(MIL-HDBK-762) Design of Aerodynamically Stabilized Free Rockets - DoD

(MIL-HDBK-762) Design of Aerodynamically Stabilized Free Rockets - DoD

(Parte 1 de 6)

MIL-HDBK-762(MI) 17 July 1990

AREA GDRQ DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited.

MIL-HDBK-762(MI)

and is available for use by all Departments and Agencies of the Department of Defense
Proposal (D Form 1426) appearing at the end of this document or by letter

1. This military handbook is approved for use by the US Army Missile Command, Department of the Army, 2. Beneficaial comments (recoomendations, additions, deletions) and any pertinent data that may be of use in improving this document should be addressed to: Commander, US Army Missile Command, ATTN: AMSMIRD-SE-TD-ST Redstone Arsenal, AL 35809, by using the self-addressed Standardization Document Improvement 3. This handbook was developed under the auspices of the US Army Materiel Command's Engineering Design Handbook Program, which is under the direction of the US Army Management Engineering College. Research Triangle Institute was the prime contractor for the preparation of this handbook, which was prepared under Contract No. DAAG34-73-C-0051.

MIL-HDBK-762(MI)

FOREWORD
LIST OF ILLUSTRATIONS
LIST OF TABLES
LIST OF ABBREVIATIONS AND ACRONYMS

Paragraph Page i xv xxiv xxv

CHAPTER 1 INTRODUCTION

1-1 PURPOSE OF HANDBOOK
1-2 CLASSES OF FREE FLIGHT ROCKETS
1-2.1 MILITARY ROCKET SYSTEMS
General
Field Artillery
Infantry
Air Defense
Armor
Aviation
Logistic
Other
1-2.2 RESEARCH ROCKET SYSTEMS
1-2.2.1General
1-2.2.2 Meteorological
1-2.2.2.3 High-Altitude Sounding
1-2.2.4 Satellites
1-2.2.5 Dispensing
1-3 OPERATIONAL MODES
1-3.1 GENERAL
1-3.2 SURFACE TO SURFACE
1-3.3 SURFACE TO AIR
1-3.4 AIR TO SURFACE
1-3.5 UNDERWATER LAUNCH
1-3.6 SURFACE OR AIR TO UNDERWATER
1-4 GENERAL ROCKET SYSTEM DESCRIPTION
1-5 OVERVIEW OF CONTENT OF THE HANDBOOK
1-1
1-1
1-1
1-1
1-1
1-2
1-2
1-2
1-3
1-3
1-3
1-4
1-4
1-4
1-4
1-4
1-4
1-4
1-4
1-5
1-5
1-5
1-5
1-6
1-6
1-6

CHAPTER 2 SYSTEM DESIGN

2-1 GENERAL
CONCEPT SELECTION PHASE
PRELIMINARY DESIGN PHASE
SYSTEM VALIDATION
2-2 REQUIREMENTS
2-3 CONCEPT SELECTION
2-3.1 COMPONENT CONSTRAINTS
2-3.2 PARAMETRIC STUDIES
2-3.2.1 General

2-1 2-1 2-2 2-2 2-3 2-4 2-5 2-5 2-5

MIL-HDBK-762(MI)

CONTENTS (cont’d)

