- / u.s 63 - A 706-181 T IS IS A REPRINT WITHOUT CHANGE OF OROP Z0-107 ~ -·r': , ·~ •' tSEARCH AND DEVELOPMENJ OF MATERIEL ENGINEERING DESIGN HANDBOOK ELEMENTS OF ARMAMENT ENGINEERING PART rwo L e - I -BALliSTICS SCIENCE & ENGE'lEEIUNG LlnL1F..' STAT.E U IVF~l7Y OF I . Y. A1' BUFFALQ HEA\oQUARTERS, U.S. ARMY MATERIEL COMMAND SEPTEMBER 1963 SUNY AT BUFFALO THE LIBRARY 30 September 1963 AMCP 706-107, Elements of Armament Engineering, Part Two, Ballistics, forming part of the Army Materiel Command Engineering Design Handbook Series, is published for the information and guidance of all concerned. (AMCRD) FOR THE COMMANDER: Major General, Chief of Staff OFFICIAL: DISTRIBUTION: Special ::.UNY AT BUFFA[ • 7 HF IBRARIES • S~l i:::~~CE A~·;J ENGIf ::::i:::R : "G LIBRARY .... • ELEMENTS OF ARMAMENT ENGINEERING PART 2, BALLISTICS SUNY AT BUFFALO • THE LIBRARY ... FOREWORD This is one of a group of handbooks covering the engineering information and quantitative data needed in the design and construction of ordnance equipment, which (as a group) constitutes the Ordnance Engineering Design Handbook Series. • The three· handbooks comprising "Elements of Armament Engineering" were produced from text material prepared for use at the United States Military Academy. They are published as part of the Handbook Series to make generally available the wealth of fundamental information contained in the text material, which is of value to those concerned with ordnance design, particularly to new engineers and to contractors' personnel. Publication of this material in its existing form avoids the necessity of extending • iii the scope of a number of proposed handbooks to include the information. For further information and more complete lists of references the reader is referred to other appropriate handbooks within the Series. Arrangement for publication of the handbooks comprising "Elements of Armament Engineering" was made under the direction of the Ordnance Engineering Handbook Office, Duke University, under contract to the Office of Ordnance Research. The copy was prepared by the McGraw-Hill Book Company, under subcontract to the Ordnance Engineering Handbook Office. • FOREWORD TO ORIGINAL TEXT MATERIAL This text has been prepared to meet a specific development and changes in the field of wearequirement as a reference for instruction in pons design. "Elements of Armament Engineering," a oneReferences cited are those available to the semester course in applied engineering analysis student as the result of study in previous courses conducted by the Department of Ordnance at at the United States Military Academy. Advanced the United States Military Academy, for memreferences are available at the Department of bers of the First (Senior) Class. It represents the Ordnance Reference Room. application of military, scientific, and engineering fundamentals to the analysis, design and opContributing authors for 1958-59 revision are: eration of weapons systems, including nuclear Maj. W. E. Rafert, Ord Corps, Asst. Professor components. It is not intended to fully orient Capt. A. W. Jank, Ord Corps, Instructor or familiarize the student in weapons employ ment or nomenclature. Capt. C. M. Jaco, Jr., Ord Corps, Instructor Of necessity, the large volume of classified Capt. J. M. Cragin, Ord Corps, Instructor data used in presentation of this course has been Capt. G. K. Patterson, USAF, Instructor omitted; hence the text is intended to serve as a • point of departure for classroom discussions. The JOHN D. BILLINGSLEY text is revised annually by instructors of the Colonel, U. S. Army Professor of Ordnance Department of Ordnance in an effort to assure that subject presentation will keep pace with August, 1958 iv • ELEMENTS OF ARMAMENT ENGINEERING PART 2, BALLISTICS • I FOREWORD This is one of a group of handbooks covering the engineering information and quantitative data needed in the design and construction of ordnance equipment, which (as a group) constitutes the Ordnance Engineering Design Handbook Series. The three· handbooks comprising "Elements of Armament Engineering" were produced from text material prepared for use at the United States Military Academy. They are published as part of the Handbook Series to make generally available the wealth of fundamental information contained in the text material, which is of value to those concerned with ordnance design, particularly to new engineers and to contractors' personnel. Publication of this material in its existing form avoids the necessity of extending the scope of a number of proposed handbooks to include the information. For further information and more complete lists of references the reader is referred to other appropriate handbooks within the Series. Arrangement for publication of the handbooks comprising "Elements of Armament Engineering" was made under the direction of the Ordnance Engineering Handbook Office, Duke University, under contract to the Office of Ordnance Research. The copy was prepared by the McGraw-Hill Book Company, under subcontract to the Ordnance Engineering Handbook Office. iii FOREWORD TO ORIGINAL TEXT MATERIAL This text has been prepared to meet a specific development and changes in the field of wearequirement as a reference for instruction in pons design. "Elements of Armament Engineering," a oneReferences cited are those available to the semester course in applied engineering analysis student as the result of study in previous courses at the United States Military Academy. Advanced conducted by the Department of Ordnance .at the United States Military Academy, for memreferences are available at the Department of bers of the First ( Senior) Class. It represents the Ordnance Reference Room. application of military, scientific, and engineer ing fundamentals to the analysis, design and opContributing authors for 1958-59 revision are: eration of weapons systems, including nuclear Maj. W. E. Rafert,. Ord Corps, Asst. Professor components. It is not intended to fully orient Capt. A. W. Jank, Ord Corps, Instructor or familiarize the student in weapons employ Capt. C. M. Jaco, Jr., Ord Corps, Instructor ment or nomenclature. Capt. J. M. Cragin, Ord Corps, Instructor Of necessity, the large volume of classified Instructor data used in presentation of this course has been Capt. G. K. Patterson, USAF, omitted; hence the text is intended to serve as a point of departure for classroom discussions. The JOHN D. BILLINGSLEY text is revised annually by instructors of the Colonel, U. S. Army Professor of Ordnance Department of Ordnance in an effort to assure August, 1958 that subject presentation will keep pace with iv L PREFACE The science of ballistics involves the study of the motion of projectiles as a particular branch of applied mechanics and related fields of physics, chemistry, mathematics, and engineering. It includes, within its scope, the natural division of this science into the subjects of interior ballistics, the motion of a projectile or missile while under the influence of a gun or thrust propulsion device; exterior ballistics, the projectile or missile in flight; and terminal ballistics, its effectiveness in defeating a target. With each successive performance dependent on that preceding, the overall ballistic performance of any missile or projectile must consist of reliable and reproducible actions in each of these phases despite conflicting design requirements in certain areas. Ballistics produces a rational foundation for the design and development of armament materiel. Therefore, a concept of the basis for the design of weapons or development of ammunition cannot be realized without a basic understanding of this science. The following chapters present information about each phase of ballistics to the extent believed necessary to pursue a study of the design and engineering analysis of components of weapon systems which satisfy the basic requirements of launch, flight, and terminal effects. Such problems are presented in Part 3 (Weapon Systems and Components) of this text. v TABLE OF CONTENTS Paragraph Page CHAPTER 1 INTERIOR BALLISTICS-GUN PROPULSION SYSTEMS .. . ····••O••• • • • oOOO•O•••oOoOoO•O•oO oO .o • • •••• oO•• 1-1 INTRODUCTION 1-1 0 o .... . ............ . 1-2 ACTION INSIDE THE GUN ........ 1-2 o ......... .. .... 1-3 DISTRIBUTION OF ENERGY .......00 ...... 0 ..... 0 1-3 1-4 PRESSURE-TRAVEL CURVES 1-3 1-5 CONTROL OF INTERIOR BALLISTIC PERFORMANCE . 1-4 1-6 IGNITION 1-4 1-7 EFFECTS OF POWDER GRAIN CHARACTERISTICS 1-5 1-701 Grain Configuration 1-6 o ........ o•••• OO ••"•• 1-702 Grain Size ....... . .. .. o •o ..... 1-6 1-703 Density of Loading 1-7 1-8 PRESSURE-TIME RELATIONSHIPS FOR GUN SYSTEMS . 1-7 1-9 EFFICIENCIES OF GUN AND CHARGE ..... 1-8 o 1-10 DEVELOPMENT OF TECHNIQUES .... ........... .. 1-8 1-11 SIMPLIFIED VELOCITY COMPUTATIONS 1-9 1-12 EFFECTS OF VARIATIONS IN THE GUN 0 PROJECTILE SYSTEM . . ................................. 1-10 1-1201 Gun Tube Length 1-11 1-1202 Gun Chamber ... 1-11 1-1203 Projectile Weight .. . . . . ...... ... .......... .................. ......... .. .. 1-11 0 . 0. 1-12.4 Density of Loading 1-11 1-1205 Sectional Density . 1-11 1-13 PRESSURE COMPUTATIONS . . ......... . ........... .. . 1-12 1-14 EFFECTS OF VARYING CONDITIONS IN SERVICE 1-12 1-1401 Temperature of . the Powder . 1-13 1-1402 Temperature of the Gun 1-13 1-1403 Erosion in Gun Bore .......................... ........ 1-13 1-15 INITIAL CHARACTERISTICS OF GUN-LAUNCHED PROJECTILES ....... ...... .......................... ... ...... o 1-16 .. .. .. . 0 ............... .. .. 1-1501 Initial Air Effects ... .. .. . . . . .. . . .. .. .. .. ... .. .. ..... 1-17 1-1502 Vertical Jump 1-18 1-1503 Lateral Jump 1-18 vii TABLE OF CONTENTS (cont) Paragraph Page • CHAPTER 2 INTERIOR BALLISTICS-THRUST PROPULSION SYSTEMS 2-1 INTRODUCTION 2-1 2-2 REACTION MOTOR PRINCIPLES ......... . .. .. .. .. .. ....... ....... .... .... 2-1 2-3 THRUST .......... .. ... .. .. .. .. ... .. .... ............ .. ............. ... .... ....... .. ............... .... 2-2 2-3.1 The Equation for Momentum Thrust . . . .. . ... .. .. .... ... . . .. .... .. ........ . 2-2 2-3.2 The General Equation for Total Thrust . . .. ... . . . . .. . . . .. . . . . . ... . . 2-3 2-4 SPECIFIC IMPULSE . . . . . . . . . .. . . .. .... . . . . . . . . . . . . . . . . . . . . . ... . . .. .... . . . .. . . . . . . . . . . . 2-3 2-5 ROCKET MOTOR THERMODYNAMICS ...... ................ ..... ... 2-3 2-6 NOZZLE DESIGN ............... ..... .. . .... . 2-5 2-6.1 Summary of Reaction Motor Performance Criteria . . ........ .. .... 2-9 2-6.2 Nozzle Configuration . . .. . . . . . . . . . . .... . . .. . . ... . .. . . . .. . . . . . .... . . ... . . .. ... . . . .... . 2-9 2-6.3 Entrance and Exit Angles . . . . . . . . . . . . . . . . . . . .. . . . . . . ... . . . . . .. .. . . . . . .. . . . . . .. . . . . . . 2-9 2-6.4 Nozzle Angl e Correction F actor ... .... .... ...... .. .. .. ...... ... ... ... .......... 2-9 2-6.5 Overexpansion and Und erexpansion .. ... .... ... .. ...... .... ............... 2-9 2-6.6 Exhaust Velocity .. . ........ ......... . ............ ....... . ....... ............ ....... 2-11 2-7 SOLID PROPELLANT ROCKETS ..... ......... ....... ....... ... ...... ... ... 2-11 • 2-7.1 Grain Geometry ... .... ... .. ... .. .... ............ ..... ... ... .. ... .. .... ... .. ..... ... ........ 2-12 2-8 SPECIAL CHARACTERISTICS OF THE SOLID PROPELLANT ROCKET ...................... ...... ........... .. .... 2-13 2-8.1 Mode of Burning ... .... .. ...... .... ...... ... ... .... .... ................................. ... 2-13 2-8.2 Temperature Sensitivity and Limits .... ... ... .".. ... .... ... ... .. ..... ... .. .... 2-13 2-8.3 Combustion Limit ..... .... ......... .... ... ... .. ................ ...................... 2-14 2-8.4 Pressure Limit .. .......... ..... ....... ... .. ........................... ............. ......... 2-15 2-8.5 Physical Changes in Storage .... ........................ ............................ 2-15 2-9 LIQUID PROPELLANT ROCKETS .. ... .. ....... .................. .. .......... 2-15 2-9.1 Pressure Feed System ..... ....... .. .. .. ... ... .. ... .... ........ .. ............... .......... 2-17 2-9.2 Pump Feed System .... .. .. ... .... ... ... ......... .. ... .... .. .......... ......... ....... ... . 2-18 2-10 SELECTION OF LIQUID PROPELLANTS ..... ... .... ........ ........ 2-18 2-11 PROPELLANT UTILIZATION ........ .... ......... .. ..... .... .... ... ... ... .... .. 2-19 2-12 JET ENGINES ....... .................... .. .. .... .... .... ..... .... .. .... .. ... ... .... ........ . 2-20 2-13 PULSE JETS . . . .. . . . .. .. . . . .. . . . . . .. . . . .. .. . . . . . . . .. . . . . . .. .. . . . . . .. . . . . . . . . .. .. . . . .. ... . . .. . . 2-21 2-14 RAM JET ... ............... ...... ... ........... .. .. .. ... .... ..... .... ....... ... ..... .... .... .. ... .. . 2-22 2-14.1 Subsonic Ram Jets 2-22 • viii TABLE OF CONTENTS (cont) Paragraph Page Chapter 2 (cont) 2-14.2 Supersonic Ram Jets 2-23 2-15 TURBO JET .. .. . .. .. ....... ........................ ... ... .... .... ..... ............ 2-24 2-16 SUMMARY OF REACTION MOTORS ..... ... .... ... ..... ...... .............. 2-27 CHAPTER 3 EXTERI OR BALLISTICS • 3-1 INTRODUCTION 3-1 3-2 DESCRIPTION OF A TRAJECTORY .......... ..... ........ ... ............ . . 3-3 3-3 AERODYNAMIC FORCES ACTING ON THE PROJECTILE ..... ..... ........ ... ..... ...... ......... ... .. .......... ... ............. .. 3-4 3-3.1 Drag 3-5 3-3.2 Crosswind Force 3-5 3-3.3 Overturning Moment 3-6 3-3.4 Magnus Force .... .... ...... ......... ... .. ...... ....... ................... .. ...... .. .. ....... . 3-6 3-3.5 Magnus Moment ...... ... ........... ..... .... .... ..... .. .... .... .. ..... .. ... ........... .. . . 3-6 3-3.6 Yawing Moment Due to Yawing ... ......... ........... .... .... ............ ... . . 3-6 3-3.7 Rolling Moment .. ....................... .. ................................ ................ . 3-6 3-4 EVALUATION OF PRINCIPLE AND MOMENTS ..... .. ......... 3-6 3-4.1 Projectile Form 3-7 3-4.2 Drag Coefficient 3-7 3-5 BALLISTIC COEFFICIENT ................... .......... ..... .. .... .. ..... .... .. .. . 3-8 3-6 BALLISTIC TABLES AND FIRING TABLES .... ...... .. .......... . 3-9 3-7 TRAJECTORY ANALYSIS .. . ... . .............. . ... ...... .............. . 3-10 3-8 BALLISTIC COEFFICIENTS FOR BOMBS ....... .................... . 3-11 3-9 TYPICAL BOMBING PROBLEM ..... .. ......... .. ... .. .... .. ................. . 3-14 3-9.1 Vertical Travel .. ................ .. .. ... .. ... ......... ... ........... ..... .. ..... ... .. ... ... . 3-15 3-9.2 Linear Travel ... .. .......... ..... .. ... ........... ..... .... .... .. .. .. ... ... .. ......... .. ....... . 3-15 3-9.3 Trail 3-15 3-9.4 Cross Trail 3-15 3-10 SPECIALIZED BOMBING TECHNIQUES ....... ... .... ............ .. ... . 3-15 3-11 STABILIZATION OF PROJECTILES ....... ....... ....................... .. 3-16 3-11.1 Fin Stabilization 3-16 ix TABLE OF CONTENTS (cont) Paragraph Page Chapter 3 (cont) 3-11.2 Roll Stabilization 3-17 3-11.3 Spin Stabilization 3-17 3-12 STABILITY AND DRIFT FOR SPIN STABILIZED PROJECTILES ..... .................. ...... ....... .. ... .. .... ... .. . 3-19 CHAPTER 4 BALLISTIC AND AERODYNAMIC TRAJECTORIES 4-1 INTRODUCTION ..... ..... .. .. ..... .. ........ .... ... ....... ... . ... ..... .. .... 4-1 4-1.1 Ballistic Missiles 4-1 4-1.2 Aerodynamic Missiles . . .. ....... .. .. ..... ... .. .. ............. .. .... ... ......... .. . 4-1 4-1.3 Hypervelocity Vehicles 4-1 4-2 BALLISTIC MISSILES .. . . .. . .. . . .. ... . . . . .. .. . .. ... . . .. . . . .. . . . . .. ... .. .. .. . . .. .... .. 4-2 4-3 SYSTEMS AND SUBSYSTEMS OF A LONG-RANGE BALLISTIC MISSILE ... .. .. . . .. .. .... .. .. . .. .... . . .. ... .. .... .. .. .... .. .. .. .. .. .... .. .. 4-3 4-4 POWERED FLIGHT OF THE MISSILE ........ ...... .................... 4-6 4-5 EXTERIOR BALLISTICS OF A MISSILE .......... .... .... .. .. . ....... 4-7 4-6 EFFECT OF EARTH'S SPIN AND CURVATURE ON TRAJECTORY LENGTH .. .. .. .. .. ...... ..... .. .. .. .. ....... .. ............ 4-7 4-7 THEORY OF BALLISTIC TRAJECTORIES ..... .. .. .. ... .. .. .. ........ 4-9 4-8 SUMMARY OF EARTH SATELLITE VEHICLES ................ 4-10 4-9 AERODYNAMIC MISSILE CONFIGURATION . . .. .. .. ... .. .. .. .. . 4-12 4-9.1 Profile Shapes 4-15 4-9.2 Plan Forms .......... .. ....... ........... ...... ... ... ..... .......... ............... ........... . 4-15 CHAPTER 5 GUIDANCE FOR CONTROLLED TRAJECTORIES 5-1 GENERAL 5-1 5-2 ATTITUDE CONTROL ........... .. ... ..... ... ...... .... .. ... .... .............. ....... 5-1 5-3 PATH CONTROL .... ... .... ....... .................. ... .... .... .... .... .... ...... .......... . 5-2 5-4 GUIDANCE FOR PREDETERMINED TRAJECTORIES .. .. 5-3 5-4.1 Preset Guidance System ........ .. ............ .. ................. ...... ........ .... .. 5-3 5-4.2 Terrestrial Reference Guidance Systems ........... .. ........ ............ . 5-4 5-4.3 Radio Navigation Guidance Systems .. .... .. ................ ............... . 5-4 5-4.4 Celestial Navigation Guidance System 5-6 • X TABLE OF CONTENTS (cont) Paragraph Page Chapter 5 (cont) 5-405 Inertial Guidance System 0 .. ... ..... ................. .................. 00 o· .. 0... 5-7 5-5 GUIDANCE FOR CHANGING TRAJECTORIES ..... ... o·o· o· o· . ... 5-8 5-501 Command Guidance System ··· · ····· ·· ··o·o· · ··· · o· o· · ··· ··· o· · ······ o·o·o· o . . . 5-8 5-502 Beam Rider ... ............... ....... ·o •••••••••••••• 0.0. 0...... ..0...... 0.0. 0...... 0.0.0.0.. .. . 5-9 5-503 Homing (Terminal Guidance) · · · ·· ···· · · · ···· ·· ········ · · ····· o· o············o··· 5-10 5-6 KINEMATICS OF INTERCEPT COURSES ... ........ o....... ... ..... 5-13 CHAPTER 6 INTRODUCTION TO TERMINAL BALLISTICS 6-1 SCOPE ·· ·········· ··········· ···········o···················································o········· 6-1 6-2 DEVELOPMENT AND USE OF TERMINAL BALLISTICS .. 6-1 6-3 TECHNIQUES OF TERMINAL BALLISTIC STUDIES ...... 6-1 6-4 MEANS OF PRODUCING DAMAGE ... ..0 ·o· . . . .. . . o·· .. . ..... .. . . 6-3 6-5 TARGET ANALYSIS ........... ...... .... .... ...... .. .. .. ..... .. .... ..... .. .. .. .. ...ooo·· · 6-3 6-6 PROBABILITY AND STATISTICAL TREATMENT OF BALLISTICS .. ....... ....... ..... ..... .. ... .. .. .. .... .... o. . .... . .. . . .. o· o· o·· · 6-4 6-601 Introduction ........ · ··· ·o·o··· ·· ·o ... · ·· o· ·· ·· · · · ··o· o·· ··o · o·o· · ····o·o······ · ·o··· · ······ ·· 6-4 6-602 Probability .· o. .. . · oo·o . ... .... o. o. . ... . o·o· . . . . . o· o.. · · ·· · oo · .. . o.. ·o·o . . . . .. · oo. o.. .. .. o· o 0... 6-4 6-603 Statistics ···· · ············· ····················· ·· ···· · ···· · · ·········· · ·······•••o•O••······ ·· ··· 6-5 6-7 PROBABILITY OF A SUCCESSFUL MISSION ...... ... ... o. o. o· o· o·.. 6-8 6-8 DAMAGE DISTRIBUTION FOR LARGE YIELD WEAPONS ....... .............. ....................................................... 6-8 0 00 ••••• • • • • • 6-9 THE DAMAGE FUNCTION ... 6-9 o . •• • • •• • • •• • • • • • •• • • • • • •• • • • • •• • • • ••• • •• •• • • • • • •• ••• 6-10 FACTORS REGULATING OVERALL SYSTEM ERRORS .... 6-9 6-1001 General ········ · ··· · ··· · ·· ········o·•· · ·· · · · ··· · ··· · o· •· ···· ·· · o· ·· ·· · o···· ···· ··o · o· ···o·o·•· O· · ·· 6-9 6-1002 Factors Considered · · · o· o·· ·· ·· o· · ··· · · ·o ·· ···· · ·o·o· · ··o·o······· · o·o··· ····o· ··· · · ·· · · 6-9 6-1003 Point Targets ......... .. ..... ..... ...... ... .... .... ........ o.... . . o........ o. ooo · ··· ·· · ·o ·o·o·· 6-10 6-10.4 Area Target Considerations ....................................... ...... .......... 6-13 6-11 THE P(f) RELATIONSHIP FOR CIRCULAR TARGETS, NON-ZERO CEP .... . .. . ... .. ..... .. ... .... .. .... .. ..... ................ .. ..... .. ... . 6-15 6-12 IRREGULAR TARGETS 6-15 xi TABLE OF CONTENTS (cont) PageParagraph CHAPTER 7 FRAGMENTATION 7-1 INTRODUCTION ······ .. ............ .......... ······ ········· ····· ···· ····· · ~1 7-2 NATURE OF THE FRAGMENTATION PROCESS .............. .. 7-1 7-3 BALLISTICS OF FRAGMENTS .............. .. .................. ..... .. ....... .... 7-1 7-4 INITIAL VELOCITIES OF FRAGMENTS ......... .. .. .. ....... ..... 7-4 7-5 DIRECTION OF FRAGMENT FLIGHT ............ ... ................ 7-5 7-6 NUMBER, TYPE , AND SIZE OF FRAGMENTS 7-5 7-7 FRAGMENT DAMAGE ..... . . .... .... .... ..... ..... .......... ............ 7-7 7-8 SHELL FRAGMENT DAMAGE ....... .. .............. ............ .. ...... .. .. 7-12 7-9 CONTROLLED FRAGMENTATION .......................... ........ 7-12 7-9.1 Direction of Flight .................. ................. ................. ...... ......... .. 7-12 7-9.2 Velocity ............................................... 7-12 CHAPTER 8 BLAST EFFECTS BY CHEMICAL AND ATO,MIC EXPLOSIONS 8-1 MECHANICS OF BLAST ... ... ........ ........ .... . . ............................ 8-1 8-2 PEAK OVERPRESSURE . . .. ... .. ... .. .. . . . . .. . .. . . . .... .. . .. .. . 8-3 8-3 THE EFFECT OF MACH REFLECTION ON AIR BURST .. 8-5 8-4 IMPULSE . . .. .. .. ... .. . .. .. .. .. . .. . .. .. .. .. .. .. ... .. ... .. ... .. .. .. . 8-6 8-5 DYNAMIC PRESSURE . ...... ................... .. ....... ....... . ............... .. 8-8 8-6 AIR BLAST LOADING .. ...... ........ ......... .. ....... ..... ......... . 8-9 8-7 DIFFRACTION LOADING .... .......... ..... .. ..... . .. .. . . .. .......... ... 8-9 8-8 DRAG (DYNAMIC PRESSURE ) LOADING ............................ 8-10 8-9 TECHNICAL ASPECTS OF BLAST WAVE PHENOMENA .. 8-10 8-10 ALTITUDE CORRECTIONS ............................ .. ................ ........ . 8-12 8-11 BLAST EFFECTS FROM NUCLEAR WEAPONS .......... .. ... ... 8-12 8-11.1 Personnel .. .. . ..... . ................... ..... .. ... ......... ....... ............... ....... .. . . 8-12 8-11.2 Military Equipment .. .. .... .............. .. ....... ... ... ... ......... . ................ 8-12 8-11.3 Structures ...... .. ............ . ... ... ... ......... ... ......... ... ... ................ ... ... ...... ... 8-13 8-11.4 Cratering .... ... .......... ... ....... ...... ......... ......... ... ......... ...... .. ... ........ ... ... . 8-13 xii TABLE OF CONTENTS (cont) Paragraph Page CHAPTER 9 THERMAL AND NUCLEAR EFFECTS OF ATOMIC DETONATIONS 9-1 INTRODUCTION .. .. ........... ..... .............. ......... .. ................. ..... ......... 9-1 9o2 UNDERGROUND BURST ..... .. ..... ..... .. ... .... .. .............................. 9-2 9-3 SURFACE BURST ... .. . . . . . . . . . ... . . . .. .. . ... . . ........ .. . . ... . .. ....... ... .... ...... .. 9-2 9-4 BURSTS IN OR OVER WATER . . . . . . . . . . . .. . . . .. . . . . . . ... . ... ...... .... ... . 9-3 9-5 CHARACTERISTICS OF THERMAL RADIATION .. ...... .. .... 9-3 9-6 MECHANISM OF THERMAL RADIATION .. ... .... ................. 9-3 9-7 ATTENUATION OF THERMAL RADIATION .......... .............. 9-4 9-8 A; . I)ORPTION OF THERMAL RADIATION .... .... ..... .. ...... ... .... 9-5 9-9 .BURN INJURY ENERGIES AND RANGES ..... .. .... ........ .......... . 9-6 9-10 EFFECTIVENESS OF SECOND RADIATION PULSE ... .... . 9-6 9-11 CHARACTERISTICS OF NUCLEAR RADIATION ............. . 9-8 9-12 INITIAL GAMMA RADIATION .... .. ... .... ... .. .. .. ..... ..... ...... ........ .... 9-9 9-13 SOURCES OF NEUTRONS AND IONIZATION CHARACTERISTICS . . . . . . . . . .. . . . . . . . . . . ... ... . . . . . .. . . ... ....... .. .. .. . . . .. . . ... . . . ... . . 9-10 9-14 NUCLEAR RADIATION EFFECTS ..... ...... ... ........ .. .... .. .. .......... 9-11 9-15 RESIDUAL RADIATION ........ .... ... .. ... .. ................ ... .. .... . .... .. .... . 9-12 9-16 NEUTRON INDUCED ACTIVITY ....... .. ... .......... ... .. .. .. .... ....... .... 9-12 9-17 FALLOUT .......... .. ........ .................. .......................................... .. .... ... . 9-13 9-18 LONG-TERM RESIDUAL RADIATION HAZARD ................ 9J15 CHAPTER 10 BALLISTIC ATTACK OF ARMOR USING KINETIC AND CHEMICAL ENERGY EFFECTS 10-1 GENERAL 10-2 TYPES OF ARMOR MATERIALS ....... ....... ... ... ...... .... .... ... .. ... .. 10-1 10-2.1 Rolled Homogeneous Steel Armor ·....... ........ ......... .... ......... ... ..... . 10-1 10-2.2 Cast Homogeneous Steel Armor .... ....... .... ... ... ......... .............. 10-1 10-2.3 Face-Hardened Steel Armor ................ .... .... ... ... ... ........ ............ 10-3 10-2.4 Nonferrous Armor Materials ... ... .................. .... ........................... 10-4 10-3 SURFACE DESIGN . . .. . . . . . . . . . . . . ..... ... . . ... . . ... . . ... . . . . . .. . . .... ... . . . .. ....... .... . 10-4) 10-4 FABRICATION OF MOBILE ARMOR STRUCTURES ........ 10-4 xiii TABLE OF CONTENTS (cont) Paragraph Page • Chapter 10 (cont) 10-5 INNOVATIONS ... 10-5 10-5.1 Spaced Armor . ············ 10-6 10-5.2 Laminated Armor ... 10-6 10-5.3 Composite Armor .... . 10-6 10-6 NECESSARY BALLISTIC PROPERTIES OF ARMOR ...... 10-6 10-6.1 Resistance to Penetration ... 10-7 10-6.2 Resistance to Shock ········ ···· ··· ......... 10-7 10-6.3 Resistance to Spalling 10-7 10-7 EFFECTS OF OBLIQUITY AND HARDNESS ON PERFORMANCE OF ARMOR ..... . 10-7 10-7.1 Effect of Obliquity Upon Resistance to Penetration ...... ........ 10-7 10-7.2 Effect of H ar dness Upon Resistance to Penetration . ..... ...... 10-10 10-7.3 Discussion ............................................... ... ... . .............. . .............. 10-11 10-8 KINETIC ENERGY PROJECTILES ········ ····· ... .. ........... ........ 10-11 10-8.1 Definition of Terms ... 10-11 10-9 GENERAL EFFECTS OF IMPACT PROJECTILE DEFORMATION .................. ···· ···· .... 10-14 • 10-10 EFFECT OF PROJECTILE DEFORMATION ON PERFORATING ABILITY ................... ... 10-17 10-11 MECHANISM OF ARMOR PENETRATION-PLATE DEFORMATION ... ···· ················· ..... 10-18 10-11.1 The Elastic Response ... . ..... 10-19 10-11.2 The Plastic Response . ........... ... .. 10-19 10-12 CAUSES OF SHATTER: MEANS OF PREVENTING SHATTER .. . ................... ................... ................................ 10-19 10-13 COMPARATIVE PERFORMANCE OF CAPPED (APC) AND MONOBLOC (AP) PROJECTILES .. ..... ... ....... ..... .... 10-20 10-14 PERFORMANCE OF JACKETED PROJECTILES ................ 10-22 10-14.1 Composite Rigid Type ......... .... . ··········· ··· ···· · .. 10-22 10-14.2 Folding Skirt Projectiles (Tapered Bore) 10-23 10-14.3 Discarding Sabot ... 10-23 10-15 OVERALL COMPARISON OF ARMOR PIERCING PROJECTILES .... .... ............ . ......... 10-23 10-16 CHEMICAL ENERGY PROJECTILES ..... 10-24 • xiv Paragraph 10-16.1 10-17 10-17.1 10-18 10-19 10-19.1 • 10-19.2 10-19.3 10-19.4 10-19.5 10-19.6 10-19.7 10-19.8 10-19.9 10-19.10 10-20 10-21 10-22 A-1 A-2 A-3 A-4 A-4.1 A-4.2 A-4.3 • A-5 A-6 TABLE OF CONTENTS. (cont) Page Chapter 10 (cant) History 10-24 THE SHAPED CHARGE PRINCIPLE ... ....... 10-24 Functioning 10-25 THE THEORY OF JET PENETRA. TION .. 10-25 FACTORS AFFECTING PENETRATION BY SHAPED CHARGE PROJECTILES ............................... ......... .................. 10-28 Type, Density, and Rate of Detonation of Explosive Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-28 Confinement of Charge . . . . . . . . . . . . ... ...... .... . Diameter and Length of Charge Back of Liner Liner Material and Thickness Included Angle of Liner . Liner Shape Rotation of the Missile ....... .. .... . Angle of Impact Standoff Distance Design and Manufacturing Problems ............. . ..... ........ 10-28 . . . . . . .. ..... ..... .. . . 10-28 ··············· ··· 10-28 .... .. ······ ... 10-29 ............... ... 10-29 ... 10-29 10-29 10-29 10-30 PERFORMANCE OF SHAPED CHARGE MISSILES . . . . . .. . . .. 10-30 HIGH EXPLOSIVE PLASTIC PROJECTILES ... ........ ....... .... . 10-31 BODY ARMOR ......... .. ··········· ···· ············ · .... ........ 10-31 APPENDIX A INSTRUMENTATION INTRODUCTION A-1 TELEMETRY ..... . A-2 VELOCITY MEASUREMENTS A-4 TIME RECORDING DEVICES A-5 Aberdeen Chronograph . . . . . . . . . . . . .. A-7 Camera Chronograph (Solenoid ) .............. . A-7 Machine Gun Chronograph ..... A-7 FIELD CHRONOGRAPH A-7 PRESSURE MEASUREMENTS .. A-8 XV TABLE OF CONTENTS (cont) Paragraph APPENDIX A (cont) A-6.1 Crush~r Gauges A-6.2 Piezoelectric Pressure Gauges .... ............ ......... ... .. ... ... ..... ... .. .. .. . . A-6.3 Strain Gauges ......... ......... ........ .. .......... ..... ... ....... ...... .. ...... ....... .... .. A-7 RECORDING OF PRESSURE OR STRAIN MEASUREMENTS ....... .... .. ...... .......... .. .. ... ......... ........ .... .... ........... . A-8 PHOTOGRAPHIC MEASUREMENTS ........... ... ............... .. .. ... . A-8.1 Microfiash ......... .. ..... .. .. .... ....... .. ................ .... ..... ..... ..... ... ...... ... .... ... . A-8.2 High Speed Photography .......... .. .... . .. ...... .. .... . .... ..... .... .... .. .. . A-8.3 Askania Theodolites, Ballistic, Mitchell, and Bowen-Knapp Cameras ........ .......... .... ....... ............. ..... ..... ........ .... ...... ..... ..... ....... .... . A-8.4 Schlieren Photography A-8.5 X-ray Photography A-8.6 Spark Photography .... ............................ ................... ................... . APPENDIX B BALLISTIC ATTACK OF CONCRETE BY USING KINETIC ENERGY AND CHEMICAL ENERGY EFFECTS B-1 INTRODUCTION ·· ···· ········· ········ ·· ······· ··········· ····· ··· ··· ·· ······· ···· ········ · B-2 DEFINITIONS . B-3 BACKGROUND ········ ······ · ··· ······· · ·· · ·· ··· ··· ········· ········ ··· ··· ······ ·· ··· ···· ·· ·· B-4 GENERAL EFFECTS OF INERT IMPACT .. .... _ ................ . B-5 GENERAL EFFECTS OF HIGH EXPLOSIVE IMPACT .. .. B-6 SOLUTION TO THE PROBLEM OF PERFORATION OF THICK REINFORCED CONCRETE ....................... ...... ...... .. .. B-7 PROBLEMS OF EMPLOYMENT ....... .. ...... .. .. .. ....... .. .. .. ... .. .. ... . B-8 EFFECT OF THE SHAPED CHARGE AGAINST CONCRETE . . ... . . . . . . .. . . . . . .. .... . . . . . .. . . .. ... ..... .... ... . . .. . . .. . . .. . . ... ... . . .... . . . . .. ... INDEX ..... ......... .............. .... ...... ... ........ , .. .... ........ .. .. ... ................... ..... . xvi Page A-8 A-8 A-10 A-ll A-ll A-ll A-ll A-ll A-16 A-16 A-16 ~ B-1 B-1 B-1 B-2 B-3 B-3 B-4 B-6 1-1 • LIST OF ILLUSTRATIONS Fig. No. Title Page 1-1 Standard gun system 1-2 1-2 Recoilless system . . . . . . . . ............. .. .. ... ....................... ....................... . 1-2 1-3 Pressure-travel (solid lines) and velocity-travel (dotted lines) curves ..................... .... . ..... .. ........................ .. .... .. ... .. ... .. .. 1-3 1-4 Pressure-travel relationship 1-6 1-5 Effects of grain configuration on pressure-travel curves. (Charge weight is equal in each case) ... . . . . . .. . . .. . . . . ... . . ... . . .. . . ... 1-7 1-6 Effects of independently varying grain size. (Charge weight is equal in each case) . . . . . . . . .. . . . .. . . . . . . . . . . . ... . . ... . . . . ....... 1-7 1-7 Pressure-time relationships determined experimentally ..... ... 1-8 1-8 LeDuc velocity-travel relationship ... ... ..... . 1-9 1-9 Advanced gas erosion at origin of rifling near 12 o'clock of 155-mm gun, M2. Note complete obliteration of lands (Extract TB9-1860-2) ............ .. . . ... ................................. 1-14 1-10 Impressions showing scoring at 12 o'clock (top) and gas erosion at 6 o'clock (bottom). Bottom also shows light scoring in the grooves. Taken from 15S-mm gun, M2 (Extract TB 9-1860-2) ........... ...... .. .. ...... ..... ....... .... .. .. .. .. .. .. .... ... .. 1-14 1-11 Muzzle velocity loss as a function of bore measurement for tubes used in 90-mm guns M1, M2, and M3 (Extract TB 9-1860-2) ..... .. ............................................. .. ... ..... .. 1-15 1-12 Remaining life as a function of bore measurement for tubes used in 90-mm guns M1, M2, and M3 (Extract TB 9-1860-2) ........ .. ... .. .. .... . 1-16 1-13( 1) Effects of projectile emerging from muzzle. ( Spark photograph of gun being fired) ..... ................. .... . ... .... .......... . 1-18 (2) Effects of projectile emerging from muzzle. (Spark photograph of gun being fired) ... . . . . . . . . . . . . . . . . . . . . . ...... . 1-19 (3) Effects of projectile emerging from muzzle. ( Spark photograph of gun being fired) . .. .. .. .. ... .. ....... .... ....... . 1-19 2-1 Reaction motor with convergent-divergent nozzle 2-2 2-2 Schematic flow diagram 2-4 2-3 Distance along nozzle . 2-7 2-4 The distribution of pressure, density, temperature, and velocity along the nozzle .. ......... .. ........ .. .... ... . . ....... 2-8 • xvii Fig. No. Title Page 2-5 Effects of underexpansion and overexpansion on nozzle performance ... ................... ............... .. .......... .... ... . . 2-10 2-6 Geometry of some rocket solid propellant charges .... . 2-12 2-7 Time-pressure and thrust-pressure relati!lnships of a re stricted burning rocket ... ... .... .............. .......... .. ... ... .... .. . ... .......... 2-14 2-8 Pressure-time curves for 3.25-inch rocket ..... .. .. .... ..... ....... . ..... 2-15 2-9 Combustion limit of rocket propellant .............. .... .... ... .... ......... 2-16 2-10 Schematic diagram of a liquid fuel feed system ...... .... ....... .. .. . . 2-16 2-11 Liquid propellant rocket motor types .......... ...... ........ ... .. .......... 2-17 2-12 Liquid rocket feed systems 2-18 .2-13 Temperature gradients 2-20 2-14 Propellant utilization system .......... . 2-21 2-15 Pulse jet in action (at sea level, 400 mph) 2-22 2-16 Subsonic ram jet in action (at sea level, 700 mph) ... 2-23 2-17 Supersonic ram jet in action (at sea level, 2700 mph) 2-24 2-18 Turbo jet in action (at sea level, 600 mph) ... . . . . . . . . . . . . . . 2-25 2-19 Turbo jet engine cycle (Brayton Cycle) on T-S and P-V planes . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. . . .. .. . . . .. .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 2-20 Comparative thrust hp ... ... . ... ... .... .... .......... .... . 2-27 2-21 Comparative fuel consumption ...... .... ... ....... ... ..... ... ... .. .. ..... .... ..... 2-28 • 3-1 General view of a flexible throat wind tunnel ... .... . .. .......... . 3-1 3-2 Schlieren photo of model in wind tunnel 3-2 3-3 A free Hight range .. ... ................ ... . 3-2 3-4 Spark shadowgraphs of 90-mm projectile fired in a free Hight range . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 3-5 Elements of the artillery trajectory 3-4 3-6 Forces on a projectile moving in still air ... ................ ... ..... .. ... 3-5 3-7 Action of magnus force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . .. .. ... .. . . . .. .. .. . . 3-6 3-8 Drag coefficient versus Mach ratio for different projectile shapes .. .. .. .. .. ... .. .. .... ...... ... ..... ...... .. ........................................... ..... ... . 3-7 3-9 Remaining velocity versus travel . . . . . . . .. . . . . . . . . . . . . . . .. . . . . .. .. . . .. .. .. .. ... . 3-9 3-10 Plots of trajectories . . .. . . . . . .. .. ... ... .. .. . . ... .... .. . .. . . .. .... .... ... . .. .... ... ... . . .. . 3-9 3-11 Flow chart for computation of firing tables .... .. ..... .... ...... ........ ... 3-12 xviii • LIST OF ILLUSTRATIONS (cont) Fig. No. Title Page 3-12 Flow chart for computation of bombing tables . . . ..... ... .... .. ... .. 3-13 3-13 Typical bombing problem ................... ... ......... .......... .... ........... .. 3-14 3-14 Low altitude bomb delivery ........ ..... ..... ... .. .. .. ...... ... ...... ..... ...... . 3-16 3-15 Forces on projectile ( CP trails CG ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-17 3-16 Comparison of spinning top and spinning projectile ......... ... 3-18 3-17 Forces on a projectile ( CP leads CG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19 3-18 Desirable yaw response-time plot ...... ... .. ....... .. ........ ................ 3-20 4-1 Regimes of atmospheric and extra-atmospheric flight ............ 4-2 4-2 Trajectories for hypervelocity vehicles (vertical scale exaggerated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 4-3 Redstone ballistic missile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4 4-4 Ballistic missile trajectory (German V -2) . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 4-5 4-5 Trajectory of an ICBM .. ...... ....... .... .... .... .. .... . ... . .... .... ... .. .. .... ... ... 4-6 4-6 Medium height trajectory ................. .......... .... ........... .......... .... .. 4-7 4-7 Short range trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 4-8 Fixed coordinate trajectory . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 4-8 4-9 Ballistic trajectory theory .. .. .. .. ... .. .. .. .. .. .. .. .. ... .. .. .. ... .. .. .. ... .. .. .. ... .. . 4-9 4-10 Ballistic trajectory theory .. .... .. ....................................... .. ......... .. 4-10 4-11 Ballistic trajectory theory ...................... .. ......... .. .......... ........ .. .. ... 4-10 4-12 Ballistic trajectory theory .. .... .. .... .. .. .... .. .... .......... .... ...... .. .. .... .. .. .. 4-11 4-13 Photographs of wind tunnel tests at Langley Aeronautical Laboratory ............................................ .... ...... ... ..... ..... .... .... ... ... .... .. . 4-13 4-14 Test in the free flight wind tunnel at Moffett Field, California .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 4-15 Heating effect of atmospheric friction ...................... .... .. .. .. ... .... . 4-14 4-16 Double symmetric supersonic airfoils ................................... ... 4-15 4-17 Supersonic aerodynamic surface plan forms ............................ 4-15 4-18 Aerodynamic steering methods ............ .. ........ ......... ... ...... .. .. ...... 4-16 4-19 Nomenclature for airfoil configuration .. .... ........ ... .. .... ... .... .. .. .. 4-16 4-20 Forces acting on airfoil at angle of attack, a ...... .. .............. .. .... 4-16 4-21 Variation of lift and drag coefficient with angle of attack for typical airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17 4-22 Illustration of Whitcomb area rule ...................... ........ .. ... .. ....... 4-18 xix LIST OF ILLUSTRATIONS (cont) Fig. No. Title Page 5-1 Guidance systems ............................... ... ... ......... .. ....... .... .... ... ... .. . 5-1 5-2 Yaw, pitch, and roll axes .. .... .. . . ... ... ....... .. ... ..... ..... ....... .... .. .. .... 5-2 5-3 Complete missile guidance system . . . . .. . . . .... .. .. . .. .... ... ...... ... .. . .. . . 5-3 5-4 Radio navigation paths . . .. . . ...... ... .. . . .. ........ .. .. ....... .... .. ....... ... .... . . . 5-5 5-5 Hyperbolic grid .... ...... . . 5-6 5-6 Schematic of celestial navigation guidance 5-7 5-7 Schematic of inertial guidance system . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . .. ... . . 5-8 5-8 Command guidance system . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . . . .. . . 5-9 5-9 Single-beam rider 5-10 5-10 Dual-beam rider 5-10 5-11 Active homing 5-11 5-12 Passive homing guidance .. ............... ... ..... ....... ..... .. ............ ..... . 5-12 5-13 Semi-active homing guidance 5-12 5-14 Geometry of intercept problem 5-14 5-15 Conditions for finite turning rate (deviated pursuit) . 5-16 6-1 Bursting shell 6-2 6-2 Shock tube 6-3 • 6-3 Damage functions for two different sets of conditions . . .. . . ... . 6-9 6-4 Point target chart, average variability ............ .......................... . 6-11 6-5 Extension chart, point targets 6-12 6-6 Two typical P(f) curves ........ . 6-13 6-7 P(f) nomograph, average variability 6-14 7-1 Detonation of a 20-mm shell ............ ... .. ... ... ..... .... ....... .. ... .... .... .. . 7-2 7-2 Static nose-down detonation of a bomb ...... .. ..... ..... .................. 7-5 7-3 Fragments from bomb, fragmentation, 220.lb, AN-M88 .... .. 7-6 7-4 Damage pattern: bomb, GP ... ................ ... ......... ........................ 7-9 7-5 Damage pattern: bomb, GP .. ...... .... ..... ............... .. .. ... .... ........ ... . 7-9 7-6 Casualties versus height of burst .bomb, fragmentation ... ..... 7-10 7-7 Shell density in area fire; superquick ground burst, 155-mm H.E. shell, M107 ..... .. .. .... ... ..... .............................................. ..... ... . 7-13 7-8 Experimental grooved ring shell body ... ... .......... ... ...... ... .. ... ....... 7-14 7-9 Uniform fragments obtained from grooved ring shell body .... 7-14 • XX LIST OF ILLUSTRATIONS (cont) Fig. No. Title Page 7-10 Uniform spacing of perforations in 5/16-inch steel plate obtained by grooved ring shell ........... .. .. ...... ......... .... ........ ..... ..... 7-15 Detonation of grooved ring shell ....... .... .. .. .. ............................. 7-16 7-11 7-12 Hand grenade ............ .. ....... .. .. ..... ...... ............. ........ ... .. ............... ... 7-17 8-1 Profile of a blast wave at a particular distance from point of detonation .. ........... .... ...... .............. .......... .. .. ...... ....................... 8-1 8-2 Schematic representation of bomb explosion ......... ............ ... 8-2 8-3 Peak blast pressure versus distance from bomb burst ............ 8-4 .. .. .. .. .. .. ...... .. ..... ....... 8-5 Blast impulse versus distance from bomb burst ........................ 8-7 8-4 Formation of Mach wave and triple point 8-6 8-6 Variation of overpressure and dynamic pressure with time at a fixed location .. ........ .... ..... .... ............ .. .. ................ .. ...... .. ..... 8-8 8-7 Stages in the diffraction of a blast wave by a structure .......... 8-~0 8-8 Relation of blast wave characteristics at the shock front ........ 8-11 9-1 Air burst of atomic bomb (20-KT) .. .... .. ... ........... ............ .. .... ... 9-1 9-2 Emission of thermal radiation in two pulses ............................ 9-4 9-3 Distances at which burns occur on bare skin .......... .. .. .... ... .. ... 9-7 9-4 Fallout from a high yield surface burst weapon ...................... 9-14 10-1 Armored infantry vehicle, right side view ............_. .................. 10-2 10-2 90-mm gun tank, M48 ....................... ....... .. .. ....... .... ....... .. .... .. ..... . 10-3 10-5 10-3 Reentrant angle effect 10-4 Formation of petalling and plugging as a result of penetration ..... .... ........ .... .......... ..... ..... ... ...... .................... ... . 10-8 10-5 Failure of a 1~-inch cast armor plate resulting from shock of impact during low temperature tests ................................ .. 10-10 10-6 Formation of spall in armor ................................. .. .. .... .. ............. 10-12 10-7 Resistance to penetration versus hardness ......................... ..... .. 10-14 10-8 Views of projectile exit regions ............................................... 10-15 10-9 Striking angle or angle of incidence ............................. .... .. ...... 10-15 • 10-10 Perforation above shatter velocity (top) and below shatter velocity (bottom ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-16 10-11 Effect of striking angle on shatter of projectile ........................ 10-17 10-12 Effect of striking velocity on shatter of projectile .. .. ................ 10-17 10-13 Effect of shatter on perforation .. .. .. ........ .. .. .................,..... 10-18 xxi LIST OF ILLUSTRATIONS (cont) Fig. No. Title Page • 10-14 Effect of yaw angle on shatter of projectile ................. . 10-20 10-15 Effect of plugging action on shatter of projectile 10-20 10-16 Effect of compressive forces on shatter of projectile .. 10-20 10-17 Projectile types . .... .... .. ......... ... .... ... . 10-21 10-18 Shaped charge (high explosive, antitank shell) .. . 10-25 10-19 Ultra high speed radiograph of shaped charge detonation (jet moves from right to left) . . .. . . .. .... . ............. .. . . .. ... . . ... ... . . . . 10-26 10-20 Jet penetration 10-27 10-21 Dependence of penetration on standoff distance . ............ .. . 10-27 A-1 Schematic telemetering system A-3 A-2 Pick-up coils for counter chronograph A-4 A-3 Views of sky screen showing aligning telescope and mount .. A-5 1 A-4 Schematic diagram of lumiline screens and counter chronograph ..................... ........................ A-6 A-5 Schematic diagram of Aberdeen Chronograph ......... ... ........ A-6 A-6 Exploded view of a crusher gauge .. A-8 A-7 Piezoelectric pressure gauge A-9 A-8 Piezoelectric pressure gauge for measuring pressures up to 80,000 psi . ... .... ... .... .......... ..... .. .... ................. ... .. .. A-9 A-9 Mounting of resistance strain gauges on a gun tube ............ A-10 A-10 Pressure strain gauge, assembled (top) and disassembled (bottom) ......... .. .. ................ ...... ..... .... A-10 A-ll Cathode ray oscillogram of pressure-time history for an artillery piece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-11 A-12 Askania cine-theodolite A-12 A-13 Askania cine-theodolite record of A-4 ( V -2) missile A-12 A-14 Mitchell photo theodolite .......... ... .... .... ......... ............................ A-13 A-15 Mitchell photo theodolite record of A-4 missile ... ................... A-13 A-16 Bowen-Knapp camera . ........ .... .... .. ... .... .. .. ... ............. ....... A-14 A-17 Bowen-Knapp record of A-4 missile at intervals of one-thirtieth of a second, showing referency system ............ A-14 A-18 Twin 4.5-inch tracking telescopes ... ... .. ... .... .. .. ... .. .... .... ... ... A-15 A-19 4.5-Inch tracking telescope record of A-4 missile ... . ... .... . .. ... A-15 B-1 Comparison of inert impact against armor and concrete . . . . . . . . B-2 • JOtii LIST OF ILLUSTRATIONS (cont) Fig. No. Title Page B-2 B-3 Effect of explosion in concrete . .. ... .... .. ........ .. ........ .................. .. . Concrete piercing fuze ......... B-3 B-4 B-4 105-mm H .E . fuzed superquick test block 3 feet thick showing relative ineffectiveness of 105-mm H.E. shell, fuzed superquick, against concrete .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. B-4 B-5( a) Effect of 105-mm H.E. shell ' with concrete piercing fuze (front view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5 B-5(b) Effect of 105-mm H.E. shell with concrete piercing fuze ( rear view ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5 B-6 Effect of shaped charge against concrete .. . .. .. .. .. .. .. ... .. .. .. .. . . . .. B-6 • xxiii CHAPTER 1 INTERIOR BALLISTICS-GUN PROPULSION SYSTEMS 1-1 INTRODUCTION Prior to the fourteenth century military life was not complicated by the study of interior ballistics. Missiles could be projected by muscle power, slings, catapults, or by elastic forces applied through bows, crossbows, and ballistas. In 1346, the English, by using gun-launched projectiles against the French, gave birth to interior ballistic phenomena. Since that time, the design of cannon has progressed from the old cast iron and bronze tubes to the modern high quality steel guns with rifled bores . With this advance has come the requirement for projecting larger missiles at ever increasing velocities and to greater ranges by varied systems of propulsion. The projection of missiles at the high velocities and other conditions demanded today, requires tremendous force. The source of the energy which supplies these forces must be readily manufactured, easy to transport, and capable of being safely applied. At various times, proposals have been made for utilization of energy provided by means other than explosives such as compressed air, electromagnetic force, and centrifugal force. Thus far, however, no results have been attained from any of these sources which approach those realized from chemical explosives. Interior ballistics (that branch of ballistics dealing with motion imparted to a missile) comprises a study of a chemical energy source, a working substance, and the accessory apparatus for controlling the release of energy and for directing the activity of the working substance. Of allied interest is the mechanical functioning of guns and accessories. · • Since unnecessary weight is an unjustified logistical extravagance, weapons are designed 1-1 to operate under greater extremes of temperature and pressure than are usually encountered in the use of non-military engines. Because the time cycle involved is quite small, there is not sufficient time for the consummation of slow processes such as heat transfer. Consequently it is necessary that the· chemical energy source must also furnish the gaseous products which in themselves constitute the working substance. This energy source may be a solid propellant as in most guns, or a liquid fuel and oxidizer source such as is currently used in rocket propulsion. As previously described in this text, propellants are studied from several ·aspects. Thermodynamic properties indicate the release of as much energy per unit weight as may be consistent with other demands. Studies of the mechanism of decom'position indicate the effects of uncontrollable parameters such as ambient temperature. Dynamics of the gases are necessarily a subject of investigation because the kinetic energy of the propelling gases is an important part of the total energy of the process. The study of motion of a projectile inside the gun tube is not a matter of simply applying Newton's laws to the motion of the projectile regarded as a point mass, but a complicated study of the rate at which the high temperature gas is evolved from the propellant; the motion of the gas so produced; and the effect of this gas on the motion of the projectile itself. The passag~ of the solid projectile stresses the tube mechanically and subjects the interior of the barrel to sliding friction. The passage of high temperature gases, in addition to the high pressures generated, heats the barrel to the extent that chemical interaction with the metal itself occurs. BALLISTICS 1-2 ACTION INSIDE THE GUN A modern gun or mortar is essentially a heat pending upon the weapon design. This muzzleengine. Its action resembles the power stroke pressure continues to act on the projectile for a of an automobile engine with the expansion of slight distance beyond the muzzle. Thus, thehot gases driving the projectile instead of a pisprojectile continues to accelerate beyond theton (Figure 1-1). When the charge is ignited, muzzle.gases are evolved from the surface of each grain A special form of this method of propulsionof propellant and the pressure in the chamber is represented by the recoilless system ( Figureincreases rapidly. Resistance to initial motion 1-2). Here controlled burning of additional proof the projectile is great, and is largely due to pellant permits discharge of gases through a nozits inertia, its friction, and the resistance of the zle at the breech. The rate of discharge of gasesrotating band to engraving. The projectile normcan be controlled by controlling propellant burnally does not begin to move until the pressure ing, thus permitting a balance of the momentumreaches values ranging from 6000 to 10,000 psi. of the gun-propellant gas-projectile system. Theinterior ballistic problem here is not only oneThe chamber volume is increased, which has of combustion but of balancing the orifice diamthe effect of decreasing the pressure; however, eter against thrust required to maintain a meanthe rate of burning of the charge increases. The velocity of the weapon at zero. The propellantnet effect is a rapid increase in the propellant weight in this case exceeds that for a comparablepressure until the point of maximum pressure is cannon by a factor of 2 to 3. The pressure-travelreached. This occurs at a relatively short discurve is designed for minimum muzzle velocitytance from the origin of rifling. Beyond that consistent with accurate exterior ballistic perpoint, pressure drops and, at the muzzle, reaches formance, thus permitting the use of a thin guna value considerably less than maximum prestube which is necessary to maintain the characsure, probably of the order of 10 to 30% de-teristic light weight of this weapon. R•coiling Pari$ +-- Fig . 1-1 Standard gun system. Fig. 1-2 Recoilless system. 1-2 • GUN PROPULSION SYSTEMS 1-3 DISTRIBUTION OF ENERGY • The energy developed by the burning of the propellant in a medium caliber gun, assuming ENERGY ABsoRBED i Translation of projectile Rotation of projectile Frictional work on projectile complete combustion, may be distributed as follows: oF TOTAL 32.00 lReflects in the area 00.14 generated under a 2.17 pressure-travel (Due to engraving of rotat.inf!; curve for t he canbands, wall friction , and non, (Figure 1-3)effects of increasing twist.) J (34.31 %). Translation of recoiling parts 00.12 Translation of propellent gases 3.14 Heat loss to gun and projectile 20.17 Sensible and latent heat losses in propellent gase~ 42.26 Propellant potential (Q.) 100.00 1-4 PRESSURE-TRAVEL CURVES In order that the projectile may leave the bore at the designated muzzle velocity, and that the pressures developed to accomplish this do not damage the weapon, all tubes are designed in accordance with a desirable pressure-travel curve for the proposed weapon. The pressure-travel curves (Figure 1-3) indi •> cate the pressure (or force if pressure is multiplied by the cross-sectional area of the bore) existing at the base of the projectile at any point of its motion. Hence, the area under any of the curves represents the work done on the projectile per unit cross-sectional area, by the expanding gases. rigin Travel of Projectile, tl Powder Chamber Fig. 1-3 Pressure-travel (solid lines) and velocity-travel (dotted lines) curves. 1-3 BALLISTICS If the areas under curves A and B are equal, then the work performed in each of these cases will be equal, and the muzzle velocities produced by each of these powders will be the same, since WORK = KE = ~ MV2 The fact that curve A exceeds the permissible pressure curve cannot be tolerated. Should it be desired to increase the muzzle velocity of a projectile, the work performed, or the area under some new curve, must be greater than the area under a curve giving a lower muzzle velocity. Such an increase in velocity is in dicated by curve C whose maximum pressure is equal to that of curve B, but whose area is greater than that under B. It appears that the ieeal pressure-travel curve would be one which would coincide with the curve of permissible pressure; however, if it were possible to design a propellant capable of producing such a result, many objectionable occurrences would take place. In addition to producing excessive erosion (a factor which would materially decrease the accuracy life of the gun), brilliant flashes and nonuniform velocities due to high muzzle pressure would result. Moreover, the powder chamber would have to be materially increased and this would affect the weight and hence the mobility of the gun. As a result of experience, the velocity prescribed for a particular gun is always somewhat below the maximum which it is possible to obtain; and the powder grain most suitable for producing this result is the one which will give the prescribed velocity uniformly from round-toround without exceeding the permissible pressure at any point in the bore. 1-5 CONTROL OF INTERIOR BALLISTIC PERFORMANCE Consideration of the desired relationships between gas pressure and projectile velocity necessary to meet the demands imposed for the achievement of desired ballistic performance, have been discussed in a general sense; however, it remains a fundamental problem of interior ballistics to determine and evaluate the influence of all variables of the problem. The solution may be based on theoretical analysis, established empirical relationships, or detailed, meticulous experimentation. The variables basic to the problem include the following: (a) Variation in chemical composition of the 1-6 In the ensuing discussions of the effects of grain design and charge weight, optimum ignition characteristics are presumed; however, the ignition problem has required extensive research, particularly in the design of ammunition for high velocity weapons. Propellant powders must be ignited by high temperature and not shock, since the latter may cause detonation. This means that heat must powder. (b) Variations in rate of reaction. (c) Variations in ignition characteristics. (d) Variation in grain geometry (surface factors). (e) Variation in charge weight (density of loading). (f) Environmental factors. The effect of chemical composition and the influence of pressure and temperature on combustion have been discussed. The influence of environmental factors must be considered ( relative to design) in terms of the extent of their influence on gun performance. IGNITION flow from the hot primer flame to the powder grain. This sensible 1-.eat, plus that due to any adiabatic compression of gases in the vicinity, is the sole source of heat available to ignite the propellant uniformly. Heat flow to the main charge is by two means: radiatiol). and conduction. In the case where one body surrounds the other, the net radiation between them may be represented as • 1-4 GUN PROPULSION SYSTEMS G = mass velocity of gas in contact with solid D = average diameter of the solid :·= cEA [C~)~-C~~)] Thus the temperature, mass, and velocity of where the gases generated are of prime importance; and when the hot gas is enhanced by the presence of incandescent solids, the radiation effects not dq, = rate of radiant heat flow d8 only augment, but exceed those obtained by c = radiation coefficient, 0.172 conduction. Under ideal conditions, each grain of powderE = emissivity or specific radiating ability in the propelling char ge would be ignited at the A. = area of radiating surface same instant by being brought into complete T1, T2 = absolute temperature of the radiating contact with the primer flame. The use of a surfaces large primer, as in large guns, requires so muchThus, radiant heat transmission varies with black powder that the firing is not smokeless.the area, and to the fourth power of the tempera Powder grains that are packed ~o closely togetherture of the radiating body. The emissivity E, may so restrict the flow of hot primer flame thatof most solids is up to ten times as high as that ignition may be irregular. From a purely theo of gases. For this reason, luminous flames which retical viewpoint, the most satisfactory primercontain large numbers of solid particles in sus would consist of an explosive gas which wouldpension in the flame radiate much more intensely permeate the entire explosive charge and liberthan nonluminous flames. This accounts in large ;lte solid particles ( s:.~ch as mixture of acetylenemeasure for the superiority of black powder for and oxygen producing carbon monoxide and inuse in primers since the products of explosion candescent carbon particles ). The best practicalcontain large amounts of solids such as potassium solution remains black powder.carbonate and sulfate which radiate intense heat, Originally, faulty ignition was a difficult probin contrast to the nonluminous flames from lem in weapons employing long cartridge cases. smokeless powders. The primer used was comparatively short, ex Heat flow by direct conduction from a hot gas tending into the case only about one-quarter of to a solid surface is described by: its length. In order to remedy this unsafe and unsatisfactory condition, new primers were de dqc = kCrAT o.25 (G)o. s (T -T.) veloped that were almost as long as the case dT I (D)0. 2 itself. These long primers have almost eliminated I 2. the slow ignition problem and have reduced thewhere amount of smoke and flash at the muzzle. No k = conductivity coefficient additional black powder is used but it is merely spread out over the longer length. In weapons CP = specific heat at constant pressure of the hot gas firing separate-loading ammunition, imperfect A. = area of the solid to which the heat is ignition has been minimized by placing a core flowing of black powder through each powder bag or T1 = absolute temperature of the hot gas by attaching an igniter to several parts of the T2 = absolute temperature of the cold surface charge. 1-7 EFFECTS OF POWDER GRAIN CHARACTERISTICS • Assuming proper ignition of all propellant composition (quickness), grain size, grain congrains, the characteristic shaping of pressurefiguration, and density of loading. Although in travel or pressure-time relationships for the gun a final design all factors may be involved, it is system, is dependent on such variables as grain of basic importance to note first, the independent 1-5 BALLISTICS •I effects of such variables. burning design (employing grains of the samePropellant compositions (single-base, doubleinitial surface area, composition, and total chargebase, nitroguanidine, etc.) were discussed in weight) results in lowered peak pressures (withPart 1, as were definitions of configurations (depeak pressure occurring later in the cycle) and gressive, neutral, and progressive burning proin higher muzzle pressure when compared withdegressive grains. For identical charge weight, pellants). Performance of gun systems is usuallydemonstrated using pressure (P)-travel (u) coareas under the curve are approximately equal.In order to meet requirements for equal initial ordinates although pressure-time relationships surface areas for the total charge, the degressiveare often used in experimental investigations. grains must be the smallest of the designs conIn each case discussed in this paragraph, initial sidered. burning rates are directly related to area exposed for the total numher of grains per charge; hence, 1-7.2 GRAIN SIZE it is difficult to consider the influence of single For. a fixed weight of charge of similar comfactors without making allowance for the total position and configuration, shaping of pressurearea initially exposed to kindling temperatures. travel relationships may be accomplished byFor any pressure-travel curve, the shape of the varying the initial area exposed to burning bycurve is affected by the variables shown in varying grain size. Similar effects illustrated inFigure 1-4. For a given pressure-travel curve Figure 1-5 result as grain size is increased(Figure 1-4) the slope of the curve in the region (Figure 1-6). ( 1) to ( 2) is dictated by ignition characteristics Similarly, comparative results of independentlyand total area initially exposed to burning: The varying composition (quickness) or web thick region (3) to (4) will be governed primarily by ness (a combination of size and configuration_ the grain configuration. · parameters) can be demonstrated. In adapting such relationships to specific gun systems, a com 1-7.1 GRAIN CONFIGURATION promise of their characteristics must be utilized. Hand and shoulder weapons require pressure Exposed burning area as a function of "pertravel relationships that minimize muzzle blast • cent grain consumed" (Figure 3-14, Part 1) offers at the expense of reaching high peak pressuresa key to the effects of configuration on pressureand, characteristically,, utilize "quick," degrestravel relationships. As indicated in Figure 1-5, sive, small-grained propellant design. High peakchanging configuration to a more progressive pressures, avoided because of design problems / /~...,...