) for Discount Rate of 12 
 
 Percent 15-39 
 
 15-18 Present Worth Factors (P) .... 15-44 
 

15-1 
 
 INTRODUCTION 
 
 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. However, when 
 it is important to make decisions and provide recommendations for the 
 most economic alternative for heating a building, some form of economic 
 analysis will be necessary. 
 
 Solar heating systems require higher capital costs than 
 conventional systems, and many economic evaluation methods attempt to 
 determine the relative merits of "paying for hardware" or "paying for 
 energy". Two simple methods and a complex method are explained in this 
 module. One first simple method is breakeven analysis, which involves a 
 comparison of unit thermal energy costs delivered by the solar system 
 and a conventional system. The second simple method involves 
 determination of a payback period required to amortize initial 
 investment for solar equipment with savings in cost of conventional 
 energy. 
 
 The more elaborate analysis, which considers a number of important 
 economic factors during the life of the system, is called life-cycle 
 cost analysis. Inclusion of many items in an analysis leads to 
 complexity; however, the economic principles of life-cycle costing are 
 presented in sufficient detail for verification by financial 
 specialists. Although various equations appear in the text, their 
 direct use is not required to complete an analysis. By following the 
 examples through the worksheets, and by using charts and tables, 
 life-cycle cost calculations can be completed in a straightforward 
 manner. 
 
15-2 
 
 OBJECTIVES 
 
 The objectives of this module are to describe methods for 
 determining solar heating costs and 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. Establish the economic feasibility of a solar system. 
 
 FACTORS IN ECONOMIC ANALYSES 
 
 An economic analysis may include some or all of the factors listed 
 below. The simple economic evaluation methods may require knowledge of 
 only a few of these factors, but life-cycle costing may involve all of 
 them. The important factors are: 
 
 1. Equipment and installation costs (or, alternatively, periodic 
 mortgage payments) 
 
 2. Operating Costs 
 
 a. Fuel Costs 
 
 b. Electrical energy costs for pumps and blowers 
 
 c. Added property tax on the solar system 
 
 d. Added insurance premium for coverage 
 
 3. Maintenance Costs 
 
 4. Credits 
 
 a. Income tax credits and/or deductions based on system 
 costs 
 
 b. Investment (for businesses) 
 
 c. Income tax credits for interest and added taxes. 
 
15-3 
 
 COSTS FOR EQUIPMENT AND INSTALLATION 
 
 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 
 mis-leading, because the total costs of such projects may include 
 considerable 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, 
 because 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, so that prices may not be representative of 
 any single project. 
 
15-4 
 
 EQUIPMENT AND INSTALLATION TIME ESTIMATES 
 Liquid-Heating Systems 
 
 Table 15-1 
 
 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 
 
 Misc. fittings 
 
 - 
 
 200 
 
 250 
 
 350 
 
 Expansion tank 
 
 - 
 
 60 
 
 80 
 
 100 
 
 Insulation 
 
 - 
 
 500 
 
 750 
 
 1000 
 
 DHW Preheat tank 
 
 each 
 
 80 
 
 100 
 
 150 
 
15-5 
 
 Table 15-2 
 Installation Time Estimates for Typical Liquid-Heating Systems 
 
 Item 
 
 Unit 
 
 Time (man-hoi 
 
 .irs) 
 
 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 
 
 30 
 
 Controls 
 
 - 
 
 8 
 
 12 
 
 16 | 
 
 Testing and balancing 
 
 - 
 
 10 
 
 15 
 
 20 
 
 1 
 
 Air-Heating Systems 
 
 Table 15-3 
 
 Typical Equipment and Material Prices (in 1978) 
 for Air-Heating Systems 
 
 Item 
 
 Unit 
 
 Price Range 
 (in dollars) 
 
 Low 
 
 Medium 
 
 High 
 
 i 
 
 Flat-plate collectors and 
 mounting hardware 
 
 ft 2 
 
 10 
 
 15 
 
 i 
 24 
 
 Storage containers 
 
 ft 3 
 
 0.5 
 
 1 
 
 i.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 | 
 
15-6 
 
 Table 15-4 
 Installation Time Estimates for Typical Air-Heating Systems 
 
 Item 
 
 Unit 
 
 T 
 
 ime (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 15-5. 
 
 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 15-6. 
 
15-7 
 
 Table 15-5 
 Equipment Costs for Components of Domestic Water Heaters (1978 prices) 
 
 Item 
 
 Unit 
 
 
 Price Range 
 fin dollars 
 
 — r 
 
 I) 
 
 Low 
 
 Medium 
 
 High 
 
 Flat-Plate Collectors 
 and mounting hardware 
 
 ft 2 
 
 10 
 
 15 
 
 24 
 
 Preheat tank 
 
 80-gallon 
 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 15-6 
 Estimates of Installation Times for Domestic Water Heaters 
 
 Item 
 
 Unit 
 
 Ti 
 
 me (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 
 
15-8 
 
 TYPICAL INSTALLED COSTS OF SYSTEMS 
 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 15-1 and 15-2. 
 
 1. 
 
 Collectors 
 
 equipment 400 ft 2 x $15/ft 2 
 
 $6,000 
 
 
 
 installation 
 
 60 hrs x $15/hr 
 
 
 900 
 
 2. 
 
 Storage Tank 
 
 equipment 
 
 
 1 
 
 ,500 
 
 
 
 installation 
 
 10 hrs x $15/hr 
 
 
 150 
 
 3. 
 
 Pipe Loops 
 
 equipment 
 
 
 2 
 
 ,070 
 
 
 
 installation 
 
 60 hrs x $15/hr 
 
 
 900 
 
 4. 
 
 DHW Subsystem 
 
 equipment 
 
 
 
 280 
 
 
 
 installation 
 
 12 hrs x $15/hr 
 
 
 180 
 
 5. 
 
 Controls 
 
 equipment 
 
 
 
 750 
 
 
 
 installation 
 
 12 hrs x $15/hr 
 
 
 180 
 
 6. 
 
 Insulation 
 
 materials 
 
 
 
 750 
 
 
 
 installation 
 
 20 hrs x $15/hr 
 
 
 300 
 
 7. 
 
 Testing and 
 balancing 
 
 
 
 
 225 
 
 
 
 Total Esti 
 
 mated Costs 
 
 14 
 
 ,185 
 
 
 
 Breakdown 
 
 of costs: 
 
 
 
 
 
 Equipment & materials 
 
 11 
 
 ,350 
 
 
 
 Labor 
 
 
 2 
 
 ,835 
 
 
 Ins1 
 
 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 15-3 and 15-4. 
 
15-9 
 
 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 
 
 3,175 
 1,125 
 
 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 14,705 
 
 Breakdown of costs: 
 
 Equipment & materials 11,420 
 
 Labor 3,285 
 
 Installed cost/unit collector area $36.76/ft 2 
 
 Domestic Water Heaters 
 
 An estimate for the installed cost of a typical solar domestic hot 
 water system in a new building with 60 ft 2 of collectors are provided 
 below. One estimate is for the installed cost of a "packaged" unit, and 
 the second is for assembling a system from separately purchased 
 components. 
 
1. 
 
 Complete 
 Complete 
 
 15-10 
 
 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 pipi 
 
 ng) 
 
 240 
 
 4. 
 