2-3.2.2 Motors
2-3.2.3 Warheads
2-3.2.4 Error Sources
2-3.3 SYSTEM SELECTION2-7
2-4 PRELIMINARY DESIGN2-7
2-4.1 PAYLOAD2-8
2-4.1.1 Kill Mechanism
2-4.1.2 Performance Characteristics2-9
2-4.1.3 Physical Characteristics2-9
2-4.1.4 Safing, Arming, and Fuzing
2-4.2 PROPULSION
2-4.2.1Propulsion Energy Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-4.2.2Motor Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-4.2.2.1 Motor Physical Characteristics
2-4.2.2.2 Performance Characteristics
2-4.2.2.3 Propellants2-12
2-4.3 AERODYNAMICS
2-4.3.1 Drag2-12
2-4.3.1.1 Wave Drag
2-4.3.1.2 Skin-Friction Drag2-13
2-4.3.1.3 Base Drag2-13
2-4.3.2 Stability2-13
2-423.3 Nonlinear Aerodynamics
2-4.4 DYNAMICS
2-4.4.1 Accuracy Trade-Offs2-14
2-4.4.2 Dynamic Loads2-16
2-4.4.3 Rocket Vibrational and Bending Considerations2-17
2-4.5 STRUCTURES2-17
2-4.5.1 Materials2-17
2-4.5.2 Structural Sizing2-17
2-4.5.3 Mass and Balance2-18
2-4.6 HEAT TRANSFER2-18
2-4.7 PERFORMANCE ESTIMATES2-19
2-4.8 SUBSYSTEM DESIGN OPTIMIZATION2-19
2-4.9 AUXILIARY DEVICES2-19
2-4.9.1 Wind and Density Measuring Devices2-19
2-4.9.2 Temperature Control Devices2-20
2-4.9.3 Firing and Firing Control Equipment
2-4.9.4 Fuze Setting Equipment
2-4.9.5 Shipping Containers
2-4.9.6 Other Devices Unique to a Given Sysem2-21
2-4.10 SYSTEM INTEGRATION
2-4.10.1 Performance
2-4.10.2 Reliability2-2
2-4.10.3 Cost2-2
2-4.10.4 Availability Data2-2
2-4.10.5 Manufacturing Considerations2-2
2-4.1 SPECIFICATIONS2-2
2-5 SYSTEM VALIDATION2-23
2-5.1 DESIGN AND DOCUMENTATION
2-5.1.1 Detailed Hardware Design
2-5.1.2 Weights and Balances2-24

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MIL-HDBK-762(MI)

CONTENTS (cont’d)

2-5.1.3 Fabrication Drawings2-24
2-5.1.4 Specifications
2-5.2 TESTING2-25
2-5.2.1 Types of Tests
2-5.2.2 Test Plan2-27
2-5.3 SYSTEM INTEGRATION2-28
REFERENCES

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CHAPTER 3 PERFORMANCE

LIST OF SYMBOLS
INTRODUCTION
PERFORMANCE PARAMETERS
3-2.1 PERFORMANCE FACTORS
3-2.2 PROPULSION SYSTEM FACTORS
3-2.3 AERODYNAMIC CONSIDERATIONS
APPROXIMATION TECHNIQUES AND APPLICABLE EQUATIONS
3-3.1 ESTIMATION OF VELOCITY REQUIREMENT
3-3.1.1 Indirect Fire Rockets
3-3.1.2 Direct Fire Rockets
3-3.1.3 Sounding Rockets
3-3.1.4 Surface-To-Air Rockets
3-3.1.5 Air-To-Surface Rockets
3-3.2 ESTIMATION OF ROCKET MOTOR REQUIREMENTS
3-3.3 SUMMARY
PARAMETRIC PERFORMANCE DATA FOR INDIRECT FIRE SYSTEMS
3-4.1 DELIVERY TECHNIQUES
3-4.2 PARAMETRIC PERFORMANCE DATA
PARAMETRIC PERFORMANCE DATA FOR DIRECT-FIRE SYSTEMS
3-5.1 DELIVERY TECHNIQUES
3-5.2 PARAMETRIC PERFORMANCE DATA
PARAMETRIC PERFORMANCE DATA FOR SOUNDING ROCKETS
3-6.1 DELIVERY TECHNIQUES
3-6.2 PARAMETRIC PERFORMANCE DATA
PARAMETRIC PERFORMANCE DATA FOR SURFACE-TO-AIR ROCKETS
3-7.1 DELIVERY TECHNIQUES
3-7.2 PARAMETRIC PERFORMANCE DATA
PARAMETRIC PERFORMANCE DATA FOR AIR-TO-GROUND ROCKETS
3-8.1 DELIVERY TECHNIQUES
3-8.2 PARAMETRIC PERFORMANCE DATA
NUMERICAL EXAMPLE