-Rapid change in surface area (degressive)\ small web thickness (many holes or smallf.i\ grains)Strong Ignition ---\.:::.1 ...,..(D'('' ..... ,_Less rapid change in surface area. (High initial surface 7" '>',.;( Larger web thickness (fewer holesarea) 1 ' or larger grains) I ' 'Pressure, P I ~Morerapid chamber expansion I ' (lighter projectile, less resis/~weak Ignition . .... ' -.... tance, etc.) /(Low initial surface ___., -- I Less rapid chamber expansionII Travel, u Fig. 1-4 Pressure-travel relationship. 1-6 • GUN PROPULSION SYSTEMS I p I u Fig. 1-5 Effeds of grain configuration on pressuretravel curves. (Charge weight is equal in each case.) Small Grain ,. -" ~M~.!dium Grains p ' ;-~..;:----~LargeGrains - / ' ' u Fig. 1-6 Effects of independently varying grain size. (Charge weight is equal in each case.) of gun tubes for cannon, are minimized by propellant designs based on "slow," progressive burning configurations of large size. 1-7.3 DENSITY OF LOADING The various types of guns, with different calibres and lengths, and each with its own muzzle velocity design, present special requirements for u u the propellant. The lengths of travel of the projectile in the bore and, consequently, the times of its travel, differ greatly. In addition, the volume of the powder chamber and the weight of the projectile introduce elements which must enter into the selection of a propellant for a gun. Since muzzle energy is directly dependent on the amount of charge burned, it becomes necessary to consider feasible means for increasing the total amount of energy (potential) released in the form of useful work done on the projectile. It is possible, by choosing increasingly large charges of slow powders, to obtain increased velocity without exceeding the maximum allowable pressure. Efficiency will be correspondingly lowered; hence it is not advantageous to fire slow powder in a gun not designed for it. The irregularity in the initial muzzle velocity is closely associated with overall efficiency which, if lowered enough, permits unburned powder to increase irregularity, muzzle blast, and flash. With slower propellants, the point of maximum pressure occurs later, thus demanding stronger and heavier construction over the length of the tube. Conversely, increasing the weight of charge of powder of given quickness increases the maximum pressure attained and causes it to occur sooner in the travel of the projectile. Despite the inherent disadvantages, the demand for high muzzle velocity dictates further development of guns with flat pressure-travel curves, as evidenced by developments using mechanism of a propellant charge traveling the tube length with the projectile. 1-8 PRESSURE-TIME RELATIONSHIPS FOR GUN SYSTEMS The frequency with which propellant burnperimental investigations, warrants a brief reing characteristics are plotted, using time as view of the comparison of this manner of a parameter, and the trend toward use of data presentation with those discussed prepressure-time relationships obtained from ex-viously. v (velocity) _..--\ --I \ \ \ p or '\ - v du ' ' ' ', 1-7 BALLISTICS For any given pressure-travel plot (analogous to pressure-volume diagrams) the relationship of projectile velocity versus travel in the gun provides the basis for relating distance and time for pressure readings. Thus, a given pressure travel diagram dictates the accelerations im parted to a projectile, and hence velocity v . The time relationship then results from the integral of an inverse velocity-travel function, i.e., t = Iau; du which permits evaluation of a travel-time relation ship. A characteristic pressure time relationship may be then determined. (A characteristic plot 1-9 EFFICIENCIES OF Two efficiencies are in general use as expressions of the overall behavior of a given gun charge-projectile combination. Piezometric efficiency is associated with the flatness of the pres mean pressure sure-travel curve, k where the mean pea ' pressure pressure is that which, if exerted against the projectile over the total length of travel, would produce the observed muzzle velocity. Useful in barrel design, a high piezometric efficiency means a shorter and lighter barrel, provided that chamber volume has been increased. It implies high muzzle pressure relative to peak pressure, but indicates final burning of the propellant near the muzzle for greater blast and risk of inferior regularity. Successive charges in a howit 1-10 DEVELOPMENT OF TECHNIQUES Until 1930, the central problem of theoretical interior ballistics was confined to a single problem: Given the characteristics of projectile and gun and a knowledge of the behavior of the charge in a closed vessel, predict muzzle velocity and peak pressure. The experimental work was based on the copper "crusher gauge" (see Appendix A) that was little changed since its invention by Novel in 1860, and the Boulenge chronograph which appeared about the same time. By 1935, perfection of piezoelectric pressure gages and the knowledge that accurate pressuretime curves would soon be obtained in guns, spurred the theoretical outlook. Closed vessel theories were replaced by treatments involving physics and physical chemistry, and the whole is shown in Figure 1-7.) Timewise, the peak pressure occurs later in the cycle, since the projectile moves at relatively low velocity during • the early phases of its travel down the gun tube. • • GUN AND CHARGE zer provide for higher piezometric efficiences as size of the charge is increased. Efficiencies of the order of 50% are common.,Values' of 40% are normal for low charge firings from howitzers and infantry mortars where regularity is of maximum importance. Values up to 60% suit A.T. gun design. The highest known values under experimental conditions have reached 75 to 90%. Ballistic efficiency, defined as the ratio of muzzle energy to the potential energy of the propellant (expressed as a percentage), is a measure of the utilization of the energy in the charge. A high ballistic efficiency is obtained by burning the charge as early as possible in the projectile travel; just the opposite of requirements for a high piezometric efficiency. 1-8 , • GUN PROPULSION SYSTEMS course of the phenomenon had to be developed, to demonstrate relations between pressure-time not only the salient features. Empiricisms relatcurves for different shapes of propellant. Con ing velocity and peak pressures can be traced tinuous refinements and applications of new back to Poisson ( 1826 ), and are associated with theories by Dr. J. C. Hirschenfelder and his the names of Vallier, Heydenreich, and Lel2uc contemporaries; vastly improved instrumentation(the latter's methods in use as late as the mid techniques which now include accurate time1940's) as being applicable over a limited range distance indicators based on doppler effects;of conditions as a way of interpolating pertourmaline pressure gages; radioactive powderformances of nearly identical guns and charges. grains; and the solution of the complex equations Re'sal's relations for shot and propellent gases, Sarrau's equation of combustion, and the Gossotof thermochemistry and dynamics by modern Liouville solution, obtained wider generality analog and digital computing machines, have from a given quantity of data. Roggle was able greatly extended current treatment of the subject. 1-11 SIMPLIFIED VELOCITY COMPUTATIONS Many formulas and equations have been deand time relationship in a manner within the veloped for the expressions of projectile velociscope of this course. They. will be used later to solve problems of recoil. The complexities of ties and powder pressures as functions of time exact technique of solving the interior ballis or distance traveled by the projectile in the bore. tic problem preclude further consideration inThe formulas to be used in this study are those this text. developed by Colonel (then Captain) Camille The LeDuc equations for velocity as a functionLeDuc, about 1895. The LeDuc formulas are of travel are based on the translation of a hyperempirical, but they are sufficiently trustworthy bolic curve (Figure 1-8 ), whose general equationto give approximations of velocities and pressures takes the form :to be expected. They have academic value in au terms of simplicity and are studied at this time v=--(1-1) to permit evaluation of pressure, travel, velocity, b+u v i' -rl I I f Fig. 1-8 LeDuc velocity-travel relationship. - 1-9 BALLISTICS where v is velocity of the projectile at any point in the bore, ft / sec u is travel of the projectile in the bore, ft a is empirical constant, ft / sec b is empirical constant, ft For muzzle conditions ( 1-1) may be written V=~ (1-2) b + u where V = muzzle velocity, ft / sec U = length of bore, ft The values of the constants a and b must be determined empirically and checked and corrected by actual test firings in order that the best approximation to the actual velocity can be determined. The positive branch of the curve approaches a as a limit. Thus, if the gun tube were of infinite length and the powder gases allowed to expand without limit, the expression _u_ would approach unity, and v would equal h+u a. This may be seen graphically in Figure 1-8. There is a definite relationship between the value of b and the travel of the projectile to the point of maximum pressure. It can be shown by calculus that when the pressure, and hence acceleration, is a maximum, the relationship u = __t exists (see Par. 1-13). 2 In practice, with the LeDuc Method a and b are determined by choosing them so as to reproduce muzzle velocity ( 1-2) and maximum pressure in a number of typical cases, and thus determine empirical relationships. For each powder manufactured, a powder constant which represents the relative quickness of the powder is determined. This value is dependent upon such factors as the web thickness, 1·12 EFFECTS OF VARIATIONS The effects of variations of the propellant on the velocity and pressure have been discussed. For a charge of given composition, grain gethe size of grain, -and percentage of remaining volatiles, and is larg~t for slow_l)owders. It mE_ • be seen that b will be directly proportional to', this ---I constant, since, for example, a slow powder (large constant) will cause the point of maximum pressure to occur farther down the bore than will a fast powder, and the magnitude of b varies with the distance to this point of maximum pressure. au From (1-1), v = b + u, the velocity for any point in the bore may be obtained. The kinetic energy of the projectile at any time is ~ w;2 , where w is the weight of the projectile in pounds. The empirical constants, a and b, are computed from the results of experimental firings adjusted to the propellant used. For example: 1/2 a = 6823 ~ (~) 1112 w where ~ = density of loading w = weight of charge, lb w = weight of projectile, lb (The constant 6823 represents the potential of nitrocellulose propellant. ) where {3 = powder constant, or a measure of the "quickness" of the powder (varies inversely as the velocity of burning) o = specific gravity of the powder (usually between 1.5 and 1.6) S = volume of the powder chamber, cu in . IN THE GUN PROJECTILE SYSTEM ometry, and grain size, the variations in performance are indicated in the following paragraphs. • m 1-10 GUN PROPULSION SYSTEMS 1-12.1 GUN TUBE LENGTH By examining LeDuc's equation it may be seen that if an increase is made in the length of the gun tube, the muzzle velocity should rise. There is an actual increase because the powder gases are all being expanded within the tube, rather than released to the air behind the projectile. Up to a certain point the gun tube may be lengthened to increase the muzzle velocity; however, there is a practical limit beyond which the additional velocity does not justify the added weight. 1-12.2 GUN CHAMBER If the volume of the powder chamber is varied for a given charge, the density of loading will vary. Such variations may occur when a different projectile is used; the projectile is not uniformly seated; or when the charge is used in a different gun. In general, an increase in the density of loading will cause an increase in velocity and maximum pressure, but will decrease the length of travel to the maximum pressure point. For example, a 1% increase in density of loading in a 120-mm gun increases the velocity 0.3%, or from 3100 ftjsec to 3110 ft/ sec. 1-12.3 PROJECTILE WEIGHT A decrease in projectile weight has an effect on the pressure-travel curve similar to that of an increase in grain size. The peak maximum pressure is lowered, its position is moved forward, and the area under the curve is decreased. The muzzle energy is lessened but the lowered shell weight has the effect of increasing muzzle velocity. The muzzle velocity varies approximately inversely as the square root of the weight of the projectile; or more accurately, y = Kw -n, n varying between 0.35 and 0.50. The lower value represents the effect of a large decrease in projectile weight. This same effect can be shown by examining LeDuc's equation for velocity and equations for a and b. (Consideration of the expression for the energy imparted to the projectile within the gun, 1/ 2 MV2 , will show that V varies inversely as (w)1 12 if the total energy imparted is the same. ) 1-12.4 DENSITY OF LOADING • A change in density of loading may result from changes in the weight of charge or changes in the volume of the powder chamber; and the 1-11 changes in the volume of the powder chamber may be caused by using a different type of gun or projectile, or by nonuniform seating of the projectile. In general, a decrease in the density of loading decreases the velocity and the maximum pressure but increases the length of travel to the point of maximum pressure. With the same gun and projectile, a change in density of loading is obtained only by changing the weight of powder charge or by nonuniform seating of the projectile. In either of these instances, for small changes, the approximate rule is: The velocity varies as the square root of the density of loading. 1-12.5 SECTIONAL DENSITY If the weight of a projectile of a given diameter is reduced, the projectile is said to have a decreased sectional density, defined as: weight (diameter)2 where the weight is in pounds and the diameter is in inches. Representative values for various projectile types and calibers are: Projectile Type and Caliber Sectional Density 155-mm HE 2.557 90-mm AP 1.892 90-mm HVAP 1.76 76-mm REP 1.104 .30 BALL M2 .237 .30 AP M2 .260 Low sectional density is desirable from an interior ballistics viewpoint but undesirable from an exterior ballistics viewpoint, since the projectile has less inertia and will be more easily retarded by the air. As a means of providing low sectional density of the projectile while it is in the gun, and increasing this factor while the projectile is in flight, methods employed have as a goal the decrease in diameter of the projectile after it leaves the gun tube. Projectile types utilizing this principle are: (a) Discarding sabot projectile. (b) Folding skirt projectile (used in a tapered bore weapon). Other methods of reducing the sectional density are the composite rigid projectile ( HVAP) and the Russian Arrowhead. In these cases, the sectional density remains low during the Hight of the projectile. BALLISTICS 1-13 PRESSURE COMPUTATIONS An expression for pressure in the gun tube may be derived from LeDuc's velocity equation. The rate of change of momentum: F = Ma PA= ( ;)(~:) p =(;g)(~:) P = pressure producing acceleration, psi A = cross-secticnal area of the gun tube, sq in. Differentiating LeDuc's equation for velocity, (b +u) a (du)-au (du) ~ ~)= dt dt ( dt b +u (b +u) 2 (du) ab = (b +u)2 dt But, du au -=v=- dt b +u Substituting in the expression above, wa2bu P=---Ag(b +u)3 (1-3) Since maximum pressure must correspond to the point of maximum acceleration, ~(~)=o dt dt or d ( a 2 bu ) dt (b +u)3 = (b+u) 3 (a2b) (du)-(a2bu) (3) (b+u)2 (du)dt dt =0 (b + u)6 or b b + u -3u = 0, whence -= u 2 Substituting in ( 1-3) above, 4 wa2 Pmaz = ---(1-4) 27 Agb As noted previously, actual tube pressure must overcome friction; force the rotating band through the rifling; impart rotation to the projectile; and produce acceleration. The actual bore pressure, which has been found experimentally to be approximately 1.04 times the pressure producing translation of the projectile [see (1-3)], is given by the formula 1.04wa2bu P(actuaI) = ----(1-5) gA(b +u) 3 Also from (1-4), the actual maximum pressure is given by the formula 4. 16wa2 p maz(actual) = ---(1-6) 27 Agb 1-14 EFFECTS OF VARY I NG CONDITIONS IN SERVICE During the service life of a gun tube, a number of variables may affect its ballistic performance in a manner which a designer may not predict, but which must be anticipated. Wear characteristics of the bore vary widely between the extremes of large, low velocity howitzers, and hypervelocity tank and anti-tank guns. Environmental conditions such as ambient temperature, gun temperature, deterioration of ,ammunition in storage, and others, thus may affect the initial 1-12 conditions for the exterior trajectory of the projectile. Examples of two methods by which such conditions are resolved to standard conditions are indicated here. Firing tables include means for absorbing the effects of nonstandard conditions into firing data,· and tube serviceability standards are used to predict service life and effects of wear on specific guns firing specific types of ammunition. • GUN PROPULSION SYSTEMS residues generated from the burning of the 1-14.1 TEMPERAJURE OF THE POWDER propellant, as well as by the-·movement of the Firing tables are based on a powder temperaprojectile through the bore. Erosion is often ture of 70°F, at the time of firing. An increase divided into three phases:in this temperature increases the potential and (a) Gas erosion. The first indications of thisthe burning rate of the propellant, giving a type of erosion are hairline cracks or a checkergreater muzzle velocity. Conversely, a decrease ing effect near the origin of rifling. This is probin the powder temperature reduces the velocity. ably caused by continued expansion and contracA tabulation of the effects of variation from tion of the metal of the gun tube in conjunction standard powder temperature is incorporated in with the brittleness of the metal caused by thethe tables to enable the necessary corrections to absorption by the gun tube of carbon and nitrobe made in the firing data. An extract from firing gen from the powder, producing a brittle carbidetables for the 105-mm howitzer is shown in or nitride. This checkering or cracking is notTable 1-1. erosion in itself but makes it easier for the hot 1-14.2 TEMPERATURE OF THE GUN gases moving at high velocity to wash away the metal. Figure 1-9 shows the checkering and gasA change in muzzle velocity will occur because erosion near the origin of rifling and the gradualof high gun temperature due to rapid fire. As wearing away of the rifling. an example, 30 rounds fired rapidly in a 90-mm (b) Scoring. Scoring is attributed to a nozzlegun will cause a breech metal temperature of about 275°F. If a round is left in the gun before or vent action of the gas esclfping past the rotating band. Sometimes tool marks or rifling defects firing, the powder will be affected by this temstart the scoring because of lesser obturation orperature; however, if the round is fired quickly, sealing by the rotating band at the defect. Oncethere will be no appreciable change in powder started, scoring, unlike gas erosion, increasestemperature and consequently, no velocity rapidly with each round although it does not change. The spontaneous firing of an overheated round left in a hot breech recess is commonly usually become evident until after several rounds have been fired. Scoring usually begins on thetermed "cook-off." upper part of the bore around the 12 o'clock 1-14.3 EROSION IN THE GUN BORE region, due to the weight of the projectile caus ing the greater clearance at the top when seated. Erosion is the process of removal of metal from the surface of a gun tube by the movement This is usually mo~e evident in guns firing at high velocities of high-temperature gases and separate-loaded ammunition. When firing is done HOWITZER. TABLE 1·1 EXTRACT FROM FI RING TABLES FOR 1 05-~ SHELL H.E. Ml MV = 7 10 FTj SEC, CHARGE 2 Change in Velocity Due To Change in Temperature of Powder Tempera ture of Change in Temperature of Change in Powder, °F Velocity, ft/ sec Powder, °F Velocity, ft/sec 0 -22 50 -6 -19 60 -3 10 0 20 -16 70 30 -13 80 +3 90 +6 40 -9 • 50 -6 100 +9 1-13 BALLISTICS .. . Fig. 1-9 Advanced gas erosion at origin of rifling near 12 o'clock of 155-mm gun, M2.Note complete obliteration of lands. (Extract TB 9-1860-2) Fig. 1-10 Impressions showing scoring at 12 o'clock (top) and gas erosion at 6 o'clock (bottom).Bottom also shows light scoring in the grooves. . Taken from 155-mm gun, M2. (Extract TB 9-1860-2) 1-14 • GUN PROPULSION SYSTEMS with a hot gun or at faster rates, after scoring has this loss is small, nearly all the range ·loss evidenced can be attributed to muzzle velocity loss. once started, scoring can become very severe. Allied to the range loss is the increase in timeDeep scoring reduces the strength of the gun of flight for the same ranges in antiaircrafttube, but most guns become too inaccurate for weapons. This is important when considered as further use before scoring becomes dangerous. Figure 1-10 shows a typical scoring at the 12 additional time for movement of the target. The loss in ·accuracy in most guns due to erosion iso'clock position in a 155-mm gun. (c) Abrasion. Abrasion is a slow mechanical insignificant except in advanced stages when rotating bands may be sheared off. wearing away of the lands after a large number of rounds have been fired. The greater wear In order to fu lly appreciate the actual values usually occurs at the 6 o'clock position at the involved in gun erosion, consider as an example origin of rifling because of the greater friction the erosion effects on a particular gun, the 90mm gun, M3, in the M46 medium tank. The between the projectile and the bore at the bot tom. This wear permits the rotating band to erosion in this gun is characterized by a smooth, even wear of the lands with scoring during latter drop, allowing a larger clearance between the top stages. As erosion occurs, the bore is enlarged. of the rotating band and the tube, accelerating The drop in velocity (based on the diametergas erosion and then scoring. between the lands, in inches, measured at aThe primary effect of erosion is a drop in peak pressure and a resulting loss of muzzle velocity, point 24.85 inches forward of the breech end of the tube) which may be expected at any degree which results in a corresponding decrease in maximum range. Under actual firin g conditions of wear, is shown in Figure 1-11 for the high with a worn gun, there is a small range loss not explosive projectile M7l, and for the armorpiercing capped projectile M82. accounted for by the loss of velocity. This may For a given weight of armor-piercing projectile,be due to increased yaw or other reasons. Since ~ ---f--'t::I _2()() 240 ,k~/ ~ v . H ~~/ v r----~-1.60 ~~ ~~1~ ~il-120 !i ~/1_ /.~ ~ ~ 80 / v/ / 4'~~----- 40 v 8ASBD (B F'IRIIO rFIDD--SHI:U. Jr1l .&liD !PC FIDD/ PRruJrCTi'I.K 82 0 ~0 ~00 l'lltC ~~Su ~i i ~ND!MN11'IQ11 a .LAIID_lDIAMKTJ!R 1 24.8[ ~~IWU) ,. ~EHDIOF ,. Muzzle velocity loss as a function of bore measurement for tubes Fig. 1•1 1 used in 90-mm guns MJ, M2, and M3. (Extract TB 9-J860-2) 1-15 BALLISTICS I' 3-740 ----.---- ~~--).700 ~~ ~Q)IJ ~ I -).660 / I ~~~ v s~i -).620 .// v ~~--3.590 / e~~ ).540 v ESTDIATED REILUNING UFE IN PERCENT I I 100 I I I I 7~ ~ . 215 0 KS'l'DIA~ RmfllHIMl UFE IN ~!VALENT FULL CHARGE ROOJIOO I I J I I I l6p0 lltoo 12po 1opo scp 6cf> 4Cfl 200 0- Fig. J-J2 Remaining life as. a function of bore measurement for tubes used in90-mm guns M J, M2, and M3. (Extract TB 9-J860-2) ~ a loss in muzzle velocity is reflected in striking graph in Figure 1-11, represented by a 243ft/ secvelocity. Therefore, armor penetration is deloss in muzzle velocity. In practical terms thiscreased, or the range at which a given thickness means that at a range of 2000 yards this projec of armor can be penetrated is decreased. Thecondemnation point for tile will penetrate only 3.6.inches of homogeneous tubes firing armorarmor instead of 4.15 inches which would be piercing capped projectile M82, occurs when the expected from a new gun. velocity has dropped to 2557 ft/sec. At this stage The remaining life expectancy in number ofwindshields may become separated from the prorounds of this 90-mm gun is shown in Figure 1-12. jectile or rotating bands may strip off while the That for the 105-mm howitzer M2A1 is based onprojectile is still in the bore. The condemnation equivalent service rounds computed for weaponspoint for the M82 APC projectile is shown on the capable of firing zone charges. (See Table 1-2.) 1·15 INITIAL CHARACTERISTICS OF GUN-LAUNCHED PROJECTILES Interior ballistic problems normally center occur while the projectile is in the vicinity ofabout the motion of the projectile while under the gun tube and must also be evaluated. Curthe influence of the launcher, while exterior balrently, most of these problems are the concern oflistics usually is associated with the Bight charinterior ballisticians; however, the subject is ofacteristics from that point to the target. The sufficient importance that it has often been calledsimplicity of such definitions fails to indicate, "transition ballistics." The launchings of guided however, the launcher influence on the initial or ballistic missiles, rockets, and for the most partconditions of the trajectory. In the case of gunprojectiles from recoilless weapons, are concernedlaunched projectiles, a number of phenomena to a far less degree. 1-16 • GUN PROPULSION SYSTEMS TABLE 1-2 EQUIVALENT SERVICE ROUNDS SHOWING EROSIVE EFFECT OF DIFFERENT CHARGES No. of Rounds Equivalent in Erosion EquivalentGun and Charge Effect to One Erosion in Firing Full Charge Decimals Tables (or Service Round) 1.00 75-mm Gun, M 2 Supercharge 1 Normal charge 6 .16 FT 75 AF 1 53 .019 Reduced charge 1.00 105-mm How., M 2 7 1 6 3 .3~ 10 .10 I<'T 105 H 3 5 4 20 .050 3 40 .0250 70 .0143 2 120 .00833 1 - 1.00 105-mm How., M 3 5 1 .34 4 3 7 .15 FT 105 L 2 3 13 .079 2 1 23 .043 thrust, thereby causing it to reach its maximum 1-15.1 INITIAL AIR EFFECTS velocity not at the muzzle, but at some short As the projectile moves forward in the barrel, distance in front of the muzzle. it pushes the air mass ·in front of it, causing the Because of its small mass and the resistance to latter to emerge first from the muzzle. The inmotion which it meets, the gas loses velocity very ternal air mass, now traveling at a high velocity, rapidly. In small arms, for example, the bullet strikes the outside air which is at rest, and creates overtakes the gas at approximately 35 em from a shock wave which develops spherically and the muzzle. Shortly thereafter the projectile overdisturbs the outside air. This condition is imtakes and pierces the report wave (the wave which produces the noise of the exploding pro mediately followed by a rush of small amounts pellant). At this instant the projectile is accom of powder gas which have forced their way panied by the normal head wave which is defined ahead of the projectile and hence emerge from the muzzle before it. As the base of the projectile as the projectile shock wave. It should be noted that a shock wave cannot form on the projectile clears the muzzle, the main mass of the propellent gas begins to pour out into the already turbulent unless the relative velocity of the projectile and outside air. At this instant the velocity of the the surrounding gaseous medium is equal to, or gas is equal to that of the projectile, but because exceeds the speed of sound. During the time the of the tremendous gas pressure present, the projectile was passing through the powder gas former increases suddenly, causing the gas to envelope, this condition did not exist, and hence no head wave was formed. However, at the • rapidly overtake and pass the projectile. During this phase the gas develops a maximum velocity instant the prqjectile pierced the report wave, the of more than twice that of the projectile and required conditions existed and a head wave was formed. consequently imparts to the latter an additional 1-17 BALLISTICS Obviously in guns with a high cyclic rate of been discusseo. The effects of the air disturbfire some exterior ballistic effect must be presances described here are directly associated withent due to gas stagnation, since the turbulence the cause and control of muzzle flash. of the gaseous medium in the vicinity of the muzzle creates a condition of instability. 1-15.2 VERTICAL JUMP The stagnation or pressure limit created in When a gun has been made ready for firing,front of the muzzle is the result of high velocity the axis of the bore forms, with the line of sight,propellent gases emerging and compressing the an angle called the angle of elevation. From theinitially still air, thus creating a marked retardaviewpoint of normal expectancy, it would appeartion effect. An envelope of gas is formed with that the projectile on leaving the bore wouldmaximum pressure existing at the intersection of follow initially the path determined by the linethe stagnation line and a prolongation of the of elevation. Such is not the case, however, foraxis of the bore. The cycle of events, described when vertical jump occurs the projectile actuallyby a related series of Schlieren photographs leaves the gun on a line of departure whose(Figure 1-13) continues as long as gas under high angle is greater than that of the line of elevation. pressure continues to emerge from the muzzle. (See Par. 3-2 and Figure 3-5, Part 2.)As the pressure subsides, the stagnation line When a projectile is launched from a gun, amoves towards the muzzle of the gun. The number of things occur which cause the phephenomenon of muzzle flash as a problem asnomenon of vertical jump. While the gun is at sociated with propellants, and the chemical andmechanical means of combating the effects have rest, the axis of the bore does not exist as a straight line but rather as a curve, concave down. Fig. J-J3 (J) Effects of projectile emerging frommuzzle. (Spark photograph of gun being fired.)Photograph No. J was taken before the bullet hademerged from the muzzle. The dark edged circle isactually a spherical shock wave. It is formed when theair column existing in the bore at the instant of firing,strikes the outside atmosphere at supersonic velocity.The gray, turbulent area within the circle is powder gas which has leaked ahead of the bullet. The darkobject at the top of the photograph is a microphonewhich was used to trigger the spark,thus taking the picture. 1-18 • GUN PROPULSION SYSTEMS The longer the gun tube, the more pronounced is this curve. A projectile passing through the bore at high velocity will cause the gun tube to be whipped rapidly upward, producing a condition similar to the straightening of a coiled hose when water under pressure is first allowed to pass rapidly through it. Due to the nature of the forces involved, as well as to the elasticity of the metal, the gun tube at the instant of projectile release is slightly concaved upward. The condition just described has been referred to as "gun tube droop." A second factor, whose vertical component contributes to vertical jump, results from the reaction of the gun tube to the rotation of the spinning projectile. With a projectile rotating clockwise as viewed from the breech of the gun, the gun tube will tend to be twisted in a counterclockwise direction. A third factor results from the sudden shifting of the center of Fig. 1-13 (2) Effects of projectile emerging from gravity of the system as the projectile speeds muzzle. (Spark 11hotograph of a gun being fired.) down the bore. This effect tends to cause the Photograph No. 2 depicts conditions perhaps a muzzle of the gun to move towards the ground.microsecond or less later than in (1 ). The bullet A fourth factor is the lack of complete carriageis still inside the barrel. stability, and this may be combined with a lack of complete rigidity with regard to various parts of the gun anr1. carriage. The problem of carriage stability will receive later treatment in this text. The factors affecting vertical jump exist, but to varying degree and direction; hence, vertical jump is determined experimentally. On a mobile carriage, such as the 105-mm howitzer, the vertical jump is 1.8 mils; for fin'd carriages it is approximately 0.4 mils. 1-15.3 LATERAL JUMP Lateral jump is defined as the difference in azimuth between the line of bore sight and the line of departure, and when it exists has a magnitude considerably smaller than that of vertical jump. It may result from some of the factors causing vertical jur.. p , but more frequently occurs as a result of an unbalanced Fig . 1-13 (3) Effects of projectile emerging from muzzle. (Spark photograph of a gun being carriage condition or a bend iu tl1e bore. ·where an unbalanced carriage condition exists, lateral fired.) Photograph No. 3 shows the bullet emerging from the muzzle. It is partially obscured by jump increases slightly with increase in gun the powder gas. The shock wave has continued traverse. In stable carriages with split trails, lateral jump is usually negligible. A bend in the to expand but is rapidly decelerating and will soon be pierced by the projectile which is re-bore is a condition comparable to droop and tarded by the atmosphere to a res ults from unsatisfactory machining operations. Suitable means exist for detecting this defect, much smaller degree. 1-19 BALLISTICS which, if serious enough, becomes a cause for is specified limits, thus held within producing gun tube rejection. Normally, bend in the bore a negligible amount of lateral jump. • • • REFERENCES 1 Corner, Theory of Interior Ballistics of Guns, John Wiley and Sons, N. Y. , Chapters I and IV. 2 Deming, Chemistry, John Wiley and Sons, N.Y. 3 F. P. Dunham, Thermodynamics, PrenticeHall, Inc., N. Y. 4 Hayes, Elements of Ordnance, John Wiley and Sons, Inc., N. Y., Paragraph 68-71. 5 F . R. W. Hunt, Internal Ballistics, Philosophical Library, Inc., N. Y., 1951. 6 Robinson, Thermodynamics of Firearms, McGraw-Hill Book Co., Inc., N. Y., Chapters XI and XII. 7 U.S. Army Technical Bulletin No. 9-1860-2, Evaluation of Erosion and Damage in Cannon Bores. 1-20 CHAPTER 2 INTERIOR BALLISTICS-THRUST PROPULSION SYSTEMS 2-1 INTRODUCTION Since World War II, the design of modern weapons has placed increasing demands on conventional systems in terms of range, velocity, accuracy, and flexibility. These demands have exceeded the capabilities of projectile-type systems as well as the capabilities of reciprocating engine-type aircraft to deliver an effective destructive missile against an enemy. In past centuries, lack of dependability and accuracy caused rejection of simple rockets as being ineffective, inefficient, and unpredictable despite their obvious potential. New propulsion techniques and modern scientific and technological advances have now, however, permitted the development of rocket motors and air breathing jet engines to the extent that modern weapons systems are increasingly centered about free rockets, guided missiles, and jet-powered supersonic aircraft which rely on the thrust-producing reaction motor as the propulsion means. Within the broad category of reaction motors lies the solid or liquid fuel rocket motor and the jet. The solid and liquid fuel rocket motor carries its own oxidizer, permitting thrust to be developed within as well as outside the atmosphere. The liquid fuel jet engine relies on atmospheric oxygen to support combustion and is represented by turbo jet, pulse jet, and ram jet designs. In this chapter the basic principles applicable to thrust propulsion by reaction motors will be discussed. Following this, the problems unique to rockets and jets are discussed separately as applicable to specific weapon propulsion requirements. 2-2 REACTION Contrary to popular beliefs, a reaction motor does not push against the air to obtain its thrust. The thrust is obtained by increasing the momentum of the working fluid and by a pressure differential. Newton's third law of motion, paraphrased, states that "For any action, there is an equal and opposite reaction." The reaction motor is propelled on the basis of this principle. Thus, jet engines may be called reaction motors. This is not sufficiently specific, however, because any body moving in a fluid works on the reaction principle if it is self-propelled. For instance, the action of a conventional propeller consists of increasing the momentum of the air, and . the propeller thrust is the resultant reaction. The ordinary propeller-driven missile or aircraft is not a form of jet propulsion because the working MOTOR PRINCIPLES fluid is not ejected from within the vehicle. If the propeller were put in a duct and the air allowed to pass through the vehicle, one would then have mechanical jet propulsion. A reaction motor consists essentially of a propellant supply system, a combustion chamber, and an exhaust nozzle (Figure 2-1). The purpose of the propellant system and the combustion chamber is to produce large volumes of high temperature, high pressure gases or heat energy. The exhaust nozzle then converts the heat energy into kinetic energy as efficiently as possible. In a solid propellant rocket the combustion chamber may contain the fuel to be burned. In a liquid propellant rocket, or in a jet engine, the combustion chamber contains the combustion reaction only. The fuel is pumped and metered in from tanks outside of the chamber. 2-1 BALLISTICS { A~l Exit • ~~Condition' .... .... / Air Inlet Diffuser I S . echon 1 \J.'!r Thermal Jets -- -..., ---- I Entrance Throat Exit Exhaust ~ Combustion f.-+ Nozzle Fig. 2-1 Reaction motor with convergent-divergent nozzle. 2-3 Thrust is the reaction experienced by the motor structure due to the ejection of high-velocity matter. Momentum is the product of the mass of a body and its velocity, and is a vector quantity. Newton's second law of motion states that the time rate of change of momentum of a body is a measure in direction and magnitude of the force acting upon it. In a rocket chamber, billions of molecules of the products of combustion are accelerated within a very short distance (the length of the rocket motor), from essentially zero velocity to exhaust velocities on the order of 6000 miles per hour. An applied force of great magnitude is required to impart such momentum to the exhaust gases. Newton's third law of motion states that there must be an equal and opposite reaction to this momentum-creating force. This equal and opposite reaction is the thrust of the rocket motor. The term thrust, which has been used fre 2-3.1 THE EQUATION FOR MOMENTUM THRUST d dV dm F = -(mV) = m -+ V -= 0 + mV, dt dt dt since V. = constant Thus F = m. V. - rha Va "" w. (V.) -wa (Va) (2-1) g g THRUST quently up to now, should be defined before proceeding further. Thrust is an applied force used to produce motion in or alter the motion of a body. It is measurable in pounds of force. It should be noted that thrust is not a measure of work or horsepower: a reaction motor which is motionless develops no horsepower. At a velocity of 375 miles per hour, one pound of thrust will develop one horsepower. The relationship is as follows: THP = thrust (lb) velocity (fps) 550 = thrust (lb) velocity (mph) 375 A rocket of the V-2 type that develops approximately 50,000 pounds of thrust at a velocity of 3750 miles per hour is developing 10 X 50,000 = 500,000 horsepower. where F = thrust in pounds of force w. = weight rate of flow of exhaust products, lb/ sec V. = velocity of exhaust products, ft/ sec g = 32.2 ft/ sec2 ina = weight rate of flow of air entering, lb/ sec Va = velocity of air entering relative to engine, ft/ sec 2-2 • THRUST PROPULSION SYSTEMS In air breathing motors, e.g., turbojets, themass of fuel is small compared to the mass of F = ~PdS = ~P;dS; + ~PodSo (2-i) air, so m. and rha are near enough to being equal so that the eql!ation becomes: where F = rh (V. -Va) (2-2) S = total surface area For rockets rha and Va are both zero, and the S; = internal surface area equation becomes: So = external surface area Pi= internal pressure F = mV. (2-3) P0 = external pressure 2-3.2 THE GENERAL EQUATION FOR TOTAL THRUST . f P;dS; = net internal force = mVe + P.A.In the equation F = mV., it was assumed s (2-5)that the exhaust pressure of the gases, p,, was andequal to the pressure of the surrounding medium,Po· In the usual case, where p, =1= p0 , there is an additional term, a function of the difference in ~PodSo = net external force = -PoA. (2-6) pressure, which must be added to make the thrust equation strictly correct. In deriving a correct Therefore, thrust equation, it can be stated as a starting F = mV.+ (P.-Po' A. (2-7) point that the thrust of a rocket motor is the reor, using the nozzle angle correction factor X, sultant of the pressure forces acting over the where XV. = V• (see Par. 2-6.4), • inner and outer surfaces. Thus, F = Xrh V. + (P. -Po) A. (2-8) 2-4 SPECIFIC IMPULSE Impulse is introduced as a measure of the per formance of the rocket motor because the amount l,p = ~ = (P. -.Po)A. +XV. (2-9) of propellant necessary is almost the same for w w g the same total impulse, no matter whether this If r.p is multiplied by the gravitational constantimpulse is delivered as a large thrust for a short g, the resultant value is defined as the effectiveduration or a small thrust for a long duration gas velocity V;, with the units ftlsec. Thus, (I= IF dt). Of particular interest to rocket design is the V, = gl,p· = g~ = g(P. -. Po)A 1 + XV. (2-10) amount of thrust delivered per weight rate of w wHow of propellant, F /t.V . This quantity is a func or assuming the nozzle correction factor as onetion of the design of the motor which is based (..\ = 1): upon the expected thermodynamic properties of the gas, defined in Part 1 (Sources of Energy) as specific impulse: V; = ~ = (P. -.P o)Al + V. (2-11) m m 2-5 ROCKET MOTOR THERMODYNAMICS The configuration of the nozzle is important the rate of How of gases through the valve. Afterto good nozzle design, but thermodynamic conthis has occurred the flow will remain steady (asiderations play as large a part. Consider Figure "steady-state How" condition will exist). After • 2-2, where, if the valve is cracked, a small flow this steady flow condition, the chamber pres of gases will enter the chamber and cause pres sure ( P,) becomes a fixed or "equilibrium" pressure in the chamber to rise until the weight rate sure value.· If the valve is opened further, moreof escape of gases through the exit section equals How will result, and after a steady state again is 2-3 BALLISTICS VALVE AT HIGH PRESSURE Fig. 2-2 Schematic reached, a new How rate and a new (higher) equilibrium chamber pressure ( P,) will exist. Thus, it might be concluded that as the How rate is increased (by stepwise valve openings) the chamber pressure increases. For a reaction motor mounting a well-designed exit section, this is always true. If a further assumption is made that the temperature of the gases in the chamber (T,) and the outside pressure (P.) remain constant, then the equilibrium temperature, equilibrium pressure, and equilibrium velocity of the gases at any one condition of steady-state How will vary with one another. However, as the gases How down the chamber and into the throat of the nozzle, the gas temperature will fall as the thermal energy of the gases is converted to kinetic energy. However, a continued increase in How rate, and a subsequent increase in equilibrium chamber pressure, will not produce an infinitely increasing velocity or decreasing temperature. Rather, above a critical equilibrium chamber pressure (Pcnt = P, ) al though chamber pressure is again increased, further velocity and temperature changes will not occur. This does not mean however, that more mass cannot be made to How through the motor. Density of the gases may and does increase as the valve opening is increased further. The mass rate of discharge is described as: m = p,A, v, (2-12) • MOTOR CHAMBER pi \ Exit Section flow diagram. is constant, then m = (constant) (Pt ) ; or the mass rate of discharge is proportional to gas mixture density. Thus, above the critical pressure the mass rate of How is a function of the thermodynamic nature of the gases discharged. The behavior of a nozzle operating above Pcnt is called "nozzling." Evaluation of motor design involves specific thermodynamic relationships. From the ideal gas law, nRT PV = nRT· P = --= npRT (2-13) • v I I and the following equations for throat pressure, temperature or velocity (P, > Pcnt ) may be derived: P 1 = P, (-2-)A:-A: 1 = .533 P, fork = 1.4 k+1 (2-14) T, = Tcrit = T; (k ! ) = .833 T;for k = 1.4 1(2-15) V, = V crit = VkrJIT, = 1100 ft/ sec fork = 1.4, t = 60°F (2-16) where k = g:, .or ratio of specific heats of the real gas mixture, in each case. where Since the larger the mass rate of discharge, the p, = density of gases at throat, slugs/ ft 3 larger the thrust of a rocket motor, it is desirable A, = area of throat, ft2 that rocket motors be operated above Pcnt· Thus, V, = velocity of gases at throat, ft/ sec for "nozzling," from ( 2-14), the critical pressure When P, > Pcnt and since in any given case A1 ratio becomes, 2-4 • THRUST PROPULSION SYSTEMS .. ~>(k+2 1)t=i (2-17) . [ 2 Jc:~l))~. k i ( . .. ) . Pat,. m = --nRT .if,P, , (2-19) k + 1 For optimum thrust conditions, chamber pres or setting all the terms on the right-hand sidesures are at least several hundred pounds per (except A,P,) equal to C..., square inch, and "nozzling" is always easily met.Using (2-12), (2-14), (2-15), and (2-16), m,the mass rate of discharge, may be expressed (2-20) in terms of the chamber temperature, pressure, where em is defined as the mass discharge coand dimension. Thus, efficient and C.., is the more generally used term,weight flow coefficient. The mass rate of dis m. = p,A, v, charge, then, is proportional (in any given syswhere tem) to only two variables: the chamber pressureand the throat area. p, ( 2 )k-t" ( 2 )-1( p, ) Other useful performance criteria include: Pt = nRT, ""' k + 1 k + 1 nRT, Thrust coefficient, CF = F/ P;A, = Cml,,, = (-2-)k=t" ~ where F = total thrust, lb (2-18) k + 1 nRT, Characteristic velocity, and c· = Vi/CF 11 Total impulse-weight ratio, V, = Vk (-2-) :;nRT;. k + 1 R.-/ W = Ft:..t = I ,,· W,,.,.!!ant By substitution, Wtota l rocket Wtotal rocket 2-6 NOZZLE DESIGN Since thrust from a rocket motor is proporsound in a gas increases with the temperaturetional to the momentum of the exhaust gases and with R. H owever, a s indicated above, theejected per second, and since momentum is equal use of a convergent nozzle puts a definite limitto mass times velocity, the efficiency or thrust on the velocity that can be obtained and thatcould be increased at no extra cost in fuel convelocity cannot be exceeded no matter how highsumption if the exhaust velocity could be maxithe pressure in the chamber is raised. mized. The means of doing this was firstdemonstrated by a Swedish engineer, Carl G. F.· The relationships between change in channeldeLaval, by the design of a convergent-divercross section area, A, and the resulting changegent nozzle. Before his discovery, engineers in speed, V, for a compressible fluid are emalways attempted to obtain supersonic velocities bodied in a consideration of isentropic flow of aby a convergent nozzle. As was shown in Par. compressible fluid in a channel of varying cross2-5, if such a nozzle is used and the pressure in section. The momentum equation, written inthe chamber of the motor is increased, a point • differential form, iswill be reached where the velocity of the gas atthe throat will reach a critical value, the maxi1mum of which is the velocity of sound in the VdV +-p dP = 0 (2-21) gas. Of course, the velocity of sound in therocket exhaust is about three times that in ordiContinuity considerations prescribe density renary air (about 1100 ft/ sec) since the speed of lationships, 2-5 BALLISTICS (2-22) • Referring to the differential expression for the velocity of sound in a compressible fluid, dP -= a2. (2-23) dp Combining equations ( 2-21) and ( 2-23), vav + a2 dpp = 0 Condition Effects and eliminating dp/p, M < 1, dA(A < 0 dV > O dP < 0 v ' p dV (V2 _ 1) _ dA = O V a2 A dV > O dP < O M > 1, dA/A > 0 dV dA v ' p or -(1-M2)= (2-24) v A dV which can be expressed in the form, M < 1, dA/ A > 0 ·-y Q p -I ~ (M2 -1) dP -dA = 0. (2-25) P A dV < 0 dP > O k M > 1, dA/ A < 0 v ' p Thus, In a practical design this phenomena creates design problems. Consider a deLaval nozzle of dV (1 -M 2) = -dA = ! (1 -M 2) dP. (2-26) any inlet pressure P,., but with a variable dis V A k P charge pressure P0 • If the discharge pressure is At very low speeds ( M < 1) the familiar inonly marginally less than the inlet pressure, the nozzle functions, not as a nozzle, but only as a compressible fluid is valid: a decrease in area venturi. This performance is shown on curve produces an increase in speed. Density changes a on Figure 2-3. are negligible. As the discharge pressure is decreased well Rewriting ( 2-22) as, below the inlet pressure, a point will be reached where a critical pressure Pc,,,, occurs at the mini(2-27) mum cross-sectional area, but the diverging sec tion smoothly diffuses the flow back at subsonic then, for M > 1, the situation is reversed. Denvelocity to the discharge pressure. This condi tion is shown by curve b. Further decrease in sity, p, decreases rapidly for a given speed in crease, so that the channel area A, must increase the discharge pressure with a well designed nozzle will smooth flow after the throat into a super as speed rises. The higher M, the greate~ the sonic rate of flow as is shown in curve c. Fordensity change for a speed change. From (2-26), discharge pressure between b and c, supersonicas dA/ A ~ 0, (a condition at a nozzle throat flow will continue for some distance, but in section) either M = 1 or dV!V = 0. Thus, order to satisfy the continuity of flow require"nozzling" is specified, as indicated above. ments for discharge of the fluid at exit pressure, In summary, the conditions justified by (2-26) a flow discontinuity will occur. This causes a shock wave within the divergent section of the and ( 2-27) are as follows: 2-6 • THRUST PROPULSION SYSTEMS • ~ ® Nozzle Nozzle CD Exit Pressure Pcrit ------------Pressure 0 @) @ • Mach Number, M 0 Fig. 2-3 Distance along nozzle. nozzle. This discontinuity causes a rise in presare avoided, are small. sure, temperature, and entropy. If the discharge Thus, in a well-designed divergent section orpressure is near the design pressure, the shock expanding cone, a means exists of increasing thewave will occur nearer the nozzle exit as in curve exit velocity up to 3 or 4 times that which wasd, supersonic velocity is maintained, although obtained at the throat. Although the mass flowthe velocity decreases sharply across the wave at the throat remains constant, the velocity offront; if it varies widely from the design presexit has increased as a result of the decrease insure it will occur nearer the throat as in curves exit pressure (Figure 2-4).e and f. If the discharge pressure is too high, The contour of the exhaust nozzle is usuallvsupersonic velocity may degenerate into subsonic • built up of straight line entry and exit portionsvelocity across the shock wave. This is shown connected by a circular arc in the throat section.in curves e and f. The losses in a smoothly conSince nozzle cooling is difficult, an effort is made verging and diverging nozzle, where shock waves to minimize the surface area exposed to the hot 2-7 BALLISTICS • I CXIfVI!RG!HT D:TION -DIV!R< ltN'I" Sl!CTIzzle, since_. separation and turbulence are accompanied by excessive drag. Therefore, the entrance and exit angles will have practical limits if the gas is to Bow along the contours of the nozzle. The overall length of the nozzle, which is a function of the entrance and exit angles, will merit consideration for such practical reasons as weight, drag, permissible size, and cost. In Figure 2-l, {3 is ordinarily on the order of 30°, while an a of near 15° seems to be optimum. It can be seen that for a given chamber and throat diameter, the length of the nozzle is a function of a and {3. Separation takes place when a exceeds approximately 40°. Therefore, a should always be less than 40°. 2·6.4 NOZZLE ANGLE CORRECTION FACTOR It is apparent that the thrust component upon which performance calculations are based is the component along the longitudinal axis of the motor. However, the exhaust gases leave the nozzle in a conical section. The exhaust velocity should be reduced to its horizontal component which is ,\v., where ,\ is the nozzle angle correction factor. The parameter ,\ is dependent upon a and has been found mathematically to be equal to ~ (1 + cos a). Typical values for ,\ range from 0.96 to 0.98. The velocity thrust component equals ,\ m v •. 2-6.5 OVEREXPANSION AND UNDEREXPANSION It is often assumed that gases are expanded by nozzles to precisely atmospheric pressure, or Pe = Po· Although it is theoretically desirable that p. = p0 , in the actual case, the exhaust pressure will not .always equal the atmospheric pressure. The exhaust gases, in all probability, will be either slightly overexpanded or underexpanded (Figure 2-5). In practice it has been found that when the exhaust gases have been expanded to a pressure which is on the order of a few pounds per square inch less than atmospheric, oblique shock waves will form. Across each of these shocks a little pressure will be recovered until eventually Pe will equal Po· Therefore shock waves prohibit overexpansion beyond a certain point. In the ·case where the gases reach the exit section of the nozzle in an under 2-9 BALLISTICS 1. 10 • 1. 00 - 0.90 v --- THRUST under over ~ F 0.80 ~pansion expansi n (F(optimum) o. 70 0 2 3 Fig. 2-5 Effects of underexpansion and overexpansion on nozzle performance. expanded condition, or p, > p0 , expansion will FP in this case will be negative and will tend to continue in the surrounding medium until the decrease F; however, F, increases as Pe depressures are equal. creases. Overexpansion is characterized by the (a) Underexpansion: ( P. > Po) . An underformation of shock waves inside and outside the expanding nozzle is one which discharges fluid nozzle. ( See lines e and f Figure 2-3. ) at a pressure greater than the external pressure, The different possible Bow conditions in a dip,., because exit area is too small. The expansion vergent nozzle section are: of the fluid is therefore incomplete within the (a) When the external pressure p0 , is below nozzle and continues outside. F11 in this case nozzle pressure p,, the nozzle will flow full but will be positive and tend to increase F; however, will have expansion (tensile shock ) waves at its F , will be less than it would be if pp were equal exit section ( underexpansion). to or less than Po because potential energy is not (b) For external pressure p0 , slightly higher converted to exhaust velocity. Most rocket than pressure p,., the nozzle will continue to flow motors in common use operate under conditions full ( Pe 2:: 0.4PJ. Oblique shock waves exist of underexpansion, particularly when launched outside the exit section. • from the ground for flight at high altitudes (sur(c) For higher external pressure, a separation face to air missiles). A further illustration is the of the jet will take place in the divergent section variation in performance of air-to-air missiles of the nozzle. The separation is axially symmet with altitude which is attributed to this characrical and is accompanied by normal or oblique teristic of nozzle performance. shock waves. As external pressure increas.~s, the point of separation travels upstream. Further, the area of the jet contracts to p reserve continuity (overexpansion). A net loss of thrust occurs. (d) For nozzles in which the exit pressure is very close to the external pressure, supersonic flow prevails throughout the nozzle (line c, Figure 2-3). The nozzle is operating at design point. (e) Properly expanded, pe _.:_ po · F11 is now Underexpanded nozzle with an equal to zero. Therefore F = F ,.. This is the maximum thrust that can be obtained by a par expansion shock forming at nozzle ticular rocket at its designed altitude, where exit. p, = Po· Thus, it is desirable from the stand (b) Overexpansion: ( p. < Po). An overexpoint of thrust, to have Pe always equal Po· This, however, is impossible for rockets of fixed dipanding nozzle is one in which the fluid is ex panded to a lower pressure than the external mensions which operate throughout a wide range of altitudes and corresponding pressures. pressure. It has an exit area which is too large. 2-10 • • I I ~ I THRUST PROPULSION SYSTEMS 2-6.6 EXHAUST VELOCITY the ideal cycle efficiency of constant pressure engine cycle operating between pressures Pc and The basic thermodynamic relationship for exhaust velocity, V c, based on isentropic flow p., and the gas constant R\ for the fluid, is reabove the critical pressure ratio is, placed by the universal gas constant R, divided by the average molecular weight of the fluid (exhaust products) M. Since V. ,...., ~· the greatest promise for Using perfect gas law relationships, this may be rewritten as , high velocity of exhaust and highest velocity thrust lies in use of fuels which offer prospects of highest combustion temperatures (within limits of motor wall strength) and low average molecular weights of exhaust products. The so-called "new," "exotic," or "zip" fuels described in Part 1 ( Sources of Energy) are specifically tailored to meet this criterion. Fuels containing free radi (2-28) cal~ offer great promise in this area. Such fuels where Tc and Pc refer to chamber (or stagnaof fluorine and boron compounds, now under ention) conditions. Thus, gineering development, offer specific impulse ratings in excess of 400 seconds, in comparison V, = I 2gkRT<, '.J(k-l)M with present standards of 350 seconds for liquid propellants and 220 to 280 seconds for solid prowhere pellants. For outer space travel, the same criterion is the basis for solar, nuclear, and ionic propulsion systems with promises of specific impulse ratings in excess of 1800 seconds. 2-7 SOLID PROPELLANT ROCKETS The simplest of reaction motors in design is temperatures (over 150°F), the grain may bethe solid propellant rocket motor. It is easy and come plastic and at low temperatures (below inexpensive to construct. In this type of rocket 20°F ), the grain may become brittle. Either of the combustion chamber contains the solid prothese conditions may cause erratic burning or pellant. Ballistite in stick form or cast Thiokol explosion, since at higher temperatures they bum might be used in a typical case. Ignition of more rapidly, and when brittle, they break with this charge by an igniter causes rapid burning resulting increases in initial burning surface. and the rapid liberation of hot gases . Rockets Recent development has appreciably improved of this type generally have high specific propelthis temperature sensitivity. lant consumption and deliver great thrust but Since a solid propellant rocket requires a relagenerally of only short duration . Internal prestively heavy casing, the ratio of the weight of the sures are often high. propellant to the total weight of the rocket is For instance, ordinary solid propellants relow, approximately 0.7. To obtain long ranges quire pressures up to 2000 psi in order to and to carry large pay loads, a large percentage of sustain combustion, and the exhaust gas temthe total weight of the rocket must be propellant. peratures reach 4000 to 5000°F. These high Recent developments of internal burning grains pressures and temperatures necessitate relatively with a slow rate of burning and low operating thick motor walls to contain them . Solid propressures should help to overcome these undepellants are susceptible to temperature extremes. sirable features . Solid propellant rockets have This is particularly true of ballistite. At high in recent years shown increasing promise for use 2-H BALLISTICS in long range missiles. In summary, the general characteristics of solid propellant rockets are: (a) Very simple design. (b) Ready to fire on short notice. (c) Propellant tends to deteriorate at temperature extremes. (d) Combustion chamber is propellant container and so must be large. (e) Relatively short burning times (.05 to 40 seconds). (f) No control over rate of burning during flight. 2-7.1 GRAIN GEOMETRY In order to attain the desired mode of burning, many grain forms have been studied and used (several are shown in Figure 2-6). Broadly speaking, solid propellant rockets may be classified in their burning into two classes: restricted and unrestricted. In the restricted burning rocket, the propellant charge is often made in the form of a solid right circular cylinder. The cylindrical side surfaces and one end face are inhibited or restricted from burning by a suitable lining or coating, and burning is allowed to proceed from one end only. This type of rocket is sometimes called "end burning" or "cigarette" burning. The duration of thrust obtained from a restricted burning rocket is roughly proportional to the length of --~0 4 .:5 MULTIPLE GRAIN HIGH VELOCI1Y3 .25CRUCIFORM GRAIN Groin Patterns . ~ . .17 0 'I 0 the charge and depends upon the chamber pressure and the type of propellant used. The thrust • obtained from such a rocket is proportional to the area of the circular burning surface and depends upon the chamber pressure, the type of propellant and the quality of design. In the unrestricted burning rocket the propellant charge is often in the form of a hollow right circular cylinder. This charge is held in place by a suitable support, grid, or trap, but is uninhibited except for the few support points required to mount it. The charge is ignited and allowed to bum on all surfaces with no attempt made to restrict the burning. The thrust from such a unit is proportional to the burning surface and depends upon the chamber pressure, the type of propellant used, and the design of the rocket unit and powder grain. The duration is proportional to the thickness of the cylindrical wall (web thickness) and depends upon the chamber pressure, the type of propellant, and the internal geometry of the combustion chamber and powder grain. Most of the other successful designs are but adaptations of these two extremes of charge design. The charges shown on the upper left in • Figure 2-6 are usually unrestricted, the two charges on the upper right hand side are restricted burning and semi-restricted burning, respectively. SINGLE GRAIN-END BURNING CONE a CYLIHDER • .......... · ~· 0 Holow Ctvciform Multiple Single Groin Star Cvlinder· Gnain Patt.m Fig. 2-6 Geometry of some rocket solid propellant charges. 