 Heat 
 exchanger 
 
 equipment 
 
 installation (included in pipi 
 
 ng) 
 
 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 materials 
 Installation 
 
 2,230 
 480 
 
 
 Ins 
 
 tailed cost/unit collector area 
 
 
 $45.17/ft 2 
 
15-11 
 
 MORTGAGE PAYMENTS 
 
 When a loan is involved in the purchase of a solar system, the 
 repayment of the loan may be the largest portion of the annual cost. 
 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 15-1. To 
 
 illustrate the use of Figure 15-1, 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 = (System cost - downpayment)x(Annual repayment factor) 
 Mortgage (from Figure 15-1) 
 
 or 
 
 $1248 = (14,185 - 2837) x (0.11) 
 
 OPERATING COSTS 
 
 FUEL COSTS 
 
 The conversion of unit costs of conventional energy forms to unit 
 costs of thermal energy ($/MMBtu) with various furnace efficiencies is 
 shown in Figure 15-2 for natural gas, propane, and No. 2 fuel oil. The 
 conversion of electrical energy costs to dollars per million Btu for 
 
15-12 
 
 Annua 
 
 Repayment! Factor 
 
 ^itmV 
 
 }7€Fl n ter e stzRaf e: 
 
 m= Years of Loan 
 
 Example: 
 
 ^Anhlual^Repaymentnpn 
 
 $ 1 0,0 @10°>foEl We rest je 25 
 
 ^gieffcflitoo 
 
 Figure 15-1. Repayment on Loan 
 
15-13 
 
 17 
 
 15 
 
 o 
 o 
 
 14 
 
 13 
 
 i5 12 
 
 1 1 
 
 
 10 
 <o 
 ■o 
 
 °> 
 
 Q 9 
 
 Z3 
 
 m 8 
 
 c 
 o 
 
 = 7 
 
 a. 6 
 
 o 
 
 V, 4 
 
 o 
 
 o 
 
 a> 
 
 c 
 UJ 
 
 — Natural Gas Energy Content is 
 
 ;-•- : -I -j- :_-j_;_ __ __j j ; ■ i 
 
 "Assumed i to be 1000 • Btu/1 1 5 }■ 
 
 Propane Energy Content is 
 
 ■ -.' Assumed to be 90 ,000 JBtu /g aJL 
 
 •■--•j#2 Fuel -OH Energy Content Js. 
 1 _J Assum'edI.to!.be_140,OOXi-Btu/gaL 
 
 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 
 Dollars/Energy Unit 
 Natural Gas- Price/100 ft 3 #2 Fuel Oil-Price/gallon 
 Propane -Price /gal Ion 
 
 1.2 
 
 Figure 15-2. Energy Cost per Million Btu for Natural Gas, Propane, and 
 No. 2 Fuel Oil 
 
15-14 
 
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 26 
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 23456789 
 Electricity 4/kWh 
 
 10 II 12 13 
 
 Figure 15-3. Energy Cost per Million Btu for Electricity 
 
15-15 
 
 resistance heating and heat pumps with various coefficients of 
 performance is shown in Figure 15-3. 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/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. 
 
 ELECTRICAL ENERGY COSTS FOR OPERATION 
 
 The cost of operating a solar heating system includes electrical 
 energy costs required for pumps, central heat distribution fan, valves, 
 and controller in a liquid system, and the blowers, motorized dampers, 
 and controller in an air system. The amount of electricity used in the 
 collection, storage, and distribution of solar heat varies from system 
 to system in the range from 5 to 10 percent of the total solar energy 
 
15-16 
 
 collected. Values lower than 5 percent may be appropriate for low-head 
 systems with small pressure drops and fractional horsepower motors. 
 
 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: 
 
 r °'Sx ^ = (Sy stem cost)x(Fraction of assessed value)x(tax rate) 
 
 INSURANCE 
 
 Insurance premium rates on houses with a solar system, at present, 
 are the same as for houses without solar systems. The solar equipment 
 is therefore 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 
 comprehensive 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 
 rates is available from local insurance agents. Very few insurance 
 companies have established insurance rates for solar systems. Damage to 
 
15-17 
 
 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. 
 
 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 two decades, 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. 
 
 INFLATION 
 
 The increases in costs for energy as well as costs for general 
 goods and services can be estimated on the basis of annual percentage 
 increases over current costs. The multiplying factors to determine 
 future costs for current energy costs are shown in Figure 15-4. The 
 horizontal axis is the number of years beyond the current year. The 
 
15-18 
 
 vertical axis is the multiplying factor over current costs, and is 
 simply the interest compounded annually, (1 + i) , where i is the 
 interest rate and n is years. 
 
 I I 
 
 10 
 9 
 8 
 
 S 7 
 
 oi 6 
 
 c 
 
 "5. 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 CO/ o\ 
 
 — o\« 
 
 > / 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 / 
 
 o 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 < 
 
 &x~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■s 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J^o, 
 
 
 
 
 
 
 
 
 
 
 
 
 2% 
 1% 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 8 10 12 14 16 18 20 22 24 26 28 
 Years Beyond the First 
 
 Figure 15-4. 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 
 15-4 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. 
 
15-19 
 
 TAX CREDITS 
 
 INITIAL INVESTMENT 
 
 A major item of tax credit is the legislation passed by the Federal 
 Government, effective 1 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 for qualified 
 systems on a principal residence of the taxpayer. For qualified solar 
 systems installed on buildings used for business, the tax credit is 15 
 percent. Additional credits are provided by different states and are 
 listed on the information sheets published by the National Solar Heating 
 and Cooling Information Center that are appended to this module. 
 
 INTEREST AND PROPERTY TAX 
 
 The deductions on state and Federal income taxes for property tax 
 and interest paid on the mortgage can result in substantial credit, 
 depending upon the "tax bracket" of the taxpayer. The amount of 
 interest paid annually on the mortgage decreases with the number of 
 years remaining on the mortgage, and can be determined from Tables 15-7 
 through 15-11. 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 
 15-10, 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 
 
15-20 
 
 money borrowed and payable in the first year. Mortgages are usually 
 repaid monthly, but for this analysis annual payment figures will 
 suffice. 
 
 The income tax savings on a Federal or state return because of 
 interest and tax payments would be: 
 
 , Income x .... , Interest andx w ,Tax rate basedx 
 ^tax credit' *■ taxes ' ^ on net income'' 
 
 INDIVIDUAL INCOME TAX RATE 
 
 The Federal income tax return provides credit for state income 
 taxes paid and many states give 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 giving credit is: 
 
 Net 
 
 /r ffQ ^. + n - wo N _ / FederaK , , State x , Federal,. w , state x 
 
 Rate ~ tax rate tax rate " tax rate tax rate 
 
 For state which do not give credit, the net effective rate is: 
 
 Net 
 
 ^^f^t,-w„A - / FederaK . , State x -. , FederaK „ , state x 
 
 Rate " tax rate tax rate " tax rate tax rate 
 
 If the Federal income tax rate is 25 percent and on a state income 
 tax return the rate is 10 percent, the net effective rate is 
 (0.25 + 0.10 - 2 x 0.25 x 0.10) = 0.30, or 30 percent. Thus, a net 
 annual income tax savings realizable on Federal and state taxes for 
 interest payment of $1133 is (0.30) x ($1133), or $340, which is a 
 significant amount in an economic analysis. 
 
15-21 
 
 Table 15-7 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-d+i)- 3 "" 1 " 1 Mortgage Term (m) = 10 years 
 
 Year 
 (j) 
 
 
 
 
 
 INTEREST 
 
 RATE 
 
 
 
 
 
 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 
 
15-22 
 
 Table 15-8 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = 1-Cl+i ) J ~ m_1 Mortgage Term (m) ~ 15 years 
 
 YEAR 
 (j) 
 
 .. ■■ «— ■ , . i , ■ .,,. . — . — — — i. ■ ■ — i — . — — i — - ■ 1 — ' ■ ■ - — 
 
 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 
 
15-23 
 
 Table 15-9 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i )J" m ~ 1 Mortgage Term (m) r 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 
 
 .320 
 
 .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 
 
 i 11 
 
 .442 
 
 .492 
 
 .537 
 
 .578 
 
 .614 
 
 .648 
 
 .678 
 
 .705 
 
 .730 
 
 .753 
 
 i 
 
 : 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 
 
15-24 
 
 Table 15-10 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i ) J ' m_1 Mortgage Term Cm) s 25 years 
 
 
 
 
 
 
 INTEREST RATE 
 
 
 
 
 
 YEAR 
 !(j) 
 
 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 
 
15-25 
 
 Table 15-11 
 
 Fraction of Mortgage Payment (A) Which is Interest 
 I/A = l-(l+i) J ~ m-1 Mortgage Term (m) = 30 years 
 
 YEAR 
 (J) 
 
 
 
 
 
 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 
 
15-26 
 
 METHODS OF ECONOMIC ANALYSIS 
 
 BREAKEVEN COST 
 
 One simple method to assess the economic competitiveness of a solar 
 system with a conventional system, is to compare the costs of delivered 
 energy. If the solar and conventional energy costs are equal, they are 
 said to "break even". In breakeven calculations a uniform annual cost 
 is applied, and in simplest terms, inflation and discount rates are 
 ignored. Usually, 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 could 
 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 15-1 
 
 A solar heating system with 300 ft 2 of collectors costs $12,000 
 ($40/ft 2 ). After taking a Federal income tax credit of $4,000 and state 
 income tax credit of $1,000, a 30-year loan is negotiated for $7,000 at 
 10 percent interest. The solar system will provide an annual average 
 useful thermal energy of 50 million Btu. Determine a (simple) breakeven 
 cost for the solar system. 
 