3-1 3-3 3-4 3-4 3-4 3-5 3-5 3-5 3-6 3-10 3-12 3-13 3-13 3-15 3-19 3-20 3-20 3-21 3-26 3-26 3-26 3-32 3-32 3-32 3-3 3-3 3-35 3-37 3-37 3-37 3-40

3-46 3-46 REFERENCES
BIBLIOGRAPHY

CHAPTER 4 ACCURACY

4-0 LIST OF SYMBOLS4-1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-1
4-4

MIL-HDBK-762(MI)

CONTENTS (cont’d)

Paragraph Page 4-2

ERROR SOURCES4-5
4-2.1 GENERAL4-5
4-2.2 PRELAUNCH PHASE ERRORS4-6
4-2.3 LAUNCH PHASE ERRORS4-2.4 BOOST PHASE ERRORS4-7
4-9
4-2.5 BALLISTIC PHASE ERRORS4-1
EFFECTS OF ERROR SOURCES4-14
4-3.1 GENERAL4-14
4-3.2 PRELAUNCH PHASE4-17
4-3.3 LAUNCH PHASE4-17
4-3.4 BOOST PHASE4-2
4-3.5 BALLISTIC PHASE4-2
DISPERSION REDUCTION4-24
4-4.1 GENERAL4-24
4-4.2 THE EFFECT OF SPIN4-27
4-4.2.1 Constant Spin Rate4-31
4-4.2.2 Constant Acceleration4-34
4-4.2.3 Constant Deceleration—Slowly Uniformly Decreasing Spin (SUDS)
4-4.2.4 Spin-Buck4-38
4-4.2.5 Very High Spin Rates4-38
4-4.2-6 Spin Techniques4-40
4-4.2.6.1 Helical Rails4-40
4-4.2.6.2 Spin-on-Straight-Rail (SOSR)4-40
4-4.2.6.3 Spin Motors4-40
4-4.2.6.4 Jet Vanes4-41
4-4.2.6.5 Canted Fins4-41
4-4.2.6.6 Spin Power Transmission4-41
4-4.2.6.7 Prespin Automatic Dynamic Alignment (PADA)
4-4.2.6.8 Autospin4-41
4-4.3 THE EFFECT OF ACCELERATION LEVEL4-41
4-4.4 THE EFFECT OF AERODYNAMIC STABILITY4-43
4-4.5 THE EFFECT OF LAUNCHER GUIDANCE LENGTH
4-4.6 PRELALINCH-PHASE DISPERSION REDUCTION
4-4.6.1 Launcher Location and Orientation4-45
4-4.6.2 Target Location4-45
4-4.6.3 External Error Sources4-46
4-4.7 LAUNCH-PHASE DISPERSION REDUCTION4-46
4-4.8 BOOST-PHASE DISPERSION REDUCTION4-46
4-4.9 BALLISTIC-PHASE DISPERSION REDUCTION4-47
ACCURACY COMPUTATION4-48
4-5.1 GENERAL4-48
4-5.2 SIX-DEGREE-OF-FREEDOM EQUATIONS OF MOTION4-49
4-5.3 REDUCED DEGREE-OF-FREEDOM EQUATIONS OF MOTION
4-564-5.4 STATISTICAL METHODS
4-5.4.1 Measures of Central Tendency4-56
4-5.4.2 Measures of Dispersion4-56
4-5.4.3 Measures of Dispersion for Several Error Sources4-58
4-5.4.4 Range and Deflection Probable Errors4-60
4-5.4.5 Probability of Hit4-61
4-5.5 ERROR BUDGET AND SAMPLE CALCULATION4-62
4-5.5.1 General4-62
4-5.5.2 Example Problem4-62

MIL-HDBK-762(MI)

CONTENTS (cont’d)