2-12 THRUST PROPULSION SYSTEMS 2-8 SPECIAL CHARACTERISTICS OF THE SOLID PROPELLANT ROCKET There are some special characteristics of solid propellant rockets which should be explained in order to fully understand the major limitations of the rocket propellants now in use. These characteristics are: (a) Mode of burning. 2-8.1 MODE OF BURNING In describing a rocket assembly containing a solid propellant, it is not sufficient to refer only to the propellant compostion to determine its characteristics. Information must also be given as to the manner in which the fuel bums under a given set of conditions established to give the desired performance. For rocket propellant calculations, the rate at which the surface of the propellant recedes in a direction normal to itself during the burning, is designated as the rate of burning and is usually expressed as inches per second. The burning rate is dependent upon the chamber pressure and increases as the pressure increases. The range of burning rates at pressures of 2000 psi for modern solid propellants varies between the limits of 1 to 2 inches per second. · A comparison between the pressure-time relationship in a gun and in a rocket will assist in understanding the pressure problem. In the case of a cannon, the pressure within the gun chamber rises very rapidly to a peak pressure of approximately 36,000 psi and, as the projectile travels down the bore of the gun, the pressure falls off quite rapidly. The time interval between the zero points of pressure is of the order of a few milliseconds. Generally, a change in ballistic performance of a cannon propellant is limited to minor changes in dimensions. This is due to the fact that in most instances both the weight of projectile and gun are fixed so as to prevent major changes in propellant design from being effective. Rockets, on the other hand, are somewhat more versatile and permit major changes in propellant design and minor changes in motor design to give the desired performance. Ideally, the time-pressure curve in a rocket motor should be rectangular; a "plateau" is (b) Temperature sensitivity and limits. (c) Combustion limit. (d) Pressure limit. (e) Physical changes in storage. The significance of each of these terms will be discussed below. about the best shape attainable. A typical timepressure relationship of a rocket is shown in Figure 2-7. The initial pressure rise within the motor chamber may be comparatively slow. Once having reached its peak, it is maintained at a constant level of the order of 1000 to 5000 psi over an appreciable length of time, or at least falls off only very slowly until,the charge is completely consumed. The order of time varies from a few seconds up to a minute or more. The limitations upon the maximum pressure are governed by the strength of the rocket tube and the maximum mass rate of discharge which can be permitted for a given end use. The pressure within the rocket ·can be readily changed by changes in propellant composition as well as burning surface. The lower and upper limits in pressure are governed by propellant characteristics which will be discussed later. 2-8.2 TEMPERATURE SENSITIVITY AND LIMITS The rate at which a solid rocket fuel burns is markedly affected by th~temperatureof the fuel. This change in the burning property will vary with each formulation and even, though to a lesser degree, with the form of grain. To design . a rocket motor properly a knowledge of the change in burning rate with temperature must be available to the designer. If a series of identical rockets are fired after being conditioned at various temperatures, it will be found that as the conditioning temperature is increased above normal (70°F), the pressure obtained within the rocket motor, when it is fired, increases; and as the temperature of conditioning is lowered, decreased pressures are obtained. Since, all other things being equal, the rate of burning is dependent upon the pressure 2-13 BALLISTICS 51-. .,.,.,. - ·-J -I IJ - 1800 leaD ........ - 1400 j 12: - 1 100 eo... , I :I ~ I Zw ;) 4 5 Pc •1465 psi C •L.54 .., •180 We • 349.511. Fig. 2-7 Time-pressure and thrust-pressure relationships of a restricted burning rocket. within the rocket chamber, it may be stated that the rate of burning varies as a function of temperature. Figure 2-8 shows the actual pressuretime curves of a 3.25-inch rocket fired at various temperatures. Excessive pressure at high temperatures and brittleness and "chuffing" (see Par. 2-8.3) at low temperatures, limit present solid propellant rockets to a temperature range from about -20 to +120°F. 2-8.3 COMBUSTION LIMIT Early in the rocket development program, considerable difficulty was encountered in obtaining uniformity of performance of rocket assemblies. As a result of a number of experimental firings it was noted that, when the exhaust nozzle throat diameter had increased beyond a certain point, erratic chamber pressures were obtained. These rTHRUST ! • r\ \ ' 1\ ' I 1 l 1 v- CH~MBER PRES:,UR • • II 2~55SECf 1 8 10 12 14 t (lee) PERFORMANCE n TIME CURVES A RESTRICTED BURNWG ROCKET 2-14 I \ ['., \ M I\ I I I _\ I ! \ ~ ~ 16 18 20 22 24 F = 26601bs. F~ I • 62912 ft.•l.l786 pressures fell considerably below the projection of the pressure curve established by the firings made at higher pressures, as illustrated in Figure 2-9. Referring to this figure, the lowest chamber pressure in the normal part of the curve, or the corresponding throat diameter, is called the combustion limit for the propellant. For exhaust nozzle throat diameters below the combustion limit the pressure curve is smooth, but after the combustion limit is reached, the pressure versus throat diameter relation is very erratic and unpredictable ( chuffing). The combustion limits for both ballistite and the composite propellants which are currently under development are near 500 psi at 70°F (ambient temperature). The single-base propellants used in conventional guns have a combustion limit of about 5000 psi and therefore THRUST PROPULSION 'SYSTEMS are not suitable as rocket propellants. 3000 ~~~l,, 2-1.4 PRESSURE LIMIT zooo I Some propellants may be safely used only at 1500 chamber pressures below some critical chamber 1000 pressure. If the critical upper chamber pressure soo is exceeded, the propellant charge seems to burn in a violent and unpredictable manner. For double-base propellants, this pressure limit is greater than 12,000 psi. Some composite propel lants have pressure limits of 3000 psi and below, which is a disadvantage in their use in certain applications. 2-8.5 PHYSICAL CHANGES IN STORAGE Double-base propellants decompose slowly on prolonged storage. Their decomposition is autocatalytic. Diphenylamine is usually added to such propellants to neutralize the catalytic effect of the initial decomposition products. It is inadvisable to store ballistite at 140°F for a period of time in excess of two weeks. Prolonged storage of this material at 120°F is not desirable. The composite propellants do not decompose chemically during prolonged storage; but in an atmosphere of high relative humidity, the sodium nitrate absorbs moisture and the charge becomes soft and mechanically weak. These propellants z ~ ~ must be shipped in moisture .tight containers and T,mr (src) must not be exposed to moisture before use. Fig. 2-8 Pressure-time curves for 3.25-inch rocket. 2-9 LIQUID PROPELLANT ROCKETS Liquid propellant rocket motors have been characterized by long development and "debugging" programs. Much of the costly and time consuming procedure is devoted to the redesign of previously satisfactory hardware in order to eliminate unanticipated "chugging" or rocket motor instability. NACA research in the field • of rocket dynamics and controls has indicated that paper designs can be translated directly into successful rocket motors if effects of rocket motor component dynamics are properly considered. The phenomenon of chugging is one of the 2-15 most serious problems associated with liquid propellant rockets. Chugging is characterized by severe oscillations in combustion, in the range of 75-300 cycles per second; these oscillations can result in rocket motor failure, missile structural failure, or guidance inadequacy. A basis for u nderstanding the nature of the instability may be achieved by examination of a simple rocket system consisting of a thrust chamber fed from a large pressurized tank, and having a very short line from the tank to the injector (Figure 2-10 ). BALliSTICS EXPERIMENTAL DETERMINED POl NTS-X a: CD "' CRITICAL 2 4 :r CHAMBER 0 EXHAUST ,----COMBUSTION LIMIT PRESSURE 1 ' ......_ ..,.1,_.~-,-----CRITI CAL THROAT DIAMETER ~-~ X I X -- I )( X )( ~- NOZZLE THROAT DIAMETER Fig. 2-9 Combustion limit of rocket propellant. Liquid Propellant Tank -+-----Combustion Chamber Fig. 2-10 Schematic diagram of a liquid fuel feed system. In this hypothetical case the pressure P1, ahead of the injector can be considered constant, but the combustion chamber pressure Pr, and therefore the pressure drop across the injector, can fluctuate rapidly with changes in combustion. Thus, a disturbance in combustion chamber pressure causes a change in the pressure drop across the injector and a corresponding change in propellant How; the change in propellant How in turn causes another change in combustion pressure. Consequently, any fluctuations in the combustion chamber pressure are amplified and the system can be unstable. For any specified rocket motor it has been found that increasing the propellant pressure at a fixed combustion chamber pressure can stabilize the system and eliminate chuggin.g. However, the stability has b een achieved at the expense of an increase in weight resulting from the heavier pumps and lines that must be used. Furthermore, the same propellant pressure does not necessarily result in stability for a larger or smaller version of the same basic rocket motor. During an NACA research project, a basic rccket system, consisting of a propellant tank, pipe lines, injector, and combustion chamber, was simulated on an electronic analog computer. It was shown that the dynamic behavior of each component has an effect upon the propellant pressure required for stability. The reason for unsuccessful scaling of rockets to either smaller or larger sizes becomes apparent, as it is shown that component dynamic characteristics do not vary proportionately with size. Proper attention to selection of components can eliminate resonances that lead to instability, and increased • 2-16 • THRUST PROPULSION SYSTEMS propellant flow velocities can substantially reflows between the walls, thereby cooling the induce the propellant pressure (and therefore the ner surface and making possible the use of thin rocket weight) required for stability. In addiwalled combustion chambers. The fuel then tion, the requirements that must be met by a enters the forward end of the combustion chamcontrol system in order to maintain rocket motor ber. The fact that the motor is cooled permits stability over a range of thrust levels, are shown. longer burning than if the motor were not cooled. Analog computer simulation of the rocket sysA further advantage of regenerative cooling is tem prior to assembly of the physical components that the fuel is preheated before injection into can greatly reduce development time and cost. the combustion chamber, with a resulting inTo overcome the problems of control, weight, crease in heat energy released on combustion. and heat of burning, liquid propellant rockets Ignition of fuel and oxidizer may be accomare used for long duration units. In liquid proplished initially by a spark plug or a pyrotechnic pellant rockets the combustion chamber may be device as was done in the V-2 rocket. Once made lighter and smaller than the solid propellant initiated, combustion is self-sustaining if the prorockets. Since this chamber need not contain the pellant is injected continuously rather than interfuels, the fuel and the oxidizer are fed from their mittently. Many fuel-oxidizer combinations are respective tanks to the combustion chamber by self-igniting on mixing and require no spark. either the pressure feed system or the pump feed Such self-igniting fuels are termed hypergolic. system. Typical liquid propellant rocket feed 2-9.1 PRESSURE FEED SYSTEM methods are shown schematically in Figure 2-11. (Most liquid propellant rocket motors have reFigure 2-12 shows how the pressure tank is generative cooling.) Regeneratively cooled connected by pip;ng to the fuel and oxidizer motors are built as a double shell, with separate tanks. The pressure tank contains either inert openings for injection of the fuel and the oxigas or ai r at high pressure. This gas is fed at a dizer. The fuel enters the rear of the motor and reduced pressure into the two tanks and forces DIRECT FEED FUEL OXIDIZER REGENERATIVE (COOLED) FUEL OXIDIZER FUEL • Fig. 2-J J Liquid propellant rocket motor types• 2-17 BALLISTICS (a) PRESSURE FEED SHORT OPERATING (b) PUMP FEED LONGER OPERATING Fig. 2-12 Liquid rocket feed systems. the fuel and oxidizer into the motor. Since liquid propellant rockets operate with a combustion chamber pressure from 250 to 500 psi, obviously the fuel and oxidizer tanks must be pressurized to some greater value to insure a flow from tanks to combustion chamber. The result is a heavy tank. In pressure feed rockets the ratio: Rm = rocket+ pay load+ propellant rocket + pay load =mass ratio is about 2:1. As the size of the rocket increases, the ratio becomes even less favorable until finally the empty weight of a pressure feed rocket is prohibitively large.. To circumvent this situa tion, a pump feed system, described later, is used. Under present conditions of development, pressure feed systems are only economical in rockets having a gross weight of about 5 tons or less. 2-10 SELECTION OF In the choice of the propellant for a particular application, account must be taken not only of the properties of the propellant components, but also of the purpose of the vehicle to be propelled and the requirements on its power plant. For ballistic missiles, bipropellants (liquid oxidizer and liquid fuel) appear to be acceptable. Of the many available liquid combinations, however, only a few turn out to be satisfactory, and no one • The general characteristics of pressure feed systems are: (a) Relatively simple design. (b) Heavily constructed tanks may be used as missile frame. (c) May be operated intermittently. (d) Better suited for relatively small rockets (less than 5 tons). (e) Cannot be stored fully fueled or pressurized for long periods of time. • 2-9.2 PUMP FEED SYSTEM The pump feed system is essentially the same as the pressure feed system except that the pressure tank is replaced by pumps to force the fuel and oxidizer into the combustion chamber (Figure 2-12). Pressure is felt only on the downstream side of the pumps; consequently, the fuel and oxidizer tanks can be of considerable lighter weight construction. LIQUID PROPELLANTS is ideal in all respects. Each propellant combination has its unique characteristics. These include performance characteristics, the physical properties of the component liquids and their end products, and such considerations as safety, ease of handling, storage, availability, and cost. Of primary importance are the performance characteristics; if they are inadequate, the propellant cannot be used • 2-18 THRUST PROPULSION SYSTEMS no matter how desirable its other characteristics may be. Furthermore, the characteristics that do not directly affect performance can often be compensated for or modified. For instance, if a liquid component has a high freezing temperature, thus complicating its use in low-temperature regions, it may be possible to add some substance that will lower the freezing point and yet not introduce unwanted side effects. Again, the cor rosive action of a highly active propellant component may be rendered negligible if tanks and pipelines made of special materials are used. It has been shown that the specific thrust may be increased by raising the temperature of the combustion products in the chamber, and by reducing the weighted average of their molecular weights. · A high gas temperature can be obtained by using a propellant mixture that yields a large quantity of heat per pound of mixture. The average molecular weight of the combustion products is determined both by the nature of the oxidizer and the fuel, and by the ratio in which they are mixed. The specific thrust will also be lowered if the combustion gases dissociate into simpler molecules and atoms, because the dissociation requires energy and thus reduces the amount available for conversion into the translational kinetic energy of the exhaust stream. Where tests indicate that effects of dissociation are appreciable, a change can be made either to a propellant having more stable reaction products or to a lower gas temperature. In addition to these basic requirements the densities of the propellants should be high, for the tank structure can then be made smaller and lighter and the liquids will also be easier to pump. Other desirable propellant properties in clude rapid and reliable ignition of the mixture, high rate of reaction, low vapor pressure, and low freezing point. Among the properties creating possible hazards are chemical instability, corrosivity, flammability, and toxicity. In view of these many restrictions, one can see why the search for suitable liquid combinations is a major problem of rocket research. Significant advances with high-energy propellants may be forthcoming if solutions can be found for the engineering problems of adapting such propellants to rocket applications and of producing them on a commercial basis, at acceptable prices. For ICBM propulsion, significant increases in performance and energy would result if reliable and practical rocket power plants could be developed for even the commonly known high-energy propellants, such as liquid fluorine and liqdd hydrogen. To reduce the rate of transfer of heat through the combustion chamber walls (an acute problem in rocket engine design), several different methods have been devised and are in use. One scheme, still under investigation, is to employ an oxidizer-fuel combination that will deposit on the inner chamber wall an inert coating capable of providing good thermal insulation and also of withstanding the scouring action of the hot gas flow. The graph in Figure 2-13 illustrates the temperature gradients to be expected in a regen eratively cooled thrust chamber provided with such an inert coating. 2-11 PROPELLANT UTILIZATION Propellant utilization is a problem that becomes important when a missile is being fired for maximum range. The problem is to insure that the maximum amount of propellant available to the rocket engines is consumed by them and to design the propellant feed system so that a minimum amount of propellant is trapped and hence unavailable for consumption. For the hipropellant rocket engines of current ballistic missiles, the problem is accentuated since the engines, because of various system and trajectory tolerances, may consume one propellant component at a relatively faster rate. Thus, when this component is completely consumed, a portion of the other one remains unburned. The effects of residual propellant can be drastic. For instance, a rough calculation shows that if one percent of the initial propellant weight remains unconsumed in a vehicle designed to have a thrust-cutoff speed of 25,000 ft/sec, the range will be reduced by about 600 nautical miles. Moreover, to maintain this cutoff speed of 25,000 ft/sec when one • '------------ 2-19 BALLISTICS combustion gas - [1., 0 distance from centerline of thrust chamber • Fig. 2-13 Temperature gradients. percent is unconsumed, the weight of propellant needed initially would be almost doubled. Figure 2-14 shows the main elements of a propellant utilization system. The most difficult problem is how to determine the amounts of oxidizer and fuel in the tanks at successive times during powered flight. When the vehicle is disturbed, as by a gust or by the control system, the resulting accelerations produce sloshing in the propellant liquids which may be appreciable 2-12 JET Because practical delivery means for a chemical or nuclear explosive are not restricted to ballistic projectiles and missiles, the aerodynamic missile with air-breathing jet engines (boosted with rocket motors) is the basis for several guided missile weapons systems. Propelled by a reaction coolant film .-----coolant bulk • inner liner ~ coolant film inert coating ~ outer case gas film ll • • even when the tanks are equipped with baffies or some other dam!?ing device. Thus, the determination of propellant levels by conventional means is difficult, if not impossible. Measurements depending upon dielectric properties of the tank contents appear to be impracticable because of the severity of the liquid motions. However, there are sensing methods that offer promise, and these are receiving extensive study and tests. ENGINES motor, the principles of thrust propulsion discussed in this chapter are directly applicable to the study of the characteristic trajectory of flight path of this family of missiles and, in particular, the analysis of systems utilizing the turbo jet, ram jet, or pulse jet engine discussed in detail in a later section of this text. 2-20 • THRUST PROPULSION SYSTEMS sensing device Ml ..,~l--sensing device regulator valve computer Fig. 2-J4 Propellant utilization system. 2-13 PULSE JETS The typical pulse jet (Figure 2-15) consists of to the name "intermittent jet" often applied to the pulse jet. It was this intermittent action that a tubular section with a set of spring loaded, one way valves in the front, and a means for injecting gave the German V-1 the name "buzz bomb" fuel, followed by a combustion chamber and a during the war, for the V-1 was propelled by this type of engine. tail pipe. The operation cycle is as. follows: Assume The operation described above applies to a that fuel has been sprayed into the combustion stationary pulse jet; however, the same cyclic chamber and is ignited by means of a spark plug. operation will take place when the engine is in motion. In this case, though, the thrust is in An explosion will result, and the gases formed create a pressure of 25 to 35 psi. The one way creased about 40% since the ramming action of valves prevent the gases from escaping forward; the air aids in increasing the supply of air and therefore they rush out the tail pipe at a high the compression. For the V-1 (in both cases) velocity. As they expand, they cause a partial intake, compression, ignition, and exhaust occur at about 40 cycles per second. Operating in the vacuum inside the combustion chamber. This action causes the valves to open and permits air static position, the German V-1 would develop about 500 pounds of thrust. When traveling at a • to enter from the front. As the air flows in, it is sprayed with fuel from jets in rear of the valve velocity of 340 mph, this same engine would bank. Because of the partial vacuum, part of the produce 780 pounds of thrust. hot exhaust gases are sucked back up the tail The most vulnerable part of the engine is the pipe and meet the air coming in through the bank of valves. Because of the short life of these valves. The returning exhaust gases compress valves, the Germans could obtain only about 30 minutes of operation. One of the improvements the new air slightly, and their heat plus residual that has been made in this country has increased burning fuel ignites the new charge of air and fuel. Thus, the action is intermittent, giving rise the life of the valves to about 7 hours. This 2-21 BALLISTICS • AI~ ENTERS WHEN YAI.ltU A~[ OP[N[D IY UPLDSIDN PASSING DOWN TO TAIL PIP[ TAIL PIPEH[~E IY RUUCTED HIGH TEM~ATURE YEUX:ITY f11PRESSURE WAVES F~OM TAIL PIPE GA!ESINC:UAS[D HERE FREQUENCY· 50 CYCLES /SECOND Fig. 2-15 Pulse jet ·in action (at sea /eve/, 400 mph). allows ample time for test runs of the motor; 50 cycles per second for an engine of the V-1therefore, a complete checkout of the system may • type, but may be as high as 280 cycles per second be accomplished prior to launching. for a miniature pulse jet.The pulse jet is limited in speed to below 450 The thrust is approximately 1Y:! pounds permiles per hour at the present. At that speed, the square inch of cross-sectional area, and is notthrust equals the drag. If it were possible to constant but decreases as the engine gains altireduce the drag and increase the speed, the tude. The thrust at 20,000 ft is % the thrust atengine could still not operate above the speed of sea level. sound, for at sonic speeds shock waves wouldinterfere with the proper action of the valves. Fuel consumption is quite high compared toThe frequency of pulses depends upon the internal combustion engines, but is much lessresonant frequency of the tail pipe, and is 40 to than that of a rocket. 2-14 RAM JET The ram jet was also developed in order to reliable. It is the most promising jet engineovercome the high propellant consumption of from the standpoint of simplicity and efficiency rockets. It is a fairly recent development, and there is yet much to be done to make it absolutely at supersonic speeds. 2-14.1 SUBSONIC RAM JETS engine through the diffuser, which is the divergAssume that the subsonic ram jet engine shown ing forward section. As air flows through thisin Figure 2-16 has been boosted up to some section it loses velocity since the cross-sectionalsubsonic speed: Air will then flow into the area increases. 2-22 • THRUST PROPULSION SYSTEMS • ------$9" F --- ATMOSPHERE EXHAUST 14.7 pli " 23 pi 14.7 pli 242fpr i~F Fig. 2-16 Subsonic ram ;et in action (at sea level, 700 mph). • • There is a certain energy in the air stream in the form of pressure energy and velocity energy. If the velocity decreases, the pressure must increase since no energy is lost. This is exactly what happens in the ram jet; · an increase in pressure occurs in the diffuser, making the pressure at the forward end of the combustion chamber greater than the pressure at the forward end of the diffuser. Fuel is continuously injected into the combustion chamber and burned. The combustion process is initiated by means of a spark plug and thereafter is self-sustaining. The gases of combustion tend to expand in all directions, but are restricted by the walls of the combustion chamber and the high pressure area at the rear of the diffuser; consequently, the gases are accelerated rearward out the exhaust nozzle. The reaction force tends to increase the pressure of the air in the diffuser. The total forward thrust of the unit, which is applied against the inside forward surface of the diffuser, is then the horizontal component of the pressure difference between the inside and the outside of the diffuser. This net pressure difference consists of two components: (a) Increase in inside pressure due to reduction of air velocity. (b) Increase in inside pressure due to combustion. 2-14.2 SUPERSONIC RAM JETS The supersonic ram jet (Figure 2-17) must be boosted to an operating velocity by some external means such as a booster rocket motor. At this speed, air enters the diffuser inlet. The diffuser is so designed that there is a decrease in air velocity as it approaches the back of the diffuser. This decrease in velocity is accompanied by an increase in pressure. Thus, a high pressure is created at the after end of the diffuser. Fuel, usually kerosene, is injected at this point by a pressure or pump feed system. This fuel, mixed with the incoming air, is ignited by a spark plug and thereafter burns continuously. The walls of the combustion chamber are subjected to combustion temperatures of approximately 3500°F; The expanding gases cannot move out the front because of the pressure barrier in the diffuser, so they expand down the tail pipe and exhaust at a greater velocity than that of the air entering the diffuser, resulting in an increase in momentum and creating a forward thrust. One critical factor in the ram jet is the design of the diffuser. Design of the diffuser for subsonic speeds is quite different from design at supersonic speeds; therefore, diffuser configuration varies for different speeds within these ranges. A ram jet needs to operate at the fixed speed for 2-23 BALLISTICS • UOOI,. SUBSONIC DIFFUSION PRCSIJRC 60"F lf.T,- OIF USER EXHAUST Fig. 2-17 Supersonic ram jet in adion (at sea level, 2700 mph). • • which it was designed. The most common type diffuser used for supersonic ram jets is the conical spike type shown in Figure 2-17. The air velocity is first reduced through an obliquely oriented shock wave to some lower supersonic value, then through a normally oriented shock wave to a subsonic value. Another major problem is the design of the fuel metering system. To maintain good combustion in a stream of air moving at several hundred -feet per second is a formidable engineering problem. Still another component of a ram jet engine presenting design problems is the flame holder, which is a gridwork placed in the 2-15 TURBO JET The turbo jet engine is by no means the simplest type of air breathing jet engine, but its history of development dates back many centuries. It became the first operational type air breathing jet engine and presently is in widespread use on all modern jet aircraft. It is also ram jet to provide shelter for the flame and to prevent the flame from being blown out. These problems can be sidestepped, however, by oper ating a ram jet.at a nearly constant altitude and speed. The problem of operation at variable speeds and altitudes is still a major one. Ram jets have operated up to 60,000 feet and may possibly reach a theoretical maximum of 90,000 feet. The speed is now limited to Mach 4 (four times the speed of sound) because at that speed the temperature caused by air friction and combustion begins to exceed the limit of presently known materials. found today as the propulsion system of several operational guided missiles. As with all air breathing jet engines, some type of compression is necessary in order to impart high velocity to the working fluid by expansion from a high pressure to a low pressure region. 2-24 THRUST PROPULSION SYSTEMS VELOCITY • 600 lll'll TfMP. • 60•f. PRESSURE -14.7 "/0 IN. 107S. Fig. 2-18 Turbo ;et in action (at sea level, 600 mph). pressure in order to provide high exit velocity, Basically, the turbo jet engine consists of five major sections: an inlet duct, a compressor, a since in order to obtain a high value of thrust, combustion chamber (or chambers), a gas turthe gases must be discharged at the highest bine, and a tailpipe ending in the jet orifice. possible velocity. The pressure-volume and There are two types of compressors in general temperature-entropy representations of the use, axial flow and centrifugal flow. The type of Brayton cycle (constant pressure heat addition)compressor used determines the general design are shown in Figure 2-19. and outline of the entire engine. The elements The whole cycle of operations iq. a turbo jetof this type engine are shown schematically in engine revolves around and is coi-Itrolled andFigure 2-18. limited by the turbine. The mass flow of airTo operate, the compressor must first be through the compressor and the compression brought up to speed in order to raise the pressure ratio both increase with increasing rpm. In in the combustion chamber to about four times that of atmospheric pressure. Fuel is then inorder to increase rpm, more energy must be availjected into the combustion chamber and ignited. able at the turbine inlet to turn the turbine faster. Since the products of combustion would be of The energy available to the turbine depends high enough temperature to cause failure of the mainly on the amount of heat released in the turbine bla des, an excess of air must be introcombustion chamber, and the amount of heat in duced to keep the temperature of the jet stream turn is limited by the ability of the turbine to at approximately 1500°F . The compressors are withstand it. coupled directly to the turbine. Hence, the hot, The advantages which accrue as a result of high-velocity gases passing through the turbine mechanical simplicity in turbo jet engines are cause it to rotate. This imparts rotation to the immediately apparent. The maintenance recompressor so that the operation may be quired, compared with the reciprocating engine, sustained. is reduced in proportion to the smaller number The turbine exhaust gases are discharged of moving parts. The symmetrical shape, light through the tailpipe to the atmosphere. The tailweight (pounds of engine per pound of" thrust), pipe provides for the build-up of a large static and small diameter, particularly of axial flow 2-25 BALLISTICS • 1 >1/. \ p / \ / \ p / 5 6' 0 // . \ p /' s v Fig. 2-19 Turbo jet engine cycle (Brayton cycle) on T-S and P-V planes. TABLE 2·1 REACTION MOTOR CHARACTERISTICS Characteristics Rocket Pulse Jet Ram Jet Turbo Jet Source of oxidizer carries own oxygen atmosphere atmosphere atmosphere Fuel (example) liquid (aniline) JP-3, 4 gasoline JP-3, 4 • (alcohol) JP-3, 4 solid (asphalt oil)(ballistite) (nitrocellulose) Booster required no yes yes no Velocity: present M = 20 M = 0.56 M = 3 M = 2+expected unlimited M = 0.80 M = 4.0 M = 3theoretical speed of light -unknown M = 4+ w/ afterburner Moving parts few reed valves few compressor and turbine Operational altitude unlimited 20,000 ft 80,000 ft 60,000 ft Burning time .05 sec to several min. limit ed by fuel limited by fuel limited by fuel Present ranges unlimited with 150 miles 5,000 miles 5,000 milesseveral stages Typical uses guided missile, target drone guided missile, aircraft,jato, rocket target drone guided missile 2-26 • • THRUST PROPULSION SYSTEMS / / / Thrust H. P. per sq. ft. _of frontal area 730 Speed (MPH) Fig. 2-20 Comparative thrust hp. compressor engines, permit installation in aerocomponents has required a vast amount of re search and experimental testing for the turbo jet dynamically clean, low drag airframes. However engine to reach its present stage of development. simple the basic design may be, each of the major 2-16 SUMMARY OF REACTION MOTORS Each jet engine therefore has its own uses. TableIt is difficult to compare the various reaction motors because no two operate at maximum 2-1 shows a comparison of the various engines. Graphs such as those shown in Figures 2-20 and efficiency under the same conditions. In addition 2-21 would be of value to the missile designer forto efficiency, other factors must be considered such as fuel consumption, thrust horsepower, determining the propulsion system to be em ployed in a particular missile. simplicity, speed, range, and operating altitude. 2-27 BALLISTICS 16 I - 14 -• 1\ ll \ ~~---+-- Specific fuel \ consumption ~f -1-·-· -·---·-~pounds per 10 ~r ·· f--·1 thrust horse power hour I 8 1\ i [\ \ 1\. k> 6 ' ~(~...'' -\[\\ K ~0I[, '~ ! I'(f"'P~ ;/(!>z ... : ' ......"' r-...... .......... ~atnj t 0 I0 150 450 750 1050 1350 1650 1950 ll50 l550 Speed{MPH) 4 ' "' Fig. 2-21 Comparative fuel consumption. ~ REFERENCES 1 Bonney, Zucrow, and Besserer, Aerodynamics 4 Liepmann and Puckett, Aerodynamics of aPropulsion, Structures and Design Practice, Compressible Fluid, John Wiley and Sons, D . Va n Nostrand Co., Inc., Princeton, N. J., Inc., Galcit Aeronautical Series, ChaptersPart II, Propulsion, Chapters 2, 4, 5, 6-8, 1-6. Merrill series. 5 Sutton, Rocket Propulsion Elements, John2 Durham, Aircraft Jet Powerplants, PrenticeWiley and Sons, Inc., N. Y., Chapter 3. Hall, Inc., N. Y., Chapters 2, 4, 5, 12, 13. 6 Vennard, Elementary Fluid Mechanics, JohnWiley and Sons, Inc., Chapter 6, Sections 3 Dr. Robert H . Goddard, Jet Propulsion, Staffs 32 thru 38. of the Guggenheim Aeronautical Laboratory and Jet Propulsion Labora tory for the Air 7 Rocket Fundamentals, Office of Scientific Technical Service Command, 1945. Rockets, Research and Deve lopment, The GeorgeAmerican Rocket Society, N. Y. Washington University, 1944, Chapters 1-3. 2-28 • CHAPTER 3 EXTERIOR BALLISTICS 3-1 INTRODUCTION the exact calculation of the trajectory, however Exterior ballistics is the science dealing with tedious, poses no serious problem particularly in the motion of a missile from the time it leaves this era of high speed digital computers which the influence of some projecting medium until it were originally designed to solve the trajectories reaches some fixed or predetermined point in space or on the ground. of projectiles and bombs. The prediction of aerodynamic forces is a matter of considerable In a larger sense, understanding this subject from a ballistician's point of view requires difficulty, and thus the primary problem in with emphasis on exterior ballistics now is the accurate and reliable a background in physics Newton's laws of motion; mechanics and the prediction of the aerodynamic forces on new analysis of dynamic forces; aerodynamics and missile designs. In the development of this basic information, the complex forces of air; mathematics, including the calculus; the principle of the gyroscope; exterior ballisticians rely heavily on highly sensitive model tests and rapid development of and some knowledge of meteorology. The pur pose of this chapter is to develop a knowledge engineering applications of compressible flow theory. Wind tunnel tests covering the subsonic of basic ballistic fundamentals leading to a region (speeds up to Mach 1), supersonic region practical conception of what takes place when a (Mach 1 to region of Mach 6), and hypersonic projectile is fired from a gun, a bomb dropped from a plane, or a rocket fired from a launcher. regions (up to Mach 10 is within practical interest) contribute importantly to solving such flow With an accurate portrayal of the inertia, gravita tional, and aerodynamic forces exerted on a proproblems (Figures 3-1 and 3-2). Free Bight ranges for model tests permit measurement of certain jectile or missile as it moves through the air, Fig. 3-1 General view of a flexible throat wind tunnel. 3-1 BALLISTICS • Fig. 3-2 Schlieren photo of model in wind tunnel. • Fig. 3-3 A free flight range. 3-2 • EXTERIOR BALLISTICS la) (b) Fig. 3-4 Spark shadowgraphs of 90-mm projectile fired in a free flight range, Velocity: (a) Mach 0.8; illustrating (a) normal and (b) oblique shock fronts. (b) Mach 2.2. optimum bomb and projectile configuration, andaerodynamic forces which can be measured only Funda with great difficulty, if at all, in wind tunnels. fin-stabilized gun-launched projectiles. These ranges permit direct tests of flight stability mental research on boundary layer and heat and provide the most accurate measurements of transfer phenomena in supersonic flight; effects projectile drag (Figures 3-3 and 3-4). Controlled of asymmetry and dynamic balance on projectile pressure and temperature ranges augment basic accuracy; spin-roll resonance data; factors inresearch methods for making interferometric fluencing drag; and aerodynamic consequences determinations of velocity distribution about of spin on spin stabilized projectiles are vital to bodies of revolution. These factors contribute the exterior ballistics p;oblems confronting conto a basic understanding of spin stabilization and temporary scientists. fin stabilization as applied to spinner rockets, 3-2 DESCRIPTION OF A TRAJECTORY of gravity of the projectile at the instant it isA trajectory may be definec;l as the curve in • released by the projecting mechanism; the tan space traced by the center of gravity of a projecgent to the trajectory at its origin is the line of tile in its flight through the air (Figure 3-5). The departure; the angle this line makes with the origin of a trajectory is the position of the center 3-3 BALLISTICS •I y I I I I QIIMrut ..... ol ~.. I Qudrul•~ 1 Aap olfaU Orilla'-I ...'~-=====--....I....-..L..-+--r-.._=::.a..=ot:...:~==:.t....-------l...--__;~-~pa~a----X •I Fig. 3-5 Elements of the artillery trojedory. horizontal is the quadrant angle of departure. The range trajectories additional factors must be con vertical plane including the line of departure is sidered, including the curvature of the earth, thethe plane of departure. In it lie the X (horizontal) and Y (vertical) axes of the coordinate system rotation of the earth, and the variation of the gravitational field with altitude. The discussion used in the computation of trajectories, whereas the Z axis lies in the horizontal plane and is in this text will be confined mainly to the gravity perpendicular to the plane of departure. To deand air effects. Long range trajectory factors scribe a trajectory completely it is sufficient to will be covered very briefly. specify the x, y, and z coordinates of the center The design of the projectile and the methods of gravity of the projectile at any time, t (i.e., at used to stabilize it have a considerable effect on every instant), after the release by the projecting the trajectory. For example, the rotation im mechanism. parted to a projectile by the rifling in the gun The factors which influence the shape of the causes it to move out of the plane of departuretrajectory of a specified projectile after it leaves due to a crosswind force resulting from gyrothe launching device are principally the earth's scopic precession of the projectile nose: The gravitational field and the characteristics of the density of a projectile has a direct influence onair through which the projectile passes. For long both its stability and range. 3-3 AERODYNAMIC FORCES ACTING ON THE PROJECTILE Consider a projectile moving in still air, as the axis of the projectile and the tangent to theshown in Figure 3-6, with its axis making an trajectory at the center of gravity of the projecangle of yaw 8, with the direction of motion. tile. The projectile will be acted on by gravityThe angle of yaw is defined as the angle between W, acting vertically downward, and an air force 3-4 • EXTERIOR BALLISTICS L Fig. 3-6 Forces on a projectile moving in gravity and R is dependent on the manner R, which will depend upon the velocity, the characteristics of the air and of the projectile, and upon the presentation of the projectile with respect to the direction of motion. If 8 were zero and the projectile symmetrical about its axis, R would point in a direction opposite to the direction of motion. In general, 8 is not zero, and thus R intersects the direction of motion. The calculations are simplified by considering R as equivalent to two components, one having a direction opposed to the motion, called the drag or head resistance, and designated by D. The other is perpendicular to the direction of motion, and is designated by L, and called "crosswind force." For a 75-mm projectile moving at a velocity of about 2200 ft/sec with 8· = 10°, D = 150 lb, L = 156 lb, and R = 216 lb. The forces D and L and the angle of yaw 8, are not restricted to the vertical plane as they appear in Figure 3-6. Instead they lie in the plane of yaw (the plane determined by the axis of the projectile and the tangent to the trajectory which intersect at the center of gravity of the projectile). The dihedral angle between the plane of yaw and the vertical plane through the tangent to the trajectory is known as the angle 3-3.1 DRAG The component of the total air resistance which acts in a direction opposed to the direction of motion of the projectile. Drag is made up of three parts: the resistance of the nose; skin friction caused by translation and rotation; and still air. Note: Relative position ol center ol ol stabilization and projectile configuration. of orientation, . The motion of projectile about its center of gravity in three dimensions is described in terms of the angle of yaw, 8 and angle of orientation, . The basic equations of motion utilizing the primary aerodynamic forces described thus far are: Fu = m dvu = -Du + Lu -mg dt F, = m dv, = -D.+ L. dt The aerodynamic forces acting on a projectile during flight influence the actual path of the trajectory as well as the orientation and velocity of the projectile upon reaching the target. The accuracy of the mathematical analysis depends largely upon the degree of stability with which the projectile flies through the air. The forces described are those of primary significance to a free flight trajectory. A more complete analysis of forces and moments acting on such a projectile follows: drag on the base (force D, Figure 3-6). 3-3.2 CROSSWIND FORCE The aerodynamic force which acts in a direction perpendicular to the direction of motion, lies within the plane of yaw, and is proportional to sin 8 (force L, Figure 3-6). 3-5 BALLISTICS 3-3.3 OVERTURNING MOMENT The angular acceleration produced by a couple, the moment of which is equal in magniwind stream tude and direction to the moment of R (located at the center of pressure, Figure 3-6) about the center of gravity of the projectile, and is proportional to sin 8. wind 3-3.4 MAGNUS FORCE A force which arises fron. the interaction of stream the boundary layer of a spinning shell and the wind stream. For a clockwise spinning tennis or baseball, interaction between the wind stream and the boundary layer permits the velocity at Fig. 3-7 Action of magnus force. the top layer of the surface of the ball to be less than the velocity at the bottom surface, and is thus associated with a higher pressure region. The ball accelerates downward. A spinning proaxis coinciding with the axis of yawing motionjectile, for example, with a counterclockwise and exerting a moment opposing the angularangle of yaw in the vertical plane, produces a velocity of the axis of the shell. component of magnus force acting to the left or perpendicular to 8 and proportional to spin rate, 3 -3.7 ROLLING MOMENT velocity, and sin 8 (Figure 3-7). Defined as that torque acting on a rotating 3-3.5 MAGNUS MOMENT projectile opposing spin. The moment of the magnus force about the Those forces normally neglected are yawingcenter of gravity. moment due to yawing, magnus forces due to 3-3.6 YAWING MOMENT DUE yawing, and magnus moment due to yawing, the TO YAWING effects being negligible for the majority of trajecA torque acting on a rotating projectile, its tories subjected to analysis. 3-4 EVALUATION OF PRINCIPLE AND MOMENTS For a given projectile shape, the dominant (Reynold's number), _!!__(Mach number), and ll. forces and moments acting on a projectile are a expressed as follows: It is normally determined as a function of u/ a, and evaluated in terms of 8 if 8 exceeds 2-3°. Drag, D = Knpd2u 2 (The necessity for investigating the latter isLift, L = K LPd2u2 sino evident when considering the exterior ballistics Overturningmoment, OM = Kmpd3u2 sino of a gun-launched projectile or rocket fired from high speed aircraft in a direction that differs where from the forward motiop of the aircraft.) Ex d = diameter, ft p = density of air, lb / ft3 amples of standard plots are shown below for o = angle of yaw, degrees or radians two projectile shapes (Figure 3-8). u = projectile velocity relative to air, ft/ sec Although the two curves in Figure 3-8 have substantially the same characteristics there are K11 , the drag coefficient (of dominant interest some marked differences. For example, projec in trajectory determinations) is a function of puf tile type A has both a sharp ogive and a boat-tail. p. 0 ,... =viscosity, lb/ft sec A comparison of the two projectiles illustrates 3-6 L EXTERIOR BAlLISTICS I I I I .25 • 20 Ko • 15 K·,, • 10 ' K I I I I """ !.---Pro ec til~'"'-' .. ..... ~ ~ ~ B I?ro ·o>ctil A .05 0 1.0 2.0 3.0 4,0 5,0u/a 6.0 7.0 8,0 9.0 Fig. 3-8 Drag coefficient versus Mach ratio for different proiectile shapes. the fact that sharp ogives are effective in decreasing drag above the speed of sound and boattailing is effective in lowering drag below the speed of sound. KL, the lift coefficient, likewise is a function of -ethe parameters, pud u-and B, as is K '"' th 1.1 'a' overturning moment coefficient. The magnitude of OM, however, also depends on the position of ' the center of gravity relative to the center of pressure of the projectile. While the mathematical statements of these functions are generally specific, the projectile form and drag coefficient (expressed in terms of Mach number) require clarification. 3-4.1 PROJECTILE FORM • The form of a moving projectile determines the way in which air will behave as it flows over the projectile's surface. A pointed projectile encounters less resistance as it penetrates the air 3-7 at high speeds than a blunt-nosed projectile, and a projectile with a tapered base allows air to flow by it more readily than one with a square base. The drag function used is one based on the shape of the projectile in question and includes a form fa ctor applicable to specific projectile shapes. 3-4.2 DRAG COEFFICIENT Th e plot of the drag coefficient against the Mach number for any type projectile will indicate an increase in the value of the . drag coefficient as the projectile approaches the speed of sound. The sudden increase in the drag is because local velocities on the surface of the projectile are greater than that of sound, and thus a shock wave is set up. At speeds greater than that of sound, the entire character of the air flow of air is changed. At lower velocities, a projectile is retarded primarily because of the BALLISTICS friction of the air stream slipping over the prosound will introduce resistance in the form of jectile surface. This produces a skin friction which shock waves. Therefore, a projectile traveling at is usually accompanied by only a slight disturbsupersonic speed encounters retardation, so far ance at the base of the projectile. As the velocity as velocity is concerned, which is the combined turbulence appears behind the projectile. This of Figure 3-4 which compares shadowgraphs of is known as wake. The projectile is then encoun a projectile flying at subsonic and supersonic tering drag from both skin friction and wake. A further increase in velocity beyond the speed of velocities. 3-5 BALLISTIC COEFFICIENT One of the most important factors which apcharges of field howitzers, the loss of velocity due pears in the formal differential equations of to air resistance is relatively small as compared a trajectory is called the ballistic coefficient, with that which is produced when the initial velocities are relatively high. Also the effept of the ballistic coefficient increases as the initial velocity increases. It is evident that projectiles to be fired with high initial velocities should be where: W is the weight of the projectile in pounds. made as heavy as other conditions will permit, d is the diameter of the projectile in inches. and should be given a shape which is aeroi is an empirical factor, called the form factor, dynamically as efficient as possible. Figure 3-10 which compares the "streamlining" (actually the indicates the effect of the ballistic coefficient on drag coefficient) of the projectile or bomb under projectiles fired with the same velocity and angle consideration, at a given velocity, with that of of elevation. The great reduction in range for an arbitrary standard at the same velocity. small values of C compared with that obtained The ballistic coefficient indicates the ability of in vacuum with c = 00 should be noted. a projectile to overcome air resistance; the larger the value of C the less the retardation. C is TABLE 3-1 VALUES OF C FOR commonly thought of as a constant. However, VARIOUS PROJECTILE TYPES since firing tables and bombing tables are made up from data taken from ballistic tables modified Form Projectile Type Ballistic to agree with data obtained from actual test and Caliber Coefficient Factor firing, it is expedient to use slightly different values of C for different sections of the trajectory. 76-mm H .E.P. 1.15 0.96 Representative values of C for various projectile 105-mm rifle, types are given in Table 3-1. H.E., A.T. 1.29 0 .76 The ballistic coefficient has a pronounced effect 90-mm AP 1.59 1.19 on the characteristics of trajectories. The curves 90-mm H.E., A.T. 1.78 1.65 in Figure 3-9 show that at relatively low initial 155-mm H .E. 2.056 1.02 velocities, such as those given by the lower zone 3-8 • • EXTERIOR BALLISTICS .,r ~ EflFCTtyGKMTYM'tilECTt.~ F1'--.t--. ltJ/11 --~- ~\ ~ -,... ~ ~I --1--r--r- ""-.... -txdata obtained from test firings. i = -E (z -w, ) + >.3y + >.2xSuch exact solutions require batteries of skilled where computing machine operators to solve the nu x = downrange distance merous trajectories that are represented in cur y = vertical distance rent firing tables and bombing tables used by combat units. The technique of solution, through z = horizontal distance to the right 3-10 • EXTERIOR BALLISTICS • wz, w, = components of wind velocity Xa, -X2, -X1 = components of angular velocity of the earth E = resistive functions of the form, p (y)uKv(M) c y = Yo ( 1 -~), where y0 is a con stant and r is the earth's radius C = ballistic coefficient, previously defined Firing tables are developed on a basis of matching a mathematical solution to the initial and final conditions of an actual firing test: (a) Conduct test firing of trajectories (up to 150 firings required). (b) Compute reduction trajectories to determine applicable values of ballistic coefficient, C. (c) Compute normal trajectories based on standard conditions (up to 3000 required) . (d) Compute variations, where p = poe-hv (air density) M = M 0e-Av (speed of sound) h = ~l A (h = 3.16 X IO-~) (e) Compute probable errors Bombing tables are developed on the basis of an accurately measured test trajectory where the drag coefficient can be experimentally determined point by point: (a) Track bomb fall and measure 6-12 points on each trajectory (10-15 drops required). (b) Compute reduction trajectories to determine the drag coefficient Kn, and ballistic coefficient C, applicable, where Kv(M) M vx2 + (ii + y)2 + i 2 d2p (y)u2 (up to 400 required). (c) Compute normal trajectories with selected K0 and C (up to 600 required) based on standard conditions. (d) Compute corrections and probable errors. 3 -8 BALLISTIC COEFFICIENTS FOR BOMBS The ballistic coefficient of a bomb relates the performance of one bomb to another, particularly in determining whether it will have a high terminal velocity. For instance, a 500-pound general purpose bomb would have a theoretical limiting velocity of approximately 1000 ftj sec. Actually, because of its shape it encounters extremely turbulent conditions when approaching that velocity or, in fact, when it passes a velocity of 800 ft/ sec. To attain this velocity, it must be dropped from an altitude of over 20,000 feet. As an experiment, an antiricochet spike attached to the nose of this bomb enabled it to attain much higher velocities. The spike was approximately 15 inches long and 1M inches in diameter. This addition to the bomb acted to deflect the shock waves that formed in front of the bomb after it entered the transonic speed zone. The addition of the spike changed the ballistic coefficient of the bomb as well as the form factor. The ballistic coefficient of a bomb is not selected in the same manner as is that of an artillery projectile. In determining a bomb's trajectory, the range, time of fall, and trail are considered separately for greater accuracy in the final computation. Usually there is a separate ballistic coefficient for range and time of flight; however, these coefficients may be incorporated into a single ballistic coefficient for certain purposes. 3-11 REDUCTIONS DIIAC loiUZZLE VELOCITY UTIMATt A IALLISTIC ltAHGE DATA' [DI!Ae COMPONENTS, fo, ~. CO(,.,ICI[NT, C . COM PUTt 011 MTW. SP£ED P110M CAGE . i£"00" C:i MW:r.;;~Ri*-OlaNIO ~11UN TRA.S:fOI/IIES~ tEXlHT OF TUS IJ4D TM: HAND KMCl NNL T• P1ICiot ~ OF DAY . --------------____ INPIJT DATA flOII ~ f"IHO x. TIUMCN CXlClN*ATD FROlool AVOIAG( BY GROU'S : , HAND COMPUTATIONS t,,X.,, z • • WEIGHT , METRO .HAND TIW&f. I n.an ~tw I'IXED ELEVATIOH. -· -·--. -· .. - GUI AlllooiUTl1 AND ELEVAroN ..ErR<>-wTiR'POCAriD-FoR HAND IWlM T~AMD MUZZLE loi.JZZLE COORDINATES EQUALLY ~INTERVALS j€C:C ' IN J uP TO SU,.,IIT. IIIAOCnl CUIOIII£TER . Xo, Yo, Zo, RANGE c);()Os£--MAG -c£iFFOEHT~ • RAMI: MD CEfLECTION FRCIJI AND DEFLECTION X. Ko , ON BASIS OF SHAPE HAND Cl ' ' OF SHELL '· '!"HEtllOLJTt. z • •nwE oF FLIGHT, .JUMP,-~-Lowf:L.iv"Ar.oN TIME OF fl.'lllfT ""*' $TOP I• · DATA ( TO CORRECT loi.JZZLE HAND tiATCH I FROM CHRONClCiltAPH [~~~_!~~~· ---------- TRENDS W x. AKO z. ~YES F':I ~ . AIRIItltST'S). ~ TO 'MIND IJ4D VARIHAICI ATlONS IN KIZZLE SPEED . WI LL COfiiSTAHT C DO~ HE IG>'T OF TlDO ,_.. GMJGf. METEOROI..OGICAL. DATlf F"'* ~NO ..-. TAICE c fOR WH01 x.1 c:J SONDt:, Dlta:TIDN FINDOt, CORRECT Wlll41N CJj[ )> MD MODOLIT'E . PRO&AIIU ERIIOR r- WGT. OF MISSLE FROM SCALE . TAKE 1'11UtA80liC FIT RlR + c ~ ~ -..., HAND () (/) .. ICJI"£S: DUe: I DATA GA~D l'tllt APflfOIMATE.l.T 10 RQ GAOII'S, $IAITAIIULATION S Olt I IIQ.I'S P£11 VfLOCITT 20«, I TO I ZDfES. F1 NO PRotiAILE TIIAJ[CTOIIo[S "I(LL, TABLE ELEIIIEHT"S 2 III[T[Qfla 0«.&1 lltoTA INQ..L.C)[ ltANGf: WM> W. , EJ1R01tS IN RANGf: (NIAC b-~" AND AND 011 atoSI WIC) Wa, ltlt t1PISifY , , All. TtloiP£RATUAE, RURRANGE:MEHTS fliOII RANG[ DATA · HTIAL fFFECTS :liiDIIAC t=-1 AND IUIIIDITY . S SCIII(TII«S A DltM f\MCTOI, G I V t, DCll IS 010SEN INSTUO OF CMOO!ING A DRAG CO£FFI~HT. - 4 flNfoL. RalUCTilN TR~CTORY IS COioiPUTt D USIIG 1 LA51' ~C fiOit IACM QROt.f'. LAST FEW ltlOUCTION TRA.I8:T'CIRIO Ym..D SUCM ft.CIAL. mu;TS AS lfl' ,~, ~•: , AMD PllRTS ~ I FINO FORIIIIA.A ~FIND FORVULA AlR T'H!IIIANO COitMCTIONS TO TH£ (:....: OF 1 CIU( TO ROTATOI 011 [Aimt AND aiDS!WIIC) F~ Of!IFT . TIM£ 011 fl.MiHT ~ S TIC '• COitllt!CTOI P"OitliLLA IS I'QH) BEFORE TIC LAST HORIIIAL. TRA.Itc:TOI'IES ARt COiolf'UTED ADOITQI.Al. ICJI"£ : TH! Mli!EI Wtnl SHADOW con"AIN SM..AII Of'PATOIS TO n.otf IN BOXES WITH -..aoow .. lOMB... TAa.t FLOW CMART Fig. 3-11 Flow chart for computation of firing tables. INITIAl. MEAIUIIE..,.,.. ltlDUCmOHI ltANM .,.TA COIIIPUTII ~IIEua. II'£ED Ml) DUO ICOOIIDU!'[ .,.,. ,.... ... Olt ·~-TilliE ""*OlllNDIIWtt'l INITIAL ll'!l'D, YI•Yt lttLIASE~ Xt, rt, Zo. IIIFACT ;....~COOfiDINATD, lit, J&, OH TIMI aF 'LI.n'). Zt, M'IICT SPIED AND AtOM Mllt:HEI.L I I.· It CMmlASIJ . . ~."',Xz,Jil, ASKANIA FlLMS . . Zt, TW C:W f\.IGKf ft . IIIIEnOROt.DGICL .,.TAI I'RON IIATCH4 l'at IO'TH ltAOIOSONCE:, DIII!CTilH ,.ICIEit IWI) LOW AND HNIH THEODOLIT! . m ALnT\IDr .,.TA f >< -1 m ;:110 0 Cf YES ;:110 ..... Of' I To lET II[W 1· 1HAND w 0:1 HOTD : >r- I METEOIIOl.OeiiCAL OATA 1NCUU ltAHGIE WWD Wa, SIMTAIIA.AnoN COMPUTE PltOBAILE c COMPUTE CIIOSS WCl W1 , A1t DENSITY , , Alit TEMPIEitATUitE, TAIILE ELDIIIENTS U) AND HIMIOITY. AfC) I IIEMOIIS fROM IEXTitA II INOitiiAL -1 n f THESE YAL\0 Ml COIIFUT'IED I"DDt IEVUIY !lCOND lt!AitRAHGIEMINTS . TltA.IECTOitiES . U)AfC) THE \AUlD C:W THIESl VMIAIUS liT IMMCT M£ ALSO CCIIIPUTIED. 5 AFl'P KD IS ACC[PTU) EXTRA IIEDUCTD T'ltA.£'nlltiES AM lUI TO OITAIN IIPnltf:lfTIAL URC\'1 C:W CttANK IN Paw 'AC!at. 4 Tl€ CNTUIOH Pat 1111m:H • THilT M AVPAQf; ltiESO.IlL fOit CHI ~( i e. SAMI lti:LIEASI CONDITIDNS) • LDI nwt THl MDeA8L1 lMOit Of' THI ltEIIDUAL.S. 5 THr AD.IISTIIlJfT'I AM: IIAOl l'at ICH PfU)S P'11D11 11GH AL1lTUDl .,.TA AMI l'at LOw RIDS P1tOM • LOW ALTl'Y\U ~. ~NOT!: THl 1GB.~CCifrMI ...M ~ TO -nee. It IIICD WITH IHAOOW If ..... TAILI n.o1 0W1T. Fig. 3-J2 Flow chart for computation of bombing tables. BALLISTICS The maximum velocity which any given freely Limit ing Velocity Ballistic falling body will attain is called the limiting (ft/ sec) Coefficient • 500 0.33 velocity, where retard ation due to the air resistance is just sufficient to balance the acceleration 1000 2.12 due to gravity. Limiting velocity should not be 1500 9.28 confused with striking velocity. Since the limit2000 15.88 ing velocity for bombs may exceed maximum speed of any plane, the striking velocity can The value of the ballistic coefficient for the never exceed the limiting velocity unless some standard 100-lb incendiary bomb is under 1, so means such as rocket propulsion is used to inthat the limiting velocity is only about 600-700 crease the velocity of the bomb. The following table shows the relation between limiting velocity ft/sec. For a heavy armor piercing bomb, a and the ballistic coefficient. higher ballistic coefficient, 5, is desired. 3-9 TYPICAL BOMBING PROBLEM When an aircraft, guided on an even forward bornb will meet resistance from the air and will receive resistance or assistance from the winds, flight roughly p arallel to the surface of the earth, dep ending on their direction. A typical bomb drops a bomb, the following occurs: The bomb will have the sam e initial forward speed as the ing problem as indicated by F igure 3-13 is aircraft but will have no vertical speed ; the established. • Bomb trajectory I I I I I ------------------\ \ \ \ \ \ \ A Point of rdrasr B Point of impact (targrt) \ C Position of planr (at timr of impact) \ ljl Drift angle \ AC Path of planr (track) AD Altitudr AG Coursr BE _Cross trail d i stancr BF Trail distance DE Actual rangr OF Whole rangr (track) Fig. 3-13 Typical bombing problem. 3-14 • EXTERIOR BALLISTICS 3-9.1 VERTICAL TRAVEL Drawn to the earth through gravitational attraction, the bomb falls with an increasing speed. This acceleration due to gravity is retarded by the increasing density of the air as the bomb nears the earth and as velocity increases. The velocity of the bomb increases as it falls earthward, but the acceleration decreases with each second of travel until there is no acceleration and the bomb falls with a constant velocity. This ultimate velocity is known as the terminal velocity of the bomb. 3-9.2 LINEAR TRAVEL The same resistance forces affect the forward , or linear, movement of the bomb. It meets the resistance caused by the density of the air and may be pushed or retarded by wind forces, depending on their direction of travel. If the bomb could be observed throughout its flight, it would be seen to retain a horizontal position parallel to the airplane for a portion of the flight and then to nose over gradually as it falls away. Due to gravitational acceleration, the angle between the longitudinal axis of the bomb and the axis of the aircraft becomes greater, depending on the time of flight. For present day bombing, it can be stated that this angle never becomes a right angle. As the bomb's downward velocity increases, the resistance forces apply greater pressure and force the axis of the bomb to point more and more toward the earth. As it approaches the earth, the bomb decelerates rapidly on its linear path. 3-9.3 TRAIL When a bomb strikes the ground or target, it will have lagged a considerable distance behind the aircraft. This distance, known as the trail, is an important factor in the construction of bombsights. The angle made by a line from the aircraft to the point of strike, and a vertical line from the aircraft to the ground is known as the trail angle. Trail is usually expressed in bombing tables as the ratio: .( .) trail distance (ft) tra11 m11s = altitude (thousands of ft) For example, given a trail distance of 1000 ft and an altitude of 25,000 ft, the trail is 40 mils. 3-9.4 CROSS TRAIL As an aircraft moves along its course, it may encounter lateral winds. In order to bring the aircraft over the target, it may be necessary for the aircraft to alter its course to compensate for the effect of the lateral wind. The stronger the lateral wind the greater the cross trail. 