15-27 
 
 Solution 
 
 At 10 percent interest, a 30-year loan will necessitate a uniform 
 annual payment of $743 to repay the $7,000 loan. With a net useful 
 annual solar thermal energy delivery of 50 MMBtu, the solar energy cost 
 is $14.86/MMBtu, and breakeven prices of 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.H/kWh 
 
 $1.25/gal 
 
 $0.94/gal 
 
 $1.04/100 ft 3 
 
 PAYBACK 
 
 Another economic measure for the solar system is the number of 
 years (elapsed time) required for accumulated energy cost savings to 
 equal initial investment (payback period). The calculations 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, a discounted payback (DPB) period can 
 be determined. In equation form, simple payback period may be 
 calculated as follows: 
 
15-28 
 
 CDR , . System Cost 
 
 bKB tyearsj ■- ( Annual Energy Costs Savings - Annual 0* and M* Costs) 
 
 Discounted payback period is the period between initial investment 
 and the time when net energy savings, appropriately inflated and 
 discounted, equal the initial investment. A nomograph to determine both 
 simple payback and discounted payback periods is provided in Figure 
 15-5. Its use is illustrated in Example 15-2. 
 
 Example 15-2 
 
 Determine the simple payback period for solar system with a net 
 investment cost (after tax credits) of $8000 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 
 inflation rate is 15 percent and discount rate is 10 percent. 
 
 Solution 
 
 The annual energy cost savings are: 
 
 80 x 10 6 Btu v $0.05 .. t1179 
 3413 Btu/kWh x kWh " * il/ ^ 
 
 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 
 
 CDD - 8000 _ 
 
 B H72-172 8 years 
 
 c and M - Operating and Maintenance 
 
15-29 
 
 Using the nomograph of Figure 15-5, 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 (l),'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 (2). Other combinations of inflation rate and 10 
 percent discount rate may be read from the nomograph by interpolating 
 between the appropriate curves. 
 
 20 
 
 15 - 
 
 
 3 - 
 
 2 - 
 
 
 
 
 i / 
 
 ^ 
 
 v! : 
 ■ I - ■ 
 
 : . : :'.:': 
 
 ;-■;■ 
 
 
 
 "*S 
 
 
 
 
 
 
 
 
 
 
 (2 s ! 
 
 
 
 f X\ y^ 
 
 
 
 
 / f 
 
 
 -— T^s 
 
 
 jf\ _^^" ,w ~ ' 
 
 — / 
 
 i / i j 
 
 i ^-^"- : 
 
 
 J^i ' 
 
 - - - • j j ■ ■ 
 
 A?Cj/I 
 
 
 ;■: J) : 
 
 — — ;-— 
 
 i 
 
 . 1 i . 
 
 
 r^ ' 
 
 1 i 
 
 — If 
 
 If s* 
 
 
 I ! ■ 
 
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 / ' 
 
 i 
 
 :- : -- ; — 
 
 
 'if 
 
 ■ »■■-■: 
 
 i 
 
 -| .. 
 i 
 
 -: 
 
 
 !~^ 
 
 fEL; 
 
 \- 
 
 : | ":"." 
 
 
 1 
 
 ZCL . 
 
 i r 
 
 1- 
 
 -:■ 
 
 _4_ ) _ 
 
 
 1 :: ! 
 
 
 
 ^1 
 
 —t 
 
 ■ 1 ! 
 
 XliX 
 
 
 
 ■ 1 
 
 
 I 
 
 
 yrs 
 
 ~Z_Z"_ 
 
 ^ 1 
 
 ~— - 
 
 
 — u t 
 
 CD 1 CO uu | 
 
 M 
 
 
 / 
 
 r- 1 oo | ol 
 
 ■•- : ;,- — i 
 
 E£j35^ 
 
 t 
 
 -j^p 
 
 i ■)■•■ )-: 
 i- i 
 
 - 1 ,-:: 
 
 — . — . — 
 
 -~i- 
 
 — i — ■- ■ - 
 
 
 
 -Hr" : 
 
 1 
 
 .::r""±. 
 
 :^l_,_ 
 
 
 f— jr 
 
 l — 
 
 1 ~ 
 
 1 
 
 i 
 
 
 
 - r 
 
 3Er: 
 
 
 — -i 
 
 —i- 
 
 ■ ■ 
 
 ]•--■- 
 1 
 
 \:::r: 
 
 — 1 
 1 
 
 i 
 
 
 Inflation Discount 
 Rate Rate 
 
 © 
 
 Investment 
 
 Cost, $ 
 rlOx I0 4 
 
 - 8 
 
 - 6 
 
 - 4 
 
 =-£ 
 
 - 4 
 
 M0XI0 2 
 
 Annual 
 Savings, $ 
 
 [-20,000 
 
 - 15,000 
 
 -10,000 
 : 8,000 
 6,000 
 
 - 4,000 
 
 - 2,000 
 
 1,000 
 800 
 
 600 
 
 10 
 
 15 
 
 20 
 
 Discounted Payback Period, yrs 
 
 Figure 15-5. Nomograph for Determining SPB and DPB 
 
15-30 
 
 LIFE-CYCLE COST ANALYSIS 
 
 The total cost of a solar heating system over its useful life 
 includes (1) capital and installation costs or mortgage payments for 
 money borrowed to pay for the installed system, (2) fuel cost for the 
 auxiliary unit, and (3) operating and maintenance (0 and M) costs. 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. 
 Whether a solar system is economically competitive with a conventional 
 system requires a comparison of the total costs of each system over a 
 selected number of years, usually the projected useful life of the solar 
 system. This life-cycle cost analysis is first explained, and another 
 type of comparison, an annual cash flow analysis, then follows. 
 
 The yearly cash flow for a residential solar heating system is: 
 
 Yearly cost _ Mortgage Auxiliary Property Insurance 
 with solar payment fuel cost tax increase premium 
 
 (15-1) 
 + Operating Maintenance _ Income tax savings for 
 costs cost interest and taxes paid 
 
 whereas for a non-solar system, 
 
 Yearly cost _ Fuel + Operating and (15-2) 
 
 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. 
 
 
15-31 
 
 Cash flow calculations should include inflation, with fuel costs 
 probably increasing 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 (15-1) or (15-2) 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 to 
 the value of first year dollars. Hence, when the present worth of each 
 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 (15-1) and (15-2) may be rewritten as follows: 
 
 C T (solar) = (ACJE 1 + C E + C E + (l-F)Lc f E f (15-3) 
 
 I a 1 oo mmft 
 
 and 
 
 C Tr (non-solar) = C E + C E + Lc.E. (15-4) 
 
 IL ocomcmff 
 
 where A is the collector area, ft 2 , 
 
 C-j- 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, 
 
 o 
 
 $/yr, 
 
 C is the first year operating cost for the non-solar 
 
 oc 
 
 system, $/yr, 
 
 C is the first year maintenance cost for the solar system, 
 
 m 
 
 $/yr, 
 
15-32 
 
 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, 
 
 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 t 
 
 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 ± r (15-5) 
 
 (l+d)\d-r) 
 
 and 
 
 P/X(d,r,n) = n/(l+r) for d = r (15-6) 
 
 where P is the present value of an annuity over n years, 
 X is the first year cost, 
 d is the discount 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 
 
15-33 
 
 Equations (15-5) and (15-6). Tables of P/X values are provided in this 
 
 module for an appropriate range of d, r, and n in Tables 15-12 through 
 15-17. 
 