4-5.5.2.1 Prelaunch Errors
4-5.5.2.2 Launch Errors
4-5.5.2.3 Boost Errors
4-5.5.2.4 Ballistic Errors
4-5.5.2.5 Additional Unit Effect Graphs
4-5.5.2.6 Example Range Error Probable (REP)
4-5.5.2.7 Example Deflection Error Probable (DEP)
4-5.5.2.8 Example Circular Error Probable (CEP)
4-5.5.2.9 Example Probability of Hit
REFERENCES
BIBLIOGRAPHY

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4-63 4-64 4-68 4-74 4-84 4-84 4-84 4-124 4-124 4-124 4-125

CHAPTER 5 AERODYNAMICS

5-0 LIST OF SYMBOLS
5-1 INTRODUCTION
5-2 GENERAL DESIGN CONSIDERATIONS
5-3 STATIC STABILITY
5-3.1 BODIES OF REVOLUTION
5-3.1.1 Nose-Cylinder Configurations
5-3.1.2 Boattail Afterbody Sections
5-3.1.3 Oversized-Head Configurations
5-3.1.4 Necked-Down Centerbody
5-3.1.5 High-Fineness Ratio Body Data
5-3.2 STABILIZING DEVICES
5-3.2.1 Fins
5-3.2.1.1 Coplanar Fins
5-3.2.1.2 Wraparound Fins and Tangent Fins
5-3.2.1.3 Fin Roll Effectiveness,
5-3.2.2 Flare-Type Afterbody
5-3.3 RINGTAILS
5-3.4 STATIC STABILITY OF COMPLETE CONFIGURATIONS
5-3.4.1 General
5-3.4.2 Fin-Body Interference
5-3.4.3 Fin-Fin Interference
5-3.4.4 Stability Tailoring
5-3.4.5 Sample Calculation Sheet
5-3.5 ROCKET PLUME INTERACTION
5-3.5.1 Definition of Problem
5-3.5.2 Effects on Aerodynamic Characteristics

5-1 5-7 5-7 5-9 5-10 5-1 5-12 5-13 5-13 5-13 5-14 5-14 5-14 5-16 5-17 5-17 5-18 5-19 5-19 5-2 5-24 5-26 5-28 5-28 5-28 5-38 5-39 5-40 5-41 5-41 5-42 5-43 5-43 5-43 5-43 5-4

5-3.5.3 Plume Simulation
5-3.6 NONLINEAR AERODYNAMICS
5-4 DYNAMIC STABILITY
5-4.1 LONGITUDINAL DYNAMIC STABILITY
5-4.2 ROLL DYNAMICS
5-4.3 SIDE FORCES AND MOMENTS
5-4.3.1 Magnus Forces
5-4.3.2 Other Side Forces
5-5 DRAG COEFFICIENT
5-5.1 WAVE DRAG

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MIL-HDM-762(MI)

CONTENTS (cont’d)

Paragraph Page

5-5.1.1 Forebody Wave Drag
5-5.1.1.1 Nose
5-5.1.1.2 Midbody Wave Drag5-47
5-5.1.2 Boattail Sections5-47
5-5.1.3 Flare5-47
5-5.1.3.1 Conical Frustum5-48
5-5.1.3.2 Split Flare5-48
5-5.1.4 Fin Wave Drag5-48
5-5.1.5 Ringtail Wave Drag5-49
5-5.2 FRICTION DRAG5-49
5-5.3 BASE DRAG5-50
5-5.3.1 Body-of-Revolution Base Drag, Rocket Jet Plume-Off
5-5.3.2 Body-of-Revolution Base Drag, Rocket Jet Plume-On
5-5.3.3 Fin-Base Drag5-5
5-5.4 DRAG CHARACTERISTICS OF COMPLETE CONFIGURATION
5-5.4.1 Interference Effect—Fin on Base5-56
5-5.4.2 Sample Drag Calculation5-56
5-5.5 PROTUBERANCE.S5-56
AIRLOAD DISTRIBUTIONS5-57
AERODYNAMIC TESTING5-67
.5-7.1 GENERAL5-67
5-7.2 WIND TUNNELS5-67
5-7.2.1 Classification5-67
5-7.2.2 Capabilities and Limitations5-68
5-7.2.3 Instrumentation5-70
5-7.2.4 Conduct of Tests5-70
REFERENCES5-72