3-10 SPECIALIZED BOMBING TECHNIQUES While the normal bombing problem is associated with the high altitude release of the weapon from a moving aircraft against a stationary target, specialized techniques have been developed to meet particular requirements of both tactical and strategic missions. Included are the skip bombing, torpedo delivery, and circle bombing techniques of World War II. The toss bombing techniques of the Korean War met the requirement for delivery of high explosive and napalm bombs into cave and bunker openings. An additional requirement placed upon the ballistician has been that of providing safe and accurate low altitude bombing techniques for tactical aircraft armed with nuclear weapons. During an approach "on the deck," the pilot locates a previously selected landmark and releases control of the plane to an automatic ~ystem which places the plane in a sharp climb at a predetermined time ; releases the bomb; and causes the aircraft to roll over and reverse course. Anticipating a blackout of the pilot, the system remains in control of the aircraft until the pilot takes over (Figure 3-14). Although flight speed over 550 mph (733 ft/sec) is hardly due to low altitude turbulence, the bomb release pattern is analogous to the trajectory of a mortar projectile. Should weather conditions obscure the initial landmark, the pilot may cross the target and immediately go into a sharp climb directly over 3-15 BAlLISTICS ..... ' ' \ 1 1 Roll I I 1r \ / I ~' Release TI /~ Point -----"*~ Pull Up Fig. 3-14 Low altitude bomb delivery. the target and use an "over the shoulder" release tion, or because of the loss of flight speed during near a point on the climb slightly beyond the the climb, dive and change his course to regain vertical. The automatic system is adaptable to flight speed, allowing the plane to leave the target area before the bomb completes its tra this requirement. At the top of the climb the pilot may roll over and reverse his original direc-jectory and detonates. 3-11 STABILIZATION OF PROJ ECTILES It is necessary that a projectile travel point are employed to stabilize projectiles and obtain first at all times; otherwise, streamlined shapes the desired type of flight; fin stabilization and cannot be utilized in order to reduce air resistspin stabilization. Most projectiles are stabilized ance. It the projectile tumbles, loss of range and by a spin imparted by the rifling in the bore of the weapon. The twist of the rifling determines unpredictable flight will result. Moreover, if the the rate of spin of the projectile and is most projectile remains pointed in the direction of flight, the design of fuzes and problems of fuze important. Projectiles launched by other means functioning are greatly simplified. Two methods may utilize fins to control flight. 3-11.1 FIN STABILIZATION force acts in a direction perpendicular to the d irection of motion. It exists because of a Since a projectile leaves the bore of a weapon d ifference in air pressure on the sides of the finsin a nose first position, the fins insure that the and exerts a force against the side on which the base will continue to follow the nose and that p ressure is greater. In such a projectile, the fins the projectile will not veer from its course to any serve to locate the center of pressure to the rear great extent. This is accomplished through an of the center of mass and thereby establish a aerodynamic force known as the "crosswind restoring moment that causes the projectile to force," which acts on the large surface area of align itself with the direction of motion of its the fins or vanes (Figure 3-15). The crosswind center of gravity. 3-16 • EXTERIOR BALLISTICS Resultant Air Center of Gravity Center of Pressure Fig. 3-15 Forces on projectile (CP trails CG). 3-11.2 ROLL STABILIZATION While it is true that well-designed and wellmade finned projectiles will trail properly, asymmetrical fins will exert an additional rudder effect. Thus, a yaw will arise, superimposed on any launching effect, and with it a crosswind force tending to displace the trajectory from that predicted for an accurately made projectile. This phenomenon is of considerable importance in evaluating the hit probability of fin stabilized projectiles and indicates the reason for extremely close tolerances and allowances currently indicated in the manufacture of fins and stabilizers for projectiles, rockets, and missiles. A practical solution to this problem which appears frequently due to increased numbers of projectiles and missiles employing fin stabilization, is to incorporate into the missile a slow spin (5-15 radians per second) which assists in distributing errors in aerodynamic surfaces over 360° of rotation (angle of orientation, cf>) , thus minimizing errors due to malalignment in production, handling, or launch. The spin rate is cited here to emphasize that roll stabilization does not reach the gyroscopic effects of spin stabilization, nor does it cause the center of pressure to shift forward of the center of gravity. Further, roll stabilization vastly complicates the path and attitude control problems for guidance of missiles (defined in Chapter 5, Part 2). 3-11,3 SPIN STABILIZATION In a fin stabilized projectile, . the center of pressure is located behind the center of gravity. The problem of stabilizing such a projectile is a matter of making certain that the center of pressure follows the center of gravity. In a spin stabilized projectile just the opposite is true. Because of the lack of fins on the projectile, the center of pressure is forward of the center of gravity. The problem of stability in this case is actually one of making center of pressure stay very close to the trajectory which is traced by the center of gravity of the projectile. Any rotating body exhibits certain patterns of behavior by virtue of gyroscopic effects. Possibly the most common exhibition of this effect is a child's toy, a top. When a top is spinning, instead of falling over in response to gravity, it attempts to fall out of the plane containing its own and the vertical axes (Figure 3-16). This attempt to fall rotates 3-17 BALLISTICS Angular Momentum Vectorl / Iw - wind -stream - Angular Precession Vector Note: Vector notation corresponds to use of right hand rul e. Fig. 3-16 Comparison of spinning top and spinning projectile. this plane about the vertical. Any point on the position, is above the trajectory. It has become axis then describes a circle about the vertical, so stable and is precessing so slowly that if cannot dip far enough to remain on the rapidly called precession. The angle that the top may dropping trajectory. As an example, the stabilitymaintain is dependent upon the speed of rotaof a small arms bullet causes it to remain pointedtion, and the precession rate is inversely proporin approximately the same direction throughouttional to spin rate. its trajectory. Thus, it strikes the ground in a A spun projectile is stable not only because it more nearly base first position. If a nose-fuzed is spinning, but also because it is spinning at a projectile were overspun, it would not strike the rate which results in the maintaining of a small target point first and would probably result in angle of yaw, ll. The rate of spin is determined a dud. by the linear velocity of the projectile while in (b) Underspun projectiles. As with the spinthe bore, and the inclination or twist of the rifling. ning top, a projectile will precess slowly when Thus, the rate of spin is a condition which is spinning rapidly and will precess more rapidly determined early in the design of a projectileas its rate of spin is decreased. Finally, if the tube combination. spin is insufficient, the gyroscopic effect will not (a) Overspun projectiles. A spun projectile be effective and the projectile will be unstable. points constantly in the direction of flight as a Before the underspun projectile reaches the deresult of the gyroscopic effect; the intensity of scending branch, it precesses rapidly and with the gyroscopic effect being dependent upon the large amplitude. Its nose rises far above the the rate of spin; i.e., the faster the rotation, the trajectory, forming a large angle of yaw. This more stable the projectile. This resulting stability, excessive yaw creates great air resistance, and in however, is desirable only when it is below a addition to causing a decrease in range, the air certain maximum limit for a projectile in flight. resistance tends to increase the yaw which If a projectile is too stable, it will fail to nose eventually develops into a tumble. over on the descending brar.ch of the trajectory. (c) Stability factor. The condition for staThis is because the trajectory drops at a faster bility of a rotating projectile (Figure 3-17) can rate than the precessing rate of the projectile A2N2 be expressed by the factor 4BMpermits. The result is that the nose, at its lower 3-18 • • Fig. 3-17 Forces on a • where A is the axial moment of inertia of the projectile, lb sec-2 ft B is the moment of inertia about a transverse axis through the center of gravity, lb sec2 ft N is the rate of spin of the projectile, radians/ sec M is the overturning moment factor caused by air force R, and is defined as GP (D + L cotll) (ft-lb). Note that the overturning moment is GP (L cosll + D sinll) and is equal to GP (L cotll + D) sinll. The stability factor may be used to predict the degree of stability which a projectile will exhibit in flight. Projectiles having a stability factor less • EXTERIOR BALLISTICS L Resultant air Direction of motion with respect to air ---Center of Pressure Center of Gravity projectile (CP leads CG). than one will be very unstable, will probably tumble, will lose range, and will produce deviations in accuracy. Projectiles having a stability factor greater than one but less than 2.5 will not tumble, will normally find the nose leading the center of gravity of the projectile throughout the trajectory, and will exhibit a desirable impact attitude for point detonating ammunition . Stability factors greater than 2.5 indicate an overstable round, one which will not track properly since the attitude of the projectile does not deviate throughout the flight (i.e., projectile lands on its base), and is found in small arms and high velocity anti-tank ammunition. In such instances, the high spin rate results in such slow precession that the trajectory is completed before the projectile can effectively nose down on its trajectory. 3-12 STABILITY AND DRIFT FOR SPIN STABILIZED PROJECTILES Deflection is motion in a direction perpendicular to the plane of fire (Figure 3-5 ) caused by two major factors: wind effects, which apply to all projectiles and missiles; and, in the case of spin stabilized projectiles, a characteristic deflection called drift. The direction is the same as that imparted by the rifling of the gun tube, right handed for U.S . weapons. The net effect is a gyroscopic precession, inherent to characteristically high spin rates, that not only reflects in the stability factor discussed previously, but the detailed treatment of the mechanism by which a projectile may stabilize itself during the initial phases of flight (considering the disturbing influences of the gun on the projectile presented in Chapter 1, Part 2). A projectile is launched with an initial angle of yaw which is attributed to the gun itself. As the projectile moves along its trajectory, the curvature of the trajectory becomes greater until shortly after the maximum ordinate is reached. After this, the curvature diminishes again. The effect of the initial curvature of the trajectory is that the air pressure is greatest under the nose of 3-19 BALLISTICS the projectile since the projectile is pointing gslightly above the trajectory. The result in terms 8 • of the gyroscopic effect will be to precess to the right. This shift of the axis to the right causes an increase in air pressure on the left side of the projectile nose which, in turn, causes a precession downward. This train of events continues, causing the axis of the projectile to oscillate about a tangent to the trajectory; however, the predomi0 nant pointing up of the projectile nose causes an Ti~ne, Sec ovemll right precession. As illustrated by Figure 3-18, in order to meet the stability criteria the 0 initial yaw of the shell must be damped out. For Downrange Distance most trajectories with quadrant angles of deFig. 3-J8 Desirable yaw response-time plot. parture less than 40°, the projectile continues to point to the right except near the gun. (For angles of departure exceeding 65°, drift to the right predominates until the maximum ordinate is reached, following which the drift may be left due to magnus forces predominating; a characteristic of summital yaw.) The summit, likewise, is a critical portion of the trajectory for fin stabilized mortar rounds which are fired at high where angles of elevation. Ki = coefficient of magnus moment and all The steady-state solution to the problem of other symbols are previously defined. Thus, the general motion consists of epicyclic orientation of a right hand spinning projectile about a tangent to its trajectory, is that it flies motion with its center at ( ~' 'I) instead of tanwith a center of motion about its axis to the right gent to the trajectory, and results in a crossward • force in the plane of yaw and a magnus force of the trajectory (angle 0 and up (angle 'I), defined as: perpendicular to it. REFERENCES 1 Hausman and Slack, Physics, Van Nostrand University of Denver Press, Chapters 11 and Co., Inc., N.Y., Paragraphs 62, 63. IV. 2 Hayes, Elements of Ordnance, John Wiley and 4 Rocket Fundamentals, Office of Scientific ReSons, Inc., N.Y., Chapter X. search and Development, The George Wash3 Kelley, Reno, and McShane, Exterior Ballistics, ington University, 1944, Chapters 4 and 5 . 3-20 • • The existence of guided missiles which fly ballistic and aerodynamic trajectories dictates specialized treatment of these flight paths. Moreover, interest in long range hypervelocity vehicles has increased with the successful launching of earth satellite vehicles. At this writing the only technically feasible means of returning a 4-1.1 BALLISTIC MISSILES A ballistic missile is herein considered as a missile which follows a ballistic trajectory after thrust cut-off. Prior to thrust cut-off, the missile may be directed to a predetermined point in space where its ballistic trajectory begins. It may also be capable of slight path corrections during its terminal fall through the atmosphere. Like the artillery projectile, it has essentially zero lift at the completion of its propulsion phase and from that point is subjected only to the influences of its momentum, gravity, and atmospheric conditions. For short ranges, the ordinate may reach 50 miles; for long ranges, the ordinate may extend to 900 miles above the earth's surface. Ballistic missiles of long range (say 5000 miles ) are called "Intercontinental" (ICBM). Intermediate range missiles (say 1500 miles) are called IRBM's. Speeds attained by ballistic missiles (and associated reentry problems) are on the order of Mach 20. 4-1.2 AERODYNAMIC MISSILES Consideration of trajectories for aerodynamic missiles must reflect the use of wings or airfoils which produce a sizable vertical lift vector. This lift vector is the major contributor in supporting the missile in flight. Aerodynamic type missiles normally fly a flat trajectory which is sometimes referred to as a supported trajectory. Generally, this type of missile uses an air breathing jet engine. Missiles of this category are often referred to as pilotless aircraft and may resemble conventional aircraft in configuration. The early CHAPTER 4 BALLISTIC AND AERODYNAMIC TRAJECTORIES 4-1 INTRODUCTION man or recovering instruments or films from a satellite orbit is by means of a vehicle decelerated and supported aerodynamically. This chapter deals briefly with ballistic and aerodynamic (cruise) missiles and with the hypervelocity vehicle which is part airplane and part spaceship. aerodynamic type missiles were restricted to subsonic speeds, but at present, speeds of approximately three times the speed of sound can be attained. The speed and altitude characteristics of aerodynamic paths in general, are shown in Figure 4-1. 4-1.3 HYPERVELOCITY VEHICLES Hypervelocity vehicles capable of tremendous speeds, have two very attractive features: short time of flight and very long range. A satellite vehicle, for example, can obtain arbitrarily long range over the surface of the earth with a finite speed (about 18,000 mph). The powered flight of a hypervelocity vehicle will probably employ rocket motors. Unpowered flight is characterized by a ballistic, orbital, skip, or glide trajectory. The principal problem connected with hypervelocity vehicles is the dissipation of heat aerodynamically produced within the atmosphere. To dissipate this heat, specialized techniques are needed, e.g., employment of a coolant fluid . The ballistic trajectory is found to be the least efficient of the several types mentioned, in that it generally requires the highest velocity at the end of powered flight in order to attain a given range. This disadvantage can be offset by reduc ing connective heat transfer to the reentry body through increasing pressure drag in relation to friction drag (i.e., using a blunt body ). Thus, the kinetic energy required by the vehicle at the end of powered flight may be reduced by mini mizing the mass of coolant material which must be carried along. 4-1 BALLISTICS Regime of High Altitude Sounding Rockets • ~Non-aerodynamic and Escape Velocity Not Orbital 400 1"'1 Ballistic Missile 0 Regime -300 >< .... lz.. " I 200 "1j "=' I .... --< 100 Too hot Tskin> zooo°F 0 5 10 15 20 25 35 40 Velocity--1, 000 Feet/sec. Fig. 4-1 Regimes of atmospheric and extra-atmospheric flight. The glide vehicle, developing lift-drag ratios Hight. in the neighborhood of 4, is far superior to the Delivery systems currently exist (and/ or areballistic vehicle in its ability to convert velocity • under development) which utilize these trajecto range. It has the disadvantage of having more tories in accomplishing the system mission of de heat connected to it; however, much of this heat livering large quantities of high explosive andcan be radiated back to the atmosphere and the nuclear warheads. The accuracy and vulnermass of coolant· material kept relatively low. ability of each type of system is a function of allThe skip vehicle develops lift-draft ratios in of the variables affecting each trajectory (Figurethe neighborhood of 4 and is comparable to the 4-2). glide vehicle in its abiltiy to convert velocity The decision as to whether a ballistic or aerointo range. Large aerodynamic loads and severe dynamic (or possible combination) trajectory aerodynamic heating are encountered by the skip will be used must precede the preliminary de vehicle during the skipping process; it is theresign work on the airframe and will greatly infore concluded that this path is less attractive fluence the choice of the other elements of thethan glide or ballistic paths for hypervelocity system. 4·2 BALLISTIC MISSILES During launch and until thrust cut-off, a balproblems confronted in the design of such a mislistic missile is supported by the vertical comsile are tremendous. The forces opposing motionponent of thrust from the propulsion system. are due primarily to gravity and drag. In suchFollowing thrust cut-off, it follows a free Hight trajectories the variation of the earth's gravitatrajectory. Although the concept is simple, the tional field at different locations on the earth's 4-2 • • TRAJECTORIES -Ballistic -Outer limit of atmosphere Surface of Earth Fig . 4-2 Tra;ectories for hypervelocity vehicles (vertical scale exaggerated). tern; and power plant requirements. surface and at different heights above the earth's surface must be considered (Figures 4-3 and It must be noted however, that a missile need not be purely aerodynamic or purely ballistic. 4-4). In general, the advantages of a ballistic missile Some missiles have a design which incorporates are the difficulty of interception due to tremenfeatures of both types to varying degrees. The drag (due to skin friction) which a long dous speeds, and the minimizing of time for range ballistic missile encounters as it re-enters cumulative error in the guidance system due to short time of flight. Disadvantages inherent in the earth's atmosphere may be excessive at the ballistic missiles include tremendous stresses set speeds involved. It is therefore necessary to inup in the airframe which require h igh structural corporate into the design a nose cone section which is insulated, dissipates heat, and/ or is strength; heating problems during reentry phase; minimum response time for the guidance sys-heat resistant. 4·3 SYSTEMS AND SUBSYSTEMS OF A LONG-RANGE BALLISTIC MISSILE A ballistic missile may be considered as an as~ thermonuclear ) that is to be delivered to, and semblage of a number of interconnected and detonated at a predetermined enemy target. The warhead, a subsyst em of the missile system, to interacting systems and subsystems that perform gether with its auxiliary equipment (subsystems) distinct functions in the accomplishment of the mission of the missile. In a military missile the such as a fuzing system, is incorporated in the payload is a warhead (high explosive, atomic, or nose cone of the missile. 4-3 BALLISTICS • • Fig. 4-3 Redstone Ballistic Missile. Delivery of the warhead to a predetermined cut-off. A control system is also necessary to target requires inclusion in the missile of a guidmaintain attitude stability of the missile during ance system. This system regulates th~ position powered flight; to prevent undesirable responses and velocity of the center of mass of the vehicle when overriding guidance signals are introduced; during powered flight, with the purpose of esand to correct deflections caused by winds, gusts, tablishing a satisfactory trajectory prior to thrust and other disturbances. 4-4 TRAJECTORIES • I 70 c 60 J ' D 50 J 40 I 30 --------------------------.~-----· Atmosphere above here too thi n either to sensibly retard missile or t o e.ct on stabilizing fins. B zo -"' lllll·e o?L EJ}6 of BurniAil I _L _L _)j " 50 ~ 45 s:: ·~ ~~ I 1 ..1 ... 400 /A 1 ~ J I I I I I " .9 350 ( v "' -;;10 u ~ 3000 I I "' " zsoo "' , ... ::s ~ I ""'-.. L 'tl ... " ~ .~ zoo 150 0 .1! I ""' ~ ........... Summit L "\. ~ ~ 100 I o' ""' \ \ _'L--_.,.., _lX_ _i 1.1 < o~\ I 5 Impact '\.Y \ \ \ ~ \ '-\ 0 Firing Point 6E 0 1 z 5 3 4 Time scale in minutes 0 5 10 15 zo 25 30 35 Range scale in miles • Fig. 4-4 Ballistic missile trajectory (German V-2) . 4-5 BALLISTICS free flight Fig. 4-5 Trajectory of an ICBM. 4-4 POWERED FLIGHT OF THE MISSILE Power produced by rocket engines is applied to an ICBM or an IRBM only during the initial portion of its flight, from the launch point to the thrust cut-off (point B of Figure 4-5). All major guidance and control of the missile must be accomplished during the powered flight, for the missile motion can be influenced only slightly when power is no longer available. The ICBM and the IRBM are launched vertically, for this simplifies the launcher required for these large vehicles and also shortens the time that they are within the sensible atmosphere. After this initial vertical climb the vehicle undergoes a programmed turn toward the target. During this turn, the guidance system begins to function and continues to do so until the desired altitude h, speed V, and angle y are attained (at B, Figure 4-5), whereupon it gives the signal for cut-off of the propulsive power. Perception and correction of vehicle attitude, exercised by the control system, are continuous during the powered flight. Both the attitude of the vehicle and the motion of its center of gravity relative to the required trajectory are adjusted by altering the direction of the thrust of the rocket engines, for instance, by putting jet vanes in the exhaust stream or by gimbaling the rocket thrust chambers. There are many sets of values of the speed V, angle y and spatial position of B that will put the nose cone on a trajectory terminating at the desired target; but some sets are more favorable • than others in respect to amount of propellant consumed by the engines or required precision of aim. It is the function of powered flight to impart to the nose cone, as accurately as possible, a favorable set of these parameters. The energy expended in propelling the vehicle during the powered flight increases with the weight of the vehicle. Because both the kinetic and the potential energies are approximately proportional to the weight of the vehicle at thrust • cut-off, it is desirable that this weight be as little as possible in excess of the weight of the nose cone. This objective is materially aided by dividing the vehicle into two or more parts, or stages, with each stage containing a rocket propulsion system. Launching is accomplished by starting the engines of the first stage and, in some designs, also of the other stages. At some time during the powered flight the first-stage engines are shut down, and this stage is jettisoned from the remainder of the vehicle. The engines of the next stage are then started, if they are not already operating, and they propel the vehicle on toward B. As the missile nears B, the engines on the last stage are shut down, and the final adjustment of the velocity needed to keep the nose cone on a trajectory that will reach the target is accomplished with rocket engines of comparatively small thrust, called vernier engines. Thus, the term thrust cut-off point (B) refers, accurately speaking, to the point where the vernier engines are shut down rather than to the shutdown point of the engines of the final stage. • 4-6 TRAJECTORIES Steep Minimum Energy Flat Fig. 4-6 Medium height trajectory. 4-5 EXTERIOR BALLISTICS OF A MISSILE The trajectory beyond the thrust cut-off point to reach the target, there are two values of the B may be divided into two segments: the free angle y that yield trajectories connecting B and flight portion, from B to the point C of reentry T. One of these trajectories is steep; the other into the atmosphere; the reentry portion from C is flat. As one decreases the thrust cut-off speed to the impact point T (Figure 4-5). For a longV, these two possible trajectories approach each range missile, the free flight portion BC is above other, the steeper trajectory becoming flatter, and the sensible atmosphere; hence, the missile durthe flatter trajectory more arched. In the limit, ing this phase is a freely falling body, the only when V attains the minimum value for which the force acting on it being gravitational attraction. missile will reach the target, the two trajectories During the reentry portion CT, aerodynamic merge into a single one of medium height (Figure 4-6). Because this medium trajectory forces also come into play, and these slow the missile and cause it to become heated. requires the smallest speed V, and therefore The length and shape of the free Hight trajecminimum kinetic energy at thrust cut-off, it is optimum with·respect to propellant requirements. tory are determined by the speed V of the missile at thrust cut-off; the angle y between the It is also more favorable in other respects. For local vertical at B and the direction of V; the the steeper trajectory the reentry speed is higher, altitude h of B; and the values of acceleration thus presenting a more formidable heating probdue to gravity g along the trajectory. lem. For the flatter trajectory the reentry path Considering a given point B and a given target through the atmosphere is longer. Both very T, one finds that for every thrust cut-off speed V steep and very flat trajectories require a more between the lowest and the highest values needed precise guidance system. 4-6 EFFECT OF EARTH'S SPIN AND CURVATURE ON TRAJECTORY LENGTH A simple picture of a free flight trajectory may 2V2 sin'Y . be obtained by considering first the case where Range = x + 6x = (cos'Y +sm'Y tan8) g (4-1) the range and time of Hight are so small that the missile can be assumed to be traveling over a flat where Ax is the additional range gained because and motionless earth, above which the accelerathrust cut-off occurs at B instead of on the ground tion due to gravity, g, is at every point the same at 0, and where 8 is the angle between the horiin magnitude and always directed normal to the zontal and the straight line drawn from B to the flat surface (Figure 4-7). For this flat earth point of impact. situation, the horizontal range from thrust cut-off As the range is increased, the effects of the to impact is given by the expression: earth's curvature and rotation become more and 4-7 BALLISTICS y y • h 0'-------~~.::.::...~-X ~----X ----!!.._Ax_ Fig. 4-7 Short range trajectory. more important. A rough picture of how these effects alter the length of the trajectory may be gained by starting with the short-range flat-earth trajectory (Figure 4-7) and adding successive corrections to it. Only the simplest situation will Fig . 4-8 Fixed coordinate trajectory. be considered: namely, that of a missile movingin the plane of thz equator. Moreover, since theinterest here is in a qualitative picture, the matheV sin y might be as much as 20,000 ft j sec. Notematical expressions for most of the corrections that for westbound missiles, this effect of thewill not be included. However, it is interesting earth's rotation would reduce the length of theto note that for as short a range as that of a shottrajectory. For motion along any parallel of latiput by an athlete at the equator, the range for tude y other than the equator, the correctioneastward projection turns out to be about an would of course have the smaller value wR cos >..inch greater than for westward projection, all eastward.else being equal. For a long-range missile the While the missile is traveling from B to F, .thedifference is proportionally still greater. point on the earth's surface directly beneath BIn Figure 4-8, one should imagine himself as has advanced from 0 to 0'. This extends thebeing out in space, off the earth, at some point trajectory to the point G because the impact area • south of the earth's equator and looking in a has been displaced downward, from OF to O'G,northward direction, parallel to the earth's axis. during the missile flight. Such an extensionIf one could stop the earth from rotating, a miswould also occur for a westbound missile.sile leaving the thrust cut-off point B would folAt 0' the apparent horizon is the line O'Hlow the same path as in Figure 4-8, except that which cuts the trajectory at H , and thus the traOX is now to be regarded as the tangent to the jectory is extended to H . Notice that this particuequator at 0 . This path is changed because the lar extension· results from a downward rotationearth actually is rotating and its surface is not or tilting of the apparent impact area with reflat. In Figure 4-8 the coordinate system XOY spect to OX during flight. For a westbound misis to be thought of as fixed in space, and not as sile the rotation of the impact area, as observedparticipating in the earth's motions. This means from 0', would be upward, resulting in a reducthat the origin 0 does not move and that the tion of trajectory length.missile leaves B at the moment when B is verThe trajectory is still farther extended, fromtically above 0 . H to I, because of the curvature of the earth,The trajectory is extended from D to F bewhich gives the missile additional time to acquirecause the horizontal component of the missile's range. This extension is positive no matter invelocity at B is increased from the locally imwhat direction the missile is traveling, and wouldparted value V sin y to V sin y + wR, where w is occur even if the earth were not rotating. Thethe earth's angular speed of rotation and R is the longer the range, the greater will be this extenearth's radius. The circumferential speed R, sion, because the separation of the spherical surwhich the missile has before launch and retains face from the plane OX occurs at an increasingduring flight, is about 1600 ftj sec eastward; this rate as the distance from 0 increases.is a sizable correction even for missiles for which The missile would reach point I only if the 4-8 • TRAJECTORIES not rotating. The other factor is the departuregravitational force on it were at every point of the missile from 0 because of its velocity wR parallel to the Y -axis. Actually this force is di rected toward the center of the earth at every resulting from the earth's rotation. This part instant of the flight. Consequently a backward of the net backward component is always west component of gravitational force sets in as soon ward, thus reducing eastward ranges and extend as the missile leaves the thrust cut-off point B, ing westward ranges. and its magnitude increases steadily with the Although our interest has been mainly to show time since the missile left B. The net effect is to in a qualitative way how the rotation and curva shorten the trajectory so that impact occurs at ture of the earth affect the range, it should be some point J rather than at I . Actually the backsaid that the method used here can be general ward component of the gravitational force is asized to cover the case of a missile projected at sociated with two different factors. One is the any latitude and in a trajectory the plane of displacement of the missile from the fixed point which is directed in any desired azimuth. For 0 as a result of its locally imparted velocity V. any case, however, the approximations involved This part of the backward component increases in deriving the mathematical expressions for the with the duration of flight, decreases as the disvarious independent correction, or perturbation, tance of the missile from the center of the earth terms are least objectionable for missiles having increases, and would exist even if the earth were small velocities at thrust cut-off. 4-7 THEORY OF BALLISTIC TRAJECTORIES Although the foregoing approach is useful for jectories will be sufficiently accurate if computed illustrative purposes, computations of trajectories with respect to a nonrotating spherical earth. of great length must of course be based on NewThus, the earth in Figure 4-9 is to be thought of tonian dynamical and gravitational theory. One as motionless in an inertial frame of reference: a starts with the assumption that the earth is a nonrotating set of coordinates in space that, for homogeneous sphere and therefore attracts a misall present purposes, may be regarded as having sile as if all the earth's mass M were concentrated its origin fix ed with respect to the center of the at its center (Figure 4-9 ). We have then a twosun. Newton's equations of motion then apply in particle problem; that of a missile of relatively their simplest for~, and from them an equation small mass m in free flight under the gravitafor the various possible free flight trajectories of tional attraction of another particle, the earth, of a missile may be derived. This equation turns out to be the general equation of a conic section. As exceedingly large mass M. Notice that the only role played here by the earth's surface is to proto whether any particular trajectory will be a vide launching and impact areas for the missile. parabola or an ellipse, is found to depend on The trajectories to be used in coordinating the whethe r the ratio of the missile's kinetic energy preliminary designs of the major subsystems of to its potential energy at thrust cut-off is equal any particular type of missile are called reference to unity or is less than unity. Knowing this, one can then show that the speed V of the missile at trajectories. For this preliminary phase the tracut-off determines the type of path as follows: A parabolic path will result if V = V2GM/ (R +h), where G is the 1\ewtonian constant of gravitation; M and R are the mass and t.he radius of the earth, respectively; and h is the altitude of the thrust surface / 1 cut-off point. Inserting in this expression the of earth 1 known values of G, llf, and R, and letting h be,~I for example, 100 miles, we find that Vis approxi\ mately 6.9 mi / sec. For this cut-off velocity and I any value of t.he projection angle "Y (Figure 4-9), / the missile will ·escape from the eart.h along a Fig. 4-9 Ballistic traiedory theory. parabolic path. • \ BALLISTICS An ellipse with its farther focus at t he earth's cen • ter (Figure4-ll) will result if V < VGM/ (R+h),that is, less than about 5 mi/ sec. It is the last case (Figure 4-11 ) that is of interest in the ballistic missile program: One canI show that to obtain maximum range for any given I I thrust cut-off speed V, the projection angle yI must exceed 45° . The maximum possible range' is half way around the earth, this being obtainedwhen y is 90° (horizontal projection), regardless Fig. 4-10 Ballistic trajectory of the altitude h of the thrust cut-off point. How theory. ever, ranges exceeding about four-tenths of theway around become increasingly impractical because of the extreme sensitivity of the range tothe angle y and speed V. To get one-fourth ofthe way around the earth when h is 100 mi, the optimum values are roughly 70° for y, 4 mij sec for V, and 0.5 hr for the Hight time.It is interesting to note the large miss distancewhich can result from seemingly 'small errors in Fig. 4-11 Ballistic trajec velocity at point B. For example, the following tory theory. data relate miss distances to the casual error atfuel cut-off for a particular ICBM traveling J.; ofAn elliptical path with its nearer focus at the a great circle (ground track ) : center of the earth (Figure 4-10) will result if VGM/ (R+h) < V < V2GM/ (R+h);thatis, Cause Effect if V is between about 5 and 7 mi/ sec. (Error at B) (Miss Distance) • A circle surrounding t he earth will result if 1 ft/ sec tangential velocity 5590 ft V = vGMj (R+h), about 5 mi / sec, and 'Y = 90°. 1 ft/ sec radial velocity 2310 ft. For other values of 'Y the path will be elliptic, 1 ft elevation 5.85 ft but not circular. 4-8 SUMMARY OF EARTH SATELLITE VEHICLES The thrust of a rocket motor has been discussed space is subjected. This must equal the time rate(Chapter 2, Part 2) in terms of Kewton's second of change of momentum of the vehicle:law where: dm dm dV -dt (vi -V) = dt (V) +dt (m) Force = ~ (mv,) = mv. + v.m. dt orTotal thrust includes a pressure term. If we -dmvi = mdV (-!-2) define an effective jet velocity vi such that 1t where V, the vehicle velocity, and vh the rocket(mvi) = pressure thrust + momentum thrust and, motor's effective gas velocity, are opposite infurther, assume steady state operation of a rocket sense.motor (vi= constant) it follows that F=m(vi-V) For a sat ell ite to maintain a stable circular= the force to which a rocket vehicle in "free" orbit about the earth, the centrifugal force must 4-10 • TRAJECTORIES air drag, gravity, maneuver, etc.) is given by ~ 18,000 Rm ~e 5000 = e3 ·6, or Rm ~36.6 ' However, this means that only 2.7% of the original r ocket (by weight ) would be structure, tanks, motors, guidance, and payload. To date this has been impossible to engineer. But the dilemma can be solved by stacking one rocket on top of another (called staging) . Staging essentially reFig. 4-12 Ballistic trajecquires the integration of (4-4) once for each tory theory. stage substituting new limits (m1, m1, V;, V1) for each integration. In view of the fact that extremely large masses . . I f Vr 2 equaI t he grav1tatwna orce, or m -r = grm of fuel are required to attain the velocities essential to maintain even a circular orbit around the where Yr = gravitational constant at radius "r". earth, a space sta tion would be an ideal startingR 2 , where point (or refueling point) for interplanetary By the inverse square law, Yr = g -2 r space ships. Exploration of the solar s~tem will g is the gravitational constant at the surface of thus be preceded by the establishment of space t he earth ; R is the radius of the eart h co nsid ered "fillin g-stations" and space ship preparation or as a sphere; and r is the radius of t he circular bits. Man's knowledge of the nature of the uni orbi t. Hence verse will be greatly increased by such fg Rz explorations. Vr = -v-1-. Of more immediate importance would be the = the velocity required to maintain a cir-use of a space observatory fo r astronomical and cul arorbitat height(r-R). (4-3) meteo rological purposes. An astronomical observatory outside the earth's atmosphere would Considering the Vr required, the question might arise: "What kind of a single stage rocket have a big advantage over one which has to "look through" the atmosphere. Telescopic defi can attain V,.?" Solving (4-2) by separation of nition is greatly impaired by the atmosphere variables, which lacks homogeneity and is in a constant state of minute vibrations. Further, the atmos (4-4) phere is practically opaque to large portions of the electromagnetic spectrum. A meteorological station which could view the earth as a ball would be able to see storm centers, cloud formations, etc.; in short, the weather situation over nearly half of the globe. Experiments in physics which require nearly complete vacuum could be performed in space: Experiments which demand zero gravity could be performed. FM radio, TV,where m; is t he mass ratio, Rm . mf microwaves, and radar are limited on earth to virtually line-of-sight operation. If three relay Restating this equation in exponential form: stations 120° apart were placed in a 24-hour or(4-5) bit, their "lines of sight" would blanket the earth v, = vr is of the order 18,000 mph for moderand hence, world-wide communications could be ate r ; vi for current motors and fuels is of the effected. order 5000 mph. Hence, the mass ratio needed Power for space stations could be supplied by to propel a rocket to orbital velocity (neglecting the sun. A large parabolic mirror could focus 4-11 BALLISTICS the sun's rays on pipes carrying some working would result in discoveries of extreme impor fluid (e.g., water). It should be remembered tance. • that a heat engine operates best when the low The military value of a space station could betemperature part of the system (sink) is at a decisive. Imagine the advantage of having avery low temperature. On the shadow side of a world-wide and instantaneously accurate situa space station, temperatures approach absolutezero. tion map! Imagine being able to see a missile atall times from launch to target! Imagine know The effects of zero gravity on chemical reacing what type of work an industrial complex istions and physical and biological processes are doing! The military importance of space stationsnot, at present, known. Perhaps studies in space is tremendous. 4-9 AERODYNAMIC MISSILE CONFIGURATION The design of an aerodynamic missile is based drag for a supersonic missile would generally inon design criteria for subsonic and supersonic dicate a slender missile body with very thinaircraft which makes the aerodynamic missile airfoils. These requirements are not whollyvirtually a pilotless bomber. For subsonic speeds, compatible with the requirements of stowagefluid flow theory has been developed to the point space for components, such as guidance and where very accurate calculation of the lift and control equipment, and with structural strength. drag forces and moments acting on an aerodyHence, compromises must be made to arrive atnamic body is possible, as long as the Mach an optimum design. number is less than about 0.8. The same is true,although to less extent, at supersonic speeds as In the design of an aerodynamic configunttion,the wing design to support large heavy bodies at long as the Mach number is greater than about 1.2. In the transonic range between 0.8 and 1.2, sustained great speed requires new techniques.The problem is somewhat different from normal the approximations made in both subsonic and aircraft design in which takeoff and landing resupersonic theory are not valid, so that design quirements are important features. work is complicated, because calculation must The rela tively high longitudinal acceleration encounteredbe based entirely upon experimental data (Figby some surface-to-air and air-to-air missiles dur ure 4-13). Moreover, the transonic region is a ing and immediately following launching, re critical one in which there is a sharp rise in thedrag coefficient and a sharp drop in the lift coquires that these missiles have great structural efficient of such magnitude that the label "sonic strength along their longitudinal axes. Certain missiles are called upon to execute turning ma barrier" has been attached to it. Fortunately, neuvers which impose great lateral accelerations this region does not constitute an impenetrable on the missile's structure. At present, sonic misbarrier. By using powerful jets and rockets of siles are being designed to withstand a maximumskillfully designed configurations, the barrier has acceleration of approximately 60 g's longitudibeen reduced simply to a region of inefficient operation. It should not be concluded that the nally, and 20 g's laterally. Accelerations of thismagnitude create stresses on the structural mem design problem has been solved completely. Exbers of the missiles far greater than the stresseshaustive research is continually supplying new encountered in conventional aircraft structures. information to form the basis for the design of For example, today's jet fighter aircraft (such asnew and better configurations for aerodynamic the F86 Sabrejet) are designed to withstand amissiles. maximum acceleration of approximately 12 g's. The final missile body design involves a comConcerning supersonic speed through the atpromise of many conflicting requirements, and mosphere, the problem of heat transfer and heatat supersonic speeds this becomes an extremely resistant materials is far greater than is generallyinvolved problem. For example, reduction of realized. It has been pointed out by leading 4-12 • TRAJECTORIES Fig. 4-13 Jet-age aeronautical scientists must assure stability in aircraft over a wide range of speed. Using a high speed research model built for special studies in the 300-mph, 7x 10-foot wind tunnal at NACA's Langley Aeronautical Laboratory, scientists evaluate stability charaderistics in subsonic flight (e.g., during landing and takeoff) of an aircraft capable of supersonic flight. Automatic recording devices in the adjacent control room measure forces exerted on the test model. The series of spot photographs show the effed of increasing speeds on the shock wave patterns over a supersonic airfoil. (Figure 4-15). Even so, much trouble was exscientists that there is virtually no limit to attain able speeds except as limited by the heating perienced when in some cases heat due to air friction caused "cooking off" (premature exeffect of atmospheric friction. At high tempera tures most materials now available lose their plosion) of the warhead. In designing the configuration of supersonic structural strength. As an example, one ballistic type missile experienced skin temperatures of aerodynamic missiles many theoretical calcula tions and much wind tunnel data must be accuover 900°F, and it was necessary for the de mulated in determining the airfoil design and thesigners to insulate the inner side of the skin with design of the plan form of the aerodynamic several inches of fiberglas in order to protect the fuel tanks and certain other missile components surface. 4-13 BALLISTICS • Fig. 4-14 A missile model " streaks along" at more than 2000 mph in an NACA supersonic free flight wind tunnel at the Ames Aeronautical Laboratory, Moffett Field, California. This vivid shadowgraph shows shocklines streaming back from the model' s needle nose and tail surfaces. During sustained flights at such highspeeds, aerodynamic heating could raise the missile's surface temperature to more than 600° F. • 1000 t I ~ :;;! 800 !! PLATI GUM SOI'T'DI! TITAIIltlll sor.'!ll! vI v LIJIIRICATIJG on. IGIIIT!S 600 I I ~ ~ 8 ~ 400 / 200 !lATill BOll.! IILIIC'r!ICIIIC E~ IXJI:S NOT FIIIICTICJI ____., / PICI'IIlLI 0 0 5Xl 100 15(0 2000 25()0 'I'IIUI Alii SI'I!D (111'11) Fig . 4-15 Heating effect of atmospheric friction. 4-14 • TRAJECTORIES -_::;__~ <> Double WedgeBiconvex Modified DoubleBic oncave Wedge Fig. 4-16 Double symmetric supersonic airfoils. Delta Rectangular Elliptical Tapered Raked Forward Fig. 4-17 Supersonic aerodynamic surface plan forms. 4-9.2 PLAN FORMS 4-9.1 PROFILE SHAPES Several plan forms for supersonic wings areThe thickness ratio is often used to describe an air foil. It is defined as the ratio of the maximum shown in Figure 4-17. For the tapered plan form, thickness to the chord length, hj c. It is generally the leading edge may be tapered, or both leading and trailing edges may be tapered; in addi about 4% for supersonic airfoils. Profile shapes are divided into two main classes: double symtion, the taper may not be the same on each edge. The wing tips for any of the plan formsmetric, that is, symmetrical about the chord and may be squared, rounded, or raked forward orperpendicular to the chord at its midpoint; and aft. Some current experiments on odd wingasymmetric, that is, unsymmetrical about the shapes are being conducted to reduc._ the aspectchord line or unsymmetrical about the perpenratio, AR. There is also research Lcin~ conducted dicular chord line at its midpoint. However, in general, supersonic profiles are symmetrical on canard configurations which utilize forward Several different geometric control surfaces while the rear fins produce the about the chord. lift; and research on blunt trailing edges for configurations of the double symmetric type are shown in Figure 4-16. The most popular of these stability ~nd control at transonic speeds. Various aerodynamic steering methods are shown in airfoils is the modified double wedge, which has the best strength properties and is relatively easy Figure 4-18. At transonic speeds it is desirable to utilize to manufacture. .4-15 BALLISTICS PLAN VIEWS A r r nn~_lt' r1H'Ilt A Arr ongem n t C First motion moves after part of • Canard A~r Frame missile in .direclton opposite to Control surfaces acl tn 01r stream noteventual dewed d irection ye t dtsturbed by lift surfaces up down rtght left l, ft >urfaces co n trol urlace' control lift ~ • • l ' Cl •"' 1 'nt 0 First motion of atrfoi l A ll a e rodynamic surfaces aftts direct1on dewed up • down. I ~I rightleft directional stability Fig. 4-18 Aerodynamic steering methods. • Fig . 4-19 Nomenclature for airfoil configuration. L Fig . 4-20 Forces ading on airfoil at angle of aHack; a. 4-16 • TRAJECTORIES --High NR ----Low NR Angle of Attack, n Fig. 4-21 Variation of lift and drag coefficient with angle of aHack for typical airfoil. swept-back wings, because, in this speed range, the compressibility of air must come into consideration and a swept back wing will forestall a sharp increase in wing drag due to compressibility of the air and the ensuing formation of a shock wave. However, at supersonic speeds this wing configuration produces undesirable windbody interference and torsional bending, resulting in center of pressure shifts. That is why many supersonic missiles have a straight wing plan form. A swept back wing is generally less stable and provides less lift than a rectangular wing. This is due to a decrease in the aspect ratio, AR, and greater body interference, since more of the wing surface is closer to the body. In wing design, the main objective is to secure maximum lift and minimum drag consistent with structural and stability requirements. An actual wing may be complicated by such considerations as taper, sweepback, twist, change of profile, and control surfaces. Basic data are usually developed in terms of a simpler structure, the airfoil. In Figure 4-19, an airfoil has been sketched to illustrate span, b, chord, c, ~amber, and thickness. Area, S, is defined as the product, be, and aspect ratio ( AR) is defined as b2j S = !!.: = ~ . be c An airfoil moving with respect to the atmosphere is subjected to the lift ( L) and drag (D) forces (Figure 4-20). The angle of attack a, lies between the direction of the relative wind and the chord line. Moment (M) acts as indicated. The expressions for these basic parameters are developed below and are similar to the expressions for cross wind force and drag developed in Chapter 3), d2 being proportional to the area S (Figure 4-20). 1 L = -p V 2SCL 2 1 D = -p V 2SCD 2 1 M = -p V2ScC/>{ 2 The coefficients depend on angle of attack, aspect ratio, profile form, and to a degree on Reynold's number (Figure 4-21). The general characteristics are illustrated for an aspect ratio of 6. The early version of the F-102 interceptor was a sharp disappointment: it would not break through the sonic barrier. Salvation came in the form of the "Whitcomb area rule," a revolutionary method of tailoring aircraft wings and fuselage to minimize interference drag in the critical transonic speed range. Airc'raft flying at low speeds push air ahead of them, but the resistance of the air thus compressed is negligible. As the aircraft approaches the speed of sound, the air compressed by its passage forms a shock wave that is forced back along the body. The pinched waist of the area-rule fuselage gives the compressed shock wave a chance to expand; this reduces the drag on the aircraft. The resulting large improvement in aerodynamic efficiency allows an aircraft like the F-102 or the B-58 to "slip" through the sonic barrier instead of needing considerably more thrust in order to "burst" through. It is regarded by the NACA, the armed services, and the aircraft industry as a major key to supersonic flight (Figure 4-22). 4-17 BALLISTICS • • • Fig. 4-22 Illustration of Whitcomb area rule. REFERENCES 1 Ley, Willy, Rockets, Missiles , and Space Travel, The Viking Press, N. Y., Chapters 11 and 12. 2 Liepman and Puckett, Aerodynamics of a Compressible Fluid, GAICIT Aeronautical Series, John Wiley and Sons , Inc. , N. Y., Chapter 4. 3 Perkins and Hage, Airplane Performance, Stability and Control, John Wiley and Sons , Inc. , N. Y. , A.P.S ., Merrill series. 4 Vennard, Fluid Mechanics, John Wiley and Sons , Inc., N. Y., Chapter 12. 5 Notes on Technical Aspects of Ballistic Missiles, Air University Quarterly Review, Volume IX, No . 3, Sept 1957. (Portions of this reference have been reproduced with permission of the Commander, Air University, Maxwell Air Force Base, Alabama.) 4-18 • When a projectile is fired from a gun at a target, it is launched in such a way that the predicted external forces acting upon it during its flight, will direct it toward the target. The target will be hit if the user has sufficient skill in choosing the correct trajectory b ased upon the ballistic characteristics of the projectile, the current meteorological conditions, and target motion. The firer can control only the launching conditions. It is completely impossible to make corrections after launch, therefore any change in target vector or meteorological conditions during flight will result in a miss; further , any error in the launch phase will also result in a miss. • The advantages of being able to control the flight of a missile after the launch stage are numerous: Launching errors are now of less importance because they can be corrected. The behavior of the target need not cause a miss because the missile can correct its course for up-to date target information. A missile that can be controlled during its flight requires a guidance • CHAPTER 5 GUIDANCE FOR CONTROLLED TRAJECTORIES 5-1 GENERAL system, or perhaps several different systems, i.e., a separate system for initial, midcourse, and terminal guidance. A guided missile guidance system accomplishes the two forms of control shown in Figure 5-l. Both attitude control and path control are necessary to achieve accuracy. This complete system will then allow the path of the missile to be adjusted after launch along a trajectory which will lead it to the target. l GUIDANCE SYSTEM I I l ATTITUDE PATH CONTROL CONTROL Fig . 5-J Guidance systems. 5-2 ATTITUDE CONTROL Attitude control is the angular orientation of the missile about its center of gravity and can be divided into three functions : yaw, pitch, and roll (Figure 5-2). (a) Yaw is the angular motion of the missile about an axis which is perpendicular to the longitudinal axis of the missile, and lies in the vertical plane passing through the missile center of gravity. (b) Pitch is the angular motion of the missile about an axis which is perpendicular to the longitudinal axis of the missile, and lies in the horizontal plane passing through the missile center of gravity. (c) Roll is the angular motion of the missile about it longitudinal axis . The necessity for maintaining attitude control can be explained as follows. First, the missile must proceed along the flight path keeping drag force to a minimum. Any unorthodox attitude of flight can be corrected by moving the missile in yaw, pitch, and roll. Next, the missile has to have a certain amount of built-in intelligence. It must know up, down, right, and left. Considering the result of a 180° roll error of the missile, the down fin is now on top and the positions of the left fin and the right fin are reversed. A command to the missile to go left actually causes the missile to go right. This shows vividly that attitude con trol must be achieved before commands for path control will effectively guide the missile to the target. Missile guidance components required to provide attitude control normally include the following: 5-1 BALLISTICS • ~YAW I I ---------ro--- PITCH I Fig . 5-2 Yaw, pitch, and roll axes. • • (a) Gyros, to provide reference directions along the principal' axis of spin for yaw, pitch, and roll motions. Normally, when properly mounted, two gyros will suffice to provide reference to these three axes of motion. (b) Differential, to detect errors between alignment of gimbal axis of gyros and axis of missile airframe to provide a signal in both magnitude and sense. (c) Computer, to compare error signals with 5-3 PATH Most guidance systems are named according to the type of path control which they have. Path control is the control of the missile's linear displacements in the lateral, normal, and range directions, referenced to an ideal flight path. (a) The lateral direction is, generally speaking, either to the left or to the right of the correct trajectory. Specifically, it is used to describe motion of the missile on a horizontal line which is perpendicular to the trajectory. When a lateral error exists, a yaw of the missile is needed to a programmed or command flight path and prepare signals, which when amplified and applied to control system will cause the missile to respond properly. (d) Controller, to amplify the small signals from the computer and energize the control system. (e) Effectors, to regulate missile response in terms of computer solutions by means of moving aerodynamic surfaces, jet vanes, gimballed motors, or activating auxiliary jets. CONTROL bring it back to the path. Therefore, yaw attitude control and lateral path control are associated. (b) The normal direction is used to describe motion of the missile along a line which is perpendicular to the trajectory (hence, the name normal is used) and lies in the vertical plane containing the trajectory. Without being exact, it might be said that the normal direction indicates whether the missile is above or below the correct path. When ·a normal error exists, the 5-2 GUIDANCE Path Feedback CCIIIIWld or t Differential Prograllllled r-0-- Flight Power Path Missile 1---Computer f--Controllerf--Effecter r-Response(Path &.Attitude) Stable Reference Attitude ~DitterentialAttitude Feedback Fig. 5-3 Complete missile guidance system. missile pitches and brings it back to the path. form of commands emanating from an outsideIt may b e seen then, that pitch attitude control source during flight. The actual path that theand normal path control are closely associated. missile is following may be determined from out (c) The range direction is simply distance side tracking, or internally mounted sensing devices. made good from the launcher to the target. In a complete guidance system the computer,There is no association between roll attitude and controller, and effectors, used for path control,range direction. are generally the same components which areThe proper flight path required to hit the used in the attitude control system. A represent target may be either programmed into the misative missile guidance system is shown insile prior to launch, or given to the missile in the Figure 5-3. 5-4 GUIDANCE FOR PREDETERMINED TRAJECTORIES The following basic guidance systems are asface missiles where a fixed trajectory of the sociated with surface-to-surface and air-to-sur-missile is predetermined prior to launch. 5-4.1 PRESET GUIDANCE SYSTEM An example of the use of a preset system was In a preset guidance system, path control sigthat of the V-2 rocket, where gyroscopes werenals or directions are generated in a predeterused to supply the signals to the control systemmined time sequence by a device within the to actuate the external fins and the jet vanes, somissile. This time sequence is determined before that the missile would follow a predeterminedmissile launch, and it cannot be adjusted once trajectory. Fuel cut-off was accomplished by anthe missile has taken off. In flight, various funcaccelerometer when the missile reached a vetions are performed which should keep the locity sufficient to carry it on a free flight path tomissile on its prescribed path to the target. the target. The firing procedure for the V-2 wasHowever, if any component does not function first to locate the coordinates of the target and perfectly, the missile probably will not hit the the launching site on a map, and then to erecttarget. the missile at the launcher with its lower side 5-3 BALLISTICS (bottom fin in flight) pointing toward the target. The missile was fired vertically and was set to tilt at a specific angle from the vertical at the end of a given time; the motor continued to accelerate the missile along the path of this angle until the particular velocity for a specific range was reached; then the motor was cut off. From then on, the missile acted like an artillery shell in flight, following a ballistic path dependent on the line of motion of the missile, the speed of the missile, and the height of the missile at fuel cut-off. At the present time there is no surface-to-surface missile either operational or contemplated which employs this type of guidance system for midcourse or terminal guidance due to its inherent poor accuracy; but, this system may be effectively used for the initial guidance phase. This type guidance system has inherently poor accuracy because it is "open loop" in nature. Since there is no feedback or comparison of the resultant path with the programmed path every component must function perfectly if the desired result is to be attained. In physical equipment this is indeed quite rare. 5-4.2 TERRESTRIAL REFERENCE GUIDANCE SYSTEMS A "terrestrial reference system" is a missile guidance system for a predetermined path. A programmer is used to reference the path of the missile to phenomena on the earth and in its surrounding medium (such as atmospheric pres sure, density, temperature, magnetic field, elec tric field, gravitational field, topography, etc.). The path of the missile can be adjusted after launch by devices in the missile which measure one or more of the above parameters; compare the measured data with programmed data; and send error signals to the control system until the proper value of the proper parameter is attained. One of the most simple, yet practical illustra tions of this system is the German V-1. This missile's course was monitored by a magnetic compass placed in the nose of the missile. If the buzz bomb turned to the right or the left, the compass created an error signal which directed its control system to bring it back on course. The V-1 maintained its altitude by measuring air density. It compared the measured air density to a programmed air density representing the desired altitude. If a difference existed, the device ~ initiated the necessary action to move the missile higher or lower. The range was set on an air log similar to a speedometer connected to a small propeller. A system of -radar map matching using the configuration of the earth's surface as a reference is a type of terrestrial reference system. This system is limited to surface targets and requires accurate radar definition and photography, as well as topography data prior to launch. Recent developments in this field have demonstrated the practicability of providing a standard guidance system for very long-range missiles and aircraft. Applications of the techniques described should appear in missile systems within the next several years. 