 The economic factors can now be expressed as: 
 
 E Q = P/X(d,r Q ,n) years, (15-7) 
 
 E m = P/X(d,r m ,n) years, (15-8) 
 
 E f = P/X(d,r f ,n) years. (15-9) 
 
 The economic factor E-, is slightly more involved and is expressed 
 
 as: 
 
 where 
 
 E 1 = a + [(I - t)p + h)]P/X(d,g,n) + 
 
 (i - a)ra - t) P/ ! x ( d *°» m ) + ( t ) p/x ( d ^'» m ) i (15-10) 
 
 U a;LU t; P/X (i,0,m) (t; P/X (0,i,m) J Ui) W) 
 
 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 15-12 through 15-17 
 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. 
 
15-34 
 
 Table 15-12 
 Values of P/X (d, r, n) for Discount Rate of Percent 
 
 Years 
 
 
 Annual Rate 
 
 • of Increase 
 
 
 
 
 
 3 
 
 6 
 
 8 
 
 10 
 
 12 
 
 10 
 
 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 
 
 i 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 
 
15-35 
 
 Table 15-13 
 Values of P/X (d, r, n) for Discount Rate of 4 Percent 
 
 Years 
 
 
 Annual Rate 
 
 of Increase 
 
 
 10 
 
 
 
 3 
 
 6 
 
 8 
 
 i 
 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 
 
 1 
 
 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 
 
 i 
 
 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 
 
 i 
 
 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 
 
 18 
 
 12.659 
 
 15.963 
 
 20.449 
 
 24.314 
 
 29.076 
 
 i 
 
 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 
 
15-36 
 
 Table 15-14 
 Values of P/X (d 9 r 9 n) for Discount Rate of 6 Percent 
 
 Years 
 
 1 
 
 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 
 
 19.360J 
 
 i 
 
 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 
 
 25.830 
 
 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 
 
 36.300 
 
 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 
 
 49.350 
 
 26 
 
 13.003 
 
 17.532 
 
 24.528 
 
 31.290 
 
 40.493 
 
 53.087 
 
 27 
 
 13.211 
 
 17.979 
 
 25.472 
 
 32.823 
 
 42.965 
 
 57.035 
 
 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 
 
15-37 
 
 Table 15-15 
 Values of P/X (d, r, n) for Discount Rate of 8 Percent 
 
 Years 
 
 Annual Rate of Increase 
 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 24 
 25 
 26 
 27 
 28 
 29 
 30 
 
 
 
 6.710 
 
 7.139 
 
 7.536 
 
 7.904 
 
 8.244 
 
 8.559 
 
 8.851 
 
 9.122 
 
 9.372 
 
 9.604 
 
 9.818 
 
 10.017 
 
 10.201 
 
 10.371 
 
 10.529 
 
 10.675 
 
 10.810 
 
 10.935 
 
 11.051 
 
 11.158 
 
 11.258 
 
 7.550 
 8.127 
 8.676 
 9.200 
 9.700 
 10.177 
 10.632 
 11.066 
 11.479 
 11.874 
 12.250 
 12.609 
 12.951 
 13.277 
 13.589 
 13.885 
 14.169 
 14.438 
 14.696 
 14.942 
 15.176 
 
 8.525 
 
 9.293 
 
 10.046 
 
 10.786 
 
 11.513 
 
 12.225 
 
 12.926 
 
 13.611 
 
 14.285 
 
 ; 14.947 
 
 | 15.596 
 
 | 16.233 
 
 ! 16.858 
 
 I 
 
 | 17.472 
 ' 18.074 
 18.666 
 19.246 
 19.815 
 20.374 
 20.923 
 21.461 
 
 8 
 
 9.259 
 10.185 
 11.111 
 12.037 
 12.963 
 13.889 
 14.815 
 15.741 
 16.667 
 17.593 
 18.519 
 19.444 
 20.370 
 21.296 
 22.222 
 23.148 
 24.074 
 25.000 
 35.926 
 26.852 
 27.778 
 
 10 
 
 10.070 
 11.183 
 12.316 
 13.470 
 14.645 
 15.842 
 17.061 
 18.303 
 19.568 
 20.856 
 22.169 
 23.505 
 24.866 
 26.253 
 27.665 
 29.103 
 30.568 
 32.060 
 33.580 
 35.127 
 36.704 
 
 12 
 
 10.965 
 12.297 
 13.679 
 15.111 
 16.597 
 18.137 
 19.735 
 21.392 
 23.110 
 24.892 
 26.740 
 | 28.656 
 
 S 
 
 30.643 
 
 i 
 
 ! 32.704 
 
 j 
 
 34.841! 
 
 37.058 
 
 39.356 
 
 41.740 
 
 44.212 
 
 46.775 
 
 49.433 
 
15-38 
 
 Table 15-16 
 Values of P/X (d, r, n) for Discount Rate of 10 Percent 
 
 Years 
 
 
 An 
 
 nual 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 ! 
 
 i 
 
 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 
 
 121.166 
 1 
 
 27.273 
 
 35.848 
 
15-39 
 
 Table 15-17 
 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 
 
15-40 
 
 Example 15-3 
 
 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 r 
 
 cost, r , is 10 percent, annual rate of increase for maintenance, r , is 
 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 15-15) 
 E m = P/X (8,6,20) = 15.596 (from Table 15-15) 
 E f = P/X (8,12,20) = 26.740 (from Table 15-15) 
 
 Example 15-4 
 
 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 (15-10), 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 
 
 
15-41 
 
 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) i|^f + (0.35) §§7357] 
 
 E 1 = 1.245 (ans) 
 
 Example 15-5 
 
 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: 
 
 A = 500 ft 2 
 
 V 
 
 = 6% 
 
 C = 26 $/ft 2 
 a 
 
 r f : 
 
 = 12% 
 
 C Q = 87 $/yr 
 
 m = 
 
 25 years 
 
 C oc - 20 $/yr 
 
 i = 
 
 10% 
 
 C m = 100 $/yr 
 
 a = 
 
 20% down 
 
 C mc = 10 $/ ^ 
 
 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 (15-13) 
 
 From Example 15-3, E n = 22.169, E = 15.596, E. = 26.740. 
 
 m f 
 
 From Example 15-4, E-, = 1.245 
 
15-42 
 
 Therefore, 
 
 C T = (500)(26)(1.245) + (87X22.169) + (100)(15.596) 
 
 + (1 - .68)(130)(10.25)(26.740) 
 
 C T = $31,075 present value (total cost) over 20 years of 
 1 life 
 
 The equation to apply to the non-solar system is 
 
 Equation (15-4). 
 
 C TC = (20)(22.169) + (20X15.596) + (130)(10. 25)(26. 740) 
 
 C Tr = $36,230 present value (total cost) over 20 years of 
 IL 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: 
 
 P o?1avings Ue = C TC ' C T " 36 > 230 " 31 ' 075 = $5155 
 
 While in Example 15-3 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 (15-1) and (15-2). 
 
 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-r (15-11) 
 
 (l+d) q 
 
 
15-43 
 
 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 15-18. 
 
 ECONOMIC ANALYSIS WORKSHEETS 
 
 There are included in this section "short" forms and "long" forms 
 for calculating annual cash flow and life-cycle costs of a system. The 
 short form enables calculation of the present worth of cumulative 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 rates of increase can be changed for any item. In using 
 the short form the inflation rates are assumed to be 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 15-12 through 15-17. 
 
15-44 
 
 Table 15-18 
 Present Worth Factors (P) 
 (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 1.467 
 
 .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 
 
15-45 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 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 15-3) 
 
 (t/kWh 
 
 c f , c f , current cost of fuel 
 
 c (use Figure 15-2 or 15-3) 
 
 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, 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 
 
 ft 2 
 decimal 
 
 _$/MMBtu 
 $/MMBtu 
 
 yrs 
 
 jdecimal 
 decimal 
 
 $/ft : 
 
 decimal 
 decimal 
 decimal 
 decimal 
 
 decimal 
 decimal 
 
15-46 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) $ 
 
 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 15-1) $/yr 
 
 26. Cr, 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 
 
 (estimate) $/yr 
 
 Non-Solar System Cost Items 
 
 31. Cp , 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 
 
15-47 Worksheet LCA-2 
 
 Sheet 1 of 2 
 
 LIFE-CYCLE COST ANALYSIS 
 
 Total Cost for Solar System 
 
 33. n 9 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 
 
 From Tables 15-12 to 15-17, determine: 
 
 37. P/X (d,g,n) 
 
 38. P/X (d s 0,m) 
 
 39. P/X (i,0,m) 
 
 40. P/X (d,i,m) 
 
 41. P/X (0,i,m) 
 
 ao f4.\r P/X (d,i,m) n _ / line 19 x line 40 ^ 
 
 **' u;L P/X (0,i s m) J ' l line 41 l 
 
 ao /, +\rlllJA&wh - r (l-line 19) x (line 38) i 
 
 w * U " z,i P/X (i,0 s 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 x = (line 9) + (line 48) + (line 46) 
 
 From Tables 15-12 to 15-17, determine: 
 
 50. E Q = P/X (d,r Q ,n) 
 
 51. E m = P/X (d,r m ,n) 
 
 52. E f = P/X (d,r f ,n) 
 
15-48 
 
 Worksheet LCA-2 
 Sheet 2 of 2 
 
 53. 
 54. 
 55. 
 56. 
 