CHAPTER 6 PROPULSION

6-0 LIST OF SYMBOLS6-1
6-1 INTRODUCTION6-4
6-2 GENERAL6-5
6-2.1 THE REACTION PRINCIPLE6-6
6-2.2 ESSENTIAL FEATURES OF CHEMICAL ROCKETS6-7
6-3 PROPELLANT TYPES6-7
6-3.1 LIQUID PROPELLANTS6-7
6-3.2 SOLID PROPELLANTS6-7
6.3.2.1 Double-Base Propellants6-8
6-3.2.2 Composite Propellants6-8
6-3.2.3 Composite Double-Base Propellants6-10
6-4 BASIC PERFORMANCE PARAMETERS6-10
6-4.1 INTERNAL BALLISTICS6-10
6-4.1.1 Propellant Burn Rate6-10
6-4.1.2 Thermodynamic Considerations6-1
6-4.1.3 Continuity Equation6-12
6-4.1.4 Propellant Temperature Effects6-12
6-4.2 NOZZLE6-13
6-4.2.1 Nozzle Design Factors6-13
6-4.2.2 Thermodynamic Relations6-15
6-4.2.3 Surface Contours6-19

viii

MIL-HDBK-762(MI) CONTENTS (cont’d)

6-4.2.4 Nozzle Erosion6-2
6-4.2.5 Jet Plume Effects6-23
6-4.2.6 Scarf Nozzle6-24
6-4.3 MOTOR CASE6-24
6-4.3.1 General6-24
6-4.3.2 Minimization of Weight6-24
6-4.4 IDEAL VELOCITY EQUATION6-25
6-4.5 THRUST MALALIGNMENT6-25
6-4.5.1 Structure Geometry and Alignment
6-4.5.2 Propellant Grain and Mass Flow Asymmetries
6-4.5.3 Test Environment6-27
6-5 DESIGN CONSIDERATIONS
6-5.1 MOTOR SIZING
6-5.2 COMBUSTION CONSIDERATIONS
6-5.3 MOTOR CASE PERFORMANCE6-34
6-5.3.1 Material Selection6-34
6-5.3.2 Safety Factor6-35
6-5.4 PROPELLANT SELECTION6-35
6-5.4.1 Thermochemical Considerations
6-5.4.2 Burn Rate
6-5.4.3 Signature6-38
6-5.4.4 Mechanical Properties
6-5.4.5 Combustion Stability
6-5.5 NOZZLE THROAT SELECTION6-39
6-5.5.1 General Considerations6-39
6-5.5.1.1 Gas Dynamics6-39
6-5.5.1.2 Structural Considerations
6-5.5.1.3 Fabrication Considerations
6-5.5.2 Propellant Grain/Burn Rate/Throat Area Interaction
6-5.5.3 Thermodynamic Considerations
6-5.6 PLUME CONSIDERATIONS
6-5.6.1 Aerodynamic Effects6-43
6-5.6.2 Thermodynamic Effects6-43
6-6 SCALING
6-6.1 GENERAL6-4
6-6.2 SCALING FACTORS
6-6.3 DISCUSSION6-47
6-7 TESTING
6-7.1 STRUCTURAL INTEGRITY TESTS
6-7.2 PROPELLANT GRAIN INTEGRITY TESTS
6-7.2.1 Mechanical Properties6-48
6-7.2.2 Thermal Properties6-49
6-7.2.3 Performance Characteristics
6-7.3 TEST FOR NEW PROPELLANT FORMULATION6-50
6-7.4 QUALITY ASSURANCE TESTING
6-7.4.1 Nondestructive Testing6-50
6-7.4.2 Destructive Testing6-51
6-7.5 ENVIRONMENTAL TESTING
REFERENCES