5-4.3 RADIO NAVIGATION GUIDANCE SYSTEMS A radio navigation guidance system is a sys tem wherein the predetermined path of the mis sile can be maintained after launch by the time or frequency measurements of radio signals. There are many variations and types of guidance systems utilizing radio signals; however, only one general type with several ramifications will be covered in this text. Radio waves travel at the speed of light. Since this speed is known and the length of time re quired to send radio signals from one point to another can be measured, then the distance be tween the two points can also be determined. Figure 5-4 illustrates two possible courses a mis sile might follow using radio navigation for guidance. The missile in Figure 5-4 (a) flies a straight line path by comparing the time of arrival of pulses that are transmitted simulta neously by radio stations at Rl and R2. If the pulses arrive at the same time, the range from the missile to Rl will be exactly equal to the range from the missile to R2, and the missile will fly along a straight line. In Figure 5-4 (b) the missile transmits pulses to a radio station at Rl. As soon as each pulse arrives at Rl, it is immediately transmitted back to the missile. The missile measures the time it takes a pulse to travel to Rl and return, and thus measures its distance from Rl. The missile then flies a course such that this radio time, and hence the distance 5-4 GUIDANCE ~Target I I I Target I I + /~~~ 6-----...L -----_'.6 R 1 I R2 I I I I I I (a) Horizontal Plane (b) Fig. 5-4 Radio navigation paths. from Rl, is always kept constant. The path the When the difference in arrival time, heard by the missile flies will be a circle. missile, indicates that the missile is crossing the · Although radio navigation may be used for heavy dotted line, and hence, the target, over circular or straight line courses, the most im signals are sent to the missile control surfaces portant application of radio navigat.ion for to cause it to pitch over to impact. guided missile use involves hyperbolic paths. In order to obtain high accuracy with radioWhen a hyperbolic path is flown by a missile, the · navigation in guided missiles, very high radiomissile will always be a fixed distance farther frequencies (VHF) are used. At these frefrom one guidance station than from the other. quencies (over 30 megacycles) radio waves areFigure 5-5 shows a grid of hyperbolas. The group of hyperbolas indicated by the solid lines propagated on a straight line from the trans is determined by radio stations Rl and R2. The mitter and do not curve around the earth. There group of hyperbolas illustrated by dotted lines is fore, as the range from the transmitter increases, • determined by radio stations R3 and R4. A mis the curving surface of the earth drops away from sile flying along the heavy solid line hyperbola the straight line radio horizon. At a range of that passes over the target may always be lo250 miles the radio horizon is 31,000 ft above the cated one mile farther from Rl than from R2. earth's surface. Although long distance radio The missile computer causes the missile to fly transmission is dependable in the very low frealong a hyperbolic path (heavy solid line) by quency region ( 10 to 100 kilocycles), the efficomparing the arrival time of pulses transmitted ciency of any antenna carried on a supersonic simultaneously by Rl and R2. The missile also missile would be infinitesimal at these frequenlistens to pulses being transmitted by R3 and R4, cies . It therefore may be seen that a missile which determine another hyperbola (heavy employing a radio navigation guidance system is dotted line) that passes through the target. limited in range. 5-5 BALLISTICS ' ' ' ' ' ' R4 ' R3 " \ ' ,, ' ',', ' Rl R2 \ ' \ \ '\ \ \ HORIZONTAL PLANE Fig. 5-5 Hyperbolic grid. 5-4.4 CELESTIAL NAVIGATION GUIDANCE SYSTEM A celestial navigation system is a guidance system wherein the predetermined path of the missile can be maintained during flight by the use of continuous celestial observation. This system is based on the known apparent position of celestial bodies with respect to points on the surface of the earth at a given time. Since the location of the launching point, the target, and the identity of the stars to be used are known before launching, any position on the surface of the earth can be determined from observations on these stars by measuring their azimuth angles and angles of elevation above the horizon with reference to time. In a guided missile the horizontal reference is 5-6 determined by a stabilized platform which is maintained perpendicular to a hypothetical line from the missile to the center of the earth, by gyroscopes and accelerometers. Automatic star tracking telescopes make the "fixes" on the stars, and ·signals proportional to the measured star angles at a given time are then sent to a computer, which compares this actual data with programmed data. The programmed data includes the star angle information for the same instant of time that the missile should reproduce if it is to proceed along the proper path. Deviations determined by the computer between the actual measured data and the theoretical programmed data produce error signals which are sent to the path control system for correction of the missile path ( Figure 5-6). • GUIDANCE \ \ , *\ I* \ \ I I Progrumed I \ I Star Angle DataAutc:aatic I StarTrackera - Computerwith 1====::: &Tor SiF&lil to Path Cootrol Time Reference s7et• Stabilized Actual Platfol'lll Star Angle Data Fig. 5-6 Schematic of celestial navigation guidance. In order to be effective the systems must be integrates it, and determines an error signalable to track stars in the daytime as well as night. which is sent to th e path control system as a disThis has been· accomplished with very sensitive tance off course. The control system of the mis,photoelectric cells. sile will react to the error signal and move themissile this same distance back on course. The 5-4.5 INERTIAL GUIDANCE SYSTEM accelerometers meanwhile detect this secondAn inertial guidance system enables a missile acceleration, the computer doubly integrates it,to follow a predetermined path by the employand when the missile gets back on course, noment of sensitive accelerometers within the miserror signal exists. The missile then continues onsile which make use of the principle of Newton's straight line flight until another error is introsecond law of motion, F = ma. An accelerometer duced.is a device which measures accelerations with Accelerometers are also used for range control.reference to a stabilized platform. Gyroscopes As the missile accelerates from zero velocity toand accelerometers are utilized to keep this its cruising speed, the accelerometer measuresstabilized platform perpendicular to a line from th e acceleration, and the computer converts thethe missile to the center of the earth. In an acceleration to distance covered along the pathinertial guidance system, accelerometers detect of the missile. \.Yhen the missile reaches cruisingaccelerations both along the predetermined flight speed and the acceleration is zero, the computerpath and perpendicular to it. This information computes distance covered on the ground byis furnished to a computer which doubly intemultiplying velocity times time. If the missileb'I'ates the acceleration as a function of time and changes velocity along the path, an accelerationdetermines distance, since or deceleration will be observed by the rangeaccelerometer and the computer will determine distance, S = JJa dt dt distance by doubly integrating this signal. WhenIf a missile is launched on a course toward a the proper range has been covered, as pro target, it will remain on this course until acted grammed into the missile prior to launch, theon by an outside force. When this outside force computer sends a signal to the control system to(such as a gust of wind) ·acts to change the dive the missile into the target (Figure 5-7) .course of the missile, an· acceleration will be exAlthough relatively simple in concept, the deperienced by the missile. The accelerometer velopment of an operational inertial guidancewithin the missile will detect this acceleration. system presents many problems in order to attainThis signal is sent to a computer which doubly required accuracy. Some of the most serious 5-7 BALLISTICS Flight • Path Azimuth PROOR.UOIED AccelerC~~teter RANGE ANDPATH DATA Stabilised Platform Error Signala To Control SJ8tea Range Accel eration Signal Fig. 5-7 Schematic of inertial g uidance system. problems are: gimbals produces torques which cause th e gyroscopes to precess causing deviations in the (a) A missile in flight is subjected to censtabilized platform. The magnitudes of these trifugal force due to rotation of the earth as well deviations are not always predictable. as the force of gravity. This makes it difficult in An inertial guidance system appears to be theattaining a true vertical for the stabilized plat most promising type of guidance for long-rangeform. missiles. It is particularly well suited. for long (b) A missile in flight is subjected to a disrange ballistic type missiles since the time of the torting force resulting from rotation of the earth guided portion of the flight is quite short. The called Coriolis force. accumulation of errors will therefore be very (c) Friction in the bearings of the gyroscope slight. 5-5 GUIDANCE FOR CHANGING TRAJECTORIICS The following guidance systems are associated sile is launched toward the general location of a moving target and is guided to contact or close with surface-to-air, air-to-air, and short-range surface-to-surface missile systems where the mis-proximity to an evasive target for a kill. 5 -5 . 1 COMMAND GUIDANCE SYSTEM designed into the computer. One of the simplest basic approaches to the A "command system" is a guidance control problem is the system used to guide a d rone system wherein the path of the missile can be changed after launch by directing signals from plane into a target. A human operator observes the drone and the target, estimates the changes some agency outside the missile. Information as required in the drone's flight path, and sends to the relative position of the target and the misradio signals to the drone which, through asile is furnished to a computer on the ground suitable control system, executes the desired which solves the intercept problem and sends commands to the missile to direct it to intercept maneuver. In a more advanced typical surfacethe target. The missile will follow an intercept to-air system, the human operator is rep laced by trajectory determined by the navigational method two radars and a computer (Figure 5-8) . One 5-8 GUIDANCE 1. TRACKING PROCESS OF CON riNUOUSL. Y DETERMINING RI:LATIV£ POSITION OF THE TARGET AND »r.tlSSILE MISSILE TRACKING RADAR TARGET TRACKING R 3. 01 RECTI NG PROC£55 OF SENDING DIRECTIONS TO CONTROL UNITS WITHIN THE MISSILE COMPUTER DIRECTING INTELLIGENCE 2. COMPUTING PROCESS OJ' USING TRACKING DATA TO P'ORMULATE NECESSARY DIRECTIONS FOR CONTROL Fig. 5-8 Command guidance system. radar tracks the target; the other the missile. The computer continuously compares the path of the missile and the target and continuously solves the intercept problem. ew direction headings are sent to the missile, either by the missile tracking radar or by a separate radio link. This type command system is being successfully employed for surface-to-air missiles, such as the operational IKE missile system. Another application of command guidance is for air-to-surface missiles where a similar system may be employed. Still another application of the command system is for surface-to-surface missiles. In this case the location of the target is known, which fixes the flight path the missile is to follow. A radar tracks the missile comparing its actual flight with the desired path and transmitting necessary corrections. This system is somewhat limited in range due to line-of-sight requirements of radar. 5-5.2 BEAM RIDER A "beam rider system" or line-of-sight system is a guidance control system wherein the direction of the missile can be changed after launching by devices in the missile which keep the missile in a beam of energy. Radars produce the most promising types of beams for this system; however, other energy beams such as light and heat might be used for this purpose. In applying the radar technique to the guidance of a surface-toair missile the beam of the target-tracking radar would have to be so modified .that adequate information is conveyed to the missile for it to determine where it is with respect to the center of the beam and guide itself toward a predeter mined position within the beam (Figure 5-9). A beam rider system is limited to short ranges because accuracy decreases as the beam width increases. One variation of the beam rider system is called the modified or dual-beam rider (Figure 5-10). In this system the missile-carrying radar beam is positioned by another target-tracking radar and computer combination. The modified beam rider system is conceived to surmount the problem of excessive transverse accelerations en countered by the beam climber in flying a continually changing line-of-sight course to the target. This occurs because the beam is constantly pointing directly at the target and moving with the target. In the modified beam rider system, it is contemplated that two radars and a 5·9 BALLISTICS • CAPTURE BEAM....----.. / // / / / / // / / / ----;; / /'" ,./ / -d:~ EL -;Jti:. EL AZ ~AUNCHER LAUNCHER Fig. 5-9 Single-beam rider. • Fig. 5-10 Dual-beam rider. computer will be us ed . The target-trackin g radar second beam than to launch the missile into the . feeds target data into the computer which calb eam that was trackin g the target. These advanculates a predicted position of the target based tages may be offset by the additional ground on target data and missile data. The second equipment required over that used in the single radar is pointed toward the predicted point and beam rider system. the missile follows this beam. This beam also 5-5.3 HOMING (TERMINAL GUIDANCE) supplies missile data to the computer. The modified beam rider system is a variation A "homing system" is a guidance control sysof the command system in which the commands tem wherein the direction of the missile can be are transmitted to the second radar instead of to changed after launch by a device in the missile the missile. The missile obeys these commands which reacts to some distinguishing characterisby virtue of its beam riding equipment. This tic of the target. A homing guidance system may system is more effective against maneuvering be used as the primary guidance for a guided targets than the normal single beam rider system. missile or it may be used in conjunction with Also, it would be easier to launch a missile into a another type of guidance system. When used • 5-10 GUIDANCE with another system, homing generally accom • plishes the guidance for the terminal or final phase of the missile trajectory. Homing guidance is used for both fixed trajectories and changing trajectories. Basically, a homing system consists of a seeker in the missile which automatically keeps pointed at some special characteristic of the target, and feeds data into a computer to keep the missile headed so as to hit the target. The important target characteristics which have been studied as means of perceiving the target are: (a) Light emissions. (b) Radio emissions. (c) Radar reflectivity. (d ) Infrared emissions. (e) Sound emissions. (f) Capacitive features . (g) Magnetic features. (h) Radioactivity. Of these characteristics, the best means of detecting targets to date are infrared radiation and radar signals. These systems are sufficiently accurate to assure a high target kill probability within their range of operation. The main drawback is range limitation in that the limit for infrared is 2 to 3 miles and for radar about 10 miles. · This limits homing, in some applications, to the terminal guidance phase, one of the systems discussed above being used for mid-course guidance. Homing systems can be subdivided into active, passive, and semi-active depending on their method of operation. An active homing system is one wherein the source of illumination of the target as well as the receiver is in the missile (Figure 5-11). A passive homing system is one wherein the receiver in the missile utilizes natural radiations from the target as in the case of heat radiations from a ship or factory (Figure 5-12). A semi-active homing system is one wherein the receiver in the missile utilizes radiations from the target which has been illuminated from some source other than the missile (Figure 5-13). All of these types are currently under development with certain types best for a given target; for example, the passive system for infrared seekers and the active or semi-active for radar seekers. Homing seekers used in antiaircraft or antimissile systems are sometimes classified according to the type of navigational course the missile flies. Any one of the common types of navigational courses, pursuit, constant bearing, or proportional, could be incorporated into a homing guidance system . ...... .... ' \ ~ !7 MISSILE SENDS OUT RADAR IMPULSES !7 !7 AND HOMES ON ECHOES .!7 .!7 Cl !7 ~--------=~~r---------------- Fig. 5-11 Active homing. 5-11 BALLISTICS GUIDANCE SYSTEM COMPONENTS ) . SCREENING DEVICE TO COLLECT TARGET RADIATION . l . SENSITIVE ELEMENT TO REGISTER SIGNAL. 3. ..EANS OF INDICATING DIRECTION OF TARGET. 4 . INTELLIGENCE CIRCUIT TO STEER. • ~ ~ ~ '\\\\IVy \~! ~\Ill/ II 'I !? LIGHT RADIO RADAR SOUND ~ HEAT Fig . 5-12 Passive homing guidance. • --.,;::;-... , .. ./ .. .../ ', MISSILE RECEIVES ECHOES AND .../ ' GOES HOME ON CENTER Of BEAM LAUNCHING PLANE SENDS v..././ \ OUT RADAR IMPULSE ~ ....../ _/./ -1_ _/ --------------- • Fig. 5-13 Semi-adive homing guidance. 5-12 -----------------. GUIDANCE 5-6 KINEMATICS OF INTERCEPT COURSES A command signal to the missile can direct the inherent characteristic of the missiJe system.missile toward the target by various intercept Four of the five most common navigationalpaths. The specific intercept path employed is methods for solving the intercept problem are asdesigned into the computer and therefore is an follows : 4 5 6 TARGET (a) Line of sight. Defined as a course inwhich the missile is guided so as to remain onthe line joining the target and point of control.MISSILE TARGET .l ~ (b) Pursuit. Lead or deviated pursuit course I is defined as a course in which the angle betweenthe velocity vector and line of sight from the missile to the target is fixed. For purposes ofew • angle ol missile heading illustration, lead angle is assumed to be zeroand only pure pursuit is described P • angle ot line o! sight ( (JJ{ = /3 ). KISSII.E TARGET l (c) Constant bearing. A course in which theline of sight from the missile to the target maintains a constant direction in space. If both missile and target speeds are constant, a collisioncourse results ( diS . dt=!S=O) . ' KISSILE~I~~L---------------- TARG=ET~~J~,_~;~,_~J 1 I I I ' I I I I (d) Proportional. A course in which the rate I' of change of missile heading is directly propor I'I tional to the rate of rotation of the line of sightfrom the missile to target • d(JM d{3 · •) I' ( dt = K dt or OM = K{3 . IIISSIU:' HCJliZONTAL 5-13 BALLISTICS The problem of analysis of Hight paths must be solved in the design stage in order to observe the characteristics of trajectory, time of flight, maximum rate of tum, and maximum lateral acceleration for a proposed system, in terms of anticipated target maneuvers, relative speeds of missile and target, and motion of point of control. Once a system is determined, the computer solves the specific problem for each encounter. Accuracy being vital to the kill probability, the inherent speed and accuracy of digital computers R lliSSILE ' ' ' ' for this purpose has speeded their development to the point of being competitive, and subse • quently superior, to analog computers for this purpose. Before any of these methods can be analyzed it will be necessary to understand the geometry of the problem (Figure 5-14) . Only two-dimensional motion will be considered, but it must be realized that the problem is a three-dimensional one. v~ T • X Fig. 5-14 Geometry of in tercept problem. In Figure 5-14: 9 is angle of heading f3 is angle of line of sight R is range or distance between missile and target v is velocity vector y is ratio of missile velocity to target velocity, subscript M refers to missile. subscript T refers to target. subscript f3 refers to direction along line of sight (LOS). subscript a refers to direction perpendicular to line of sight. 5-14 GUIDANCE Several relations between the parameters of the problem are now observed. The range R, at any given time: R = la' (v~T -v~M) dt + Rinitial (5-l) Interception will take place only if R is always decreasing and for R to decrease v~r -v~M < 0, or negative. From Figure 5-14 the following relations may be determined: dR · - = R = v~r-vdM dt = Vr COS (er -{3) -VM COS (eM -{3) = VM [~COS (er-{3)-COS (eM-{3)] (5-2) and d{3 {3= dt R vr sin (er -{3) -vllf sin (eM -{3) R vM [~sin (er-f3) -sin (eM-{3) J R (5-3) The characteristics of the four navigational methods follow. (a) Line of sight (beam rider). A beam rider always Bies the line of sight from a tracker on the ground to the target and requires associated ground equipment which may be jammed. However, new developJY1ents such as pulse-doppler radar, may effectively counter the enemy's jamming ability. Turning rates are always finite when y > 1, hence, lateral accelerations must be determined as functions of altitude, range, relative missile velocity, and angle of line of sight, B. (b) Pure pursuit. The missile is always headed toward the target along the line of sight: ellf = {3, then V~M = VM ·eM= {J~er, in other words, interception takes place from the tail of the target (unless the target is met head on ) . The missile must maneuver but the pursuit coqrse is the simplest to mechanize in a guidance system. With pure pursuit navigation the lateral acceleration of a missile attacking a non-maneuvering target will be infinite at the instant of intercept if the missile velocity is more than twice the target velocity. The lateral acceleration will be zero at the instant of intercept if the missile velocity is less than twice the target velocity. From these conclusions, it is realized that unless some miss distance is allowable, it is impractical to use a pursuit course when the missile velocity exceeds twice the target velocity, since it is impossible for a missile to attain an infinite lateral acceleration. (c) Deviateq pursuit. A deviated pursuit course, often referred to as fixed lead navigation or constant bearing navigation, is a course in which the angle between missile velocity vector, VJ1 and line of sight (eM -f3) is fixed. Thus, if ll = f3 -eM• (5-2) and (5-3) become, respectively (5-4) Vr sin{3-VM sino (5-5) R Figure 5-15 shows a plot of the relationship between y and sinll which must exist in order that ~ remain finite (Region II) or zero. It is seen that only for 1 = y ~ 2 will it be possible to select a /l which does not yield an infinite turning rate. Of course in practice, when turning rates called for are in excess of the maximum missile turning rate, the missile will remain in its maximum tum until it cuts across the line of the target path and then re-enters the proper course or is lost. Since lateral acceleration, a,11 = VM /3, characteristics of turning rate apply to lateral accelerations when VM is constant. (d) Constant bearing. The missile is navi gated so that the target always has the same . d{3 . beanng, dt = {3 = 0. For a nonmaneuvering target moving with constant velocity, this means that a missile with constant velocity will ideally be directed onto a straight-line collision course. A perfect constant bearing course is impossible to attain in an actual system, however, due to inherent system errors and dynamic lag. A constant bearing course is utilized for the antiaircraft artillery fire control problem, where 5-15 BALLISTICS 10 -Infinite y cos & REGION I: > 2 Turning Rate 5 y s 2 = 1 REGION II y cos 8 0 sin S (1 -y 2 sin2 S Fig. 5-15 Conditions for finite turning rate (deviated pursuit). the computer determines 8AI• the direction to point the guns in order to accomplish intercept. This met: od is not satisfactory for use with guided missiles. (e) Proportional. The angular velocity iJM, of the missile is a constant K, times the angular velocity, i3 of the line of sight; iJM = KiJ. Hence, 8.11 = K{3 + 80 • Both pursuit and constant bearing navigation methods are special cases of proportional navigation. For example: When K = 1 and 8o = 0, 8M = {3, which is pursuit navigation. When K = m, then~ = 8 M a> stant bearing navigation. • It could be shown that for a maneuvering target and a variable speed missile, the required missile rate of tum, iJM, is always finite when K ;;=:: 4. Considering a realistic interception problem, proportional navigation is probably the most • satisfactory, although the computer setup will be more complex than for a pursuit or constant bearing course. Most operational and developmental air defense guided missile weapon systems, employing command or homing guidance system, are designed with some type of proportional navigation. • = 2 = 0, which is con- REFERENCES Locke, A. S., Principles of Guided Missile Design, D . Van Nostrand Co., Inc., Chapter 12. 5-16 CHAPTER 6 INTRODUCTION TO TERMINAL BALLISTICS 6-1 Terminal ballistics is concerned with the principles underlying the effects of weapons on targets to include penetration, fragmentation, detonation, shaped charge, blast, combustion, and incendiary effects. In designing weapons and ammunition, maximum desired terminal effect is a primary objec- SCOPE tive. A proper balance of many factors is essential to accomplish this purpose. The most important of these factors are shape, weight, and material used in the projectile; type and weight of explosive charge; fuzing system; and terminal velocity. Data on performance as influenced by these factors, with the exception of fuzing, are discussed in this section of the text. 6-2 DEVELOPMENT AND USE OF TERMINAL BALLISTICS The science of terminal ballistics has lagged behind th e companion sciences of exterior and interior ballistics primarily because of difficulties in obtaining basic data for study. Rapid advances in th e fields of radiograp hy and high speed photography have relieved the situation somewhat, but the problem of securing good data remains complex. For example, direct observation of the end product is possible only in fragmentation studies. Mechanisms by which these results were achieved can be determined only by statistical analysis of fragment distribu tion. However, new developments and improvements in recording techniques are helping to increase our knowledge of th e subject. Studies previously initiated were intensified during World War II and are now being continued for th e purpose of accumulating a greater store of technical data pertinent to terminal ballistics. Much of this data, relating to the performance of ammunition and the vulnerability of targets, has been published in a wide variety of documents for the benefit of both the ammunition designer and consumer. This has been of real value to combat unit personnel who plan and direct th e application of firepower. In th e final analysis, it is the responsibility of commanders or staff officers to select the proper ammunition from among the many types placed at their disposal by th e technical services; it is also th e commander's responsibility to use it properly. It is hoped that an appreciation of th e principles to be brought cut in this text will impress the student with th e essential economy involved in a terminal ballistic viewpoint; economy of effort, time, materials, and manpower. 6-3 TECHNIQUES OF TERMINAL BALLISTIC STUDIES • Because terminal ballistic effects ordinarily appear as instantaneous events to th e layman, the time factor in terminal ballistic investigations has often been the limiting factor; i.e., the ability to physically record detailed reactions which take place during time intervals of the 6-1 order of several microseconds. Experiments are conducted to determine the principles governing the number, size, velocity, and spati al distribution of fragments (Figure 6-1 ) resulting from detonations of cased high explosive charges, in order to gain knowledge BALLISTICS Fig. 6-1 Bursting shell. that will permit optimizing of effects on enemy ies of effects against personnel, structures, targets. Thick wall enclosed chambers, instrustructural members, aircraft, and the air-blast mented optically and electrically, and lined with coupling into the ground for relatively long durathicknesses of materials to trap fragments are tions. In addition to the timing devices and basic to these investigations. Penetration effects sensitive pressure pickups, a basic technique inof small· missiles and fragments demand knowlvolves large shock tubes to reproduce shock edge of air drag parameters of fragments and wave forms that can be scaled accurately to repsub-missiles. resent types of shock fronts that result from both Investigations concerning the production and conventional and atomic explosions (see Figure prevention of fire damage to military materiel 6-2). must be conducted concurrently. The physical The study of shaped charge and high velocity nature of the detonation process within explosives jets involves investigations in a variety of scientific fields. These include the physics of plasticity involves studies of detonations by various types of initiators with physical measurements by use of metals at very high strain rates; the physics of X-ray, electrical, and optical techniques. of interactions between metals and high explosives; and the field of instrumentation design Detonation studies include the mechanism for the formation of air shock from explosions. for highly specialized applications. Included are Studies of the propagation and effects of shock multiple flash radiographic techniques which produce X-rays of 10-7 seconds duration to ob waves in earth, rock, air, and other gases under varying conditions are required for the design tain a series of successive pictures of a jet or of blast producing weapons, and for the design collapsing liner. The jet velocity is often in exof structures capable of withstanding the efcess of 23,000 feet per second. Optical techfects of such weapons. The effects of detonation niques in shaped charge and detonation studies of small charges under varying conditions are include rotating mirror cameras, Kerr cells, found from actual experiments. Extrapolations image convertor systems, Faraday electro-optical are made by appropriate scaling laws to obtain shutters, and ultra high speed framing type effects of full scale weapons. The studies of cameras. These are all directed to record events blast waves extend from the surface of an exin terms of exposure time ranging from 1/ 10,000 plosive to extended distances, and include stud-to 1/ 1,000,000 part of a second. 6-2 TERMINAL BALLISTICS Fig. 6-2 Shock tube . 6-4 MEANS OF PRODUCING DAMAGE Whatever the type of weapon considered and (c) Blast, the effect caused by the sudden rewhatever the nature of the target attacked, damlease of large amounts of energy in a fluid age can be produced by one or more of the medium. physical phenomena associated with the bring(d) Debris, set in motion at relatively high ing to rest of a missile, with the detonation of velocities. an explosive, with nuclear fission, or with chemi(e) Heat, in the flame of the blast, or radiant cal or bacteriological action. It is conven~ent to heat. classify these phenomena as follows : (f) Fire, which may result from the effects of (a) Fragmentation, or the action of relatively an explosive, or may be induced by special in small particles, usually from the case of a bomb, cendiary weapons. rocket, warhead, or shell. (g) Chemical action, particularly from smoke (b) Impact, which pertains to the penetration or poisonous gases. or perforation of an object by a relatively large ~h) Bacteriological action. metallic body, such as an armor-piercing shot. (i ) Radioactivity. 6-5 TARGET ANALYSIS The technical aspects of producing target damto the strategist, the tactician, or the local comage by the many mechanisms described above mander. Its vulnerability may lie in terms of must include methods or standards by which personnel, control equipment on the target, a specific effects on targets can be realized. A tarcontrol center or command post, the logistical get must be considered in terms of its importance lines which supply the target, or the economic 6-3 BALLISTICS potential which it supports. Likewise, defensive measures against attack at all levels play a critical role. Target intelligence from the strategic and tactical levels must include details of target vulnerability. Vulnerability studies of friendly and potential enemy weapons are highly scientific processes; for example, aircraft vulnerability studies indicate the best hope of kill against enemy planes, and likewise, indicate the most vulnerable areas of our own aircraft which can often be minimized by redesign. Armor is evaluated in terms of mobility, armor protection, main weapon accuracy, and tactical employment. Basic data are concurrently fed into computers for playing of mathematical war games. Similarly, the problem of the human target ex 6-6 PROBABILITY AND STATISTICAL TREATMENT OF BALLISTICS 6-6.1 INTRODUCTION Computed trajectories for gun launched projectiles, rockets, bombs, and missiles are based on a rigorous mathematical analysis; accurate data resulting from meticulously instrumented £light tests; and the overwhelming contribution of electronic digital computers to solve the basic equations of motion. The user, however, requires additional fire control data (range and deflection probable error or dispersion data) . The designer and the weapons analyst demand performance in terms of hit and kill probability, including all variations resulting from human or systems errors in handling and processing data to the gun or launching device. The following is a brief treatment of the mechanism by which such information is evaluated and used. The total problem is one of statistical analysis which is not only the basis for evaluating these performance parameters, but is the basis for the acceptance and the surveillance of all United States ammunition and other mass produced items under procurement, and in world-wide storage. 6-6.2 PROBABILITY If a possibilities are each equally likely and if, of the a, exactly b possess some .unique attribute, tends far beyond the consideration of the effect of one round delivered against an enemy soldier. • Incapacitation of enemy troops requires wound ballistic studies which include vulnerability of the human body; effects of body armor; and armament of friendly troops in terms of weight of principal weapon, weight of ammunition carried, weapon accuracy, training time required to reach proficiency with the weapon, and logistical requirements. The optimizing of these parameters may answer such proposals as the arming of the infantryman (in an effort to give him a greater combat effectiveness) with a high velocity rifle of small calibre which will be light, fire accurately at short ranges, and for which he may carry twice or three times the amount of ammunition now prescribed. • • b c, then it is said that the probability of c is a written P (c) = ~ a For example, if, of 10 pencils, 3 are red (let the attribute red be denoted by R) , 4 are blue (B), 3 are green (G), then the probability of selecting a red pencil at random is: ~, i.e., P(R) = .3 10 These data may be tabulated thus: RRRBBBBGGG Obviously, 3 + 4 P(R or B) = = .7 = P(R) + P(B) 10 This is known as the Sum Rule. Further, the probability of R, B, or G is l (or a certainty); whereas the P (yellow) = 0 (impossible). Now, denote hard lead pencils by H and soft by S and retabulate: RRRBBBBGGG HHSHSSSHHH 6-4 TERMINAL BALLISTICS This tabulation tells one that 2 red pencils are hard and one is soft. Thus, if one selects a red pencil, then 2 P(H) 3 This is known as the conditional probability that a pencil is hard on the hypothesis that it is red, and may be written: P (HIR) = P (H given R ) = PR(H ) = .667 The probability that a random choice will be both red and hard is .2, i.e. P(R H) = no. of hard red pencils = ~ ' total no . of pencils 10 The Product Rule is now stated by example: :~ 2 2 P (R, H ) = P (R) X P (HiR) = -X -= 3 10 10 6 2 2 = P (H ) X P (RiH) = lO X 6 = 10 = probability a random choice is hard and red. If 2 random variables, e.g., X and Y, are statistically independent, then P( X) = P(XjY) and it follows, P(Y) = P(YjX ). In this case, the product rule may be written : P(X,Y) =P(Y,X ) = P(Y) X P(X). In this example, the ten pencils collectively are known as the parent population. The one pencil randomly selected is the sample of size n = 1. The manner in which the sample is selected is of major importance. If the mathematics are to be valid, nothing one does, objectively or subjectively, must prejudice the data. f of r unds 6-6.3 STATISTICS To analyze a set of data in an effort to discover trends or predict performance, one tries to answer the following questions: ( 1) "Where is the center of the distribution, or what is a representative single-number description of the data?" (2) "What is the dispersion, variation, or spread?" (3) "Is the distribution skewed or symmetric?" This text considers the answers to (1) and (2) only, and infers probabilities from the answers. There are several ways of answering the questions posed in (1) above; e.g., mean (average), mode or median. The most useful of these, the mean or average, is centroidal, i.e., is located at the balance point of the data. For a symmetrical frequency distribution, mean, mode, and median are essentially the same. Imagine an experiment in which a number of rifle rounds are fired over a fixed range at a single target point. Measure, to the nearest inch, the horizontal and vertical distances from the center of hull's eye to the actual strike point of each round and tabulate these data as follows: High or Low Left or Right Round No. (High is+) (Right is +) 1 +1 0 2 -2 +1 3 +2 0 4 0 0 5 -1 -2 6 0 +1 7 0 0 8 -1 -1 9 +1 -1 10 0 0 / 11 +3 +3 12 0 0 These data may be graphed as histograms: -z -1 o t1 +Z +l -3 -z -1 o +1 +Z +3 HIGH-LOW LEFT-RIGHT 6-5 BALLISTICS Note that, implied in measuring to the nearest inch, is the fact that the measurement "0" really means within -0.5 in. to + 0.5 in. It is apparent that, if the average miss is not 0, there is an aiming error, therefore it is useful to compute the averages for the data presented. Let the individual data be denoted by x with a subscript. Then the mean or average is given by: X = X t + X 2 + . .. + X1 2 =_!_ f X ; (o-1) 12 12 i-1 Thus, XH-L = _! = .25 inches high , is the a verage 12 miss high or low, a nd XL-R = _!_ inches right , 12 is the average miss left or right. Therefore, based on these scant data, one can say that there is apparently no aiming error because both x's are within -0.5 to + 0.5 inches. If asked "What is the probability of being within ~ inch of a horizontal line through the center of the bull?" one might answer, "From the first histogram, 5 of the 12 rounds fired fell within ~ inch. Based on these scant data, P (vertical error < .5 in.) = %2 in. Further, one might infer that essentially all rounds will fall within 3.5 in. since 12 out of 12 in our sample fell within 3.5 in. of the horizontal center line." The area of each histogram is 12 rounds. Dividing the ordinates by 12, in effect, divides the area by 12 making it equal one. In short, the graph has been normalized, i.e. , the total area has been made to equal one. This normalization changes the frequency distribution (histogram) to a probability distribution in which the area between two values of miss distance equals the probability that any given round will fall within those two values . There are obvious weaknesses in the technique employed thus far. First, measurements to the nearest inch are not very precise. Further, a sample size of 12 is not large enough. Therefore, imagine firing a very large number of rounds (say oo) measuring each miss distance precisely. In this case, the histograms will smooth out into continuous, rather than stepped, curves. The sum of a large number of independent random quantities practically always satisfies the normal law, i.e., approximates extremely well to a function of the forme-"'' . The normal frequency function is given by 6-6 1 (z-m)~ f(x) = --== e -l --; • V27ru where m is the true mean or average of t.he population, and u is the true standard deviation of the population. 8 = standard deviation of the sample = root-mean-squared deviation = -1 ~ ~(X; --x)"-' Js. a b" 1ased estimate o f" u, i-t ~n . but S ~ u when the sample size n is large. By employing the standardized variable, x -m h I f" d ' 'b · t = ---, t e norma requency Jstn uhon u becomes: 1 f (t) = --e -~~~~ vl21r t The following properties of the normal curve are easily verified: (a) Maximum ordinate occurs at t = 0 (or • .c = m ). (b) Curve is symmetrical about t = 0 (or x = m). (c) The " tails" of the curve rapidly approach the horizontal axis. (d) There are two inflection points at t = ± 1 (or at x = m * u) . (e) Total area under f(t) is 1, i.e., +co I_ ! e -12tz dt = 1. V271" -co (f) The probability of a random value of t lying between A and B equals the area under f(t) between A and B, i.e., B P(A ~ t ~ B) = ~ f(t)dt • TERMINAL BALLISTICS B A t TABLE 6-1 AREAS UNDER NORMAL CURVE Table 6-1 gives values of jf(t)dt for several FROM -oo TO t = x -m ) -00 values of t. By use of this table, P(A ~ t ~B) (1 can be found. , I Further, if it is desired to know what values l=x-m I ft e-t2t2rft 'I ll t=x-m iof t would delimit some fractional part of all q I .f oo v21r u events this too can be determined from the table. -00 It is important to recall that the parameters -3.5 .0002 II I -1.5 I .0668 m and u, essential to the use of probability tables, -3.4 .000:3 -1...1 .0808 are population values. These must be approxi-3.3 .0005 I -1.3 .0968 mated from experimental or sample data. The -3.2 .0007 -1.2 .1151 best estimate of m is the average of the sample -3.1 .0010 -1.1 .1357 data, x. However, the best estimate of u is given -3.0 .001:3 -1.0 .158i by -2.9 .0019 -.9 .1841 I ~ -2.8 .0026 .8 I .2119 -n ~-n~1" --2.7 .0035 I --.7 ! .2420 ---~ (xi-x)2n-l n-1 n 1 .0047 -.6 .27-13 u ~ --s= -2.6 -2.5 .0062 ~ -.5 I .:{085 -2.4 .0082 -A .3-1-16 ' -2.3 .0107 -.3 I .3821 -2.2 .0139 -.2 I .-1207 It is enlightening to note from Table 6-1 that -2.1 .0179 I -.1 I I .-1602a normally distributed random variable will fall I -2.0 .0228 i 0.0 .5000 within 1u of the mean [1 -2 ( .1587)] · 100% I of the time, or 68.26% of the time. Areas, or I + .I :=1-£-.1 -1.9 .0287 I I probabilities can be summarized as follows: • - Area or -1.8 I .0359 I + .2 00 Interval Probability I i 1-.3 -1.7 .0-1-16 I .3 1=1 t = -1 to + 1 or x = x -u to x + u .6821i II + I t = -2 to +2 or x = x -2u to x +2u .9545 -1.6 .05-18 I + .-1 -00 I t = -3 to +3 or x = x -3u to x +3u .99n 1=1-1-.0 -1.5 .0668 + .5 Mortars, bombs, rockets, and guided missiles, i.e., missiles approaching the target plane from :I -00 a nearly vertical direction, present very nearly Note: circular dispersion patterns. It is therefore conOnly integrals for nega tive values of t are given; I.J~· 00 venient to define a circular error probable CEP symmetry and the fact that J f (t)dt = 1, we have which gives that value of miss distance within which 50% of the rounds or missiles will fall. It -00 ! +to= _ ~-to may be seen from Table 6-1 that +t = .6745, 1 gives the limits of the centrally located half of -CD -CD 6-7 BALLISTICS t values. If it is assumed there are no aiming errors (i.e., m = 0) then 0t = .6745 = x~o - CT or X~o = .6745uz = probable error of X. Similarly, Y~o = .6745uu = PE11 CTz = = CT CT11 (Since, a circular dispersion pattern is hypothesized.) It is shown in more advanced texts that • 1 CEP := 1.1774u A knowledge of statistical analysis of errors (in terms of standard deviation and probable error) is helpful because the performance of weapon system components (e.g., CEP, range and deflection probable error, fuzing error, etc.) is expressed in such terms. Actual data for specific systems are classified and presented only in classroom discussions. • • 6-7 PROBABILITY OF The knowledge that a single round will succeed in its mission is influenced by a considerable chain of circumstances. Consider, by way of illustration, a flat trajectory weapon with a deflection standard deviation of 1 mil, firing on a target 6 yards wide, at a range of 1000 yards. If the weapon is properly aimed at the center of the target, an allowable error of 3 standard deviations exists. This is sufficient allowance to practically insure a hit, since it has been shown that a probability of .9973 exists for limits of ± 3u. This example has been over-simplified. In reality, .9973 is the probability of a hit on the hypothesis (or condition) that the aim is correct; thus, the probability of a given weapon hitting a target is dependent on the aim. Aim is clearly a function of crew training, crew eyesight, and proper functioning of the fire control equipment. Consider the same system manned by a perfect crew with the further condition that the projectile is a high explosive shell. The probability of killing the target is the joint probability of proper functioning of the high explosive train on the hypothesis of a hit. Thus, by the Product Rule, A SUCCESSFUL MISSION the P (kill) = P (hit) X P (proper functioning of high explosive train). The problem can be further compounded by introducing the probabilities of proper performance of each link in the chain of events which precedes a kill. Included in the chain would be a factor for the hardness or softness of the target, i.e., the probability of a definite kill for one round. The latter involves the appropriateness of attacking the given target with the given terminal ballistic effect. Hence, the net kill probability might take the form P(kill) = P (proper mechanical functioning) X P (proper crew performance). X P (hit on the hypothesis of proper aim) X P (kill on the hypothesis of a hit). Fortunately, most of these probabilities are, or with sufficiently energetic training and discipline may be made, high. The two dominant factors are 'obviously the size of the target and th e ac curacy of the delivery system, both expressed in terms of probable error or standard deviation. 6-8 DAMAGE DISTRIBUTION FOR LARGE YIELD WEAPONS When an atomic weapon is detonated over a will vary with distance from ground zero from given target it may be expected, except for unvirtually complete damage to virtually no damduly high bursts, that there will be a zone (exage. Similarly, outside of the zone of probable tending radially from ground zero) in which damage, there will be a zone of no damage. The there will be almost certain damage to the target. lines of demarcation between these zones will It may also be expected that, outside of the cernot be capable of precise definition. However, tain damage zone, there will be a zone of probthese zones will usually exist. It is possible to able damage in which the actual damage imposed determine the distance from ground zero at which 6-8 TERMINAL BALLISTICS the probability of damage is that desired or required. In doing this it is convenient to work with that distance at which the probability of damage is about 0.5. Three damage levels, light, moderate, and severe, used to describe the degree of damage tactically important are defined as follows: (a) Light. Superficial, can still perform mission. (b) Moderate. Out of action for present engagement but can be repaired. (c) Severe. Permanently out of action. The required damage levels are moderate and severe. The damage radius (Rn) is that radius (from ground zero) within which as many target elements escape the specified damage as sustain it outside. Rn = Rr,o where R50 is the radius at which the probability is .50 that a target element will sustain the specified damage. 6-9 THE DAMAGE FUNCTION The relationship between probability of damage and distance from ground zero as it exists for a given set of conditions, is known as the damage function applicable to that set of conditions. As conditions vary, e.g., different targets, different effects, different burst conditions, it may be expected that the curve representing the damage function will change. These changes will evidence themselves in the slope of the damage curve and in the magnitude of R/)' Consequently, the relative size of the zones of certain damage and of probable damage change. The slope of the curve is related to a variability factor. The proper variability depends upon the variation in target response expected from the type of effect being utilized. The plot in Figure 6-3 shows three curves of a family of curves, each of which corresponds to different target responsiveness. The curve for the target, shown by a solid line, is annotated ~ Zone certain damage --1 of 1, 0 .....::--<." 0,9 0,8 o. 7 0, 6 o. 5 0,4 o.' o.a 0, l 0 Zone of Zone of no probable damage damage ---+--Least Variable ~MostVariable rom ground zero Fig. 6-3 Damage functions for two different sets of conditions. with zones of damage and radius of damage Rn. The least variable target, shown by a dotted line, is more discriminating, i.e., the zones of damage are more sharply delimited . The most variable ·target has an extensive zone of probable damage. 6-10 FACTORS REGULATING Most delivery systems are subject to delivery errors which, in some cases, are quite large. The probable delivery error must, therefore, be taken into account in determining the probable varia 6-1 0.1 GENERAL The selection of the weapons system, a weapon, and its delivery means, is vital to the s~ccess of a planned atomic strike. The procedure used in selecting the weapons system is referred to as a target analysis. The atomic weapons staff officer performs the target analysis in order to OVERALL SYSTEM ERRORS tion of the actual ground zero from the planned, or desired, ground zero. This is important in planning the utilization of weapons as it may greatly affect the amount of damage to the target. present to the commander, recommendations on weapon systems to use and the details of their employment. 6-10.2 FACTORS CONSIDERED There are many factors that need to be considered in the selection of a weapons system. Generally, they can be broken down into the two 6-9 BAlliSTICS categories of technical and tactical factors. Un Some of the systems are inherently more accurateder any given situation certain of the factors may than others. This factor may govern in some • assume greater importance than others thereby cases where troop safety assurances cannot otherexerting a greater influence on the choice of a wise be met. The air delivery system is inherparticular weapons system. ently flexible, yet, because of possible enemy (a) Mission or objective of the attack. The countermeasures, weather, or navigational probmost important factor in weapon selection is the lems, the selection of such a delivery system mayobjective of the attack. Other factors may have be unsound. Additionally, the problems of conan important bearing which will require some trol and coordination make it desirable that themodification in final weapons systems selection delivery means be under the control of the armybut, unless the objective of the attack is met, the commander. The gun delivery system is accurateattack will not be successful. The results desired in delivery, and not affected by weather or subfrom the attack are determined and clearly stated ject to interception, but is limited in use by itsby the commander. Many considerations includrange capabilities. Each system available in anying the mission, type of maneuver, target nature particular situation must be judged in the lightand vulnerability, and strength and disposition of the objective of the atomic attack.of opposing forces, will influence the command(e) Weapon characteristics. The characteriser's decision as to the type and amount of damtics of the weapons will also affect the final choiceage needed against the entire target or any in some situations. For example, a certain weaelements thereof. In arriving at the stated obpon may be the only one that has an underjective the commander is assisted by his staff. ground burst capability whereas another weapon (b) Troop safety or other command limitamay be the only one capable of being pretions. The second factor, troop safety or other positioned.command limitations, also plays an important (f) Economy. The third technical factor thatpart in the selection of a weapons system. The must be considered is economy. The smallesttactical disposition of friendly troops and the weapon which will achieve the desired results,protection from the effects of atomic weapons all other factors being equal, should be chosenavailable to them must be considered in relation for reasons of economy. As an example, an at • to the size of the atomic weapon and the actack is being considered on troops in forests, andcuracy of the delivery means available. In areas it has been determined that a casualty radius ofcccupied by civilians, humanitarian consideration · 1300 yards is needed. Atomic weapons should bemay make it desirable to avoid or minimize civilconsidered wh ich will give the required casualtyian casualties or material da!llage in certain radius. All other factors being equal the smallareas. Minimizing damage to installations such est yield weapon with the required casualtyas bridges, communication centers, and other faradius should be selected.cilities which may be of future value to friendly 6-10.3 POINT TARGETSoperations, may also be specified by command A point target may be a single element such as limitations. The avoidance of obstacles, either a building or a bridge, or it may be a small areaby radioactive contamination or from rubble may target. The term small is a relative term. A be another limitation of the objective of the target is small only by comparison with the radiusatomic attack. The commander may well specify of damage (RJJ). Thus, a very hard target (oneany of the above as limitations or results not derequiring high effect values) of 200 yards radiussired from the atomic attack; this, in turn, may is not a small target when attacked with a weamodify the final selection of a weapons system. pon of RJJ of 400 yards. A target of RJJ = 200 (c) Weapon availability (logistics). Weapon yards is small when compared with an RJJ ofavailability affects the final selection not only 1500 yards. The assumption that an area targetfrom the viewpoint of actual weapon availability can be treated as a point target is based on judgbut also from the viewpoint of the characterisment and the requirement for accuracy.tics of the weapons. Problems involving the probability of damage (d) Delivery system capabilities. Various deto point targets are solved by means of the basiclivery systems have different characteristics. point target chart, Figure 6-4, or the point target 6-10 • • • .-- z 0.. "'u -ten' m :::» ::0 ~ z)> r ?' OJ)>rr (JI 1·4 -tI I I I I ~">"1/ /1 I I I I I () F= 4 POINT TARG£T PROBABILITY CHART-AVERAGE VARIABILITY (JI I 1.3 I J..< I ,...,/ I I I I I I (I ) (2) EXPECTED FRACTIONAL DAMAGE TO AN AREA TARGET CONSIDERED TO BE A POINT TARGET. 7.5 . I 0 .5 1.0 1.5 2.0 2.5 3.0 3 .5 4 .0 4 . 5 5.0 5.5 6.0 6.5 7.0 .I DISTANCE FROM DGZ TO TARGET CENTER /CEP c:P Fig . 6-4 Point target chart, average variability. BALLISTICS Ill fIll fIIIIIIIIIITTT 111111111111 mnnJlllllllll II11111111111111 s: PROBAIIUTY OF DAMAGE TO POINT TARGETS ZEROCEP en (Anrac• nrt•~ility) I s: I I !f "'! II g: ~ it+ Hf ti ~.± h-I .. s: . t-· ~ :i .. 1 T I ! II ~ ~-+.! 1-l-·liI . I. Ill ,,I-H. I ...! ! Hj . :I . rlH .. ""ttt ... -'-. ~ ... ~ .. • l .... :::! ! :il tt ·ll·t-1 1 -... . .. -04 •• . . . . .... • l-L • • 0 • . . . . ...'ltif-:-! ' . . . . . :: r: . . .. . . . . . .. i~ ~! . . ....... . ::J'. ·~ ...... ... . ::~ ;. :.:-q :. r~~;:.:_ · 1-t--: .. ·-..... . . .. --~ .... .... . . ·--·---. --· ......... . -... . .·-. .... .4 -, ~-+ . . .... . .. . . . .. . . • -r •• • 1 . -• H-l ~-" .... . . . . ..- . . . . .. . . . . . . . ~~= -' ~ ... -. --.. ---- . . . ... ---!.:.t! t+ 1 ± --. .. .. --·--. . ~.:· . .... -::_:.~~i ?:E~:! r.-·'5.;.:: ~ :.~.:... ·:.·r T. -, •. r! I ••·r. ~t-l+ I . •. . . • I· ~- · •~· I :t* :i:r. t .• ~ -+--~' r-,; ~ g-· r=;-~; 'h-+ ---H a :1-"+ ~..::-±~::t. . -ft:r_. • •.. . i Sf: j ~.t ... -r -+-' t----.. . •· .... .r+++ 1 •.• ' m11i !I i: I ~:.: ..re-t--f-r..! ~ . . l : 'T: ·r ',.; ~--e::;~: ~ t---; ~::r" !-c , I r-, , .... ci i if 1 1 II! I N ci Ff, HI ' rTf:.::.=.~---ci '+ llllllllillllllllllllllllITTTTTT I I I J I I I I -C> I 0 2.0 1.9 1.8 1.1 1.6 l.S 1.4 1.3 1.2 1.1 1.0 .9 .8 .7 .6 .S .4 .3 .2I DISTANCE ROM DCZ TO TAlCET CENTtR/DAMACE RADIUS {*) 0 • Fig . 6-5 Extension chart, point targets. 6-12 TERMINAL BALLISTICS extension chart ( Figure 6-5). The basic point target chart, Figure 6-4, provides means for finding the probability of damaging a point ta rget, or a small area assumed to be a point, when the delivery error ( CEP), damage radius ( Rn), and p distance (d) from DGZ are known. The ex l. 0 ~-:: ------........ tens ion chart, Figure 6-5 is used whenever values ......._ _ are off the bas ic point target charts, and it must 0.8 -----1---" \be used when there is no delivery .error. The I I I probability contours of the point target chart I I give directly the probability of damage to a tar~ I o.5 -----r-- get consid ered as a point. If the·target is a single 1 I I I \ elemen t, the probability (P) of damage reprep I I sents the ass urance that the element will sustain I I : severe or moderate damage depending on the 0.2 -----~-----,--criteria used. Where a small area targe t consist1 I ing of several elements is considered a point ~----~~----~--~----~~~£ 0. 3 f 0. 6 0. 75 I. U target, the probability (P) of damage to the point may also be construed as the average frac tional damage which would occur if the attack were r epeated a la rge number of times under Fig. 6-6 Two typical P(f) curves. The dotted curve identical conditions. As an example, if the probindicates the P(f) curve for the larger yield weapon ability of causing casualties to an infantry com(hence, the larger Rn). pany (considered as a point target) were de termined to be 60%, and if it were estimated that 150 troops were in the company area, then, on the average, 90 of them would be casualties. 6-10.4 AREA TARGET CONSIDERATIONS of at least 10% damage to a target will be greaterThe determination of damage occuring to (or than the probability of at least 90%damage, unbeing imposed on) an area target is more comder the same conditions. The degree of partial plex than for a point target. In the case of the damage to the target as a whole (i.e., to all point target, since the target either will or will target elements) is called fractional damage. not be damaged, there are but two pertinent Hence, generalizing the foregoing statement: the probabilities; the probability of damage and the probability of a large fractional damage will be probability of no damage. In the case of area less than the probability of a small fractonal damtargets however, the target may be totally damage. This r elationship can be illustrated by what aged, partially damaged, or not damaged. There is called the P(f) curve for the circumstances at issue ( P r eferring to probability of damage; and is a probability associated with every degree of f referring to fractional damage). Fractionalpartial damage to the target as a whole, as well damage is not to be interpreted with respect toas a probability of complete damage and a proball target elements. A typical P(f) cu.-ve is illusability of no damage. trated in Figure 6-6, which illustl ates the folSince atomic weapon effects are evidenced lowing relationships between probability ( P) spherically about the point of detonation, they and fractional damage (f): are evidenced circularly on the ground about p f ground zero. Consequently, target shape is im0.30 portant. For simplicity, area target considera0.80 0 .50 0.60 tions are limited to circular targets. It is reasonable to expect that the probability 0.20 0.75 6-13 109 I 10 PROBABILITY SCALE FOR d • 0 1 I 8 I I I INDEX I ~~A9 / V L7 -.--1 1 1 I . ./ ./V I I .01 .02 .03 .0!5 .I .2 .3 .4 .S .6 .7 .8 .9 .9!5 .99 ~ 8 6 1 ' 1 1 I ' '1 ,111 lduull!!d!!lol!!lol""l""l""!dmlu!!lll' I .,....V /./~~'l.~~~ : 7 !5 P (f) NOMOGRAPH, CIRCULAR TARGETS, AVERAGE VARIABILITY _/~/~~~~ 4 I I 1 NOMOGRAPH FOR FINDING PROBABILITY OF AT /~~/r /~~'1'~/..V 4LEAST A GIVEN FRACTIONAL DAMAGE (f) TO3 A CIRCULAR TARGET. ~ .V~1'4./.fi II) / /V./ ' 'l 3 ~ 2.!5 I I ~~ ~/........ ~~~R 25 ~ ca:: 0 ~RAJTIONAL OA~G~~ ~~~/~~~r;l' 2 ..... ~ ~ "' .99 ~vv~ ~~v;;~ ::;C) 1.!5 .9!> V V ""'/./)//,//, 1!5 ~..... a::c ..... J9.-V..,.vt::~.,~~v'i! /j/ · ~ II) ~v~_.....vv~"' /v11 ..... :::) II) Q I 70 ........ ~"""" ..,; v :::) OJ c .9 'e.O f-""'" "' / / 1/ / I9 Q )>9' .8 !