 57. 
 
 (A)(C HE,) = (line 34 x line 11 x line 49) 
 
 a i 
 
 C o E Q = (line 29 x line 50) _____ 
 
 C m E m = ( line 30 x line 51 ^ 
 
 (l-F)(L)(c f )(E f ) = [ )( )( )( ) 
 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 C T = line 53 + line 54 + line 55 + 1 ne 56 - line 22 
 
 Total Cost for Non-Solar System 
 
 58. 
 
 C oc E o = line 32 x line 50 
 
 59. Lc f 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) 
 
15-49 
 
 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 15-7 through 15-11 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 
 
15-50 
 
 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. 
 
15-51 
 
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15-52 
 
 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 
 Worksheet LCA-1. The costs in succeeding years are determined by 
 multiplying 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 15-18. 
 
 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]. 
 
 
15-53 
 
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15-54 
 
 EXAMPLE 15-6 
 
 Determine the life-cycle cost and energy cost savings of a 
 liquid-heating solar system with 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 
 $/ft2 of collector. 
 
 6. r,, 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. 
 
15-55 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project ^Hn 
 
 V> 
 
 £»M Kc^ide ur 
 
 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 15-3) s.O 1 /kWh 
 
 7. c f , c f , current cost of fuel (a**) 
 
 c (use Figure 15-2 or 15-3) 
 
 Terms of Loan 
 
 8. m, term of the loan for solar system 
 
 9. a, downpayment £id % 
 
 10. i, interest rate on loan \f) % 
 
 Economic Data 
 
 * 
 
 \0%i3 M MBtu/yr 
 P { , Q M MBtu/yr 
 2 r 1 3 M MBtu/yr 
 
 t>00 ft 2 
 
 ■ b% decimal 
 
 SA.GS $ /MMBtu 
 \3.00 $/MMBtu 
 
 £t? y rs 
 (^«5^ decimal 
 
 (J, 1(3 d ecimal 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 17. 
 18. 
 19. 
 
 C , installed cost of solar system per 
 unit area 
 
 r f , estimated auxiliary fuel inflation 
 rate 
 
 r , r , estimated electric energy 
 inflation 
 
 g, r . estimated general inflation 
 
 3 1 . SZ- $/ft 2 
 
 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 
 
 \5 % 
 
 is- % 
 
 1 % 
 
 Q,0$ 
 
 decimal 
 
 0.&O=£_ decimal 
 
 , 32- decimal 
 
 0,0% 
 
 decimal 
 
 0,35" 
 
 decimal 
 
 o.lo 
 
 decimal 
 
15-56 
 
 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) 
 
 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 15-1) 
 
 26. Cr, 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) 
 
 nr 
 
 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) 
 
 1 0,110 $ 
 Ar } OOQ $ 
 
 \4rpQ $ /yr 
 _Hl__$/yr 
 
 ± 1 7 $ /yr 
 
 1*2- 
 
 [00 
 
 $/yr 
 
 $/yr 
 
 l6"53- $ /yr 
 
 M $/yr 
 
15-57 Worksheet LCA-2 
 Sheet 1 of 2 
 
 LIFE-CYCLE COST ANALYSIS 
 
 Total Cost for Solar System 
 
 33. n, total years of analysis pt y rs 
 
 34. A, collector area (line 4 of LCA-1) 5~DO f t 2 
 
 35. L, annual heat load (line 3 of LCA-1) (2fjL3 M MBtu 
 
 36. F, fraction of annual heat provided 
 
 by the solar system (line 5 of 
 
 LCA-1) . £ft d ecimal 
 
 From Tables 15-12 to 15-17, determ >e: 
 
 37. P/X (d,g,n) [4,1 (, Q 
 
 38. P/X (d.O.m) q,D77 
 
 39. P/X (i,0,m) 9. Oil 
 
 40. P/X (d.i.m) 3 3,72 7 
 
 41. P/X (0,i,m) 9 J1J4J 
 
 A9 / + np P/X (d,i ,m) 1 _ / line 19 x line 40 x s\ /\ <v j 
 
 4 ^' UjL P/X (0,i,m) J " [ line 41 } V-VV [ 
 
 a<> n ^i -P/X (d,0,m) 1 _ r (l-1ine 19) x (line 38)- , 
 4J * u ' tJL 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 x = (line 9) + (line 48) + (line 46) 
 
 From Tables 15-12 to 15-17, determine: 
 
 50. E Q = P/X (d,r Q ,n) 
 
 51. E m = P/X (d,r m ,n) 
 
 52. E f = P/X (d,r f ,n) 
 
 0, 
 
 U\ 
 
 c 
 
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 0, 
 
 62xs 
 
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15-58 
 
 Worksheet LCA-2 
 Sheet 2 of 2 
 
 53. 
 54. 
 55. 
 56. 
 
 57. 
 
 (A)(C KEJ = Uine 34 x line 11 x line 49) \1 , 5tc5 $ 
 
 ArO^ $ 
 
 (l-F)(L)(c f )(E f ) = (JOji^il^Qu^ \?L f 22$ $ 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 C T = line 53 + line 54 + line 55 + line 56 - line 22 
 
 C E Q = (line 29 x line 50) 
 
 c m E m = (line 30 x line 51) 
 
 mm 
 
 33p7E $ 
 
 Total Cost for Non-Solar System 
 
 58. C n £ = line 32 x line 50 
 
 oc o 
 
 59. Lc f Ex = 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) 
 
 5>4~ $ 
 
 *4,443$ 
 
15-59 
 
 EXAMPLE 15-7 
 
 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<t/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/ft 2 . 
 
 6. r f , fuel 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. 
 
15-60 
 
 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 
 
 heating 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. 
 
15-61 
 
 Worksheet LCA-1 
 Sheet 1 of 2 
 
 DATA SHEET FOR ECONOMIC ANALYSIS 
 
 Project Z>Olqv '[ 
 
 Building Data 
 
 1. Annual space heating load lQJLl3 M MBtu/yr 
 
 2. Annual DHW heating load £), Q M MBtu/yr 
 
 3. Total H and DHW load (add lines 1 & 2) U^- 3 M MBtu/yr 
 
 Solar System Data 
 
 4. Collector area 4^0 f t 2 
 
 5. Fraction of annual heating load 
 
 supplied from solar <5u d ecimal 
 
 6. c , current energy cost for electricity 
 
 Energy Prices 
 
 (useTigu"re'l5-3J~ ~S~ < £/kWh~ LfL^L $ /MMBtu 
 
 7. c f , Cp . current cost of fueled) . 
 