>O ~ v l/ / 1 / "8 a::c ,.... ~ ~ "' a:: .7 . 40 v"' v / L ll ..7 C) (/) c . v ~ I I "' -4 c2 .6 -~o vv I I .6 ":1c () 0 .!5 c (/) .20 0 .!5 Ro I -.4 V .4 -RoRr . 10 ..,;V / Rr 2 ..~I I I I I I I I II II I I I I I .0!!5 I t:H1 I I I I I I I 1111-~: .2I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1.2 .I !5 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I t15 .I1.01 .01!5 .02 .02!5 .03 .04 .0!5 .06 .07 .08 .I .15 .2 .2!5 .3 .4 .!5 .6 .7 .8 .9 I 1.!5 2 2.!5 3 !5 6 .I 7 8 9 10 CIRCULAR ERROR PROBABLE /TARGET RADIUS, (CEP/Rrl Fig. 6-7 P(f) nomograph, average variability. • • --------• TERMINAL BALLISTICS 6-11 THE P(f) RELATIONSHIP fOR Figure 6-7 has been designed to enable determination of the P(f) relationship for circular targets of radius RT when attacked with a weapon of damage radius Rn, delivered with a circular probable error ( CEP ), provided the desired ground zero (DGZ) coincided with the target center. Often one is not concerned with the entire P(f) curve but rather with a specific point on CIRCULAR TARGETS, -NON-ZERO CEP it. For example: it has been decided to impose a 40% fractional damage on a designated target and that there b e a 90% assurance (probability) of attaining at least that damage. This nomograph, together with the probability scale associated therewith, enables determination of the required Rn to comply with the commander's desires, provided the DGZ is the target center. 6-12 IRREGULAR TARGETS (a) Targets which are not generally circular in shape may be considered as follows: 1. Rectangular targets. Targets roughly rectangular in shape with the long side less than two times the short side can be reduced to an equivalent circular area without serious error. In using the charts and nomograph, RT should be equated to the radius of the circle of equivalent area. If the sides of the rectangle are X and Y, then, XY)t/2 _ RT = ---:;-= o.s64 vxY ( 2. Elliptical targets. If the long axis is less than twice the short axis, the area may be equated to that of a circle with no serious error. (RT = ~yab, where a and b are the lengths of the major and minor axes, respectively.) The area may also be found by approximation, by planimetering, or by counting grid squares. (b) Irregular targets which are not amenable to reduction to a circular target of equivalent area must be considered as a system of points. Targets such as marching troops or armored columns, or other very linear or irregular targets, can only be solved by considering a series of points within the area of concern and determining the average probability of damage. The greater the number of points considered, time permitting, the more accurate the determination of damage will be. The damage determined will be that which can be expected on the average. REFERENCES 1 Burr, Engineering Statistics and Quality ConCraw-Hill Book Co., Inc., N.Y. trol,,McGraw-Hill Book Co., Inc.,'N.Y., 1953. 4 Scarborough and Wagner, Fundamentals of 2 Freund, Modern Elementary Statistics, PrenStatistics, Ginn and Co., Boston. tice-Hall, Inc., Englewood Cliffs, N.J. 5 Woodward, Probability and Information 3 Goode and Machol, System Engineering, Me-Theory, McGraw-Hill Book Co., Inc., N.Y. • 6-15 CHAPTER 7 FRAGMENTATION 7-1 INTRODUCTION When a charge of high explosive detonates inside a closed metal container, the container is blown into fragments. These are hurled outwards at high velocities and in effect become projectiles with a capacity for inflicting damage upon nearby objects. Capacity for damage depends upon fragment size, velocity, and distribution. A container which erupts into dustlike particles or into a few very large pieces is of little value. Knowledge of the fragmentation process is therefore basic to the design of many types of missiles. Terminal ballistic studies attempt to determine the laws and conditions governing the speed and distribution of fragments; the sizes and shapes that result from the bursting of different types of containers; and the influence of the bursting charge fragmentation. 7-2 NATURE OF THE FRAGMENTATION PROCESS Upon detonation of the high explosive in a missile, the metal case expands very rapidly because of the internal pressure of the expanding products of the detonation. Flash radiographs of a tetryl loaded 20-mm shell, detonated statically, illustrate the phenom 7-3 BALLISTICS Fragmentation is not the only result of detonation of explosive missiles, since only forty percent of the gas energy normally is absorbed in the fragmentation process. The balance of the available energy is consumed in the creation of a compressive wave in the air surrounding the projectile. The fragments resulting from detonation of a missile are propelled at high velocity, and within a very short distance from the center of explosion, pass through the shock wave which is retarded to a greater extent by the air. The velocity of the shock wave in air is dependent upon peak pressure in the shock wave front and the pressure, temperature, and composition of the undisturbed air. Its velocity is reduced according to the square of the distances from the center of explosion until, at a considerable distance, enon of fragmentation as it occurs in artillery shell. There are nine pictures (Figures 7-1, (a) to ( i) incl.). Figure 7-1 (a), the reference picture, shows the shell before detonation. Exposure time is approximately one microsecond ( 1/ 1,000,000 of a second). OF FRAGMENTS the velocity becomes equal to that of sound in air. It is apparent that it is difficult to obtain ballis tic data on individual fragments; nor is it neces sary. Statistical analysis of the fragmentation of the whole container provides essential practical data. The ideal fragmentation missile is one which would break up into uniform fragments with a size and velocity fulfilling predetermined tactical requirements. This ideal has not yet been attained, but the size and shape of frag ments can be controlled to a limited extent. The problem of determining optimum fragments illustrates the need for fragment flight charac teristic (drag) as well as the vulnerability of the prospective target in terms of fragment mass and striking velocity. 7-1 BALLISTICS Fig. 7-1 (b) Shell two microseconds after initiation of the bursting charge. Fig. 7-1 (c) Five microseconds after initiation showing the shell case in the process of swelling. Fig. 7-1 (d) Eleven microseconds after initiation cracks can be seen in the shell case which has expanded to almost twice its original girth . Fig. 7-1 (e) Twenty microseconds after initiation showing continued lateral movement of the shell case fragments. The expanding gases are escaping through the failure cracks. • Fig. 7-1(a) Shell before detonation. • • Fig. 7-1 (f) Thirty-four microseconds after initiation showing continued growth of fragmentation perpendicular to the longitudinal axis of the projectile. Fig. 7-1 (g ) Thirty-nine microseconds after initiation . Fig. 7-1 Detonation of a 20-mm shell. (Sheet 1 of 2) 7-2 FRAGMENTAT ION Fig. 7-1 (h) Fifty-four microseconds after initiation showing the extent to which the fragments fly off in the direction perp endicular to the surface of the casing. The disc shaped side spray which exceeds the nose and tail spray in intensity of fragmentation is the main instrument of damage in most missiles. Fig. 7-1 (i) Ninety-two microseconds after initiation showing the wide variance in size and shape of fragments. All the fragments have by now received their initial velocities . • Fig. 7-1 Detonation of a 20-mm shell. (Sheet 2 of 2) 7-3 BALLISTICS 7-4 INITIAL VELOCITIES OF FRAGMENTS The initial velocity of a fragment depends mainly on: (a) The C j M ratio where C is the mass of explosive per unit length of projectile and M is the mass of metal per unit length of projectile. (b) The characteristics of the explosive filler (brisance, power) . Table 7-~ illustrates the relationship b etween C j M ratio and initial velocities (V0) determined from a series of tests using cylinders of an internal diameter of 2 inches and uniform wall thicknesses as indicated. The explosive filler used was TNT. TABLE 7-1 FRAGMENT VELOCITIES FROM VARYING CONTAINER WALL THICKNESSES Inches Wall Thickness Y2 % ~ U6 Ys C/ M .165 .231 .286 .500 .775 Vo (ft/ sec) 2870 3240 3800 5100 6100 Initial fragment velocities can be estimated experim entally by measuring fragment penetration into a material such as soft pine or celotex, and adjusting estimated velocity in terms of fragment mass, shape, and drag coefficient. Semi-empirically, the approximate initial velocities are, I c I C/ M V = K \jM + C/ 2 = K \j1 + 1/ 2 C/ M where V = initia l fragment velocity, ft / sec K = constant associated with t he power and brisance of t he explosive used C and M , as defi ned above The primary reason for the relatively low velocities of fragments from the container with the greatest wall thickness, is that a large part of the energy released by explosion is absorbed in rupturing the cylinder. However, the table could be changed considerably either by the use of different explosives, particularly those whose power and brisance differ, or by different wall material such as cast iron versus forged steel. Explosive power is usually considered as ability • to do work over an area, a property more dependent on oxygen balance and after-burning than on rate of detonation . On the other hand, brisance has been defined as the ability to create destruction in the immediate vicinity of the explosion, which quality appears to be determined by the speed of establishment and the magnitude of pressure in the detonation wave. TABLE 7-2 COMPARISON OF FRAGMEN TATION OF 90-MM M71 SHELL USING TNT AND COMPOSITION B Compo- T~T sition B Loading Loading Fragments (Pi t Fragmentation Tests) 700 998 Fragment Velocity (Panel Penetration Tests) 2367 ft / sec 3231 ft / sec Perforation in Steel • Plates (at equal radii) 120 164 The best way then to achieve high initial velocities of fragments is to have a high C j M ratio, usually obtained in practice by the use of a thin walled container. This is not always possible however, since in many cases projectiles must be designed with thick walls to withstand setback forces or they may be purposely designed to give larger fragments. In these cases a more powerful explosive is needed having a higher brisance than that used in a thinner walled cylinder. Explosives containing RDX, for example, have both high brisance and good power. They are ideal then for producing high velocity fragments, although for certain applications they are too sensitive. Velocities of fragments from an air burst have higher values than those obtained from detona tion upon impact due to the velocity of the mis sile at the time of detonation. This fact is one of the reasons why VT or time fuzing provides more effective fragmentation effects. • 7-4 FRAGMENlATION Fig. 7-2 Static nose-down detonation of a bomb. 7-5 DIRECTION OF FRAGMENT FLIGHT The fragments from a missile usually fly in a direction perpendicular to the surface of the casing. For an artillery projectile, this can be readily seen by referring again to Figure 7-1 (i). Figure 7-2 shows the static detonation of a large bomb suspended nose down with nose about seven feet from the ground. The tracks of the fragments are made luminous by their heat. Note the black smoke, which represents the unoxidized solid products of the explosion, an indication of the incomplete oxidation of the explosive charge. The cone of tracks, opening upward in Figure 7-2, is called the 45° spray and originates from that section of the casing that connects the cylindrical part with the tail. The fragments almost parallel to the ground constitute the main side spray and originate from the cylindrical side walls of the bomb. The picture does not do full justice to the great density of fragments in the side spray. The slight upward deflection of the entire side spray is due to the fact that the bomb was detonated statically, nose down, and the detonation started from the bomb nose. If either the bomb or shell had been detonated while in Hight by VT fuze action, the side spray would have had a slight forward thrust; the resultant of the radial initial velocity of the fragments and the forward velocity of the bomb or shell. 7-6 NUMBER, TYPE, AND SIZE OF FRAGMENTS • The damage that will be produced by a fragment with a given velocity depends on the mass of the fragment. It is therefore necessary to know approximately for each missile the distribution of mass among all the fragments large enough to cause damage. Mass distribution of missile 7-5 fragments is determined experimentally by means of static detonations in which the fragments, or a portion of them, are caught in sand pits. Usually, the side spray contains the most important part of the fragmentation. Such a spray will, in general, have a different mass distribution from BALLISTICS .,.....,... 04......... \. ~ .l,,• .....),.,.. • ::::::::::: ...,..... ..........4 a •• ..... a m:m:::: "' ••• • • ltfllm(U ~f• lilt• t I •• • • ~ e • • a • ;:;::::i:ii Fig. 7-3 Fragments from bomb, that of fragments from the whole missile. In the static detonation of bombs, portions of the side spray, nose spray, or tail spray are collected in a sand pit. The fragments are separated fr om the sand by sifting through metal screens of four mesh to the inch . The fragments thus obtained, few of which have masses less than one gram, are then weighed and classified according to their masses into no more than six classes. Such sorting is shown in Figure 7-3 which represents recovery of fragments of an M88 220-lb fragmentation bomb loaded with Composition B. In general, the shape of the fragments varies exceedingly. Many of them appear flat, their smallest dimension corresponding to the thickness of the swollen case, stretched by the expansion that follows detonation. Present fragmentation bombs have a light casing wrapped with a metal helix of square cross section in order to control to some extent the size, and therefore the distribution of mass among the fragments. When the bomb bursts, the helix is broken into pieces of comparatively uniform size as compared to ::::::::::: ' • •-~'' • • • • • ,.ae I •• a a ::~:::::::: ••• ••••• •o••••••a.••••• ::!:~:;:~:; ••• ••••• liJAtellllea-ae 0 ~!a::::::! ... \1 • • • •••••••• •••*• a ::::;::::H • u • 4' • • a • :J ...• t•1 a I e I f mnt::~:l ••• • J 1 •' ... 1 •• •••• • W:!li~:t: ''" •~••"' ... ••• ....... . ....._. •••• <:' -·•••••••••••• :~w::::~: ••• ~c-•• •••••,Dttlt\1•• •••uuuu • u at.rll ~ t e·11 ••• t •••1 1 1 · !~m:::':: ut ' u • ~ t•tt )AIIIIIIII a m:m:::::!: ::t:: ...........,,. :m::::n: ~ .. • •• '' ••••••,•••.,... f i!ili:Hiii ::: f~:t~ 't•L~~·tttlllttAl i I · :muu::r lal-talt 1 lrt llll)tll ~..........-= ······· .. . .. ,.... •••••••'*" a&• •••tl It I • It• ·111 • .····-·····........... •••• ,••, ......... ...,......,... •••, ......~ llf• ..,.,.......,. •• e e. t 5 I • I • 8 • • fragmentation, 220-lb, AN-M88. the fragments of a general-purpose bomb. Fragments will vary from dust-like particles to relativel y large pieces in GP bombs, where the size of fragm ents is not controlled. While adjustment of the Cj M ratio in shells can be used to change the degree of fragmentation of the shell wall, the size and number of fragments resulting from the shattered wall can also be adjusted by altering the material used in the wall. For example grey cast iron, an inherently brittle material, shatters into very small sand-sized pieces which have low killing power. Also they have little momentum and thus short range. This is unfortunate since the casting of shell bodies is desirable from a mobilization point of view. A vital factor in the design of any ammunition item is its ability to be readily adaptable to quantity manufacture during mobilization or war. This country has a broad base of industry which could cast she~l bodies. On the other hand, because forging is a widely used commercial 7-6 -----------------------------------------~ FRAGMENTATION J • method of fabrication, the industry of this country can support very large scale manufacture of forged shell bodies . In like manner in recent years, cold swaging and cold extrusion processes have been looked upon with favor as suitable methods of shell manufacture. Metal which deforms without splitting in these pressure forming processes is, on the whole, tough and hard to shatter. Hence, some advantage in both production and fragmentation might be realized if ~ cast iron were available which could be made to shatter into fragments of optimum size. Spheroidized cast iron, in which the carbon distribution ( in nodular distribution as well as in Fe,1C) can be controlled by heat treatment, shows some promise in fulfilling this requirement. With rigid metallurgical control (fractures at the nodules which act as stress risers), such cast iron can be made to give fragments of desirable size. 7-7 FRAGMENT DAMAGE In evaluating the effectiveness of fragmentation of specific weapons (bombs are used as an example), the types of damage considered are casualties, and normal perforation of mild steel of ~-inch, ~-inch, and ~-inch thickness. A casualty may be defined as a hit by a fragment with at least 58 foot-pounds of energy. (This rule of thumb f1as been superseded by wounding criteria of much greater refinement for use by weapons designers and fragmentation effectiveness studies.) Normal perforation of mild steel occurs when a fragment, traveling perpendicular to the face of the plate, passes completely through the plate of the indicated thickness. Damage in which there is perforation of ~-inch mild steel is effective against airplanes on the ground. Damage in which there is perforation of ~-inch mild steel is effective against trucks. Damage in which there is perforation of M-inch mild steel is effective against light armored vehicles, railway rolling stock, and targets of similar resistant nature. The fragment damage shown in Table 7-3 gives the number, B, of effective fragments per square foot of target area at a given distance r from the burst of a 220-lb. bomb, based on an initial fragment velocity of 4420 feet per second. The numbers, B, are averages for different directions from the burst, and are side wall directions. They apply only to a considerable number of bursts with random orientation of the bomb axis relative to the target. The actual density of fragments in the most dangerous d irection from the bomb is about six times the average densities, B, given in the table. As distinguished from fragment damage tables, damage patterns of typical individual cases, as shown in Figures 7-4 and 7-5, illustrate how the terminal velocity of the bomb, the angle of fall, and the height of burst influence fragment distribution. Both fragment damage tables and damage patterns presuppose a graze or air burst with no shielding of the target. Consequently, in using such data allowance must be made for target shielding and the penetration of the bomb into the ground before burst. The amount of this penetration will depend upon the remaining velocity, the angle of fall of the bomb, the nature of the soil, and the type of bomb and fuze. The optimum height of burst which will give the maximum number of personnel casualties may be read from Figure 7-6. When a fuze for regulating the height of burst is available and causes a known dispersion in the height of burst, it is possible to use Figure 7-6 to determine the mean height to which the burst should be adjusted. Air bursts are recommended against men in foxholes or open trenches and against personnel shielded by rough terrain. The type of shielding labeled "10° foxholes" is believed to be that most commonly encountered and corresponds to the shielding afforded men in foxholes when the men are somewhat below the level of the ground, or to the shielding afforded prone men by rough terrain. A "10° foxhole" is defined as a foxhole in which an occupant would be unharmed by fragments with an angle of fall less than 10 degrees. Hastily dug-in positions on level ground would correspond to "0° foxholes," as would trenches in which the heads of men are even with the ground. 7-7 BALLISTICS TABLE 7-3 FRAGMENT DAMAGE: CASUALTY AND PERFORATION EFFECTIVENESS OF BOMB, FRAGMENTATION, 220-lb, AN-M88; COMPOSITION B LOADING; INITIAL FRAGMENT VELOCITY 4420 FT/ SEC • Average For the Lightest Distapce Total Number of Effective Fragment From Number of Effective Burst Effective Fragments Weight, Velocity, in Feet Fragments per sq ft oz ft / sec r N B m v Casualties 40 8650 .706 .0073 2850 50 8000 .418 .0101 2420 60 7400 .268 .0134 2100 80 6500 .133 .0217 1650 100 5800 .0757 .0322 1360 150 4500 .0261 .0609 988 200 3700 .0121 .0857 832 300 2800 .00406 .137 658 500 1920 .00100 .268 471 700 1500 .00040 .446 365 1000 850 .00011 .808 271 Perfo ration of Ys-inch Mild Steel 20 8200 2.16 .0088 4420 30 7300 1.06 .0140 3720 40 6600 .538 .0205 3260 60 5600 .203 .0364 2640 80 4650 .0948 .0568 2240 100 3750 .0489 .0845 1970 150 2300 .0133 .188 1550 • 200 1750 .00571 .335 1300 300 990 .00144 .720 1040 400 420 .00034 1.14 915 600 28 .00001 2.13 770 Perfo ration of %;-inch Mild Steel I 20 4100 1.34 .0718 4420 30 3600 .522 .0917 4040 40 3180 .259 .112 3750 60 2520 .0914 .162 3270 80 2100 .0428 .220 2910 100 1860 .0243 .289 2640 150 1350 .00783 .517 2180 200 820 .00268 .822 1870 250 330 .00069 1.22 1640 300 67 .00010 1.72 1490 Perforation of 7'2-inch Mild Steel 20 1220 .398 .580 4420 30 1090 .158 .660 4220 40 920 .0750 .750 4020 60 650 .0236 .925 3710 80 420 .00857 1.11 3480 100 250 .00326 1.33 3260 120 120 .00109 1.55 3080 140 60 .00040 1.79 2920 170 26 .00012 2.20 2710 200 13 .00004 2.65 2530 • 7-8 FRAGMENTAT ION -I CIIOUNO IUIIST .. lt[MAINING V(lOCfTY H0 rl• AlTIT UD£ 01 llt(l[A$( 20000 n .. / ~HOt\ 0 ..... ... • AT LIAST 1 HIT I'IR 1 SQ. n • .. AT LIAST 1 HIT I'IR • SQ. n •D Af LIAST 1 Hrt -10 SQ. n RA PO 109276 Fig. 7-4 Damage paHern: bomb, GP. HIIGKT « IUIIST lO n . IIIJWIIIIOG Vll.OCITY 110 1/o~ A&.muD( « R[U:AS[ ZO.OOO n. u ,. .... .... .... 400 AT.T I'IRI SQ. n . .. AT LEAST I HIT l'f:R • SO. n ~ AT LIAST I HIT I'£R 10 SQ. 1': I'(III'QIIATION 0' II I ·I N MILD SK(L AT LIAST 1 HIT I'£R ZS SO. n. AAPO 109271 CA~UA&.na • Fig. 7-5 Damage poHern: bomb, GP. 7-9 BALLISTICS • -w...f/J0 V 860V• .., -75° V 1040 II• "' -45° v-100 V• • • 10 20 40 50 60 70 80 90 100 HEIGHT Of BURST · FEET ItA liD toe2.. Fig. 7-6 Casualties versus height of burst-bomb, fragmentation. The optimum heights of burst for various types desired. In this table the groups of bombs comof bombs run approximately as follows: pared are those normally carried in the same station of the bomb bay. The figures given are Optimum Height of ratios of effective hits of the type indicated for Bomb Filler Burst, No Dispersion the bombs compared. The type of explosive 20-lb Frag (TNT) 20-30 ft charge used in each bomb was given in the pre90-lb Frag (Comp B) 30-50 ft ceding paragraph. 100-lb GP (Amato!) 30-50 ft An examination of the data given indicates 260-lb Frag (Co mp B) 35-70 ft that at low or medium altitudes a 20-pound 500-lb GP (Amato!) 30-GO ft fr agmentation bomb is preferred against person nel or lightly protected targets. For low altitude Table 7-4 will be useful in making a choice of bomb for ground burst against unshielded tarbombing, the parachute on a 23-pound fragmentation bomb greatly improves its effect over the gets according to the type of fragment damage 7-10 FRAGMENTATION TABLE 7-4 FRAGMENTATION COMPARISON: RATIOS .OF EFFECTJVE HITS OBTAINED FROM VARIOUS BOMB COMBINATIONS AT VARIOUS ALTITUDES OF RELEASE Ra tio of Fragments From Bombs Compared Causing No. a nd Type of Alt itudeBombs Compared of Attack ·- Casualties Ys" perf. >i" perf. Yz" perf. Six 20-lb frag Low* 1.83 2.38 0.94 .... One 100-lb GP 10,000 ft 3.00 • 0 • • 2.48 .... 20,000 f t 1.67 1.19 . . . . .... 30,000 ft 1.05 0.79 . . . . • • 0. Six 20-lb frag Low * 1.03 0.96 0.52 . . . . One 260-lb frag 10,000 ft 1.41 0.88 . . 0. . ... 20,000 ft 0.68 0 .40 .... . .. .30,000 ft 0 .51 0.35 . . . . . . . . One 100-lb GP LO\\" 0.56 0.40 0.55 .... On e 260-lb frag 10,000 ft 0.47 0 .35 0.49 . . . . 20,000 ft 0.41 0 .33 0.47' . . .. ~0, 000 ft 0.48 0.44 0.61 •I .... Twenty 20-lb frag Low* 1.05 1.07 0.69 . . . . Six 90-lb frag 10,000 ft 1.05 0 .81 . .. . • • • 0 20,000 ft 0.79 0.66 .. . . . ... 30,000 ft 1.08 0.65 . .. . . .. . Twenty 20-lb frag Low* 1.91 2.05 1.12 . . .. One 500-lb GP 10,000 ft 2.88 2.13 . ... . . .. 20,000 ft 1.86 1.38 . . . . • 0 •• 30,000 ft 1.46 0 .99 •• 0 . . . . . ·--- Six 90-lb frag Low* 1.81 1.92 1.45 0.28 One 500-lb GP 10,000 ft 2.74 2.64 1.80 .. . . 20,000 ft 2.34 2.09 1.32 • 0. 0 30,000 ft 1.36 1.51 0.98 . . . . --·----------· Two 100-lb GP Low 0.79 0 .65 0.67 . .. . One 500-lb GP 10,000 ft 0.78 0.66 0.68 .. . . 20,000 ft 0.85 0.71 0.74 ... .30,000 ft 0.93 0 .75 0.78 . . . . Two 260-lb frag Low 1.42 1.61 1.21 0.85 One 500-lb GP 10,000 ft 1.65 1.87 1.39 0 .98 20,000 ft 2.09 2.14 1.58 • 1.13 30.000 ft 1.91 1.70 1.27 0.91 *For low altitude bombing, the effectiveness of fragmentation bombs will he greatly increased if the parafrag(23-lb 1\140 or !20-lb M86) is substituted for the corresponding fin-stabilized-frag. 7-11 BALLISTICS nonparachute bomb which, except for having clusters of six, and when so used will be particufins instead of a parachute, is identical. When larly effective if the required damage is, at most, released from high altitudes, a fragmentation equivalent to perforation of }4-inch mild steel. bomb is reduced in effectiveness. The bombs are When this bomb is used in individual suspension, used in accordance with the type of damage substitution of the 120-pound parafrag may give required, consulting specific fragment damage increased effect from low altitudes. For heavier tables and damage patterns discussed previously. damage the large fragmentation bombs or the A 90-lb fragmentation bomb may be used in 500-pound GP bomb may be used. 7-8 SHELL FRAGMENT DAMAGE The analysis of fragment damage from artillery range, and that the effective damage of the target shells is very similar in principle to the preceding requires fragments which will perforate ~-inch analysis involving bomb fragment damage. As in mild steel, it can be determined from Figure 7-7 the case of bombs, tables of fragment damage that the minimum number of shell for this range and damage patterns, both of which give data on would be required if charge 5 and high angle fragmentation effect, have been prepared for all fire are used. standard high explosive artillery shells. In general it may be stated that ground burstsIn addition, tables of shell density in area fire are recommended in most cases where the tarare available which give the number of shells gets are relatively unshielded. Air bursts arerequired per unit area to accomplish specified recommended against men in foxholes or openeffects under various conditions for both air and trenches and against personnel shielded by roughground bursts. Such a table for the 155-mm terrain. For the 155-mm shell, the optimum Howitzer firing HE shell M107 (ground burst) is shown in Figure 7-7. Assuming that an area height of burst against shielded personnel is target ( 100 ft X 100 ft) is assigned at 10,000 yd:: between 25 and 50 feet. 7-9 CONTROLLED FRAGMENTATION From the discussion thus far, the important (b) The velocity of fragments. characteristics of missiles designed for fragmen( c) The direction of flight of fragments. tation are: It can thus be stated that a controlled fragmentation missile will be one in which the configura (a) The mass distribution (number, size, and tion, direction of flight, and velocity of each shape) of fragments. fragment can be predicted. 7-9.1 DIRECTION OF FLIGHT 7-9.2 VELOCITY The direction of flight of fragments will deThe velocity of fragments is the next point to pend on the shape of the missile. The best shape be considered. From the discussion in Par. 7-4, is one that directs the flight of fragments so as above, it was explained that the initial velocity to give the maximum effective area of fragment of the fragments depends on the charge-mass spray. Unfortunately, the shape of the missile ratio of the missile as well as on the type of ex is not governed by the terminal ballistic considplosive used. The charge-mass ratio of a missile eration alone, and therefore some compromise is inherently governed to some extent by design in the ideal shape of missiles is necessary to meet considerations other than purely terminal bal interior and exterior ballistic requirements. listic requirements, as is the type of explosive 7-12 FRAGMENTATION 4 .0 155H , Wt SO PDF SHELL DENSITY AREA FIRE . SO GROUND BURSTS 3 .5 NO SHIELDING - LOW ANGLC: FIRE ~--HIGH ANGLE FIRE 3 .0 2 .5 DAMAGE TYPE PERF. l t 4 ·1N . MILD STEEL SO'~'• BY NUMBER OF VULNERABLE TARGET 2 .0 ELEMENTS <2 SO . FT. l WIDTH OF FRINGE-29 FT. -~ 2 .50 f-'~--,.-------~-------_;_---t--PERF~~=~;EM~~ESTEEL . SO"'" BY NUMBER OF -~ VULNERABLE TARGET ;;; ~ 2.25• ELEMENTS 12 SO. FT.l WIDTH OF FRINGE-34 FT. .... z :::> "'... IL 2 .0 0... "' 5 0... "' "' 1.75 C. I I -' -'... :I: "' I I I ... 0 "'... 1.50 I I _..,, -'"" , __, --.... ""' CD 2 :::> zb 1.25 DAMAGE TYPE0 .9 CASUALTIES SO'!'o BY NUMBER ·OF ENEMY PERSONNEL WIDTH OF FRINGE-37 FT . 0 .8 0 .7 0 .6 0 .5 I I I I I I I / ,/ .,. ,I ____,..,~' "' 0 . 4 L-----------------------------------------------------------------~ 0 2 4 & 8 w ~ 14 16 18 RANGE IN THOUSANDS OF YARDS RA PO 109322A • Fig. 7-7 Shell density in area fire; superquick ground burst, 155-mm HE shell, M107. 7-13 BALLISTICS • Fig. 7-8 Experimental grooved ring shell body. • I -· • Fig. 7-9 Uniform fragments obtained from grooved ring shell body. 7-14 FRAGMENTATION used. For instance, sensitivity of the container and of the explosive to set back, among other considerations, presents a limitation of the type of explosive used and on the charge-mass ratio. A direct mechanical control of the number, size, and shape of fragments offers the best opportunity for controlling the fragmentation effec tiveness of missiles. As mentioned in Par. 7-6, above, such control has been achieved, to a degree, in standard fragmentation bombs by wrapping a metal helix of square cross section around the charge. More recent methods of governing the mass distribution of fragments , although still in th e experimental stage, offer considerable chance for improved control. They are: (a) Use of notched wire of square cross section. (b) Use of grooved rings of square cross section. The first control method listed above is similar in principle to our standard fragmentation bomb case design. Figure 7-8 is an illustration of the body of an experimental grooved ring shell. The grooves are equally spaced around each ring, being relatively shallow in depth and triangular in cross section. The rings are assembled on the liner and pressed together as tightly as possible. Retainers are fitted sufficiently tight on the liner to hold the rings in place. Figure 7-9 illustrates the relative uniformity of the controlled size of fragments achieved by the grooved ring method. It should be noted that the close uniformity in size and shape of fragments will result in greater uniformity of striking velocities. This, to repeat, is a direct res ult of the more nearly uniform initial velocities and uni form presentation areas offered by the fragments as they fly through the air, which results in more uniform retardation during flight. Size, and therefore mass control, of fragments has been achieved in both notched wire and grooved ring shell by accurate spacing of the notches or grooves. This spacing is based on the assumption, thus far borne out in test firings, that there is an optimum width of fragment for each size and type of shell. Figure 7-10 illustrates the uniform spacing of perforations, achieved with the experimental Fig. 7-10 Uniform spacing of perforations in ~&-inch steel plate obtained by grooved ring shell. shell in Figure 7-8, when it was placed eight feet above a mild steel plate ( 6 ft X 8 ft X 5/ 16 in. ) and detonated statically. Large holes indicate perforations. Figure 7-11, showing nine spark radiographs of the detonation of the grooved ring shell illustrated in Figure 7-8, depicts the progress of controlled fragmentation. Pictures (g) and (i) of Figure 7-11 are side views, while the other pic tures are top views. As a matter of interest it is well to compare these p~ctures with the spark radiographs of uncontrolled fragmentation in Figure 7-l. The comparison suggests that one accomplishment of controlTed fragmentation, at least for the grooved ring type, is a higher degree of uniformity in size, shape, and intensity of fragmentation . If the grooved ring missile were detonated in a position such that the target was in the side spray region, probability of target damage would be higher. A current item of materiel employing the controlled fragmentation device of the rectangular 7-15 BALLISTICS • Fig. 7-11 (a) Fig . 7-J J (b) Fig . 7-JJ (c) Fig. 7-11 (d) Fig. 7-11 (e) • Fig. 7 -11 (f) Fig. 7-J J (g) Fig . 7-11 (h) Fig . 7-JJ (i) Fig . 7-J J Detonation of grooved ring shell .. 7-16 F~AGMENTATJON Fig. 7-12 Hand grenade. grooved wire, easily fabricated, and highly effecing optimum-sized fragments, sub-projectil es, or tive when matched to the weight and brisance of aerodynamic bodies into the target. The student the explosive, is illustrated in Figure 7-12. is alerted to be aware of the need for possible Security classification precludes illustration of solu tions to the problem of fragmentation in his many additional and practical schemes for proappraisal of conventional and developmental amviding controlled fragmentation andj or deliver-munition. REFERENCES No general, unclassified references are available . • 7-17 CHAPTER 8 BLAST EFFECTS BY CHEMICAL AND ATOMIC EXPLOSIONS 8-1 MECHANICS OF BLAST When a conventional explosive charge or nuclear detonation occurs in air, expanding gases, often referred to as a flame front, burst forth and compress the surrounding air, thus initiating a shock wave. The gases themselves have little inertia, cool rapidly, and will have lost most of their velocity at a distance of 40 to 50 times the diameter of the charge. The belt of compressed air in the shock wave has initially a high outward velocity which it loses rapidly at first . The shock wave, except for its .intensity, has all the characteristics of a sound wave, and travels through the surrounding air in the same manner; that is, without the transmitting medium moving along with it. The shock wave is bounded by an extremely sharp front called the shock front which represents a discontinuity in density, pressure, and temperature of the medium through which it passes. Here the pressure rises abruptly from atmospheric to a peak pressure, then declines to atmospheric pressure. This phase is known as the positive or pressure phase of the shock wave. The pressure continues to decline to subatmospheric pressure and then returns to normal. The second phase is called the negative or suction phase. Figure 8-1 shows a typical pressure-time record of a blast wave at a particular distance from point of detonation. The negative phase of a shock wave is caused by the air and gases of detonation moving outward as a strong wind behind the shock front. They are prevented by their own inertia from slowing down quickly enough, as the pressure of the core of the gases subsides . The rarefication thus formed propagates outward, trailing the positive phase. After the positive phase passes, the wind reverses in direction and blows toward the point of detona IIII'ULS£. OR 'OSITIYE IMI'ULSE • AYEUGE PRESSURE X OUR AT I011 o AREA u•DER TRUE EXCESS PRESSURE FOR OURATIO• Of ,OSITIY[ 'HAS£ IOIMAL ~~------~~~~~~ ATII05r11ERIC ~~ DUUTIOII : AIR DISTURBANCES ...___ OF THE - •EGAT lYE PMASE DIJE TO FRAGMENTS : POSITIY£ PHASE I PASSING THE GAGE 1 AT SUPERSONIC I vEL0 c I T y .I I TIME, THOUSAIDS Of A SECO•D I I 0 10 15 25 • TYPICAL PRESSURE-TIME RECORD fOR THE lUST fROM A 80H8 Fig. 8-1 Profile of a blast wave at a particular distance from point of detonation. 8-1 BALLISTLCS ' , • e,_,. flltQIIT• ',, IIIGit. tJI IM-//PIC TUIIt[ Of TH( 01 V(L.OQTY •, MTu.D llllf IHSlAHTAHlOUS ..... woo-eoo n 1 Sl.t \ ,.,.,._,..,, /' SITUATI(IH tllf""'''DlD ,, ......,,01'~ '. ..,....,arwcOt · .-.c.-sr Ql S(C.) UT[IIt IIOtlll fX""-00($ 1114ile* 01 ·,~ ........ AT TH( [ftC) 01 A AOW f1f Tflt[(S • _,.. ICISI -· • • Fig. 8-2 Schematic representation of bomb explosion. tion, gradually decreasing in velocity as the pressure returns to normal. Figure 8-2 shows the effect of this action on an object in the path of the shock wave. An atomic detonation resembles a high explosive detonation in that the explosive effect is the result of the very rapid liberation of a large quantity of energy in a relatively small volume. But atomic detonations differ in three important aspects: first, the amount of energy is thousands of times as great as that produced by even the largest high explosive weapons ; second, the energy released consists of blast, intense heat, light, and penetrating nuclear radiation; and third, under some burst conditions residual radioactivity may be produced which may be significant from a military and civil defense point of view. While the pressure-time relationships as depicted in Figure 8-1 are applicable to atomic detonation, the accompanying thermal effects may often initiate slight pressure rise near the target area immediately prior to the passage of the primary blast wave, and augment damaging effects. This wave, when present, is referred to as the precursor wave. The blast from an explosion in air can be visualized as a sphere bounded by the shock front (probably less than a lOOOth of an inch thick) l>epeath which is a layer of compressed air, the positive phase; and then a thicker layer ·of rarefied air, the negative phase. The core of the sphere is filled with air of normal atmospheric pressure except in the early stages. At first the sphere expands very rapidly, its radius increasing initially as much as 20,000 feet per second in some cases. Then it slows down, until 8-2 BLAST EFFECTS eventually the increase stabilizes at the speed of sound, llOO feet per second at 60°F. As the sphere increases in size, the two layers under the shock front gradually increase in thickness but decrease in pressure difference until they finally degenerate into sound waves. Because of the shape of the charge and the manner in which the explosion is initiated, the blast wave may not spread out from the explosion in a perfectly spherical manner; that is, there is some difference in pressure off the nose, tail, and sides, but for practical purposes, the assumption that the energy spreads out evenly in all directions is justified. 8-2 PEAK OVERPRESSURE The physical characteristics of a shock wave are usually measured by the peak overpressure and impulse of the positive phase at various distances from the point of explosion. The peak pressure is the pressure jump at the shock front, the highest pressure in the shock wave, and it is usually measured in pounds per square inch above atmospheric pressure. The positive phase is usually of very short duration; for example, about 0.0008 seconds at 10 feet from a 100-lb GP bomb, and 0.05 seconds at 400 feet from a 4000-lb LC bomb. The negative phase lasts considerably longer (5 or 6 times the positive phase) but the maximum negative pressure is only a fraction of the maximum positive pressure. • Ballistic data for specific weapons tabulate peak pressures (side-on) and positive impulses. Pressures registered by a pressure gauge placed side-on to the direction of blast are commonly referred to as the hydrostatic or side-on pressures. The pressure that would be registered by a gauge set face-on to the blast would be more than twice the side-on pressure owing to the reflection of the shock wave. At points relatively close to the bomb, where the peak pressures are high, the pressure registered by a face-on gauge woud be considerably more than twice the side-on pressure because of the wind effect, i.e., the actual movement of the air in the direction away from the explosion. Near the explosion where the wind is great, it will be strong enough to hurl even large objects for considerable distances. Where the side-on pressure is only 5 lb per square inch, the face-on will be about twice as large; whereas for a side-on pressure of 100 lb per square inch, the face-on pressure will be five times as large. The peak pressure existing in a shock wave decreases rapidly as the shock wave moves out • ward from the center of explosion. Among the factors contributing to this decrease in pressure are the irreversible heating of air passing through the shock front and thereby extracting energy from it; and the increasing surface area of the shock front which reduces the energy per unit area (expanding sphere). If r represents the d istance from the center of the explosion to the point of peak pressure, the following laws approximate the effect of in creasing distance: (a) Close to the center of explosion where pressure exceeds 10 lb per square inch, peak pressure varies roughly as 1j r2 • (b) Farther from the center of explosion where peak pressure has dropped to the range of 5 to 10 lb per square inch, peak pressure varies as 1j r3 / 2 • (c) At considerable distance from the center of explosion where peak pressure is below 1 lb per square inch, peak pressure varies approximately as 1j r6/ 5 . Figure 8-3 shows a plot of peak blast pressure versus distance from the point of detonation for various sizes of high explosive bombs. Note that different sizes of bombs will produce the same peale pressure at different distances. This may be < ~ompared with the effects of a 20-KT yield air burst atomic weapon where an overpressure of 5 psi or greater extends to a distance of 6000 feet from ground zero. Peak pressure may be related to charge weight ( w) or yield ( Y) of an explosion, as a measure of the amount of energy released. The effects of two different weights or yields of explosive charge may be related as follows: For chemical reactions, the peak pressures will be equal at distances that are in the ratio of the cube root of the weights; i.e., if the pressure from a charge of w 1 lb is P1 lb per square inch at distance r 1 feet, then for a weight of w2 lb the 8-3 BALI:-ISTICS 1000 --- ---- -·· f-. -u. _. _a: .L -f--1--·--.. • -·-_-:Bl:l IBS \--- --·---· -·-···-· ---·-- PE lK BL~ST 'VS t--·- DIS: ANCE PROI BCil BUB ST ,...... 100 (T~1,4:!AD;I!l ) -· --- f--- . ~ -. -··-. \ ,. ·--· ·----·-1---f- ~ . \ 0' • \ -· ~ I -1\ \ \ E-4 1\ 10 ~ ~ -f--"' ~ I'... ~ ~ • . ............ t------1----t-- 1 DISTANCE PRC&l POINT OF DETONATION (!!=_) 100 1b G.P. 0 10 '10 50 100 AN~30 250 lb G.P. 0 50 100 150 AN~57 500 1b G.P. AN-M43 or 0 so 100 150 200 ~64 1000 1b G.P. AN-MJJ. or 0 so 100 150 200 2SO AN~65 2000 lb G.P. AN-M34 or 0 so 100 1SO 200 250 3SO AJI-K66 J I • I t I I I I I l I I 1 ! I '' 4000 1b L.c. o 50 100 150 200 2so 300 3SO 400 4SO soo AH4156 t I I 0 I l t I I , I I I I I I I 1 I I ' _ I t I I l I I , I I I ' ' • I I ' ! I I , ' , I ' I I I I I I I , ' I Fig. 8-3 Peak blast pressure versus distance from bomb burst. 8-4 • BLAST EFFECTS TABLE B-1 RELATIVE BLAST EFFECTIVENESS OF VARIOUS EXPLOSIVES, TNT 100* Peak Pressure Effectiveness Against Load-Bearing Wall Construction Explosive (at Equal Distances) Radius Area Torpex (RDX/ TNT/ AL: 42/ 40 / 18) 122.5 125 156 HBX (RDX/ TNT/ AL/ Wax: 40/ 38/ 17/ 5) 117.5 120 144 Minol (NH4KOa/ TNT/ AL: 40/ 40/ 20) 115 117.5 138 Tritonal (TNT / AL: 80/ 20) 112.5 117.5 138 DBX (NH4NOa/ RDX/ TNT/ AL: 21 / 21 / 40/ 18) 112.5 112.5 127 RDX Comp B (RDX/ TNT: 60/ 40) 110 110 121 Ednatol (Halite/ TKT: 57/ 43) 105 105 Ill TNT 100 100 100 Picratol (Expl. D/T~T: 52/ 48) 100 100 100 Amatex (I\H4~0a/RDX/TKT: 43/ 9/ 48) 100 97.5 95 Amato! (NH1NOa/ TI\T: 50/ 50) 95 87.5 77 • Extracted from TM 9-1907, dated July 1948. pressure will be P1 lb per square inch at a distance r:! feet where The data in Figure 8-3 refer to TNT fillings. r1 (:~Y1 3 r2 = The relative blas t effectiveness of other exploFor nuclear reactions sives is indicated in Table 8-1. 8-3 THE EFFECT OF MACH REFLECTION ON AIR BURSTS While consideration must be given to underthe incident wave, to form a third wave which has ground, underwater, and surface bursts as well, a vertical front at ground level. The third wave it is of major importance in the discussion of is called a Mach wave and the point where the overpressure to recognize th at when a bomb is three waves intersect, the triple point. The Mach detonated at some distance above the ground, wave grows in height as it spreads laterally, and the shock wave spreads out almost spherically the triple point rises, describing a curve through until it strikes the ground. It is reflected by the the air. The point of origin and path of the triple ground surface as shown in Figure 8-4. At a point depend on the size of the explosive charge • certain distance along the ground from the point and its height above the ground. At the triple immediately below the bomb, the reflected wave point, where the incident wave is reinforced by combines with the original shock wave, called the reflected wave, both the peak pressure and 8-5 BALLISTICS MACH REFLECTION impulse are a maximum, and considerably higher than that exerted by the original shock wave at the same distance from the point of explosion. As the Mach wave grows in height it absorbs the incident and reflected waves. Ultimately, at distances very large compared to lhe height of burst, the whole configuration of shocks becomes approximately a single spherical shock wave in tersecting the ground perpendicularly. Utilizing this phenomenon of Mach reflection makes it possible to increase considerably the radius of effectiveness of a bomb. By detonating a weapon at the proper height above the ground the maximum radius at which a given pressure or impulse is exerted can be increased in some 8-4 As indicated in Figure 8-1, a physical characteristic of a shock wave that is of basic importance, is the impulse of the positive phase. As a measure of both the intensity of the pressure and its duration, it is equal to the area under the pressure-time curve of the positive phase. It is • cases by almost 50% over that for the same bomb • detonated at ground level. The area of effectiveness is thereby increased by as much as 100% under some conditions. Ballistic data are used to determine the height of burst necessary to maximize the horizontal distance at which a given impulse can be obtained. The optimum height for an air burst, and the amount by which its effectiveness will be increased depend on the size of bomb, and the strength and height of the target structure. The use of air burst on some types of targets, such as city areas, also tends to increase the area of effectiveness of a blast bomb by reducing the shielding effect that buildings and other structures have on one another. IMPULSE approximately equal to one-half the peak pressure multiplied by the duration of the positive phase and is measured in units of pound-milliseconds per square inch. The impulse of an explosion will be equal at distances that vary as the two thirds power of the ratio of the weights • Fig. 8-4 Formation of Mach wave and triple point. 8-6 BLAST EFFECTS :50 00 20C 500 1000 DISTANCE FROM BURST (FEET) Fig. 8-5 Blast impulse versus distance from bomb burst. or yields ( Y); i.e., if the impulse from u,>1 lb is 11 lb-sec per square inch at r 1 feet, then the impulse from a charge of w 2 lbs will be equal to I~ at a distance r2 such that Provided minimum values of impulse required to destroy a specific type of structure are known, the radii to which these values are satisfied as a function of explosive charge weight or yield can be determined from the above relationships. A sample tabulation of blast impulse for bombs is shown in Figure 8-5. 8-7 BAlLISTICS TABLE 8-2 OVERPRESSURE, DYNAMIC PRESSURE, AND WIND VELOCITY IN AIR AT SEA LEVEL Peak Overpressure I Peak Dynamic Pressure Maximum Wind Velocity (pounds per square inch) (pounds per square inch) (miles per hour) 72 80 1,170 50 40 940 30 16 670 20 8 470 10 2 290 5 0.7 160 2 0.1 70 8-5 DYNAMIC PRESSURE Although the destructive effects of the blast wave have usually been related to values of the peak overpressure, there is another quantity of equivalent importance called the dynamic pressure ( q = ~pu2 ). For a great variety of building types, the degree of blast damage depends largely on the drag force associated with the strong (transient) winds accompanying the passage of the blast wave. The drag force is influenced by certain characteristics (primarily the shape and size) of the structure, and is generally dependent upon impulse. The dynamic pressure is a function of the wind velocity and the density of the air behind the shock front. Both of these quantities are related to the overpressure under ideal conditions at the shock front (see Par. 8-8) . For very strong shocks, the dynamic pressure is larger than the overpressure, but below 69 pounds per square inch overpressure at sea level, the dynamic pressure is smaller. Like the peak shock overpressure, the peak dynamic pressure decreases with increasing distance from the explosion center, although at a greater rate. Some indication of the corresponding values of peak overpressure, peak dynamic pressure, and maximum blast wind velocities in air at sea level is given in Table 8-2. At a given location, the dynamic pressure changes with time in a manner somewhat similar to the change in the overpressure, but the 8-8 1 • ., ... ::J .,"' VI ... 0.. , .-Dynamic Pressure Ambient Arrival Time Fig. 8-6 Variation of overpressure and dynamic pressure with time at a fixed location. rate of pressure decrease behind the shock front is different. This may be seen from Figure 8-6 which indicates qualitatively how the two pressures vary in the course of the first second or so following arrival of the shock front. Actually, the wind velocity (and the dynamic pressure) will drop to zero at a somewhat later time, due largely to the inertia of the moving air, but for purposes of estimating damage the difference is not significant. • BLAST EFFECTS 8-6 AIR BLAST LOADING The behavior of an object or structure exposed to the blast wave from a nuclear explosion may be considered under two main headings. The first is called the loading, i.e., the forces which result from the action of the blast pressure. The second is the response, or distortion of the structure due to the particular loading. As a general rule, response may be taken to be synonymous with damage since permanent distortion of a sufficient amount will impair the usefulness of a structure. Damage may also arise from a movable object striking the ground or another object which is more or less fixed. For example, tumbling vehicles are damaged primarily as they strike the ground. Further, glass, wood splinters, bricks, pieces of masonrv, and other objects loosened by the blast wave and hurled through the air form destructive missiles. Indirect damage of these types is, of course, greatly dependent upon circumstances. Direct damage to structures due to air blast can take various forms. For example, the blast may deflect structural steel frames, collapse roofs, dish-in walls, sha tter panels, and break windows. In general, the damage results from some type of displacement (or distortion) and the manner in which such displacement can arise as the res'ult of a nuclear explosion will be examined below. For an air burst, th e direction of propagation of the incident blast wave will be perpendicular t<:> the ground at ground zero. In the regular reflection region, the forces exerted upon structures will also have a considerable vertical component (prior to passage of the reflected wave). Consequently, instead of the loading being largely lateral (or sideways) in nature, as it is in th e Mach region, there will also be an appreciable downward force initially, which tends to cause crushing toward the ground, e.g., dishedin roofs, in addition to distortion due to translational motion. 8-7 DIFFRACTION LOADING When the front of an air pressure wave strikes the face of a building, reflection occurs. As a result, the overpressure builds up rapidly to at least twice (and generally several times ) that of the incident shock front. The actual pressure attained is determined b y various factors such as the strength of th e incident shock and the angle between the direction of motion of the shock wave and the face of the building. As the shock front moves forward , the overpressure on the face drops rapidly toward that produced by the blast wave without reflection. At the same time, the air pressure wave bends or diffracts around the structure so that the structure is eventually engulfed by the blast, and approximately the same pressure is exerted on all the walls and the roof. The developments described above are illustrated in a simplified form in Figure 8-7. This shows, in plan, a building which is being struck by an air blast (Mach) wave moving in a horizontal direction. In Figure 8-7 the shock front is seen approaching the structure with the direction of motion perpendicular to the face of the building exposed to the blast. In Figure 8-7b the wave has just reached its front face, producing a high overpressure. In Figure 8-7c the blast wave has proceeded about half way along the building, and in Figure 8-7d it bas reached the back. The pressure on the front face has dropped to some extent and it is building up on the sides as the blast wave diffracts around th e structure. Finally, when as in Figure 8-7e the shock fron t has passed, approximately equal air pressures are exerted on all the walls (and roof) of th e structure. If the structure is oriented at an angle to th e blast wave, the pressure would immediately be exerted on two faces, instead of one, but the general behavior would be the same as just described (Figures 8-7£, g, h, and i ). The damage caused during the diffraction stage will be determined by the magnitude of the loading and by its duration. The loading is related 8-9 BALLISTICS to the peak overpressure in the blast wave and this is consequently an important factor. If the • structure under consideration has no openings, as has been tacitly assumed so far, the duration of the loading will be very roughly the time re t~G¢G:Vt quired for the shock front to move from the front to the back of the building. The size of the structure will thus affect the diffraction load ing. For a structure 75 feet long, the diffraction loading will operate for a period of the order of one-tenth of a second. For thin structures, e.g., ~~px9!telegraph or utility poles and smokestacks, thediffraction period is so short that the correspondFig. 8-7 Stages in the diffraction of a blast waveing loading is negligible. by a structure. 8-8 DRAG (DYNAMIC PRESSURE} LOADING During the whole period that the positive tween nuclear and high explosive detonations.phase of th e air pressure wave is passing (and For the same p eak overpressure in the blastfor a short time thereafter) a stmcture will be wave, a nuclear bomb \·viii prove to be more desubjected to the dynamic pressure loading, or stmctive than a conventional bomb, especiallydrag loading, caused by the strong t ransient for buildings which res pond to drag loading.winds behind the shock front. Like the diffracThis is because the blast wave is of much shortertion loading the drag loading, especially in the duration for a high explosive bomb, e.g., a fewMach region, is equivalent to a lateral (or transthousandths of a second. Because of the in • lational) force acting upon the structure or obcreased ltmgth of the positive phase of the blastject exposed to the blast. wave from weapons of high energy yield , suchIt is the effect of drag loading on structures weapons cause more destruction than might bewhich constitutes an important difference be ex pected from the peak overpressures alone. 8-9 TECHNICAL ASPECTS OF BLAST WAVE PHENOMENA The characteristics of the blast wave have been the overpressure, the dynamic pressure, and thediscussed in a qualitative manner in the earlier density of the air behind the ideal shock front.parts of this chapter. The remaining sections will The blast wave properties in the region of regbe devoted to a consideration of some of the ular reflection are somewhat complex andquantitative aspects of blast phenomena in air. depend on the angle of incidence of the waveThe basic relationships among the properties of with the ground and the shock strength . For aa blast wave, having a sharp front at which there contact surface burst, when there is but a single is a sudden pressure discontinuity, are derivedfrom the Rankine-Hugoniot conditions based on hemispherical (fused ) wave, and in the Mach the conservation of mass, energy, and momentum region below the triple point path for an air at the shock front. These conditions, together burst, the various blast wave characteristics atwith the equation of state for air, permit the the shock front are uniquely related. It is forderivation of the required relations involving the these conditions, in which ther e is a single shockshock velocity, the particle (or wind) velocity, front, that the following results are applicable. 8-10 • BLAST EFFECTS 1, 000 10, 000 100 700 7,000 70 400 4,000 40 200 2,000 20 ~ ...... tOO l' 000 10 (f) ...... p.. p.. 700 (f) 70 7 Q) Q) ;:l Vl '"' ;:l Vl 4 Q)Vl '"' 40 400 Vl ill p..'"' p..'"' u -o ill 20 200 2 E - u ., c Q) > ::::: Cl ill 100 a:; 10 1.0 70 7 0. 7 4 0.4 2 0.2 40 20 I 0 0 . 1 l. 4 7 10 20 40 70 100 Peak Overpressure (PSI) Fig. 8-8 Relation of blast wave characteristics at the shock front. The shock velocity U, and the particle velocity the air behind the shock front is related to the (or peak wind velocity behind the shock front) ambient density, p0 , by u, are expressed by p 7 + 6p / P o U = ao (1 + 6p / 7 P 0)I!2 Po 7 + pl P o The peak dynamic pressure q, is defined as and 5 p2 q =-. 2 7Po + p The variations of shock velocity, particle (or where p is the peak overpressure (behind the peak wind) velocity, and dynamic pressure with • shock front) , P0 is the ambient pressure (ahead the peak overpressure at sea level, as derived of the shock), and a0 is the ambient sound vefrom the foregoing equations, are shown graphi locity (ahead of the shock). The density, p, of cally in Figure 8-8. 8-11 BALLISTICS When the blast wave strikes a surface, such as It can be seen from this expression that the value • ~ that of a structure, at normal incidence, i.e. , head on, the instantaneous value of the reflected overpressure, Pr, is given by r = (7Po+ 4p) p 2 P 7Po+ p 8-10 ALTITUDE The foregoing equations apply to a strictly homogeneous atmosphere, that is, where am.bient pressure and temperature at the burst point and target are the same for all cases. If the ambient conditions are markedly different for a specified explosion , as compared with those in the reference explosion, then correction factors must be applied. The general relationships which take into account the possibility that the absolute temperature, T, and ambient pressure, P, are not the same as T0 and P0, respectively, in a reference ( 1-kiloton) explosion, are as follows. For the overpressure, 8-11 BLAST EFFECTS FROM NUCLEAR WEAPONS Because the most severe blast effects on personnel, equipmen t, and structures come as a re 8-11.1 PERSONNEL Personnel can be injured by blast in two ways. Primary blast injuries resulting from the direct action of the blast overpressures on the human body, and secondary injuries resulting from Hying debris. It requires approximately 100 psi overpressure to cause significant primary injury. Overpressures of this magnitude are not experienced even at ground zero from an air burst weapon and at very short distances from ground zero from surface burst weapons. Therefore, primary blast injuries are not significant from the point of view of personnel casualties. Secondary blast injuries are caused principally by collap sing buildings and debris or equipment Hung about by the blast, or by the persons being picked up and hurled against stationary objects or the of Pr approaches 8p for large values of the incident overpressure (strong shocks) and tends toward 2p for small overpressures (weak shocks) (see Figure 8-8) . CORRECTIONS where the p's refer to the respective overpressures at a given distance. The corrected values of distance for a specified pressure are then given by d = do (W) l/3 (~0)'1 3 and for arrival time or positive phase duration at the appropriate scaled distance by 13 12 t = toWll l (~0)' (~0)' suit of atomic detonations, such effects will be illustrated for atomic weapons. ground by the high winds accompanying the detonation. For instance, a 5 psi overpressure is accompanied by wind gusts up to 160 mph peak velocity. Secondary blast injuries are similar in effect to those due to mechanical accidents or blas t from high explosive detonations. 8-11.2 MILITARY EQUIPMENT All types of equipment can be damaged by blast if the peak overpressures are high enough. Wheeled vehicle damage consists of frame distortion, and wheel, body, and engine damage. The rupture of fuel tanks may cause fire to occur. Overturning contributes to the damage. Armored vehicles are very resistant to blast damage. However, even these vehicles may b e damaged in the areas of very high peak manner 8-12 BlAST EFFECTS TABLE 8-3 BLAST EFFECTS RADII IN YARDS FROM GROUND ZERO Weapon Type Built-up Areas and Command Military Tanks and Yield Burst Personnel Therein Posts Vehicles Artillery 2 KT *High Air 800 1400 negligible negligible **Low Air 600 1100 500 200 20 KT High Air 1800 3000 negligible negl~ible Low Air 1300 2300 1100 4 0 100 KT High Air 3000 5100 negligible negligible Low Air 2300 3800 1900 750 .100KT High Air 5200 8800 negligible negligible Low Air 3900 6700 3300 1300 5MT Low Air 8300 14,000 7200 2800 Surface 8300 14,000 7200 2800 •High Air Burst. This height of burst in this table is based on 2000 feet for the 20-KT weapon. Normally height of burst is scaled as the cube root of th(' ratio of yields. ' • •Low Air Burst. This height of burst in this table is based on one and one-half times the fireball radius for the 20-KT weapon or 675 feet. For other yi('ld s it has been assumed that fireball volume is directly proportional to yield . as are tanks (Table 8-3) . Lighter weapons and the surface or under the ground is the formation field equipment, since they are more easily blown of a crater; however, the particular result of nu about, are damaged at greater distances from a clear explosions should be examined in somewhat , burst than is artillery. Aircraft in flight may be closer detail. The mechanical energy of the ex seriously damaged if engulfed by a blast wave. panding fireball throws earth upward and out The gust loads resulting from the wind as well ward. The heavier particles of earth and rock as the overall squeezing effect my cause intoler fall back into and in the vicinity of the crater. able structural damage. This results in high radioactive contamination 8-11.3 STRUCTURES in the crater area. Some of the energy of the expanding fireball is dissipated into the earth Buildings and structures react to blast in a itself as a shock wave in the ground. The effects manner determined by their type of construc tion, design, strength, size, and the peak overof the gJ:ound shock wave are similar to a mild pressures to which they are subjected. The drag earthquake but are more localized. Destruction characteristics of the target will be a function of of underground structures is complete in the resulting damage. Collapse of structures, parcrater itself, and militarily significant damage ticularly light masonry and brick, produces the caused by ground shock may extend beyond the greatest number of incapacitating (secondary) crater for considerable distance. How far, deinjuries to personnel in and around these strucpends on soil characteristics, type of structure, tures. and yield of the weapon. Table 8-4 shows crater dimensions for the various nuclear weapons 8-11.4 CRATERING capable of being burst on or under the surface A characteristic of all explosives detonated on of land targets. 