 T TC (use Figure 15-2 or 15-3) U-OU $ /MMBtu 
 
 Terms of Loan 
 
 8. m, term of the loan for solar system jj_Q_ y rs 
 
 9. a, down payment \Q % . \0 d ecimal 
 
 10. i, interest rate on loan { % /) , Id d ecimal 
 
 Economic Data 
 
 11. C . installed cost of solar system per , ^ , 
 
 a unit area 3(o. (J? $ /ft 2 
 
 12. r f , estimated auxiliary fuel inflation 
 
 rate Xlavle^ % 
 
 13. r , r , estimated electric energy 
 
 inflation vJArJg/s % 
 
 14. g, r , estimated general inflation 
 
 rate Vav-ie^% 
 
 15. p, property tax rate (based on 
 
 market value) . 03 d ecimal 
 
 16. h, insurance premium rate , Op 3 d ecimal 
 
 17. Federal income tax rate for owner '25 d ecimal (first year) 
 
 18. State income tax rate for owner d ecimal 
 
 19. t, effective income tax rate 
 
 {i.e., (line 17) + (line 18) - 
 
 - [2 x (line 17) x (line 18)]} Qj2^2 d ecimal (first year) 
 
 20. d, market discount rate , \ rt d ecimal 
 
15-62 
 
 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) 
 
 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 15-1) 
 
 26. C f , 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) 
 
 nv 
 
 Non-Solar System Cost Items 
 
 31. Cr , 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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 \*\ 
 
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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. c , current energy cost for electricity 
 
 (use Figure 15-3) 
 
 C/kWh 
 
 7. c f , c.p , current cost of fuel 
 
 T TC (use Figure 15-2 or 15-3) 
 
 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, 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) $ 
 
 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 15-1) $/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 
 
 (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 
 
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) f t 2 
 
 35. L 5 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 
 
 From Tables 15-12 to 15-17, determine: 
 
 37. P/X (d.g.n) 
 
 38. P/X (d,0,m) 
 
 39. P/X (i,0,m) 
 
 40. P/X (d,i,m) 
 
 41. P/X (0,i,m) 
 
 a.9 / + \rP /X (d,i,m)i / line 19 x line 40 x 
 
 ^' {Z)l P/X (0,i,m) J ' { line 41 ' 
 
 a-} M + Nr P/X (d.O.m)- . _ r (l-1ine 19) x (line 38)- , 
 
 43 * (1 " t)L P/X (i 9 0,m) J - [ line 41 } 
 
 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) 
 
 From Tables 15-12 to 15-17, determine: 
 
 50. E Q = P/X (d,r Q ,n) 
 
 51. E m = P/X (d,r m ,n) 
 
 52. E f = P/X (d,r f ,n) 
 
Worksheet LCA-2 
 Sheet 2 of 2 
 
 53. 
 54. 
 55. 
 56. 
 
 57. 
 
 (A)(CJ(E,) = (line 34 x line 11 x line 49) 
 
 a 1 
 
 C Q E = (line 29 x line 50) 
 
 C m E m = ( line 30 x line 51 ^ 
 
 (l-F)(L)(c f )(E f ) = ( )( )( )( ) 
 
 (1 - line 36) x line 35 x line 7 x line 52 
 
 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 o 
 
 59. Lc f E f = 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) 
 
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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 
 „ .SOLAR ^ 
 
 INFORM*ATtON obiter 
 
 ■:■/":. 
 
 ■Wfr v 
 
 3/30/80 
 
 The Center is operated by the Franklin Research Center tor the U.S. Department of Housing and Urban Development and the 
 U.S. Department ot Energy. The listings contained herein are based on information known by the Center at the time of 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 INCENTIVE/. 
 
 An energy conseivation 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 energy 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 
 (^16) 322-3R90 
 
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 establishes 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 tor heating space or water or for generating electricity. For single- 
 family dwellings the credit equals 25% of eligible expend'tures 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 water 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). 
 
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 soiar 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 State 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 will 
 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 installed 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 guidelines) 
 
 Contact (for sales tax 
 information) 
 
 Ohio Department of Energy 
 30 E. Broad Street. 34th 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 multifamily 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). 
 
19 
 
 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 
 
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 apply 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 
 a'e 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 of 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 of 1979). 
 
 Contact Local taxing authority 
 
 LAND USE 
 
 This law subjects solar easements to the same legal 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 
 
 Tnis 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 tne 
 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 8910 
 Madison. Wl 53708 
 (608) 266-1911 
 
 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 16 
 
 OPERATIONAL CHECK-OUT 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
16-i 
 TABLE OF CONTENTS 
 
 Pa^e 
 
 INTRODUCTION 16-1 
 
 OBJECTIVE 16-1 
 
 GENERAL PROCEDURE 16-2 
 
 VISUAL INSPECTION 16-2 
 
 FINAL CHECK . 16-3 
 
 OPERATIONAL CHECK-OUT 16-4 
 
 PERFORMANCE TEST 16-4 
 
 AIR SYSTEMS 16-6 
 
 INSPECTION CHECK LIST - COLLECTORS 16-6 
 
 INSPECTION CHECK LIST - PEBBLE-BED HEAT STORAGE UNIT . 16-7 
 
 START-UP PROCEDURES - AIR HANDLER 16-8 
 
 PERFORMANCE CHECK 16-11 
 
 PERFORMANCE ANALYSIS 16-13 
 
 LIQUID SYSTEMS 16-14 
 
 PUMPS 16-15 
 
 HEAT EXCHANGER 16-16 
 
 ANTIFREEZE SOLUTION 16-16 
 
 LIQUID LEVELS 16-17 
 
 CORROSION INHIBITOR 16-18 
 
 DRAIN-DOWN SYSTEMS 16-18 
 
 Collector Loop 16-18 
 
 Storage Tank ........ 16-19 
 
 Sensors and Controls ...... 16-20 
 
16- ii 
 
 Page 
 
 PERFORMANCE CHECK 16-21 
 
 APPENDIX A16-1 
 
16-1 
 
 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. 
 
 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. 
 
16-2 
 
 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 perim- 
 eter 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; 
 
16-3 
 
 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 
 
16-4 
 
 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 
 
16-5 
 
 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 perfor- 
 mance. 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. 
 
16-6 
 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 - C0LLECT0RS (1) 
 
 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 (IV 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. 
 
16-7 
 
 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. 
 
16-8 
 
 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. 
 
16-9 
 
 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,, 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. 
 
16-10 
 
 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 VL 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. 
 
 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 
 
16-11 
 
 c. The dampers inside the AU 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 top 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 
 
 (D Flexible 
 the Solar Heating Flow Schematic shown on the next page v '* 
 
 tubing is then inserted for connection to a manometer or sensitive 
 
 ^ 'Courtesy of The Solaron Corporation, used by permission. 
 
16-12 
 
 SOLARON 
 COLLECTORS 
 
 MO-U 
 
 Ll 
 o 
 
 CO 
 
 Sol 
 
 VOptional 
 Summer Bypass 
 
 HW COILs H0-4 
 oron Air Handler-^^\ 
 
 rT-I^H 
 
 /"" TV^Air Plenur 
 
 / jF 3 ~ — 38 
 
 / r Heat Storoge ~« 
 
 ED 
 
 Rock 
 
 & 
 
 £«=»_ 
 
 ^Air Plenum- 
 
 project name: Typical Prnjprt. date.. 
 
 PROJECT TYPE. RES'L X_ COMM'L IND'L 
 
 AGRI OTHER 
 
 location: Sunbeam Valley, California 
 
 COLLECTOR ARRAY:_2_HIGH X 12 WIDE = 468 SQ.ft 
 
 serviceman: I. Deal Heaven! y 
 
 company: SUPERIOR SUNBEAMS. INC. 
 
 PHONE () 
 
 BD-2^ BD-14 Fi ^, er L AJL_J 
 
 SOLAR HEATING FLOW SCHEMATIC 
 
 = Open 
 P.O. = Partially Open 
 C s Closed 
 
 SEQUENCE OF OPERATIONS 
 
 HEATING FROM COLLECTOR 
 
 HEATING FROM STORAGE 
 
 STORING HEAT 
 
 HEATING WITH AUX. FURNACE 
 
 WATER HEATING (SUMMER) 
 
 PO 
 
 P.O. 
 
 PO. 
 
 D-4/ 
 
 9^c 
 
 2^e 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 ON 
 
 Solaron 
 
 air 
 handler 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 ON 
 
 ON 
 
 ON 
 
 OFF 
 
 ON 
 
 OFF 
 
 OFF 
 
 OFF 
 
 OFF 
 
 ON 
 
 OFF 
 
 FOR HEAT PUMP SYSTEMS: MD-2 Closed, MD-3 0pen, BD-I Closed 
 
 
 AIR HANDLER 
 
 SOLAR 
 
 AUX 
 
 Design CFM 
 
 Design Ext SP 
 
 Fan RPM 
 
 HP 
 
 Motor RPM 
 
 Volt 
 
 Phase 
 
 FLA 
 
 SF 
 
 SFA 
 
 Insul. Class 
 
 Motor Mfg 
 
 Model No 
 
 936 
 0.80" 
 
 
 
 1160 
 1/2 
 
 1725 
 
 
 
 
 115 
 1 
 6.0 
 1.25 
 6.8 
 R 
 GE 
 '4T0051 
 
 
 
 
 
 
 
 
 
 
 T, (CFM S0 | ) + T 2 (CFM QUX - CFM S0 | ) 
 CFM aux . 
 
 T, = I30°F 
 T 2 = 68° F 
 T 3 = 117° F 
 
 TEMPERATURE & STATIC PRESSURE MEASUREMENTS 
 
 STORING HEAT! Mo,0 5 r £ mps - 
 
 HEATING FROM 
 STORAGE 
 
 HEATING FROMJ Motor Amps 
 COLLECTOR 5.3 
 
 POINT 
 
 °F 
 
 STATIC 
 ^PRESSURE 
 
 S.P 
 
 DIFF. 
 
 POINT 
 
 °F 
 
 STATIC 
 PRESSURE 
 
 S.P. 
 DIFF. 
 
 POINT 
 
 °F 
 
 STATIC 
 PRESSURE 
 
 S.P 
 DIFF. 
 
 1 
 
 >< 
 
 r 0.00" 
 
 X 
 
 1 
 
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 - 
 
 -.19" 
 
 
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 2 
 
 138 
 
 -.34" 
 
 
 2 
 
 - 
 
 -.01" 
 
 
 2 
 
 - 
 
 -.94" 
 
 > .69 
 
 
 3 
 
 132 
 
 + .35" 
 
 3 
 
 130 
 
 -.29" 
 
 
 3 
 
 _ 
 
 -.20" 
 
 
 >.19 
 
 ).14 
 
 ) .04" 
 
 4 
 
 68 
 
 + .16" 
 
 4 
 
 68 
 
 -1R" 
 
 4 
 
 
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 5 
 
 66 
 
 + .06" 
 
 
 5 
 
 
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 5 
 
 66 
 
 -.34" 
 
 
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 ) .00 
 
 ).42" 
 
 6 
 
 141 
 
 -.25" 
 
 6 
 
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 122 
 
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 7 
 
 
 
 
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 8 
 
 
 
 
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 117 
 
 + .18" 
 
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 (?) COPYRIGHT 2-1978 SOLARON CORP., DENVER, CO. 80222 
 
16-13 
 
 PERFORMANCE ANALYSIS 
 Air Heating System 
 
 Collector 
 
 1. Area, A ft 2 
 
 c 
 
 2. Inlet temperature, T. 
 
 3. Outlet temperature, T 
 
 4. Pressure drop across blower, Wp 
 
 5. Flow rate, V 
 
 6. Air density, p 
 
 7. Specific heat, c 
 
 8. Heat delivery rate: 
 Q c = (mc p )(T o - Ti )(60) 
 
 = V • pc (T -T.)(60) Btu/hr 
 
 DO 1 
 
 B. Collector Efficiency: 
 
 Solar radiation on horizontal 
 [ H 
 
 °F 
 
 °F 
 
 in W.G. 
 
 cfm 
 
 .07 
 
 lb/ft 3 
 
 .24 
 
 Btu/(lb 
 
 2 
 
 surface, I u Btu/(ft -hr) 
 
 2 
 or on tilted surface, I T Btu/(ft *hr) 
 
 Collector efficiency 
 Q c 
 
 h = T-|- x 100 % 
 
 c 1c 
 
16-14 
 
 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. 1 i qui d-to- liquid heat exchanger 
 
 3. valves and piping for draining and venting. 
 
 ^Courtesy of The Solaron Corporation, used by permission. 
 
16-15 
 
 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 
 
16-16 
 
 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 
 
16-17 
 
 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. 
 
16-18 
 
 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 
 atmospheric 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 
 
16-19 
 
 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 
 
16-20 
 
 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 
 
16-21 
 
 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 
 
16-22 
 
 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. 
 
16-23 
 
 PERFORMANCE ANALYSIS 
 
 
 Liquid Heating System 
 
 Collector 
 
 i 
 
 1. 
 
 Area, A Q 
 
 2. 
 
 Inlet temperature, T. 
 
 3. 
 
 Outlet temperature, T Q 
 
 4. 
 
 Pressure drop across pump 
 
 5. 
 
 Fluid or flow rate, G 
 
 6. 
 
 Specific heat, c 
 
 7. 
 
 Fluid specific weight, y 
 
 8. 
 
 Heat delivery rate: 
 
 ft 2 
 
 _°F 
 _ psi 
 
 _ gpm 
 
 _ Btu/(lb-°F) 
 lb/gal 
 
 Qc = G VVV( 60 > Tf 
 
 Collector Efficiency: 
 
 1. Solar radiation on horizontal 2 
 surface, I„, or Btu/(ft -hr) 
 
 H 2 
 
 tilted surface, I T Btu/(ft -hr) 
 
 2. Collector efficiency 
 
 n^rj- x 100 * 
 
 c ^c 
 
A16-1 
 
 v 
 
 APPENDIX 
 
A16-2 
 
 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 
 
A16-3 
 
 Yes No 
 
 C. Thermal Storage Units: 
 
 1. Container materials are sufficiently durable 
 
 2. Contamination of air or water is adequately protected 
 
 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 
 
A16-4 
 
 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 17 
 
 INTRODUCTION TO SOLAR COOLING 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 

17-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 GLOSSARY OF TERMS 
 
 Page 
 17- ii 
 17-iii 
 
 INTRODUCTION 
 
 OBJECTIVE 
 
 CATEGORIES OF SPACE COOLING METHODS 
 
 DEFINITION OF TERMS .... 
 
 REFRIGERATION SYSTEMS 
 
 ABSORPTION REFRIGERATION . 
 
 Temperature Restrictions . 
 
 Types of Lithium-Bromide- Absorption 
 Refrigeration Systems 
 
 SOLAR RANKINE-CYCLE ENGINE 
 
 HEAT PUMP 
 
 EVAPORATIVE COOLING 
 
 EVAPORATIVE COOLING THROUGH ROCK BED 
 EVAPORATIVE COOLING WITH ROOF PONDS AND SPRAYS 
 
 DESICCANT COOLING (DEHUMIDIFICATION) 
 
 TRIETHYLENE GLYCOL OPEN-CYCLE DESICCANT 
 SYSTEM 
 
 SOLID DESICCANT SYSTEMS 
 
 REFRIGERATION COOLING WITH ROCK BED OR WATER STORAGE 
 
 REFERENCES 
 
 17-1 
 17-1 
 17-1 
 17-2 
 17-3 
 17-5 
 17-6 
 
 17-7 
 
 17-8 
 
 17-10 
 
 17-10 
 
 17-10 
 
 17-11 
 
 17-13 
 
 17-13 
 17-15 
 17-15 
 17-18 
 
17-ii 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 17-1 Vapor-Compression Air-Conditioner Schematic . . 17-4 
 
 17-2 Absorption Air-Conditioner or Chiller — 
 
 Schematic Drawing ....... 17-5 
 
 17-3 Rankine-Cycle Vapor-Compression System . . . 17-9 
 
 17-4 Evaporative Cooling with Rock-Bed Storage . . 17-12 
 
 17-5 Schematic of Triethylene Glycol (Liquid 
 Desiccant) Open-Cycle Air-Conditioning 
 System . . . . . . . . . 17-14 
 
 17-6 Solid Desiccant Dehumidification and Cooling 
 
 System ("MEC" System) 17-16 
 
17-iit 
 
 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 
 
17-1 
 
 INTRODUCTION 
 
 The withdrawal of heat from the air within a building enclosure by 
 a process which results in a temperature or humidity lower than that of 
 the natural surroundings is termed space cooling or air-conditioning. 
 Cooling systems powered by solar energy are examined in this module. 
 
 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. 
 
 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 cli- 
 matic factors and in the opportunity for joint use of some of the solar 
 
17-2 
 
 heating equipment. The discussion in this module concerns principally 
 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 -r 0.6). 
 