8-13 BALLISTICS TABLE 8-4 CRATER DATA • Crater Dimensions Radius of Type I Weapons of in Average Soil I Ground Shock (Yield) in Average Soil Burst Radius (yd) Depth (ft) (yd) 20-KT surface 140 210 280 20-KT underground 170 -150 400 1-MT surfar.~ 515 765 1450 5-MT surface 880 1305 2500 REFERENCES 1 Oldenberg, Introduction to Atomic Physics, 2 Effects of Atomic Weapons, Department of the McGraw-Hill Book Co., N.Y., Chapter 19. Army Pamphlet 39-3, May 1957. • • 8-14 CHAPTER 9 THERMAL AND NUCLEAR EFFECTS OF ATOMIC DETONATIONS 9-1 INTRODUCTION When an atomic weapon detonates in the air, a large sphere of hot, luminous gases is formed. This is called the fireball. The size of the fireball depends on the yield. The fireball from a nominal 20-KT weapon is about 300 yards across at maximum size and is about 30 times as brilliant as the sun at noon. Initially, the fireball contains all the energy of the detonation. Because of the very high temperature of the fireball, it radiates its heat (and light) out into the target area. The heat and light are referred to as thermal radiation; its emission from the fireball occurs in the first few seconds of detonation. For one test shot in Nevada the flash of light was observed 400 miles away. The detonation process releases large amounts of nuclear radiation in the form of gamma radiation, alpha particles, beta particles, and neutrons. This nuclear radiation is emitted or radiated from the fireball in the first moments of the detonation. Most of it appears in the target area in the first two seconds after detonation; after one minute no significant nuclear radiation is received in the target area. The fireball continues to give off nuclear radiation, principally gamma radiation, 45,000 Feet 5000 Feet Approx. scale WIND (SIDE VIEW) J for some time, but after one minute the fireball has risen so high that the gamma radiation does not reach the g;·ound. The nuclear radiation which emanates from the fireball in the first minute or so after the detonation is called instantaneous nuclear radiation. As the hot fireball expands rapidly in the first moments of detonation, it pushes a large volume of air outward. This outward push generates a blast wave in the air which continues to travel in the air with a velocity approximately equal to the speed of sound. The initial rapid rate of rise of the fireball causes air to be drawn inward and upward. Dust and dirt from the target surface are also drawn up to form the stem of the atomic cloud (see Figure 9-1). Approximately half of the energy of the detonation appears as blast; one-third as thermal radiation; and the rest as nuclear radiation. The characteristics of these principal weapon effects will be discussed in subsequent sections. Shortly after detonation the fireball rises and cools. Its rate of rise is quite rapid and it reaches a high altitude in a few minutes. The cooling and condensing of the fireball results in the mushroom head of the familiar atomic cloud. VERY SMALL PARTICLES Fig. 9-1 Air burst of atomic bomb (20-KT). 9-1 BALLISTICS 9-2 UNDERGROUND BURST When an atomic weapon is detonated below the earth's surface, the expansion of the fireball imparts to the surrounding earth a force upward and outward. A large volume of the earth is thrown out, leaving a crater. Some of the earth falls back into and around the crater. The fireball vents up through the ground; however, by the time it comes up through the surface, the fireball has given up most of its mechanical shock energy to the ground in the formation of a crater. Therefore, air blast resulting from an under• ground burst is very much less than from an air burst. Except for a relatively weak flash that appears when the fireball vents the surface, almost all the heat and light (thermal radiation ) is released into the ground in an underground burst. Hence, above ground, thermal effects may be small or negligible. The nuclear radiation products released by the detonation process are entrapped or absorbed • by the ground. The soil which absorbs the nuclear radiation is thrown upward and outward. When it falls back to the ground it contaminates the area with residual radioactivity. From an underground burst, then, there is in the target area no significant thermal radiation, greatly reduced blast effects, cratering, and no instantaneous nuclear radiation. When the earth in the vicinity of an underground burst is thrown upward, it produces a column of characteristic appearance. The heavier particles in the column fall back to earth and produce a concentric cloud of dust which expands outward from the burst point. This cloud is called the base surge. The finer dust particles of the column remain suspended in the air as a cloud for some time before eventually falling to earth. The atomic cloud from an underground burst does not rise as high as the cloud from an air burst; moreover, it is colored by the fine particles of soil entrapped in it. • • 9-3 SURFACE BURST The characteristics of a land surface burst are, in general, intermediate between those of an air burst and an underground burst. Consider first a contact surface b urst on land. Since the fireball, in a surface burst, forms above the ground, its rapid expansion generates a blast wave. However, some of the mechanical energy of the expanding fireball is transmitted to the earth under the fireball so that air blast from a surface burst differs from air blast from an air burst. Since the weapon detonates close to the earth, the air blast is very strong near the burst point but the blast pressures fall off more rapidly with increasing distances from burst point. Some cratering, however, will be accomplished. A 20-KT yield bomb detonated on the surface would produce a crater about 75 feet deep and 100 yards in diameter. The thermal characteristics of a surface burst are essentially the same as for an air burst, i.e., just about as much heat and light are radiated in each case for weapons of the same yield. The area of effectiveness of thermal radiation in a target area is less from a surface burst than from an air burst. This is due to the fact that thermal radiation from a surface burst weapon arrives in the target at very acute angles of incidence and minor terrain irregularities, buildings, and even equipment provide effective shielding. The instantaneous nuclear radiation emanating from the fireball of a surface burst weapon is essentially the same as from an air burst weapon of the same yield. However, since the fireball expands against the earth's surface, a considerable portion of the earth under the detonation is vaporized and irradiated. This vaporized irradiated earth is drawn up by the rising fireball. The combination of vaporization of a portion of the earth's surface and the scooping effect of the expanding fireball produces a crater, similar to but smaller in size than the crater from an underground burst. The heavier particles of rock and soil thrown out by a surface burst will fall back around the burst area. Since the soil has been irradiated it will contribute to residual radioactivity in the area. The vaporized earth drawn up into the fireball will condense when the fireball cools; fall to earth downwind, producing residual radioactivity in the area of fallout. 9-2 THERMAL AND NUCLEAR EFFECTS 9-4 BURSTS IN OR OVER WATER When an atomic weapon is burst in the air over water, the blast, thermal radiation, and instantaneous nuclear radiation are essentially the same as for an air burst over land. When an atomic weapon is detonated under the surface of a body of water, the column thrown upward consists of water, or if the underwater burst occurs in shallow water, earth from the bottom. The column of water falling back onto the surface produces a base surge of mist and spray. Some of the energy of the fireball as it expands under water is transmitted to the water and is propagated outward as water shock and water waves on the surface. There is no appreciable thermal or instantaneous nuclear radiation from an underwater burst, and air blast is less than from an air burst. The water, thrown upward in the column, is irradiated and entraps fission fragments. When this water falls back to the surface, it contaminates the area with residual radioactivity (fallout). The base surge contributes to the residual radioactive contamination. If the fallout and base surge occur over large volumes of water, the residual radioactive contamination is soon diluted and dissipated. If the underwater burst occurs in a harbor or near enough to shore, the fallout may occur over land which would cause more concentrated contami nation and would remain for longer periods. When an atomic weapon detonates at or near the surface of water, the thermal instantaneous nuclear radiation and blast effects will be essentially those of a land surface burst. However, some of the mechanical energy of the expanding fireball will generate water waves and underwater shock. No crater will form unless the water is shallow. A large volume of water will be vaporized and drawn up into the cloud. When this condenses, it will be deposited as fallout. 9-5 CHARACTERISTICS Most of the flash of light and heat from an atomic detonation is emitted in the first second of the detonation although some continues to be emitted as long as the ball of fire is visible. As has been mentioned, approximately one-third of the energy liberated in an atomic detonation is in the form of heat energy. In many cases the intense flash of light will be the first warning of an atomic detonation in the area but the thermal radiation will have already been emitted. The thermal radiation, like light, travels in straight lines and is stopped by any object or material which can cast a shadow . It has little penetrating power. Thus, even light-weight clothing may offer protection from such radiation. As the thermal radiation travels outward from the fireball, it decreases in intensity. This re- OF THERMAL RADIATION duction in intensity is due to absorption of the radiation by particles of dust, smoke, and haze in the air. The burning that might result from an atomic detonation, then, will be less when the air is hazy than if it is clear. A smoke screen, therefore, may be an effective shield in lessening the effects of thermal radiation from an atomic weapon. Personnel who are facing in the general direction of an atomic detonation may experience a temporary blindness, called flash blindness. Essentially normal vision returns in a half hour or less. At night, even personnel facing away from an atomic detonation (eyes open and uncovered) may experience flash blindness but it will not persist as long as in personnel facing the detonation. 9-6 MECHANISM OF THERMAL RADIATION Immediately after the ball of fire is formed, phenomena associated with the absorption of the it emits thermal radiation. Because of the very thermal radiation by the air in front of the ball high temperatures, this consists of ultraviolet of fire, the surface temperature undergoes a (short wave length) as well as visible and incurious change. The temperature of the interior frared (long wave length) rays. Due to certain falls steadily, but the surface temperature of the 9-3 BALLISTICS ball of fire decreases more rapidly for a small fraction of a second. Then, the apparent surface temperature increases again for a somewhat longer time, after which it falls continuously. In other words, there are effectively two surfacetemperature pulses; the first is of very short duration, whereas the second lasts for a much longer time. The behavior is quite general, although the duration times of the pulses increase with the energy yield of the explosion. Corresponding to the two temperature pulses, there are two pulses of emission of thermal radiation from the ball of fire (Figure 9-2). In the first pulse, which lasts about a tenth part of a second for a one-megaton explosion, the temperatures are mostly very high. As a result, much of the radiation emitted in this pulse is in the ultraviolet region. Moderately large closes of ultraviolet radiation can produce painful blisters, and even small closes can cause reddening of the skin. However, in most circumstances, the first pulse of thermal radiation is not a significant hazard with regard to skin burns for several reasons. In the first place, only about one percent of the thermal radiation appears in the initial pulse because of its short duration. Second, the ultraviolet rays are readily attenuated by the intervening air, so that the close delivered at a distance from the explosion may be comparatively small. Further, it appears that the ultraviolet radiation from the first pulse could cause significant effects on the human skin only within ranges at which other radiation effects are much more serious. The situation_with regard to the second pul-se is, however, quite different. This pulse may last for several seconds and carries about 99 percent of the total thermal radiation energy from the bomb. Since the temperatures are lower than in the first pulse, most of the rays reaching the earth consist of visible and infrared (invisible) light. It is this radiation which is the main cause of skin burns of various degrees suffered by exposed individuals up to 12 miles or more from the explosion of a one-megaton bomb. For bombs of higher energy, the effective damage range is greater. TIME AFTER EXPLOSION "' z 0 i=! :s Q <"' 10.0 ..:I~ ~~ '1.0 "'< 200 z -irtl 0 ...... U) 100 0 IfII 70 . .....:l p.. X l!fJ w . 40 !J7 20 f-1// v 10 7 Jr; 1 4 IIJ I IvI 2. ' •I 1 III I ' 0.1 0.2 0.4 0.7 1.0 2 4 7 10 20 40 70 100 SLANT RANGE FROM EXPLOSION (MILES) Fig . 9-3 Distances at which burns occur on bare skin. the whole of the second pulse, from the minimum so that when the separation is great enough, no through the maximum and down to the second damage will be smtained. The part of the minimum, is significant. thermal pulse which can be most easily de Due to the decrease in thermal energy received creased to significance occurs toward the end, per unit area at increasing distances from the when the intensity of the ball of fire has become fireball , more distant objects will receive less relatively low. Hence, at some distance from energy than those closer in. As objects are the explosion, the tail end of the thermal pulse located farther and farther away from the exmay be ineffective in causing damage, although plosion, the thermal energy received from all the high-intensity part, especially that around portions of the pulse is proportionately reduced, the temperature maximum , is still capable of 9-7 BALLISTICS inflicting injury. Closer to the fireball, the tail of the pulse will also be dangerous and the high intensity region will be even more so. At all distances from the explosion, the most dangerous part of the thermal pulse is that which occurs around the time of the second temperature maximum of the fireball. It is here that the thermal radiation intensity of the ball of fire is greatest. Consequently, the rate at which energy is delivered to objects at any distance from the explosion is also greatest. In other words, from a given explosion, more thermal energy will be received in a certain period of time around the temperature maximum than at any other equal period during the thermal pulse. These facts are important in relation to the efficacy of evasive action that might be taken by individuals to reduce injuries due to thermal radiation. From what has been stated above, it is apparent that it is desirable to take such action before the temperature maximum in the second thermal pulse is reached. In the case of an explosion in the kiloton range, it would be necessary to take shelter within a small fraction of a second if an appreciable decrease in thermal injury is to be realized. The time appears to be too short for evasive action to be possible. On the other hand, for explosions in the megaton range, shelter taken within a second or two of the appearance of the ball of fire could reduce the severity of injury due to thermal radiation in many cases, and may even prevent injury in others. Although personnel can sustain flash burns at relatively great distances from an atomic detonation, a number of factors tend to minimize the effectiveness of thermal radiation as a predictable mechanism for the production of casualties in 9-1 1 CHARACTERISTICS OF NUCLEAR RADIATION The explosion of a nuclear bomb is associated are immediately absorbed (or captured) by with the emission of various nuclear radiations. various nuclei present in the bomb, and this These consist of neutrons, gamma rays, and capture process is usually also accompanied by alpha and beta p articles. Essentially, all the the instantaneous emission of gamma rays. The neutrons and part of the gamma rays are emitted remainder of the gamma rays and the beta in the actual fission process: These radiations are particles are liberated over a period of time as produced simultaneously with the nuclear exthe fission products undergo radioactive decay. p losion. Some of the neutrons liberated in fission The alpha particles are expelled, in an analogo us a tactical unit. Clothing, particularly combat uniforms, provides considerable protection from • thermal radiation except on exposed face and hands. From a 20-KT weapon, for example, personnel will not be burned through military clothing beyond 1,500 yards from ground zero. In contrast, third degree burns on exposed skin can be sustained out to 2200 yards, second degree burns out to 3000 yards. Any shadow-producing object or terrain featu re will provide protection from thermal radiation (though not necessarily from blast or nuclear radiation). An individual in a foxhole or trench, behind a tree, rock, or terrain irregularity, or even prone in a shallow fold in the ground will not be burned if the shielding object is between him and the fireball (see Table 9-2). TABLE 9-2 TH ERMAL EFFECTS RAD II IN YARDS FROM G ROUND ZERO I N WHI CH PERSONNEL CAN SUSTAIN INCAPACI TATI NG BURNS Weapon Type Troops in Troops in Yield Burst Foxholes Open 2 KT High Air 300 1000 Low Air 400 1000 • 20 KT High Air 600 2200 Low Air 850 2200 100 KT High Air 1100 4000 Low Air 1400 4100 500 KT High Air 1800 6900 Low Air 2100 7000 5MT Low Air 4100 14,800 Surface 4200 14,200 • 9-8 THERMAL AND NUCLEAR EFFECTS manner, as a result of the decay of the uranium (or plutonium) which has escaped fission in the bomb. The initial nuclear radiation is generally defined as that emitted from both the ball of fire and the atomic cloud within the first minute after the explosion. It includes neutrons and gamma rays given off almost instantaneously, as well as gamma rays emitted by th e radioactive fission products in the rising cloud. It should be noted that although alpha and beta particles are present in the initial radiation, they have not been considered. This is because they are so easily absorbed that they will not reach more than a few yards at most, from the atomic cloud. The somewhat arbitrary time period of one minute for the duration of initial nuclear radiation was originally based upon the following considerations: As a consequence of attenuation by the air, the effective range of the fission gamma rays and of those from the fission products from a 20-kiloton explosion is very roughly two miles. In other words, gamma rays originating from such a source at an altitude of over two miles can be ignored, as far as their effect at the earth's surface is concerned. Thus, when the atomic cloud has reached a height of two miles, the effects of the initial nuclear radiations are no longer significant. Since it takes roughly a minute for the cloud to rise this distance, the initial nuclear radiation was defined as that emitted in the first minute after the explosion. The foregoing arguments are based on the characteristics of a 20-kiloton nuclear bomb. For a bomb of higher energy, the maximum distance over which the gamma rays are effective will be larger than that given above. However, at the same time, there is an increase in the rate at which the cloud rises. Similarly, for a bomb of lower energy, the effective distance is less, but so also is the rate of ascent of the cloud. The period over which the initial nuclear radiation extends may consequently be taken to be approximately the same, namely one minute, irrespective of the energy release of the bomb. Neutrons are the only significant nuclear radiations produced directly in thermonuclear reactions. Alpha particles (helium nuclei) are also formed, but they do not travel very far from the explosion. Some of the neutrons will escape but others will be captured by the various nuclei present in the exploding bomb. Those neutrons absorbed by fissionable species may lead to the liberation of more neutrons as well as to the emission of gamma rays, just as described above for an ordinary fission bomh. In addition, the capture of neutrons in nonfission reactions is usually accompanied by gamma rays. It is seen, therefore, that the initial radiations from a bomb in which both fission and fusion (thermonuclear) processes occur consist essentially of neutrons and gamma rays. The relative proportions of these two radiations may be somewhat different than for a bomb in which all the energy release is due to fission ; but for present purposes the difference may be disregarded. Although the energy of the initial gamma rays and neutrons is only about three percent of the total explosion energy, compared with some 33 percent appearing as thermal radia tion, the nuclear radiations can cause a considerabl e proportion of the bomb casualties. 9-12 INITIAL GAMMA RADIATION The gamma rays produced in fission, and as a result of other neutron reactions and nuclear excitation of the bomb materials, all appear within a second (or less) after the nuclear explosion. For this reason, the radiatio:1s from these sources are known as the prompt or instantaneous gamma rays. • The fission fragments and many of their decay products are radioactive isotopes which emit gamma radiations. The half lives of these radioactive species range from a millionth of a second (or less) to many years. Nevertheless, since the decay of the fission fragments commences at the 9-9 instant of fission, and since, in fact, their rate of decay is greatest at the beginning, there will be an appreciable liberation of gamma radiation from these radioisotopes during the first minute after the explosion. In other words, the gamma rays emitted by the fission products make a significant contribution to the initial nuclear radiation. However, since th e radioactive decay process is a continuing (or gradual ) one, spread over a period of time which is long compared to that in which the instantaneous radiation is produced, the resulting gamma radiations are referred to as the delayed gamma rays. BALLISTICS The instantaneous gamma rays and the portion hand, are mostly--emitted at a later stage in theof the delayed gamma rays which are included explosion, after the bomb materials have vapor • in the initial radiation, are nearly equal in ized and expanded to form a tenuous gas. Theseamount, but they are by no means equal fractions radiations thus suffer little or no absorption beof the initial nuclear radiation transmitted from fore emerging into the air. The net result is thatthe exploding bomb. The instantaneous gamma the delayed gamma rays, together with thoserays are produced almost entirely before the produced by the radiative capture of neutronsbomb has completely blown apart. They are, by the nitrogen in the atmosphere, contributetherefore, strongly absorbed by the dense bomb about a hundred times as much as do the prompt materials, and only a small proportion actually gamma rays to the total radiation received at aemerges. The delayed gamma rays, on the other distance from an air (or surface) burst. 9-13 SOURCES OF NEUTRONS AND IONIZATION CHARACTERISTICS Although neutrons are nuclear particles of finally emerge. They have fairly high speeds, butappreciable mass, whereas gamma rays are the actual (average) distance the neutrons travelelectromagnetic waves analogous to X-rays, their is relatively large, and so some time elapse before harmful effects on the body are similar in characthey reach the outside of the ball of fire. Howter. Like gamma rays, only very large doses of ever, the delay in the escape of the promptneutrons may possibly be detected by the h u man neutrons is no more than about i hundredth partsenses. Neutrons can penetrate a considerable of a second.distance through the air and constitute a hazard Neutrons, being electrically neutral particles,.that is greater than might be expected from the do not produce ionization or excitation directlysmall fraction (about 0.025 percent) of the in their passage through matter. They can, howexplosion energy which they carry. ever, cause ionization to occur indirectly as aEssentially, all the neutrons accompanying a result of their interaction with certain lightnuclear explosion are released either in the fi ssion nuclei. When a fast neutron collides with theor fusion process. All of the neutrons from the nucleus of a hydrogen atom, for example, thelatter source and over 99 percent of the fi ssion neutron may transfer a large part of its energy • neutrons are produced almost immediately, probto that nucleus. As a result, the hydrogen nucleusably within less than a millionth of a second of is freed from its associated electron and movesthe initiation of the explosion. These are referred off as a high-energy proton. Such a proton isto as the prompt neutrons. capable of producing a considerable number ofIn addition, somewhat less than· one percent of ion pairs in its passage through a gas. Thus, thethe fission neutrons, called the delayed neutrons, interaction of a fast neutron with hydrogen (orare emitted subsequently. Since the majority of with any substance containing hydrogen) canthese delayed neutrons are emitted within the cause ionization to occur indirectly. By a similarfirst minute, however, they constitute part of the mechanism, indirect ionization, although to ainitial nuclear radiation. Some neutrons are also small er extent, results from collisions of fastproduced by the action of the gamma rays of neutrons with other light nuclei, e.g., carbon,high energy on the nuclear bomb materials. oxygen, and nitrogen. (The ionization resultingBut these make a very minor contribution and so from the interaction of fast neutrons with hydrocan be ignored. gen and nitrogen in tissue is the main cause ofAlthough the prompt fission neutrons are all biological injury by neutrons.)actually released within less than a millionth of Neutrons in the slow and moderate speeda second of the explosion, as noted above, they ranges can produce ionization indirectly in otherare somewhat delayed in escaping from the enways. When such neutrons are·captured by thevironment of the exploding bomb. This delay lighter isotope of boron (boron-10), two electriarises from the numerous scattering collisions cally charged particles, a helium nucleus (alphasuffered by the neutrons with the nuclei present particle) and a lithium nucleus of high energyin the bomb residues. As a result, the neutrons are formed. Both of these particles can producetraverse a complex zigzag path before they ion pairs. Indirect ionization by neutrons can 9-10 • THERMAL ANb NUCLEAR EFFECTS also result from fission of plutonium or uranium isotopes. The fission fragments are electrically 9-14 NUCLEAR Nuclear radiation produces ionization in substances exposed to it. With th e exception of photographic film, most inanimate materials are unaffected by the ionization produced by nuclear radiation. Living tissue, however, may be destroyed by it. The damage done to an individual by nuclear radiation is dependent on the amount of radia tion received ( the dose ) and the time during which the dose is received. Doses of radiation received from immediate nuclear radiation are called acute doses. D oses received over a period of 12 hours have the same biological effect as doses received all at once and are also acute doses. Doses of radiation received over periods of time longer than 12 hours are called chronic doses. The effects of chronic radiation doses are somewhat different from acute doses. Acute radiation doses are the more important from a tactica l point of view. Radiation doses are expressed in terms of a unit ca lled the roentgen. To give an idea of its value, the average dental X-ray delivers five roentgens to the patient's jaw, but only five thous andths of a roentgen of stray radiation to more remote parts of the body. Bodi ly damage resulting from radiation depends in part on the volume of the body exposed. However, from atomic weapons , the characteristics of the radiation are such that very often the whole body receives the radiation. Doses of interest are, therefore, described as acute whole body doses. Individuals receiving high acute whole body doses of radiation develop initial symp toms of radiation sickness shortly after exposure. The time of appearance of these initial symptoms varies with the dose ; the higher the dose, the sooner the symptoms appear. Initial radiation sickness symptoms are nausea and vomiting which, if the dose is high enough, may be severe enough to make an individual noneffective. The initial symptoms of radiation sickness may disappear after a few hours, depending on the dose received , and there is an apparent recovery. After a period of from a few days to two weeks, called the latent period, radiation sickness symptoms reappear with increasing severity. This second period varies from a few weeks to several months. charged particles (nuclei) of high energy which leave considerable ionization in their paths . RADIATION EFFECTS Dea th may occur during this period. Table 9-3 shows the effects of various acute whole body doses. TABLE 9-3 EFFECTS OF ACUTE WHOLE BODY DOSES Acute EffectsDose 5000 r 5000 r produce immediate and persistent noneffectiveness until death . 1000 r Initial sickness appears in 1 hour or less. :\o survivors are expected. 650 r Initial sic kness appears in all personnel within 4 hours and lasts for about 1 day . Death ensues in about 2 weeks in about 95% of the cases. Survivors a re noneffective for (j months. 450 r Initial sickness appears in all personnel during first day. About 50% deaths can be expected but this may be red uced by adequate medical treatment. Survivors are noneffectiYe for 6 months. 300 r Initial sickness during first day in all personnel. Abo ut 25% deat hs may be anticipated but this may be reduced by adequate medical treat ment . Survivors are noneffective for 3 months . 200 r Ini tial sickness during first day in about 50% of personne l. Second period of sickness appears after about 3 weeks and lasts for 1 or 2 weeks. Ko deaths anticipated unless recove ry is complicated by poor health , other injury, or infection . 100 r Initial sickness in about 2% of personnel. All are able to perform duty. 9-11 BALLISTICS 9-15 RESIDUAL RADIATION Residual nuclear radiation , as distinguished from instantaneous, is defined as that which is emitted later than one minute after detonation. Residual radiation is predominantly gamma. Alpha . and beta particles may also be emitted but their importance is negligible if even the simplest precautions are taken against residual gamma radiation. The atomic cloud is highly radioactive and may be a hazard to aircraft crews until it is dispersed. The most significant residual radiation from the point of view of tactical use of atomic weapons is that which persists in the target area. Fission products constitute a very complex mixture of some 200 different forms (isotopes) of 35 elements. Most of these isotopes are radioactive, decaying by the emission of beta particles, and frequently accompanied by gamma radiation. About 1% ounces (0.11 pound) of fission products are formed for each kiloton (or 110 pounds per megaton ) of fission energy yield. The total radioactivity of the fission products initially is extremely large, but it falls off at a fairly rapid rate as the result of decay. At one minute after a nuclear explosion, when the residual nuclear radiation has been postulated as beginning, the radioactivity from the H ounces of fission products, from a one-kiloton explosion, is comparable with that of a hundred thousand tons of radium. It is seen, therefore, that for explosions in the megaton energy range the amount of radioactivity produced is enormous. Even though there is a decrease from the one-minute value by a factor of over 6000 by the end of a day, the radiation intensity may still be large. 9-16 NEUTRON The neutrons liberated in the fission process, but which are not involved in the propagation of the fission chain, are ultimately captured by the bomb materials through which they must pass before they can escape; nitrogen (especially) and oxygen in the atmosphere, and various elements present in the earth's surface. As a result of capturing neutrons many substances become radioactive. They, consequently, emit beta particles, frequently accompanied by gamma radiation, over an extended period of time following the explosion. Such neutron-induced activity, therefore, is part of the residual nuclear radiation. The activity induced in the bomb materials is highly variable, since it is greatly dependent upon the design or structural characteristics of the weapon. Any radioactive isotopes produced by neutron capture in the bomb residues will remain associated with the fission products. When neutrons are captured by oxygen and nitrogen nuclei present in the atmosphere, the resulting activity is of little 0r no significance as far as the residual radiation is concerned. Oxygen, for example, interacts to a slight extent with fast neutrons, but the product, an isotope of nitrogen, has a half life of only seven seconds. It will thus undergo almost complete decay INDUCED ACTIVITY within a minute or two. The radioactive product of neutron capture by nitrogen is carbon-14; this emits beta particles of relatively low energy but no gamma rays. Nuclear explosions cannot add appreciably to the fairly large amount of this isotope already present in nature, and so the radiations from carbon-14 are a negligible hazard. An important contribution to the residual nuclear radiation can arise from the activity induced by neutron capture in certain elements in the soil. The one which probably deserves most attention is sodium. Although this is present only to a small extent in average soils, the amount of radioactive sodium-24 formed by neutron capture can be appreciable. This isotope has a half life of 14.8 hours and emits both beta particles, and, more important, gamma rays of relatively high energy. In each act of decay of sodium-24, there are produced two gamma ray photons, with energies of 1.4 and 2.8 Mev, respectively. The mean energy per photon from fission products is 0.7 Mev, although gamma rays of higher energy are emitted in the early stages. Another source of induced activity is manganese which, being an element essential for plant growth, is found in most soils even though in small proportions. As a result of neutron capture, • 9-12 THERMAL AND NUCLEAR EFFECTS the radioisotope manganese-56, with a half life of 2.6 hours, is formed. Upon decay, it gives off several gamma rays of high energy in addition to beta particles. Because its half life is less than that of sodium-24, the manganese-56 loses its activity rapidly. But, within the first few hours after an explosion, the manganese may constitute a serious hazard, greater than that of sodium. A major constituent of soil is silicon, and neutron capture by silicon leads to the formation of radioactive silicon-31. This isotope, with a half life of 2.6 hours, gives off beta particles, but gamma rays are emitted in not more than about 0.07 percent of the disintegrations. It will be seen later that only in certain circumstances do beta particles themselves constitute a serious radiation hazard. Aluminum, another common constituent of soil, can form the radioisotope aluminum-28, with a half life of only 2.3 minutes. Although isotopes such as this, with short half lives, contribute greatly to the high initial activity, very little remains within an hour after the nuclear explosion. When neutrons are captured by the hydrogen nuclei in water, the product is the nonradioactive (stable) isotope, deuterium, so that there is no resulting activity. As seen above, the activity induced in oxygen can be ignored because of the very short half life of the product. However, substances dissolved in the water, especially salt 9-17 The tremendous heat resulting from the detonation of a nuclear device in the atmosphere produces a lighter-than-air bubble of intensely hot gases which serves not only to carry aloft the debris resulting from the fissions and the disintegration of the bomb casing and auxiliary equipment, but also to suck up great amounts of soil and dust, much of which is rendered radioactive. As the gases rise, they cool by radiation , by adiabatic expansion, and by entrainment of the surrounding air. The resulting atomic cloud apparently consists of an ascending toroidal ring with debris, dirt, and water droplets circulating about this ring, upward in the center and downward at the outer edges. For relatively low air bursts, the surface material, as a result of the (sodium chloride) in sea water, can be sources of considerable induced activity. The sodium produces sodium-24, as already mentioned, and the chlorine yields chlorine-38 which emits both beta particles and high-energy gamma rays. However, the half life of chlorine-38 is only 37 minutes, so that within 4 to 5 hours its activity will have decayed to about one percent of its initial value. Apart from the interaction of neutrons with elements present in soil and water, the neutrons from a nuclear explosion may be captured by other nuclei, such as those contained in structural and other materials. Among the metals, the chief sources of induced radioactivity are probably zinc, copper, and manganese, the latter being a constituent of many steels and, to a lesser extent, iron. Wood and clothing are unlikely to develop appreciable activity as a result of neutron capture, but glass could become radioactive because of the large proportions of sodium and silicon. Foodstuffs can acquire induced activity, mainly as a result of neutron capture by sodium. However, at such distances from a nuclear explosion and under such conditions that this activity would be significant, the food would probably not be fit for consumption for other reasons, i.e., blast and fire damage. Some elements, i.e., boron, absorb neutrons without becoming radioactive, and their presence will tend to decrease the induced activity. FALLOUT effects of thermal radiation and blast, rises as a column of dust pulled up by the central updraft. The ascending mass of air and debris continues to rise until it has cooled to equilibrium with its environment and lost its upward velocity, usually within six to eight minutes. Typically, just after the ascending motion has ceased, the cloud of radioactive debris consists of a long, slender stem, capped by a broader mushroom top. Often, especially in the case of low air bursts, the stem and top are not joined (Figure 9-1). Although considerable debris is contained in the stem, the subsequent history of the debris depends on many factors, including the size distribution and fall velocity of the particles; the nature of the wind field; the eddy diffusivity; and 9-13 BALLISTICS H+1 H+Z H+3 Ht4 H+S H+6 H+7 H+S 10 Or/hr TIME (hours) fallout begins 0 1 0 zo 30 40 50 60 70 80 90 100 110 1ZO 130 Miles downwind Fig. 9-4 Fallout from a high yield surface burst weapon. Note: Based on J5 knot scaling wind dose rates normalized to one hour after detonation. the scavenging of particles by precipitation. The problem of fallout of radioactive particles resulting from atomic explosions divides itself into two major categories: (1) fallout in the vicinity of the burst site (close-in fallout); and (2) distant fallout, that which occurs beyond about 200 miles. The term fallout refers to the deposition on or near the surface of the earth, of radioactive particles resulting from the detonation of a nuclear device. It includes deposition due to the direct gravitational fall, deposition resulting from vertical currents and eddies in the atmosphere, and to particles scavenged from the atmosphere and deposited by falling precipitation. The latter phenomenon is referred to as rainout. The movement of the atomic cloud is governed by the wind field. At any given level the trajectory of the primary cloud, (i.e., that portion of the initial cloud which moves approximately horizontally with the winds and is unaffected by diffusion or fallout) may be partially predicted by conventional meteorological techniques. The determination of the movement of all the debris is a much more complex problem. It is, of course, apparent that all of the particles will eventually fall; the larger particles will reach the ground soon after the burst while the smallest may remain airborne almost indefinitely. Knowledge of the size distribution and fall velocity of the particles is so incomplete that only qualitative estimates are available. Horizontal and vertical wind shears coupled with fallout and diffusion can result in a very rapid spreading of the cloud 9-14 in many instances. In other cases, where mixing is inhibited by stable stratification or little wind shear exists, relatively concentrated patches of debris can be carried for long distances in the upper troposphere. The size and shape of the area contaminated by fallout is governed by the yield of the weapon, the height to which the cloud ascends, and the strength and direction of the winds at various altitudes. Figure 9-4 shows the fallout pattern that can be expected to result from a high yield weapon detonated on the surface. • Fallout intensities decay rapidly for the first few hours; after six hours the rate of decay is much slower. Table 9-4 shows, for various times after detonation, the fraction of the dose rate at one hour to which fallout decays. TABLE 9-4 DECAY FACTORS FOR FALLOUT Time After Fraction of Detonation Dose Rate at in Hours 1 Hour 1 1.00 1.5 0.62 2 0.44 4 0.19 6 0.11 8 0.08 10 0.06 12 0.05 • THERMAL AND NUCLEAR EFFECTS 9-18 LONG-TERM RESIDUAL RADIATION HAZARD Of the fission products which present a potential long-term hazard from either the testing of nuclear weapons in peacetime or their use in warfare, the most important are probably the radioactive isotopes cesium-137 and strontium 90. Since both of these isotopes are fairly abundant among the fission products and have relatively long half lives, they will constitute a large percentage of any world-wide fallout. Of course, the activity level due to these isotopes at late times in the local fallout pattern from a surface or subsurface burst will be considerably larger than in the world-wide fallout from a given nuclear burst. Cesium has a radioactive half life of 30 years and is of particular interest in fallout that is more than a year old because it is the principal constituent whose radioactive decay is accompanied by the emission of gamma rays. The gamma rays are actually emitted, within a very short time, by a high-energy state of the decay product, barium-137. The chemical properties of cesium resemble those of potassium. The compounds of these elements are generally more soluble than the corresponding compounds of strontium and calcium; and the details of the transfer of these two pairs of elements from the soil to the human body are quite different. Cesium is a relatively rare element in nature and the body normally contains only small traces. Consequently, the biochemistry of cesium has not been studied as extensively as that of some of the more common elements. It has been determined, however, that cesium-137 distributes itself within living cells in the same way as potassium, so that it is found mostly in muscle. Based on one experiment with several human subjects, the current estimate of the time required for normal biological processes to reduce the amount of cesium in the body by one-half, i.e., the biological half life, is 140 days. Because of the penetrating properties of the gamma rays from the decay of cesium-137, the radiation is distributed more or less uniformly to all parts of the body. Although the radioactive decay of cesium-137 is accompanied by gamma ray emission, the relatively short time of stay, together with most of the cesium being in a less sensitive location in the body, indicates that for the same amount of stratospheric fallout, the residual cesium-137 will be less of a general pathological hazard than the residual strontium-90. Attention will now be given to what is probably the more serious long-term radiation hazard. Because of its relatively long radioactive half life of 28 years, and its appreciable yield in the fission process, strontium-90 accounts for a considerable fraction of the total activity of fission products which are several years old. Thus, even such material as has been stored in the stratosphere for several years will be found to contain a large percentage of this radioactive species. Strontium is chemically similar to calcium, an element essential to both plant and animal life; a grown human being, for example, contains over two pounds of calcium, mainly in bone. As a consequence of the chemical similarity, strontium entering the body follows a path similar to calcium and therefore is found almost entirely in the skeleton, from which it is eliminated very slowly. Thus, the half life of strontium in human bone is estimated to be about ten years. The probability of serious pathological change in the body of a particular individual, due to the effects of internal radioactive material, depends upon the intensity and energy of the radioactivity and upon the length of time the source remains in the body. Although strontium-90 emits only beta particles (no gamma rays), a sufficient amount of this isotope can produce damage because once it gets into the skeleton it will stay there for a long time. As a result of animal experimentation, it is believed that the pathological · effects which may result from damaging quantities of strontium-90 are anemia, bone necrosis, and certain types of cancer, possibly leukemia. It is the combination of physical and chemical properties of strontium-90, namely, its long radioactive half life and its similarity to calcium, together with the nature of the pathological changes which can result from concentrations of radioactive material in the skeleton, that make strontium-90 the most important isotope (so far as is known) as a possible cause of harmful long-term effects of 9-15 BALLISTICS fallout. Genetic effects due to strontium-90 are relatively insignificant. In the first place, owing to their very short range in the body, the beta particles from this isotope in the skeleton do not penetrate to the reproductive organs. Further, the intensity of the secondary radiation (bremsstrahlung) produced by the beta particles is' low. • Finally, the amount of strontium-90 in soft tissue, from which the beta particles might reach the reproductive organs, is small and may be neglected in this regard. • • REFERENCES 1 Otto Oldenberg, Introduction to Atomic Phys2 Effects of Atomic Weapons, Department of the ics, McGraw-Hill Book Co. , N. Y., Chap. 19. Army Pamphlet 39-3, May 1957. 9-16 CHAPTER 10 BALLISTIC ATTACK OF ARMOR USING KINETIC AND CHEMICAL 10-1 A specialized field of terminal ballistics and one in which new developments are of critical importance concerns consideration of the means available to accomplish defeat of protected targets, primarily armor and concrete. These two defensive devices, along with the bunkertype field fortifications that were so effective in battles throughout the Pacific regions in World War II and the Korean War, frequently require special techniques for attack. Included in the types of weapons suitable for attacking such targets are napalm or fire bombs which are a tremendously effective psychological weapon 10·2 TYPES OF Armor is generally thought of as being steel, and almost all armor in use is steel. However, research indicates the possibility of aluminum, titanium, and other light metals being used for armor, particularly where weight savings would 1 0-2.1 ROLLED HOMOGENEOUS STEEL ARMOR For a number of years the most common type of armor used in the construction of combat vehicles has been rolled alloy steel produced and heat-treated so as to give it, as ·nearly as possible, the same chemical and physical characteristics throughout its structure. Chemically it consists of steel with the following alloying elements added: 0.50-1.25% chromium; 0.5-1.5% nickel; 0.3-0.£)1; molybdenum; 0.8-1.6% manganese; and 0.30% carbon. It is usually used as plate, furnishing yonveniently flat walls on which to base the design of the inside of the vehicle, although it can be bent to a limited extent to form curved surfaces. It is more easily produced in large quantities than either face-hardened or cast ENERGY EFFECTS GENERAL and one which threatens personnel with fire and suffocation. These weapons however, are not of the highly specialized variety as are kinetic or chemical energy type rounds. Successful attack of any target is dependent upon the characteristics of the target itself, hence this phase of terminal ballistics is divided into two parts : Chapter 10 for the study of the defeat of armor; and Annex B to Part 2, th e defeat of concrete. Both the offensive and defensive aspects of both types of material will be considered because both may be in the hands of the attacker and the defender in future combat. ARMOR MATERIALS offset the increased cost of these materials over steel. In addition, certain nonmetals show promise as armor materials, particularly in the role of body armor. The three major applications of steel as armor include: homogeneous steel and can be welded into a vehicle structure with little difficulty. It has high toughness and ductility and affords the best protection against the shock of impact of relatively large caliber projectiles as well as the blasts of high explosive missiles. The bow armor of the armored infantry vehicle (Figure 10-1) is an example of rolled homogeneous armor. 10-2.2 CAST HOMOGENEOUS STEEL ARMOR Chemically, cast homogeneous armor is virtually the same as· rolled homogeneous armor. It is given its shape by casting in a mold and receives its optimum ballistic properties by subsequent heat treatment. The advantage of cast armor is that it can be molded into almost any shape, 10-1 ~u· s HATCH 0 ~ o:J )> ,.... ,.... VI -4 () VI • - Fig.10-1 Armored infantry vehicle, right side view. • BALLISTIC ATTACK OF ARMOR CAL. .50 HB BROWNING! MACHINE GUN M2 -~===oi;U~ • RAPO 168781 Fig. 10-2 90-mm gun tank, M48. furnishing curved surfaces of any desired thickness. The high convexity possible with cast ~ armor is illustrated in Figure 10-2. The oval shaped turret and elliptically shaped hull of this vehicle are both single, homogeneous steel armor castings. On the other hand, since the effect of heat treatment depends upon the thickness of the cast section, it is more difficult from a manufacturing viewpoint to obtain the proper ballistic properties in castings since they have great variations in thickness. Also, castings cannot be hotworked (a process which refines grain s~ructures and eliminates casting cavities); therefore they are not as tough and shock-resistant as rolled armor. In general, rolled armor is about 15% better in resistance to shock and penetration than cast armor. However, this advantage is offset to some extent by the varying angles of obliquity and irregular shapes possible in castings. These variations in shape considerably decrease the penetrating ability of certain types of projectiles. • In vehicle design it may be practical and desirable to use a combination of homogeneous plate and castings which can be joined by welding into the finished form. The M48 tank has a floor of rolled flat plate welded to a cast hull. 10-3 10-2.3 FACE-HARDENED STEEL ARMOR Face-hardened armor is characterized by an extremely hard outer face with a relatively soft, tough back. It is usually manufactured from rolled homogeneous plate by a surface carburizing process. The advantage of using face-hardened armor lies in its ability to shatter projectiles striking its hard surface, thereby greatly reducing their ability to penetrate. Face-hardened armor has very limited shock resistance due to its brittleness resulting from high hardness. It is more difficult to manufacture than homogeneous armor, since carburizing necessitates heating in a furnace for a considerable period of time. It is also difficult to weld because of its high surface carbon content, very often cracking in welding or afterwards from residual stresses set up within the plate. Because of these difficulties, facehardened plate is rather expensive and cannot be manufactured or fabricated in tonnages com parable to homogeneous plate. Its principal application is for protection of personnel against small arms fire and its use as gun shields on mobile guns and on armored personnel carriers (Figure 10-1). BALLISTICS • 10-2.4 NONFERROUS ARMOR MATERIALS During and since World War II, considerable research has been devoted to investigating the armor application o{ light metals, principally titanium, aluminum, and magnesium alloys, and also of certain nonmetals such as nylon, fiberglass, and silicate aggregates in mastic binders. The interest centered upon the relative protection that would be given against various types of ballistic attack compared with that provided by an equal weight of steel. These investigations proved definitely, that for weights of material permissible in body armor, steel is inferior to combinations of aluminum and nylon for protection against small caliber bullets and high explosive shell fragments. The alloys of certain light metals show future promise for use as aircraft armor where the importance of weight saved would offset the disadvantages of substituting a more expensive, strategically critical material in place of steel. For protection against shaped charges and against shock from high explosive projectiles and mines, where bulk and thickness are more important than the strength of the material, plastics, glass, and ordinary silicate rock in a mastic binder offers greater protection than an equal weight of steel. None of these nonferrous armor materials has yet come into general usage; however, their future is assured by the improved protection which is provided, on an . equal weight basis, against certain types of attack. The search for lighter armor materials is continuous, because weight is one of the most important factors in the use of armor. 10-3 SURFACE DESIGN In addition to providing the maximum advantage of obliquity, the apportionment of protection in accordance with the expected severity and directions of attack, and the uniformity of protection from any one direction of attack, the optimum design in an armor structure will also provide for an overall convex surface. This requires avoiding re-entrant angles and irregularities such as joints between sections, sudden changes in thickness, sudden changes in obliquity, installed components, and attachments welded to either the inside or outside surface of the armor. A flat or a convex surface tends to reject impacts at obliquities and is by far preferable to a concave surface containing a re-entrant angle (Figure 10-3) which tends to catch attacking projectiles, thereby increasing the dangers of ricochet and bullet splash. The latter condition often causes an attacking projecile to be turned against a surface which provides less protection and which in most cases would not be exposed to attack. Moreover, re-entrant angles often cause a thinner wall section not exposed to direct attack to suffer penetration when attacked by the blast • of a high explosive projecile. Surface irregularities, either inside or outside the vehicle, tend to create weaknesses in the armor and therefore should b e avoided. A flat, smooth wall of constant thickness offers the best resistance to severe attack, principally because the shock of impact can be uniformly absorbed over the entire area. Any irregularity, whether it be a reinforcing brace, a protective bead, a sudden change in thickness, a sudden change in obliquity, or a welded joint, tends to restrict uniform deformation and may set up, near the irregularity, stress concentration of sufficient magnitude to cause failure. • 10-4 FABRICATION OF MOBILE ARMOR STRUCTURES Almost all fabrication of structures of homotank when the armor is struck on the outside) · geneous armor (and therefore, the greatest perconstitute a hazard to the crew and to equipment centage of all armor fabrication) is accomplished within the tank, and since welded joints in homoby arc welding. Since flying boltheads, nuts, and geneous armor can be made ballistically stronger rivetheads (detached from the inside wall of the than either bolted or ·riveted joints, whenever 10-4 BALLISTIC ATTACK OF ARMOR TURRET WITH REENTRANT ANGLES TURRET WITHOUT REENTRANT ANGLES Fig . 10-3 Reentrant angle effect. practicable, bolts and rivets have been abandoned in favor of arc welding, which produces a joint far superior in ballistic strength to any other method of welding. In the fabrication of structures employing face-hardened armor, the heat developed during the arc welding operation affects the hardened face of the armor, causing it to become more brittle in the region adjacent to the weld and thus making it less resistant to both penetration and shock in the vicinity of the joint. For this reason other methods of fabrication which afford greater ballistic strength may be preferable, despite their disadvantages. Methods in general use are: arc welding, bolting, riveting. It is of interest to note that an attempt has been made to increase the ballistic strength of a welded face-hardened armor joint by masking the edges of the plate during the face-hardening process so that the finished plates have edges of homogeneous armor. This practice, however, may result in considerably lowering the resistance to penetration of the masked area as compared to that of the basic face-hardened armor. The principal requirement of an armor joint, insofar as its ballistic properties are concerned, is its resistance to shock. In order to prevent general rupturing of the armor structure when the vehicle is struck by an attacking projectile, the joints between the armor plates and/ or casting should be of such design, and of such ballistic strength, that they will withstand as severe a shock test as the basic armor without permitting the plates and/ or castings to separate. The welding procedure to be used for any particular joint should be selected on the basis of its inherent ability to provide the maximum resistance to both shock and penetration in all areas affected by the welding. 10-5 INNOVATIONS • All during its history, armor has been unable ing weapons. In almost every period marked by to keep pace with improvements in armor attack-military progress, new developments in arms and 10-5 BALLISTICS ammunition have created additional difficulties even before satisfactory solutions to old and existing armor problems had been found. Because this situation is particularly true today, the 10-5.1 SPACED ARMOR Apart from the development of new materials, further consideration of the question suggests that a solution to the problem may result either through the use of spaced armor or through some new development in composite armor. While experience indicates that the latter approach offers little or no chance of success, there is always a possibility that the discovery of new materials and methods may change the picture sufficiently to permit a solution. During World War II the Germans used spaced armor to a limited extent. Whether or not it can be advantageously used in the future depends upon further investigation and development. Spaced armor consists of two or more plates located at relatively great distances from each other. In order to defeat armor piercing projectiles, the initial plate must either break up the attacking projectile or turn it sufficiently from its trajectory to prevent penetration. In order to defeat hollow charge projectiles, the initial plate must be able to withstand the attendant forces so that the energy released will be adequately dissipated before a secondary plate can be attacked. Altern :~.te protective concepts include the use of externally mounted spikes to spoil stand off distance of incoming rounds; detonation of small shaped changes against the jet of the attacking rounds; resilient screens; and coatings of violently oxidizing material to cause disposal of the jet. Any investigations which may be conducted must include such factors as silhouette, method of support, weight, jettisoning, and mobility. 10-5.2 LAMINATED ARMOR Laminated armor of layer-upon-layer of steel question arises as to what changes in armor might be made in an effort to defeat, or at least reduce, the destructive effect of modern projectiles. is basically inferior to a single piece of armor of the same overall thickness. This phenomenon has been verified by repeated test firings with little hope existing for increased ballistic performance of armor through the use of laminated plate. 