17-3 
 
 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 17-1. 
 
 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 
 17-2 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 
 
17-4 
 
 o 
 O 
 
 in 
 
 o 
 o. 
 o 
 
 > 
 
 c 
 o 
 
 i_ 
 0> 
 
 i_ 
 »♦- 
 
 q: 
 
 a) 
 
 EVAPORATOR 
 
 Warm Air 
 from Rooms 
 75° F 
 
 Cool Air 
 
 to Rooms 
 
 55° F 
 
 PRESSURE 
 
 REDUCING 
 
 VALVE OR 
 
 RESTRICTOR 
 
 { m Low Pressure Refrigerant, 
 Li qui 
 
 El 
 
 id and Vapor, 40° F 
 
 CONDENSER 
 
 Liquid Refrigerant, 100° F 
 
 Atmosphere 
 
 High Pressure Refrigerant Vapor, 120° F 
 
 Figure 17-1. Vapor-Compression Air-Conditioner Schematic 
 
17-5 
 
 SOLAR 
 COLLECTOR 
 
 ^> 
 
 I. GENERATOR 
 
 LIQUID 
 SOLUTION 
 
 PUMP 
 5. RECOUPERATOR 
 
 PUMP 
 
 2. CONDENSER 
 
 EXPANSION 
 VALVE 
 
 RETURN TO 
 „ COOLING TOWER 
 
 COOL AIR 
 OR WATER 
 
 I 4 4 
 
 3. EVAPORATOR 
 
 •* — A A A A 
 
 4. ABSORBER 
 
 !£! 
 
 MM 
 
 WARM AIR 
 OR WATER 
 
 COOLING TOWER WATER 
 Figure 17-2. 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 
 
17-6 
 
 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 17-2. 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 
 
17-7 
 
 usually between 160°F and 210°F. The heat input rate to the generator 
 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. 
 
17-8 
 
 Figure 17-2 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 17-3, 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 
 
17-9 
 
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17-10 
 
 experimental and developmental stages and not yet available as a 
 
 commercial 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 opera- 
 tion are described in Module 11. 
 
 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. 
 
17-11 
 
 An evaporative cooler coupled with a rock-bed storage unit is shown 
 in Figure 17-4. 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 ized retracting insu- 
 lating 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 
 
17-12 
 
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17-13 
 
 metal roof (ceiling) for radiation into the living space below. In 
 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 17-5. Moist room air is dehumidified by contacting it with a 
 solution of tri ethylene 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 tri ethylene 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 
 
17-14 
 
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17-15 
 
 may be used to heat the air stream. Heat is recovered from the glycol 
 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 crys- 
 tals, and "molecular sieve" zeolite granules are all commercially used 
 in air-drying applications. Figure 17-6 shows how one of these pro- 
 cesses 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 investi- 
 gated, 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 
 
17-16 
 
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17-17 
 
 conventional cooling machines. A heat pump or vapor-compression 
 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. 
 
17-18 
 
 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 
 Solar Energy for Heating, and Night Radiation for Cooling a 
 Building", Proceedings, United Nations Conference on New Sources of 
 Energy, Volume 5, pp. 148-158, Rome, 1964. 
 
 4. Chung, R. , Duffie, J. A., and Lbf, 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 
 Dehumidification" , 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 
 SIZING, INSTALLATION, AND OPERATION OF SOLAR HEATING AND COOLING SYSTEMS 
 
 FOR 
 RESIDENTIAL BUILDINGS 
 
 MODULE 18 
 
 FUTURE PROSPECTS FOR SOLAR HEATING 
 AND COOLING SYSTEMS 
 
 SOLAR ENERGY APPLICATIONS LABORATORY 
 COLORADO STATE UNIVERSITY 
 FORT COLLINS, COLORADO 
 
18-i 
 
 TABLE OF CONTENTS 
 
 LIST OF FIGURES 
 LIST OF TABLES . 
 
 Page 
 18- ii 
 18- ii 
 
 INTRODUCTION . 
 
 OBJECTIVE 
 
 SOLAR COLLECTORS 
 
 SELECTIVE SURFACES . 
 EVACUATED TUBE COLLECTORS 
 TRANSPARENT HONEYCOMBS 
 CONCENTRATING COLLECTORS . 
 
 THERMAL STORAGE 
 
 HEAT EXCHANGER . 
 
 SYSTEMS 
 
 18-1 
 
 18-2 
 
 18-2 
 
 18-2 
 
 18-4 
 
 18-6 
 
 18-8 
 
 18-8 
 
 18-12 
 
 18-13 
 
18-1 i 
 
 LIST OF FIGURES 
 
 Figure Page 
 
 18-1 Types of Evacuated Tube Collectors .... 18-5 
 
 18-2 Transparent Honeycomb Collector .... 18-7 
 
 18-3 Direct Contact, Liquid-Liquid Heat Exchanger . . 18-13 
 
 LIST OF TABLES 
 
 Table Page 
 
 18-1 Selective Surfaces Characteristics .... 18-3 
 
 18-2 Properties of Phase-Change Heat Storage Materials . 18-10 
 
 18-3 Properties of Possible Collector Fluids . . . 18-14 
 
18-1 
 
 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. 
 
18-2 
 
 OBJECTIVE 
 
 This module contains descriptions of new concepts and developments 
 in solar heating and cooling systems that could improve overall per- 
 formance and economy. Its objective is to provide the trainee a basis 
 for anticipating future developments and improvements in the systems 
 described 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, thereby improving cost effectiveness 
 of the collectors. Although already used in numerous commercially 
 produced collectors, further improvements in optical properties and 
 
18-3 
 
 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 estensively 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 18-1. 
 
 Table 18-1 
 Selective Surfaces Characteristics 
 
 r 
 
 Coating 
 
 Absorptance for 
 Solar Radiation 
 
 Emittance for 
 
 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 
 
18-4 
 
 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 
 18-1. 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 
 
18-5 
 
 GLASS ENVELOPE, /VACUUM 
 
 SELECTIVE 
 COATING 
 
 GLASS DELIVERY TUBE 
 
 ,TM 
 
 (a) Owens-Illinois Sunpak Double-Walled Evacuated Collector Tube. 
 
 METAL HEAT 
 TRANSFER FIN 
 
 -VACUUM 
 
 HEAT TRANSFER FLUID 
 
 (b) General Electric TC-IOO Solartron" Double-Walled Evacuated 
 Collector Tube. 
 
 EVACUATING TUBE 
 
 END CAP, 
 
 SODA GLASS 
 TUBE 
 
 COLLECTOR TUBE 
 
 (c) Sanyo Single-Walled Evacuated Collector Tube with Unidirectional 
 Flow. 
 
 , VACUUM 
 
 ^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 18-1. Types of Evacuated Tube Collectors 
 
18-6 
 
 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 
 
18-7 
 
 GLASS COVER 
 
 STEEL FRAME 
 
 PIPING 
 CONNECTION 
 
 TRANSPARENT 
 HONEYCOMB 
 
 ABSORBER PLATE 
 
 FIBER GLASS 
 INSULATION 
 
 Figure 18-2. 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 
 
18-8 
 
 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 
 
18-9 
 
 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 18-2 
 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 col- 
 lector 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 tem- 
 perature. Although higher collector efficiency is obtained at low 
 temperature, most space heating systems cannot advantageously use water 
 
18-10 
 
 
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18-11 
 
 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. 
 
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 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 
 
18-12 
 
 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° to 
 20° 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 18-3. 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 
 
18-13 
 
 COLD WATER 
 FROM LOAD 
 
 TOP OF LIQUID 
 (SURFACE) 
 
 PERFORATED 
 PLATE 
 
 J^O/VATER HEAT 
 STORAGE AND 
 LIQUID BUBBLES 
 
 CONICAL 
 BOTTOM 
 
 WATER LIQUID 
 INTERFACE 
 
 PUMP 
 
 LIQUID 
 
 Figure 18-3. Direct Contact, Liquid-Liquid 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 16-3, 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-ton) 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 
 
18-14 
 
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 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. 
 
 * U. S, GOVERNMENT PRINTING OFFICE 1380 329-854/6632 
 

 PENN STATE UNIVERSITY LIBRARIES 
 
 AQQ007D' 
 
 L422^3