10-5.3 COMPOSITE A·RMOR Since World War II considerable experimentation has been conducted to establish data pertinent to the terminal effects of various kinetic energy, H.E., A.T., and H.E.P. rounds on armor in use or in the development stage. One should consider the possible future utilization of nonferrous metals and steel plate by the intimate bonding of two or more of them into a composite form providing the maximum possible protection against all types of rounds, with the composite armor affording better protection per unit of weight than steel. This opens the door for • composite armor of aluminum or magnesium alloys affording as much protection as steel for shock and penetration of kinetic energy rounds; silicate aggregates in mastic binders affording protection from H .E. and A.T. rounds; and resilient materials for shock action. Combinations of materials in a composite form obviously will require great strides in fabrication techniques as well as increased performance over that pr~sently possible. However, with continued technological advancements, the future may well see the fabrication of composite armor as a partial answer at least in the search for maximum protection against the multiplicity of rounds currently available. • 10-6 NECESSARY BALLISTIC PROPERTIES OF ARMOR The necessary ballistic properties which are tration, resistance to shock, and resistance to required of armor consist of resistance to pene-spalling. 10-6 BALLISTIC ATTACK OF ARMOR 10-6.1 RESISTANCE TO PENETRATION 10-6.3 RESISTANCE TO SPALLING Resistance to penetration is that property Resistance to spalling is that property which which prevents a projectile from passing partially tends to resist cracking, flaking, or breaking away of the armor plate, particularly on the inner or entirely through armor plate. When penetration occurs, either a cylindrical plug is driven surface opposite the point of impact. In general, from the back of the plate or the metal is pushed where spalling occurs, the diameter of the openaside, some of it flowing towards the exposed ing on the rear sudace of the plate is considerably face where it forms a lip, and the remainder greater than the caliber of the projectile which being pushed towards the unexposed sudace caused penetration. In substance, resistance to (back) forming a convex protrusion which may spalling is a measure of the soundness of the be expelled in one piece or as scattered fragsteel and the quality of its heat treatment ments (Figure 10-4). (Figure 10-6). The three physical properties in armor which10-6.2 RESISTANCE TO SHOCK have the greatest influence on its ballistic Resistance to shock is that property which properties are: permits armor to absorb, without cracking or (a) Hardness: the ability of the armor to resist rupturing, the energy expended against it by indentation.either an attacking projectile of relatively large (b) Toughness: the ability of the armor to caliber, or the explosion of a high explosive proabsorb energy before fracturing.jectile. Because of the very high velocities at (c) Soundness: the absence of local flaws, which projectiles strike and at which high order cavities, or weaknesses in the armor. Unsound explosions take place, this energy must be ab ness is not so often found in rolled armor as in sorbed in an extremely short period of time. Low cast armor, because of the mechanical working temperature decreases the shock resistance of which has been done during the hot-rolling armor by making it more brittle and thus less able to absorb the shock (Figure 10-5). process. 10-7 EFFECTS OF OBLIQUITY AND HARDNESS ON PERFORMANCE OF ARMOR The ballistic properties of armor depend upon projectile is said to be undermatching in relationseveral factors: the type and thickness of the ship·to armor thickness; if T/ D is equal to 1, the armor; the ratio of the thickness of the armor to projectile is said to be matching; and if T/ D is the caliber of the projectile (T/ D ratio); the type less than 1, the projectile is overmatching. When of projectile; the striking velocity; the obliquity T/ D ratio is varied, there is considerable differof impact; and the hardness of the armor. ence in the displacement of metal as the projectile The ratio between the armor thickness (T) and pushes through the plate. The performance of the diameter of the projectile (D) is expressed as different caliber projectiles is roughly compathe T j D ratio. If T j D is greater than 1, the rable when the T/ D ratio remains constant. 10-7.1 EFFECT OF OBLIQUITY UPON curves begin to rise more and more rapidly. The RESISTANCE TO PENETRATION sharp rise is attributable to the failure (fracture or shatter) of the projectile thereby increasingWhen the obliquity of impact against a given resistance to penetration. The location of the thickness of armor is increased, resistance to beginning of the rapid rise and the steepness of penetration is also increased. Basically, little or the curve at any particular obliquity depend upon no change in resistance to penetration occurs as several factors already mentioned: the T/ D ratio, the obliquity begins increasing from 0° until the hardness of the armor, and the type of prosomewhere in a range of from 10° to 20° the jectile. In general, high obliquity impact causes 10-7 ..._____________________ __ - BALLISTICS • / @- / Formation of bulge. Formation of petalling on back and front of plate. • !22406 ROSE PETALLING ROSE PETALLING ROSE PETALLING PROJECTILE IN PLATE ALL PETALS OFF • Fig. 10-4 Formation of petalling and plugging as a result of penetration. (Sheet 1 of 2.) 10-8 BALLISTIC ATTACK OF ARMOR Formation of plugging. PUNCHING STARTED .PUNCHING Fig. 10-4 Formation of peta/ling and. plugging as a result of penetration. (Sheet 2 of 2.) • 10-9 BALLISTICS • Fig. 10-5 Failure of a 1ll2-inch cast armor plate resulting fromshock of impact during low temperature tests. a projectile either to ricochet or to shatter, there • increases; and where matching projectiles are by greatly reducing its ability to penetrate. In concerned, little change in resistance to penetraaddition, if the projectile does penetrate, it must tion at normal impact occurs over a considerabledisplace a greater volume of metal to perforate range in hardness. These relationships are illusarmor on an oblique path rather than taking the trated in Figure 10-7, wherein an undermatchingshortest path through; that is, a path normal to ( 20-mm) projectile, a matching ( 37 -mm) prothe surface. Thus a piece of armor plate 2 in. jectile, and an overmatching (57-mm) projectilethick, sloped at 55 °, may afford as much protechave been fired against various hardnesses oftion as a piece of armor plate 5 in. thick with no armor one and one-half inches ( 38-mm) in thickslope. Interior space and other design consideraness. These differences are generally accountedtions limit the amount of slope possible on for by the fact that face-hardened armor willvarious armored components. often shatter undermatching monobloc projectiles, whereas homogeneous armor is less likely 10-7.2 EFFECT OF HARDNESS UPON RE to shatter them. However, due to the brittleness SISTANCE TO PENETRAnON inherent with hardness, face-hardened armorAn increase in the hardness of a given thickshows poorer elastic and plastic response thanness of armor may result in an i~crease, in a dehomogeneous armor, and hence is less likely tocrease, or in no change at all in resistance to resist penetration of an intact projectile. A most penetration depending upon the T j D ratio. important factor in selecting the hardness desiredWhere undermatching projectiles are concerned, in a particular piece of armor is the caliber ofresistance to penetration at normal impact inprojectile that the armor must withstand. Lightlycreases as hardness increases; where overmatching armored vehicles such as personnel carriers andprojectiles are concerned, resistance to peneself-propelled artillery generally employ facetration at normal impact decreases as hardness hardened armor since they can only hope to 10-10 • BALLISTIC ATTAC K OF ARMOR withstand small arms fire and shell fragments 10-7.3 DISCUSSION which would be undermatching. Since the resistance to shock is a measure of the ability of armor to absorb energy, the obliq No m~thematical relationship has yet been uity of attack has little effect other than that atestablished to link the effects of obliquity and hardness upon resistance to penetration, for no high obliquity impact, the armor will absorb less energy in deflecting the projectile into rico two sets of conditions among type and thickness of armor and type and model of projectile neceschet than if the projectile imbedded itself. Howsarily produce exactly the same result; therefore, ever, the hardness of armor has great effect upon Figure 10-7 cannot be given general application. its shock resisting properties. Armor of the higher The designer of a combat vehicle should establish hardnesses tends to be more brittle and to crack under severe shock of impact or blast, while armor requirements only after a study of a comarmor of the lower hardnesses tends to be moreplete tabulation of data for each type and thicktough and ductile and to withstand greater shock. ness of armor and each caliber and model of But armor of too low hardness cannot provideprojectile to be considered. Due to the magni tude of the effect of increased obliquity upon sufficiently high resistance to penetration or massive deformation, so a compromise is necessary. resistance to penetration, every advantage should The hardness of armor and obliquity of attackbe taken of the effect of obliquity in the design of all combat vehicles, gun shields, and other have little effect upon resistance to spalling, as spalling is essentially dependent upon the sound armor structures. Wherever possible, armor surness of the steel and the quality of its heatfaces presented to attack by enemy fire should be treatment. However, once perforation has beeninclined at the highest obliquities permissible obtained, armor plate of the higher hardnesses within the limitations of the other design con will generally spall more (Figure 10-8). siderations. 10·8 KINETIC ENERGY PROJECTILES (e) Shatter. The breaking of the projectile 10-8. 1 DEFINITION OF TERMS into a number of pieces by complex sh earing (a) Penetration-perforation. In considering actions rather than by brittle failure. the effects of missiles on targets it has been found useful to distinguish between penetration and (f) Shatter velocity. That striking velocity at which the projectile, for a given angle of in perforation. The term penetration is reserved for the entry of a missile into the armor without cidence, will shatter into two or more parts when passing through it. The term perforation implies striking a given type of armor. the passage of the missile completely through ( g) Angle of incidence or striking angle. The the armor. angle measured between the normal to the armor (b) Target. That materiel or personnel whose at the point of impact, and the tangent to theinjury or destruction will nullify or lessen the trajectory at the same point (see Figure 10-9). effectiveness of the enemy. In the specific case of a tank the target may be the crew, ammuni(h) Striking energy. The kinetic energy postion, fuel system, radios, fire control equipment, sessed by the projectile at the instant of impaCt armament, or structural or moving parts such as due to its mass and striking velocity. The kinetic the engine, power train, track, etc. The target energy of rotation of the projectile is usually itself is usually highly vulnerable if its protective ignored.armor can be perforated. (i) Armor piercing cap. A metal cap affixed(c) Striking velocity. Velocity of the projecto the nose of a projectile in order to increase thetile at the instant of impact. velocity at which shatter will occur by decreasing(d) Residual velocity. Velocity of the proinitial impact stress due to inertia. jectile after perforation. 10-11 '------------ BAlliSTICS • • Tensile and shear stresses in fo rmation of spa// Separation into layers during formation of spa// Spall Fig. 10-6 Formation of spal/ in armor. (Sheet 1 of 2.) 10-12 BALLISTIC ATTACK OF ARMOR • Example of displacement of backspa/1 from armor Fig. 10-6 Formation of spa// in armor. (Sheet 2 of 2.) 10-13 BALLISTICS THE EFFECT ON HARDNESS UPON RESISTANCE TO PENETRATIONWITH UNDERMATCHING, MATCHING, AND OVERMATCHING PROJECTILES. 1-1/2-INCH ROLLED HOMOGENEOUS ARMOR TESTED WITH20-mm A.P. M75, 37-mm A.P. M74, AND A.P.C. M51 AND 57-mm A.P.C. • M86 PROJECTILES, AT NORMAL IMPACT. ..ci ,.; z 1700 0 .... 37mm A.P.C. M51" II. "'"" "'"" .'-.. .'-..'pc;-I-> 4. ·"'-" " " .'-.."'"' ~ ~.·UAl ~"" > "'"" ~ ~"' ~ (,) 33-·"' -.'-.. .". .'-.." .'-.." "' ~"-"" "" "'-' " "' .'-.."" ""'III: ,"\,. ::-....' 0.-' ·"' y ." .'-.. ·" ·""-'' " .'-.. ·"'-IV"" ·"'-·"' " :"'\: .Y ·"' > ""' "·" """ """ "~ ......_....._ ""~ "' .".' """.Y·" [57" I C!) v -LIMIT VELOCITY (NO SHATTER) r\..". !2(XX) "~ ---LIMIT VELOCITY ( W/ SHATTER) :g ~~v -SHATTER VELOCITY ~ ar: I ; 1250 0 .3 0.!5 .e 1.0 1.3 1.!5 ARMOR THICKNESS IN INCHES Fig. 10-13 Effed of shatter on perforation. With pieces of intermediate thickness, between 0.8 and 1.35 inches in the present example, all results are possible; the projectile can perforate plates of these thicknesses at relatively low velocities (i.e., at long range) , but will fail at higher velocities (i.e., at short :~;ange) because of shatter. At still higher velocities perforation can again be achieved in spite of shatter, although in the case illustrated, these velocities are often above the muzzle velocity of a standard gun. When perfora~on can be obtained at velocities above and below, but not within a certain interval, the interval is called a shatter gap. The shatter velocity in the above example is much higher than usually encountered because the graph is based on data obtained at normal incidence with a sharp nosed projectile. With 1G-11 MECHANISM OF ARMOR The versatile behavior of armor plate is largely responsible for its ability to withstand perforation. If armor plate failed in a single way, one could determine the physical property which governed its ballistic behavior. A change in a }REG ION OF "SHATTER GAP" BALLISTIC LIMIT W/0 SHATTER projectiles having more conventional nose shapes, or in oblique attack, shatter may occur at velocities even below the muzzle velocity of the standard gun. The 2-pound projectile used by the British in the Libyan Campaign failed to perforate German tanks when fired at point blank range, but was successful at long ranges. This resulted from the occurrence of a shatter gap which extended well below 3400 ftj sec, the muzzle velocity of the gun. The effect of firing a projectile at a velocity above its shatter velocity is only to increase its effectiveness at long range at the sacrifice of good performance near the muzzle. Particularly for hypervelocity projectiles, prevention of shatter for striking angles up to 55 degrees is the principal problem in the design of armor piercing projectiles. PENETRAliON-PLATE DEFORMATION single physical property that improves the plate's resistive power with · respect to one type of failure, often lowers its resistive power with respect to other types of failure. Plate responds under impact as follows: 10-18 BALLISTIC ATTACK OF ARMOR 1 0-11.1 THE ELASTIC RESPONSE the dart type and the plugging type. In the dart This response is characterized by the initiation type of plastic· response the penetration may be of compression waves moving through the ma-likened to that of a long sharp dart or conicalwedge. On passage of the projectile through the terial at the speed of sound in steel, a = yE/ p, plate the material is in effect shouldered asideapproximately 16,000 feet per second. If the with no forward motion being imparted. In thewave characteristics are of sufficient magnitude, plugging type of plastic response a mass of thethe plate may exhibit failure by fracture or by plate material, in the form of a plug, is pushedspalling (i.e., failure in tension, the stresses genforward ahead of the advancing projectile. Actuerated being in excess of the ultimate strength a1ly, under usual conditions of perforation, theof the steel). This latter phenomenon is eviplastic response is a combination of both thedenced by the throwing off of plate fragments plugging and the dart type. Part of the platefrom the back of the plate. It should be noted material is pushed aside and part is pushed aheadthat perforation is not a condition essential to of the projectile. When ordinary A.P. ammunicause spalling. Further, if the resulting fragtion is fired against face-hardened plate most ofments (spall) have sufficient velocity, their effect the material is moved forward rather than sideon the protected target is considerable. The ways. maximum energy which can be absorbed by the The energy necessary to achieve perforationelastic response is something under 1/ 5 of the increases almost linearly with an increase intotal energy which can be absorbed by the plate. hardness of plate for a given plate thicknessIf the plate is to prevent perforation, the remainto caliber ratio until a critical plate hardness ising 80% or more of the striking energy must be • reached at which point the energy requiredabsorbed by the plastic response. The spalling to perforate begins to decrease. This decrease ismechanism is also the basis for the effectiveness associated with a gradual change in the type ofof high explosive plastic rounds described later. plate reaction from one in which the dart type of 10-11.2 THE PLASTIC RESPONSE plastic response is dominant to one in which theplug type dominates and places a limit on the There are two main types of plastic response, practical hardness of homogeneous plate. 10-12 CAUSES OF SHATTER: MEANS OF PREVENTING SHATTER The projectile designer must present at the The yaw of the projectile at time of impact is aface of the target a projectile having, for any factor contributing to shatter (Figure 10-14).given diameter, a maximum striking energy. This With an extreme yaw condition existing, the nosemay be accomplished by the provision of suitable of the projectile on impact suffers a drasticform characteristics which lessen resistance in change of direction. So rapid is this change thatflight while maintaining stability. Since the ultithe preponderant mass of the shot behind themate goal of the projectile is destruction of the nose is unable to accommodate and thus tends totarget, it must, by virtue of its striking energy, continue in the original direction. This resultses tablish the maximum possible stre~s in the plate. in severe longitudinal bending stresses in theTo accomplish this vital condition, it must preprojectile which may cause fracture. Resistance·sent a minimum area to the plate during the en • to this bending stress may be increased by propertire period covering its contact with the plate. steel selection and a suitable length to caliberThis is possible only if the projectile is of such ratio.strength as to resist shattering. It follows, there Figure 10-15 illustrates the manner in whichfore, that resistance to shatter is the most implugging penetration of the plate may causeportant characteristic which an A.P . projectile fracture. · Fracture in this case results on the surmust possess. face away fom the plate whereas the yaw effect 10-19 BAlliSTICS t../ / TRANSVERSE BE NOING FORCE / PLATE / Fig. 10-14 Effect of yaw angle on shatter of pro;ectile. FO,.CE TENOING TO "IGttT P"OJECTILE ---/---l PLUG Fig. 10-15 Effect of plugging action on shatter of pro;ectile. presented fracture possibilities on the surface nearest the plate. The inertia principles causing the fracture and the remedies are the same. • Fig . 10-16 Effect of compressive forces on shatter of pro;ectile. A third cause of the projectile failure (Figure 10-16) lies ·in the creation of compression waves in the projectile upon impact. Reflection of the wave at the base of the projectile results in a standing wave. The amplitude of vibration of this wave may be of such magnitude ~s to cause fracture. The problem of shatter has been ameliorated by the use of armor piercing caps. An armor piercing cap is, as the name implies, a cap fitted over the nose of the projectile. The cap is made • of alloy steel, differentially hardened from striking face to base. This treatment permits the cap to present a hard surface to initial impact, setting up a tremendous stress in the target plate. The tough interior of the cap aids in absorbing the impact shock. That the cap itself is shattered in the process is of secondary interest only, though it may bring about slightly lowered performance on the attack of homogeneous plate. The results are twofold: The cap also provides a relatively favorable stress distribution over the nose of the body of the projectile which lessens the tendency of the projectile to shatter. 10-13 COMPARATIVE PERFORMANCE OF CAPPED (APC) AND MONOBLOC (AP) PROJECTILES The purpose of the armor piercing cap is to prevent shatter. In cases where the monobloc (Figure 10-17) does not shatter, the use of a cap is a detriment. On the other hand, if shatter of the monobloc is likely to occur, then the cap, by keeping the main body of the projectile intact, will decrease the limit energy required for perforation by the projectile as a whole, despite some loss in perforating ability due to the disintegration of the cap. Thus, the limit energy 10-20 BALLISTIC ATTACK OF ARMOR IDEALIZED PROJECTILE TYPES tAPP(O Ja,CKUED PROJ(CTil( PAOJ£G11L( CAVITY c ...__BOURRILET RI NG A -ARMO R-I IE• CJ. •CAPPED PROJECTILE, WITH EXPLOSIVE FILLER -ARMOR-l'IERCI 'G-CAPFED PROJECTILE, EMP TY G -A MO -PIERCJ. 'G SHOT D-H YPE! V LOCJfY ARMOR-PIERCING SHOT (COMPOSITE RIGID • Fig. J0-J7 Pro;ectile types. 10-21 BALLISTICS TABLE 10-1 COMPARATIVE RESISTIVITY OF -ARMOR PLATE • Thickness of Homogeneous Armor Plate (Inches) Defeated by AP Shot Fired at 2800 ft / sec Muzzle Velocity I Obliquity Range (Yards) ! Striking Velocity oo I 60° 55° 30° 20° 0 2800 3.2 4.2 5.0 6.2 6.7 500 2680 2.9 3.5 4.5 6.0 6.5 1000 2570 2.7 3.3 4.3 5.7 6.2 1500 2460 2.2 3.2 4.2 5.4 6.0 3000 2140 L4 2.6 3.5 5.0 5.3 Comparative Thickness of Homogeneous Armor Plate (Inches) Defeated by • • Round APC HVAP (J) HVAP (2) may be either Projectiles Fired at 1000 yds Range I Obliquity Muzzle Velocity Shell Velocity I I 2800 2560 3R50 2850 I 3850 3200 I increased or decreased by the attachment of a cap, and unless the conditions of impact are specified no answer can be given to the question of whether a capped or ·a monobloc projectile perforates a greater thickness of armor. Recent findin gs based upon scale model firing tests show that capped projectiles surpass monobloc projectiles for attack of heavy homogeneous armor in the obliquity range of 0° to 40°. In the 10-14 PERFORMANCE OF 10-14.1 COMPOSITE RIGID TYPE In order to take advantage of the increased striking energy made possible by the use of a smaller caliber, higher velocity perforating missile, designers have made use of the principle of the subprojectile as shown in Figure 10-17. Here the jacket around the smaller caliber tungsten oo 60° 55° 30° I 1.9 2.5 4.7 6.1 2.1 2.9 7.8 10.2 2.9 3.3 8.8 11.2 higher range of 40° and up, monobloc projectiles perforate a greater thickness of armor. The apparent superiority of monobloc projectiles at greater obliquities results from the tendency of the monobloc nose to shatter causing the remainder of the projectile to tip more nearly normal to the plate. Perforation is achieved by p unching action in spite of partial shatter of the projectile. In this obliquity range the capped projectile has a strong tendency to ricochet. JACKETED PROJECTILES carbide core, or subprojectile, enables the missile to derive the full benefit of the propellent gases. Further, since the jacket or carrier is generally made of aluminum, the lighter overall weight of the complete projectile coupled with the use of high potential propellants results in a higher muzzle velocity. The decrease in overall weight, 10-22 BALLISTIC ATTACK OF ARMOR while helping to give greater muzzle velocity, tapered bore guns and also increases tremenalso results in a lower inflight ballistic coefficient, dously the time and costs of production of bothC, than is found in the discarding sabot type of gun and ammunition. In addition the tube isround. Such projectiles, hypervelocity ( HVAP), short lived. The Germans made use of this prinare fired at high muzzle velocities (above 3500 ciple, however, in some of their weapons.ftjsec). They have excellent armor piercingqualities if used at normal battle ranges, how10-14.3 DISCARDING SABOT ever, their armor piercing abilities fall off rapidly In the discarding sabot type of armor piercingat longer ranges due to the low ballistic coprojectile (Figure 10-17) the jacket or carrierefficient. Since the jacket of this type projectile falls away from the subprojectile or core whenis rigidly attached to the core (which has a the projectile leaves the muzzle, allowing thediameter about half that of the gun) and does tungsten-carbide subprojectile to proceed towardnot fall off until in contact with the target, the the target. Since the diameter of the core is HVAP projectile is also known as the composite approximately half that of the complete projecrigid or compo-rigid type. tile, and since the carrier is made of a light metalsuch as aluminum, the overall weight of the com 10-14.2 FOLDING SKIRT PROJECTILES posite missile is much less than that of a mono (TAPERED BORE) bloc projectile of the same caliber. Consequently, This type of projectile (see Figure 4-17) is the muzzle velocity of the missile will be greaterfired through a tapered bore which may either than that of a monobloc projectile of equal cali-.be built into the gun or which may be added to a her. Since the smaller subprojectile presents a standard gun by means of a special muzzle atsmaller area to be retarded Ly air while on itstachment. The taper serves to swage down the way to the target, its ballistic coefficient C willflanged skirts which extend from the main body be high and it will have a low rate of loss ofof the projectile as a jacket. As a result, the muzzle energy, arriving at the target with a high emergent caliber is much less than the original striking energy. As a net effect the subprojectilediameter. In this way, the accelerating pressure is effective over a much longer range than theof the powder gases acts on a large area in the composite rigid type. gun bore, while a small (emergent) area is pre The principal disadvantage of the sabot typesented to the resisting pressure caused by air is the danger that discarding pieces of jacket may resistance in flight. This type of projectile has, therefore, the advantage of good exterior ballisstrike friendly troops. Another important short tics from the standpoint of ballistic coefficient. coming is that the sabot is not always uniformly However, the swaged down skirts make imperfect discarded at the muzzle resulting in deflection contact with the projectile body thus creating of the projectile from its flight path. Further en generating points for retarding shock waves at gineering studies are being conducted to improve high velocities. There are two other serious disuniformity of stripping the jacket from the sub advantages of the folding skirt type. The taper projectile with marked improvements in tech prohibits the use of standard ammunition in niques foreseeable. 10-15 OVERALL COMPARISON OF ARMOR-PIERCING PROJECTILES The foregoing discussion of the various types sufficiently versatile that we can afford to relyof armor piercing projectiles should not lead to completely on it.the conclusion that any one type is so much bet For example, the tungsten-carbide cores ofter than all others that it can completely replace composite rigid projectiles are readily fractured them. Each type possesses certain advantages by skirting plates set at high obliquities in frontwhich under favorable conditions make it the of the main armor. In addition, it should be best for those conditions. No one of the types is pointed out that the superiority of performance 10-23 BALLISTICS of this type of projectile over steel shot bodies is plate at high angles of obliquity. As a result of these firings an experimental-monobloc projectile • greatest in the short range attack of greatly over formed by cutting off the nose of a standard matching face-hardened armor plate at low ob liquity. The trend toward very high obliquity, monobloc and adding a windshield has been pro longer range attack of faster tanks, having more duced in limited quantities for further trial. nearly matching homogeneous steel armor proWhen the whole situation is summed up it tected by skirting plates, is accompanied by a amounts to this: we need all types of projectiles; marked decrease of the formerly great superiarmor piercing (AP), armor piercing capped ority of the HVAP projectile. ( APC ) , composite figid ( HVAP), discarding sabot ( DS), shaped charge ( H.E., A.T.) and Recent comparison firings of AP, APC, and HVAP projectiles indicate that the AP (mononew classified types. Any of these would be the bloc) shot is consistently more effective against best round for the particular type of structure rolled, cast homogeneous, and face-hardened which it was designed to meet. 10-16 CHEMICAL ENERGY PROJECTILES greater effect on steel plate than soltd blocks of 10-16.1 HISTORY this material. While considerable time elapsed The discovery of what is now variously rebetween the publications of the work of Munroe ferred to as the shaped charge effect, the hollow and that of Neumann, it is generally believed charge effect, the cavity effect, or the Munroe that the same conclusions were arrived at indeeffect, dates back to the 1880's in this country. pendently by each investigator.Actually, the essential features of this effect had Up to the start of World War II, the open been observed about 1800 in both Germany and literature contains precious little on the subject. Norway, although no great use was made of it In fact, it was not until about 1940 that we hear and it was temporarily forgotten. of it again in this country, at which time a Swiss • Knowledge of the shaped charge in this engineer, H. A. Mohaupt, brought over the idea country stems from the work of Dr. Charles of a projectile carrying an explosive charge in the Munroe, who, while working at the Naval Torform of a hollow cavity. Research work in this pedo Station at Newport, Rhode Island, in the country probably stemmed from this idea, in 1880's, discovered that if a block of gun cotton which thin-walled steel cones of 45° apex angle with letters countersunk into its surface is detowere used as liners for the cavity. A greatly innated with its lettered surface against a steel tensified program of research on this subject was plate, the letters are indented into the surface of promptly initiated by the Ordnance Department the steel. and it was not long before a number of laboratories over the country became engaged in study Apparently nothing was done toward further study of this effect, but between 1910 and 1914, a ing both the theoretical and practical aspects of number of German patents were granted for the the phenomenon. It should also be noted that by application of what essentially was the hollow the late 1930's, the Germans had become consid charge effect. Particularly notable was the work erably advanced in their stud y of this phenomof Neumann, whose work was based on tests enon, and it is now known that this work was made using blocks of TNT having conical indenconsidered to be of such importance as to be tations. He found that such blocks produced a classified as top secret. 10-17 THE SHAPED CHARGE PRINCIPLE which force their way into the target material Up to this point, we have discussed the proband are designed to emerge undeformed at the lem of penetration and perforation by missiles 10-24 • BALLISTIC ATTACK OF ARMOR inner face. In such cases the undeformed missile is the instrument of damage, and the degree of damage is dependent on the striking velocity of the missile. The shaped charge missile differs from the types of armor piercing projectiles already discussed, in that the thickness of material it can perforate is essentially independent of its striking velocity. In fact the missile remains at 10-17.1 FUNCTIONING When this missile strikes a target, the base fuze operating on the non-delay or inertia principle, detonates the charge from the rear. A detonation wave travels forward and the metal liner is collapsed starting at its apex. The collapse of the cone results in the ejection of a long, narrow jet of the products of explosion and metal particles from the face of the liner at velocities from 10,000 to 39,000 ftj sec. This process is illustrated in Figure 10-19 by the series of ultra high speed radiographs of an . experimental shaped charge lined with a 45° steel cone, radiographed at successive times to depict the mechanism of cone 10-18 THE THEORY When a jet strikes a target of armor plate of mild steel, pressures approximating 250,000 atmospheres are produced at the point of contact. This pressure produces stresses far above the yield strength of steel and the target material flows out of the path of the jet as would a fluid . There is so much radial momentum associated with the flow that the diameter of the hole produced is considerably larger than that of the jet. Fig. 10-18 Shaped charge (high explosive, antitank shell). the outer face of the target, producing a jet which is the instrument of damage. A shaped charge missile consists basically of a hollow liner of inert material, usually metal and of conical, hemispherical, or other shape, backed on the convex side by explosive. A container and · a fuze and detonating device are included (Figure 10-18). collapse. The charge was 50/ 50 pentolite having a base diameter of ~ inch. The time noted in microseconds for each radiograph denotes the time after the detonation wave passed the apex of the cone. The jet breaks up into fine particles early in the process of its formation, but retains its jetlike characteristics. There is a gradient in the velocities of the particles along the jet. The particles in front move faster than those in the rear causing the jet to lengthen, and thereby re ducing its average density with time. The jet is followed by the major portion of the now completely collapsed cone. The latter is generally referred to as the slug. OF JET PENETRATION The difference in diameter between the jet and the hole it produces depends upon the characteristics of the armor plate. Thus ·a larger hole is made in mild steel than in armor plate. However, the depth of penetration into a very thick slab of mild steel will be only slightly greater than that into homogeneous armor. As the jet particles strike they are carried radially wit~ the target material. The jet is used 10-25 BALLISTICS • 5N 9,. 2S Pe • Fig. 10-19 Ultra high speed radiograph of shaped charge detonation (jet moves from right to left). up from the front and becomes shorter and shorter until finally the last jet particle strikes the target and the primary penetration process stops. The actual penetration continues for a short time after cessation of jet action because the kinetic energy imparted to the target material by the jet must be dissipated. The additional penetration caused by this afterflow is called secondary penetration. Its magnitude depends upon target strength. It is mainly responsible for the small differences observed between the depths of penetration in mild steel and in homogeneous armor, although there is probably some difference in the primary penetration as well. Since the stresses produced by the jet are much greater than the yield strengths of most target materials, both the target and the jet can be considered as fluids. While some exceptions will be found to the following rule, the depth of primary penetration P' depends primarily on several factors: the length of the jet, L; the density of the target material, p; and the average density of the jet, Pi· Actually it has been found that P' is proportioned to Lyp/ p 10-26 BALLISTIC ATTACK OF ARMOR B B~r!tm&. __ s8 (a) Hollow charge and explosive train prior to T Charge initiation of explosion. E R (b) Hollow charge undergoing process of a highexplosion. The detonatiqn wave initiated by the detonator and booster has passed over most of theliner which is in the process of collapsing tQ_form the jet and slug. At this stage, the principal linermass in the jet has been formed from the apex of the liner. A Detonation Velocity (c) Relative velocities of jet, liner, and slug particles during the process of cone collapse would be asobserved from a moving point, A, based on equatinghorizontal components of momentum about A. Note the relative high jet velocity and motion of particles of the liner towards point A. .Fig.10-20 Jet penetration. The strength of the target material does notseem to have any appreciable effect on the depthof primary penetration, however it should benoted that the jet density, Pi• is dependent to alarge degree on the density of the cone, particlesof which are dispersed throughout the primaryjet. As illustrated in Figure 10-20 (a) (b) (c),the cone tends to invert in the early process ofjet formation. Security restrictions limit discussion of developments in cone design and configuration, however certain basic parameters andvariables affecting jet performance are indicatedin the following paragraphs.The standoff distance is defined as the distance Fig. 10-21 Dependence of penetration on standoff from the base of the cone to the surface of the distance. • target when the detonation occurs. This distanceis extremely important in obtaining maximumpenetration of the jet. An increase in standoff of primary penetration. This is true up to adistance allows an increase in the length of the certain distance. Beyond that distance the jetjet L, but at the same time decreases the average spreads somewhat due to irregularities in thedensity Pi· The product of these two quantities cone and charge, which decrease the depth ofremains substantially constant, so that from the primary penetration. Examination of Figure 10expression given above, it would appear that an 21 will show clearly how penetration varies withincrease in standoff distance increases the depth standoff distance. 10-27 BALLISTICS TABLE 10-2 EXPLOSIVE PENETRATION POWER Density Detonation Rate Relative Standing in Explosive (grams/ cc) (m/ sec) Penetration Efficiency I I Comp B 1.68 8000 1st Pentolite 1.64 7640 2nd Ednatol 1.62 7500 3rd TNT 1.59 6900 4th TABLE 10-3 LINER MATERIALS Approx Sp Gr Hole Depth, Hole Width, Metal Group of Liner Metal mm mm I Copper and copper alloys 8.5 58 14 Deep drawing sheet steel 7.7 55 15 Zinc 7.2 51 17 Sheet iron 7.8 47 16 Aluminum and its alloys 2.7 29 23 Magnesium alloys 1.7 23 25 10-19 FACTORS AFFECTING PENETRATION BY SHAPED CHARGE PROJECTILES • The critical factors affecting penetration by shaped charge missiles are as follows: 10-19.1 TYPE, DENSITY, AND RATE OF The net effect of confinement is to increase peneDETONATION OF EXPLOSIVE tration by 10 to 15%. CHARGE 10-19.3 DIAMETER AND LENGTH OF While the depth of penetration is indicated CHARGE BACK OF LINER to be more closely related to detonation pressure than to the rate of detonation, it may be said The length of the charge should be at least four times the diameter. The Munroe effect is that the greatest effect will be produced by that not dependent on the presence of a liner (i.e., explosive having the highest rate of detonation. paper could be used to form the contour of the Table 10-2 illustrates the relative effect of four explosive ) but the material of the liner actually different castable explosives. contributes in a large measure to effective per While the rate of detonation is of prime importance in selecting a high explosive filler, other formance, penetration being a function of Pi· properties of the explosive must be taken into 10-19.4 LINER MATERIAL AND THICKNESS consideration. Among these are sensitivity to initiation, po1,1rability, and thermal stability. The type of metal used for a liner and the thickness of this metal liner have also been found 10-19.2 CONFINEMENT OF CHARGE to affect the penetrating action of a given shaped Confinement is inherent in a military projeccharge. Cones of different w~ll thickness but all tile. Its effect on shaped charge action is to deof 90° apex angle were prepared from each of crease loss of pressure laterally, increase the approximately twenty different metals and metal duration of application of pressure, and probably alloys. All the charges were fired at a constant to improve the shape of the detonation front. standoff. The data given in Table 10-3 are based • 10-28 BALLISTIC ATTACK OF ARMOR on the hole depth and width obtained with the charges employing liners 1 mm in thickness. It was found, at least in this series of tests, that the de'pth of penetration of charges prepared using cones of each of the different metals in creased with liner thickness up to 1 mm, and that further increases in liner thickness beyond this had no appreciable effect on the depth of penetration. Several points should be noted in these data. First, the depth of penetration appears to be re lated to the specific gravity of the liner metal. Secondly, there was no appreciable difference in the penetrating power of charges employing cones of metals within the same group, i.e., cop per and copper alloys. Thirdly, as the depth of penetration decreas~d, the width of the hole in creased, so that the hole volume in all cases was practically unchanged. These results were ob tained under a given set of conditions. A change in these conditions might well alter the relative effectiveness of cones prepared from different metals. For specific applications, such as static demo lition charges, glass liners are utilized because the performance of such liners insures more cylin drical holes for the insertion of an additional standard charge, and also because the possibility of a hot slug being wedged in the hole cannot be tolerated. 10-19.5 INCLUDED ANGLE OF LINER American ammunition varies from 42° to 60°. Foreign ammunition varies from 18° to 90°. 10-19.6 LINER SHAPE Different shaped cavities and liners react in different ways. For example, a conical liner collapses from the apex and leaves approximately 70 to 80% of the liner to follow behind the jet as a slug. Hemispherical liners on the other hand appear to turn inside out, most of the liner being projected in the jet, with only random bits of residue left behind. The jet velocity from hemispheres is only about ~ that from cones, but the mass of the jet is approximately 3 or 4 times as great, with the result that total jet energies are comparable. The only standard round of am munition designed with a hemispherical (or modified hemispherical) liner is the 57 -mm recoilless rifle. All other types employ a conical shape. 10-19.7 ROTATION OF THE MISSILE Particles making up a jet are given a tangential velocity due to rotation of the missile during for mation of the jet. This tangential velocity com ponent causes spreading of the jet and therefore lessens penetration. Projectiles having conical liners may lose as much as 50% or more of their effectiveness due to rotation. Projectiles having hemispherical liners are somewhat less affected by rotation because of the difference in the mechanism of liner collapse and the greater mass of the jet. In general, penetration is reduced as spin increases from 0 to about 200 rev/ sec, after which further spin has little effect. As is already known, artillery projectiles require rotation (about 10,000 rpm) for stability and conse quently the effectiveness of shaped charge rounds is considerably reduced. The rotational velocity has less of a detrimental effect on depth of pene tration if standoff distance is small. 10-19.8 ANGLE OF IMPACT For each type of shaped charge projectile there is a critical angle of impact beyond which depth of penetration is markedly reduced and is non uniform from round to round. This is primarily due to variability of performance resulting from fuze action. 10-19.9 STANDOFF DISTANCE For a given shaped charge projectile one of the most important factors governing depth of penetration is the standoff distance. Proper projectile design providing correct standoff distance allows sufficient room for the fuze to function properly and the cone to collapse and form a jet of proper density, thus maximizing the possibility of perforation of the target. Factors such as proper striking velocity, resistance offered. by the material of which the round is made, variance of density of the jet due to rotation of the projectile, plus other variables must be considered. Failure to consider all factors affecting the formation of the high pressure high velocity jet would materially affect sound performance. Figure 10-21 shows typical craters produced in mild steel by static charges fired at various standoffs. Depending upon liner shape, liner material, and lack of spin, up to six times the cone diameter may provide optimum standoff distance. The dependence of best performance on standoff distance poses a fuzing problem, especially 10-29 BALLISTICS in the case of rotating, shaped charge, artillery projectiles. Conventional artillery weapons normally impart a higher muzzle velocity to projectiles than is desirable for shaped charge projectiles. High striking velocities of shaped charge projectiles may result in the collapse of the ballistic cap upon impact. If the projectile is fuzed with an inertia type base fuze, the time necessary for the fuze to initiate the bursting charge may permit an appreciable decrease in the standoff distance as the cap collapses. In order to overcome this condition, some recent designs have provided a nose instantaneous fuze to initiate the detonation of the charge. Since, with this type of missile, the charge must be initiated at the rear in order to provide a proper directional impulse for the detonating wave, the liner must be open at the apex and the bursting charge must have an open channel in it to allow the wave to reach the booster at the base of the charge. This axial void does not adversely affect either the detonation wave or the collapse of the liner. On the contrary it appears to slightly enhance effectiveness of the charge due to forming a somewhat concave detonation front. 10-19.10 DESIGN AND MANUFACTURING PROBLEMS In the design of efficient shaped charge ammunition, still more variables must be taken into consideration, such as shell wall thickness, ogive strength and length, fu ze time, and others. ~t is not intended to throw confusion into an understanding of the action of shaped charge ammunition by mentioning variable after variable, but to point out strongly that the design, construction, and action of such ammunition is by no means simple but rather is a complexity of gove~ning fa ctors, each of which has its own sig nificant effect. Involved in the internal construction of shaped charge ammunition, there are a number of factors which have an adverse effect on penetration. Among these might be mentioned ( 1 ) misalignment of explosive charge axis with cone axis ; (2 ) metal liners of uneven thickness; ( 3) formation of an uneven layer of explosive around the b ase of the cone; and ( 4 ) cavities or low density areas in the explosive charge. It is known that any one of these may cause either poor jet formation or else a jet which tends to go off obliquely from the extended cavity axis. Particular mention might be made of the necessity of using an explosive filler having good fluidity when casting into the component. A castable explosive which has a high viscosity or which tends to be mushy even at the high temperature of standard melt kettles, may solidify too quickly when poured into the shaped charge cavity and thus not form a perfect layer around the base of the cone. The adverse effect of poor loading is more apt to be noticed in the performance of small weapons than in larger calibers. 10-20 PERFORMANCE OF SHAPED CHARGE MISSILES The fact that performance of shaped charge missiles is independent of striking velocity as such, and therefore of range, would appear to make these charges ideal for antitank artillery. However, as previously noted, when shaped charge missiles (H.E., A.T.) are caused to rotate by the rifling in the guns from which they are fired, their performance drops 30 to 7ctJ,. Non-rotated, fin stabilized, shaped charges can be made to perform almost as well when detonated by impact as when detonated statically, providing the striking velocity is not so great that the operation time of the fuze will allow the cone liner to become deformed before complete detonation. Various theories have been offered as to what happens inside a tank perforated by the jet of a shaped charge missile. Tests quite definitely show that for shaped charge missiles having explosive charges weighing 15 pounds or less there is no appreciable blast effect, pressure rise, or temperature rise inside the tank. The jet does not spread out in a cone shaped spray from its exit in the armor plate. If the jet perforates the armor plate with sufficient energy to spare, it does continue along its original path. Ammunition, fuel, etc. , in the path of the jet will often be set afire. Crew members in the path of the jet will be severely injured, but it is entirely possible for one man to be severely injured or killed • 10-30 BALLISTIC ATTACK OF ARMOR and the man immediately adjacent to him, but out of the path of the jet, to escape unscathed. It is entirely possible for a tank to be perforated from such an angle that no harm results to the crew or tank except for a small hole in the armor. Damage is actually produced by the tiny, hot, high velocity fragments of liner metal making up the jet. Depending upon the quality of the ar 1 0-21 HIGH EXPLOSIVE The high explosive plastic projectile is primarily an antitank round which uses a comparatively new principle to defeat armor. The spalling or chipping of the interior tank surface caused by this round is completely effective without necessarily penetrating the extt--;....-1 ~q, c CD ~ c 0 f• X ; Q f. • . . • ~ 0 tf CD ]Lnf ~ -~:. . . . . 1 r-- -" ;,• . ..... ·· --.. -·-J. I I I 10 YOw • WEIGHT aF EXPl.OSIVE ,,...a4e ..• ' • •• • I. .. I .. .. .. • Fig. B-6 Effect of shaped charge against concrete. element from a portion of the M-78 fuzes, the are readily identined by a spot of white paint on new fuze being named the fuze, C.P., M-78, the tip. In actual employment, the white tipped Non-Delay. Each box containing twenty M-78 fuzes should be used first, until hits are obtainedfuzes contains four of the non-delay type, which on the concrete target. B-8 EFFECT OF THE SHAPED CHARGE AGAINST CONCRETE The effect of the shaped charge against contion depth which results in massive concrete'. crete is shown in Figure B-6. Depth of penetraA weak thick wall will resist penetration bet tion produced resulted from charges with axes ter than a thin strong wall, since there is com perpendicular to the slab face. Shaded band inparatively little difference in concrete density cludes values 20% above and below the mean between the two and penetration appears to bevalue. Because of scabbing on the rear face (see dependent on density. Additional protection isinset sketches) perforation often results even afforded concrete against shaped charge attackwhen slab thickness is greater than the penetra-by the addition of steel plates front and back. REFERENCES No general, unclassified references are available. B-6 • INDEX Accelerometer, 5-7 Aerodynamic forces 3-4 ( see Forces, aerodynamic) Aerodynamic missiles, 4-1 configuration, 4-12 plan forms, 4-15 profiles, 4-15 steering, 4-16 trajectories, 4-1 Air blast loading, 8-9 Air effects, 1-17 Airfoils , 4-15 forces on , 4-16 lift and drag coefficients, 4-17 nomenclature, 4-16 Air-to-surface missile, 5-9 Armor, 10-1 ballistic attack, 10-1 ballistic properties, 10-6 obliquity, 10-7 penetration, 10-18 petalling, 10-8 plugging, 10-9 resistivity, 10-22 shatter, 10-19 fabrication, 10-4 penetration, 10-18 elastic response, 10-19 plastic response, 10-19 surface design, 10-4 ( see also Design of armor) types, 10-1 body, 10-31 cast steel, 10-1 face-hardened steel, 10-3 nonferrous, 10-4 rolled steel, 10-1 Artillery trajectory, 3-4 • Atomic detonations, 9-1 blast effects, 8-12 cratering, 8-13 equipment, 8-12 genetic, 9-16 personnel, 8-12 structures, 8-13 injuries from, 9-6 surface burs~ 9-2 underground burst, 9-2 water bursts, 9-3 Ballistic attack of concrete, B-1 Ballistic cameras, A-ll Ballistic coefficient, 3-8 for hom bs , 3-11 Ballistic missiles, 4-1 el'terior ballistics , 4-7 flight, 4-6 systems , 4-3 Ballistic tables, 3-2, 3-9 Ballistic trajectories, 4-1 theory of, 4-9 Ballistics, armor, 10-6 penetration resistance, 10-7 shock r esistance, 10-7 spall resistance, 10-7 Ballistics, exterior, 3-1, 4-7 Ballistics, fragments, 7-1 (see also Fragments) Ballistics, interior, 1-1 Ballistics, terminal, 6-1 Ballistics, transition, 1-16 initial air effects, 1-17 lateral jump, 1-19 vertical jump, 1-18 Bipropellants (see Liquid propellants) Black body radiation, 9-5 Blast effects radii, 8-13 Blast impulse, 8-7 Blast pressure, 8-4 Blast wave, 8-1 technical aspects, 8-10 Body armor, 10-31 Bombing problems, 3-14 altitude corrections, 8-12 burst height, 7-10 crater d ata, 8-14 cross trail, 3-15 linear travel, 3-15 low altitude, 3-16 1-1 Bombing problems (cont) Diffraction loading, 8-9 stabilization Discarding sabot projectiles, 10-23 (see Stabilization) Distribution of energy, 1-3 trail, 3-15 vertical travel, 3-15 Doppler effect, A-7 • Bombing tables, 3-13 Drag coefficient, 3-7 Bombing techniques, 3-15 Drag loading, 8-10 Bowen-Knapp cameras, A-ll Drift stabilized projectiles, 3-19 Brayton cycle, 2-26 Earth satellites, 4-10 Bremsstrahlung, 9-16 Edge effect, B-2 Bursting shell, 6-2 Energy distribution, 1-3 Capped projectiles, 10-20 Engines, jet (see Jet engines ) Celestial navigation, 5-7 Erosion, 1-13 Cesium, 9-15 effects, 1-17 Charge efficiency, 1-8 gas, 1-14 Chemical energy projectiles, 10-24 Exhaust velocity, 2-11 Chronographs, A-5 Explosiv~charge detonation, 10-28 Aberdeen, A-7 camera, A-7 Exterior ballistics, 3-1, 4-7 field, A-7 machine gun, A-7 Fallout, 9-13 Coefficient, ballistic, 3-8 Firing tables, 1-13 drag, 3-7 calculations, 3-11 • Command guidance, 5-8 Fission fragments , 9-9 Composite rigid projectiles, 10-22 Force, aerodynamic, 3-4 Composition B, 7-4 Coriolis, 3-10, 5-8 Coriolis force, 3-10, 5-8 crosswind force, 3-5 drag, 3-5 Courses, intercept magnus force, 3-6 (see Intercept courses) magnus moment, 3-6 Crusher gauge, A-8 overturning moment, 3-6 rolling moment, 3-6 Damage distribution, 6-8 yawing moment, 3-6 function, 6-9 Foxholes, 7-7 pattern, 7-9 Fragmentation, 7-1 Data analysis, 6-5 comparative, 7-8 Design of armor, 10-4 controlled, 7-12 composite, 10-6 innovations in, 10-5 Fragments, ballistics of, 7-1 laminated armor, 10-6 damage, 7-7 spaced armor, 10-6 dispersal, 7-5 initial velocity, 7-4 Detonation, 20-mm shell, 7-2 bomb, 7-5 quantitative data, 7-5 grooved ring shell, 7-16 recovery of, 7-6 1-2 • Fuel, rocket, 2-12 burning, 2-13 combustion limit, 2-14 pressure limit, 2-15 storage, 2-15 temperature sensitivity, 2-13 Fuzed shells, B-5 Fuzing, ballistic missile, 4-4 Gamma radiation, 9-9 Gas erosion, 1-14 Gauges, crusher, A-8 piezoelectric, A-8 strain, A-10 Grain characteristics, 1-5 configuration, 1-6 loading density, 1-7 size, 1-6 Gravitational force, 4-11 Guidance, 5-1 attitude control, 5-1 changing trajectory, 5-8 path control, 5-2 terminal, 5-10 trajectory, 5-3 Guidance systems, 5-1 active homing, 5-11 beam rider, 5-9 celestial navigation, 5-6 command, 5-8 dual-beam rider, 5-10 homing, 5-10 inertial, 5-7 intercept problem, 5-14 kinematics of, 5-13 passive homing, 5-12 preset, 5-3 radio navigation, 5-4 semi-active homing, 5-12 single-beam rider, 5-10 terrestrial reference, 5-4 Gun action, 1-2 Gun efficiency, 1-8 • Gun systems, 1-10 causes of wear, 1-12 gun bore erosion, 1-13 gun temperature, 1-13 powder temperature, 1-13 density of loading, 1-11 1-3 gun chamber, 1-11 gun tube length, 1-11 projectile weight, 1-11 sectional density, 1-11 Hand grenade, 7-17 Heat engine, 4-12 High explosives, 8-5 High explosive impact, B-3 High explosive projectiles, 10-31 High speed photography, A-ll Histograms, 6-5 Homing guidance, 5-11 Hyperbolic grid, 5-6 ICBM, 4-1 Ignition, 1-4 direct conduction, 1-5 radiation, 1-5 Impact, high explosive, B-3 inert, B-2 projectile, 10-14 Impulse, specific, 2-3 Inertial guidance, 5-8 Inert impact, B-2 Instrumentation, A-1 Intercept courses, 5-13 constant bearing; 5-15 deviated pursuit, 5-15 line of sight, 5-15 proportional, 5-16 pure pursuit, 5-15 Interior ballistics, 1-1, 2-1 (see also Jet engines ) control of, 1-4 Ionization, 9-10 IRBM, 4-1 Jacke ted projectiles, 10-22 Jet engines, 2-20 principles, 2-1 pulse jets, 2-21 ram jets, 2-22 (see also Ram jets) Jet engines (cont) Momentum thrust equation, 2-2 specific impulse, 2-3 Metzzle pressure, 1-4 thrust, 2-2 Muzzle velocity, 1-15 turbo jets, 2-24 Neutron particles, 9-9 Kinematics, 5-13 induced activity, 9-12 Kinetic energy projectiles, 10-ll sources, 9-10 Newtonian constant, 4-9 Lateral jump, 1-18 N ike missile, 5-9 LeDuc equations (projectile velocity), 1-9 Nozzles, 2-5 Limiting velocity, 3-14 angle correction factor, 2-9 Liquid fuel feed system, 2-16 configuration, 2-9 convergent-divergent, 2-2 Liquid propellant rockets, 2-15 design, 2-5 chamber pressure, 2-16 distance along, 2-7 motors, 2-17 entrance and exit angles, 2-9 pressure feed system, 2-17 pressure distribution along, 2-8 pump feed system, 2-18 schematic flow diagram, 2-4 Liquid propellants, 2-18 Nuclear radiation, 9-8 requirements, 2-19 effects of, 9-llutilization, 2-19 fallout, 9-13 Liquid rocket feed system, 2-18 long-term hazard, 9-15 neutron induced, 9-12 residual, 9-12 .\1ach number, 3-6 sources of, 9-10 reflection, 8-5 region, 8-9 wave, 8-6 Ogive, 3-6 Measurement, pressure, A-8 Orbits, satellite, 4-10 velocity, A-4 Oscillogram, A-ll Missile, IRBM, 4-1 Overpressure of shock wave, 8-3 Nike, 5-9 Redstone, 4-4 Overspun projectiles, 3-18 V-2, 4-5 Overturning moment, 3-7 Missiles , aerodynamic (see Aerodynamic missiles) Peak pressure of shock wave, 8-3 Missiles, ballistic Perforation of concrete, B-3 (se e Ballistic missiles) Photographic measurements, A-ll Missiles, configuration, 4-12 high speed photography, A-llaerodynamic steering, 4-16 Schlieren photography, A-16 airfoils, 4-16 spark photography, A-16 plan forms, 4-15 X-ray photography, A-16 profile shapes, 4-15 Piezoelectric gauges, A-8 Mitchell camera, A-ll Pitch axis, 5-1, 5-2 Moment, magnus, 3-6 overturning, 3-6 Powder grain effects, 1-5 · rolling, 3-6 density of loading, 1-7 yawing, 3-6 grain configuration, 1-6 1-4 • Powder grain effects (cant) • grain size, 1-6 Precession, 3-18 Pressure calculations, 1-12 Pressure measurements, A-8 recording of, A-ll Pressure-time relationships, 1-7 for 3.25-inch rocket, 2-5 Pressure-travel curves, 1-3 Pressure-travel relation, 1-6 Probability, 6-4 damage distribution, 6-8 damage function, 6-9 of successful mission, 6-8 product rule, 6-8 sum rule, 6-4 Product rule, 6-8 • Projectiles, 10-21 form, 3-7 impact of, 10-14 limiting velocity, 3-14 penetration, 10-25 performance, 10-23 capped projectiles, 10-20 composite rigid, 10-22 discarding sabot, 10-23 jacketed projectiles, 10-22 tapered bore projectiles, 10-23 stability factor, 3-18 terminal velocity, 3-15 types, 10-19 capped, 10-20 chemical energy, 10-24 composite rigid, 10-22 discarding sabot, 10-23 drift stabilized, 3-19 jacketed, 10-22 kinetic energy, 10-11 overspun, 3-18 shaped charge (see Shaped charge projectiles) spin stabilized, 3-19 tapered bore, 10-23 underspun, 3-18 Projectile velocity computation, 1-9 Propellants, combustion limit, 2-16 energy of, 1-3 liquid, 2-18 selection of, 2-18 utilization of, 2-19 solid, 2-13 changes in storage, 2-15 combustion limit, 2-14 mode of burning, 2-13 pressure limit, 2-15 temperatures, 2-13 utilization system, 2-21 Pulse jet, 2-22 characteristics, 2-26 Radar, 5-9 Radiation, nuclear (see Nuclear radiation) Radiation, thermal (see Thermal radiation) Radioactive decay, 9-14 (see also Fallout) Radio navigation paths, 5-5 Ram jets, 2-22 characteristics, 2-26 subsonic ram jets, 2-22 supersonic ram jets, 2-23 Reaction motors, 2-20, 2-27 characteristics, 2-26 principles, 2-1 Rebound, B-1 Recoilless gun system, 1-2 Redstone 'missile, 4-4 Reynold's number, 3-6, 4-17 Ricochet, B-1 Rocket fuel, 2-26 (see also Fuel, rocket) Rocket fuel consumption, 2-28 Rocket motors, 2-3 characteristics, 2-26 impulse-weight ratio, 2-5 thermodynamics, 2-4 thrust, 4-10 thrust coefficient, 2-5 Rockets, liquid propellant, 2-15 pressure feed systems, 2-17 pump feed system, 2-18 Rockets, · solid propellant, 2-11 characteristics, 2-13 grain geometry, 2-12 1-5 Rocket staging, 4-11 Roli axis, 5-1, 5-2 Satellites, 4-10 Scabbing, B-1 Schlieren photography, 3-2, A-16 Shaped charge projectiles, 10-24 angle of impact, 10-29 angle of liner, 10-28 confinement of charge, 10-28 design and manufacture, 10-30 detonation of charge, 10-28 effect against concrete, B-6 functioning, 10-25 liner dimensions, 10-28 liner shapes, 10-29 penetration, 10-28 performance, 10-30 rotation, 10-29 size of charge, 10-28 standoff distance, 10-29 Shatter, 10-19 Shock to armor, 10-7 Shock tube, 6-3 Shock velocity, 8-11 Shock wave overpressure, 8-3 Solid propellant rockets (see Rockets, solid propellant) Spalling, 10-7 Spark photography, A-16 Specific impulse, 2-3 Spin stabilized projectiles, 3-19 Stabilization, 3-16 fin, 3-16 roll, 3-17 spin, 3-17 stability and drift, 3-19 Staging, rocket, 4-11 Statistics, 6-5 Strain gauges, A-10 Striking angle, 10-15 Strontium, 9-15 Subsonic ram jet, 2-23 Sum rule, 6-4 Supersonic airfoils, 4-15 Supersonic ram jet, 2-24 Surface-to-surface missile, 5-9 • System errors, 6-9 Tapered bore projectiles, 10-23 Target analysis, 6-3 Ta~gets, 6-12 area considerations, 6-13 extension chart, 6-12 point chart, 6-11 types, 6-10 circular, 6-15 irregular, 6-15 point, 6-10 Telemetry, A-2 Temperature effects, 1-13 Terminal ballistics, 6-1 area target considerations, 6-13 circular targets, 6-15 damage function, 6-9 irregular targets, 6-15 statistical methods, 6-4 system errors, 6-9 target analysis, 6-3 Terminal guidance, 5-10 • Terminal velocity, 3-15 Theodolites, A-ll Thermal radiation, 9-3 absorption, 9-5 attenuation, 9-4 damage radii, 9-8 dose effects, 9-11 emission, 9-4 injuries, 9-6 mechanism, 9-3 second radiation pulse, 9-6 temperature pulses, 9-4 Thiokol, 2-11 Thrust, 2-2 momentum, 2-2 total, 2-3 Thrust cut-off, 4-7 Time-pressure relations, 2-14 Time recording devices, A-5 Aberdeen chronograph, A-7 1-6 Time recording devices (cont) camera chronograph, A-7 field chronograph, A-7 machine gun chronograph, A-7 TNT, 7-4, 8-5 Total thrust equation, 2-3 Trajectories, 3-3 aerodynamic, 4-1 analysis, 3-10 artillery, 3-4 ballistic (see also Ballistic trajectories) fixed coordinate, 4-8 guidance, 5-3, 5-8 hypervelocity vehicle, 4-3 ICBM, 4-6 medium height, 4-7 physical effects upon, 4-7 plots of, 3-9 short range, 4-8 Transition Ballistics (see Ballistics, transition) Turbo jet characteristics, 2-26 engine cycle, 2-26 turbine, 2-25 Underspun projectiles, 3-18 V-1 missile, 2-21 V-2 missile, 4-5 Velocity, exhaust, 2-11 fragment, 7-4, 7-12 muzzle, 1-15 projectile, 1-9 terminal, 3-15 Velocity computations, 1-9 Velocity measurements, A-4 Velocity, exhaust, 2-11 Vertical jump, 1-18 Whitcomb area rule, 4-17 Wind tunnel, flexible throat, 3-1 Schlieren photo, 3-2 Wind tunnel tests, Langley Aeronautical Laboratory, 4-13 Moffett Field, California, 4-14 X-ray photography, A-16 Yaw angle, 3-4 axis, 5-1, 5-2 plane, 3-5 response, 3-20 1-7