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MIL-HDBK-762(MI)

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CONTENTS (cont’d)

CHAPTER 7 STRUCTURES

LIST OF SYMBOLS
GENERAL
MASS AND BALANCE
7-2.1 MASS AND CENTER-OF-GRAVITY ESTIMATION
7-2.2 TRANSVERSE MOMENT OF INERTIA
7-2.3 ROLL MOMENT OF INERTIA
LOAD
7-3.1 TRANSPORTATION AND HANDLING LOADS
7-3.2 LAUNCH LOADS
7-3.3 FLIGHT LOADS
STRUCTURAL DESIGN ANALYSIS
7-4.1 CONCEPTUAL DESIGN
7-4.2 PRELIMINARY DESIGN
7-4.2.1 Structural Components
7-4.2.1.1 Motor Case
7-4.2.1.2 Nozzle
7-4.2.1.3 Propellant
7-4.2.1.4 Payload
7-4.2.1.5 Payload Nose Fairing
7-4.2.1.6 Fins
7-4.2.2 Preliminary Load Estimation
7-4.2.2.1 Mass Distribution
7-4.2.2.2 Moment of Inertia
7-4.2.2.3 Airloads
7.4.2.2.4 Shear Diagram
7-4.2.2.5 Bending Moment Diagram
7-4.2.2.6 Axial Load Diagram
7-4.2.3 Stress
7-7
7-7
7-9
7-9

7-2 7-2 7-2 7-25 7-25 7-25 7-29 7-29 7-29 7-29 7-29 7-31 7-32 7-36 7-36 7-37 7-38 7-39 7-39 7-42 7-46 7-47 7-48 7-48 7-49 7-53 7-53 7-56 7-56 7-59 7-59 7-60 7-61 7-62 7-64 7-6 7-68 7-70 7-70 7-72 7-72 7-73 7-7 7-7 7-7

Motor Chamber
End Closure
Nozzle
Payload
Fin
Propellant Grain
7-4.2.4 Materials
7-4.2.4.1 Structural Materials
7-4.2.4.2 Physical Properties of Structural Materials
7-4.2.4.3 Manufacturing Techniques
7-4.2.4.4 Mass-Per-Cost Factors
7-4.2.4.5 Propellants
7-4.2.5 Safety Factors
7-4.2.6 Mass and Size Estimating Relationships
7-4.2.6.1 Payload
7-4.2.6.2 Propellant Mass Estimation
7-4.2.6.3 Motor Sizing
7-4.2.6.4 Motor Inert Masses
7-4.2.6.5 System Considerations
7-4.3 STRUCTURAL MODELING FOR SYSTEM ANALYSIS
7-4.3.1 Load Representation

MIL-HDBK-762(MI)

CONTENTS (cont’d)

7-4.3.2 Structural Models
7-4.3.2.1 Lumped Parameter Models
7-4.3.2.2 Finite Element Models
7-5 DYNAMIC ANALYSIS
7-6 AEROELASTICITY
7-7 HEAT TRANSFER
7-7.1 INTRODUCTION
7-7.2 THE ROLE OF HEAT TRANSFER ANALYSIS
7-7.3 PHYSICAL SITUATION
7-7.3.1 General
7-7.3.2 External Heating
7-7.3.3 Internal Heating (Case and Nozzle)
7-7.3.4 Exhaust Plume Heating
7-7.3.5 Propellant Effects
7-7.3.6 Heating Interval
7-7.4 MECHANISMS OF THERMAL PROTECTION
7-7.5 MATERIALS
7-7.5.1 Case Insulations
7-7.5.2 Nozzle Insulations
7-7.6 DESIGN REQUIREMENTS AND CONSTRAINTS
7-7.7 APPROACH TO THERMAL ANALYSIS
7-7.8 ANALYTICAL TECHNIQUES
7-7.8.1 General
7-7.8.2 Nozzle Thermal Techniques
7-7.8.3 Complex Analytical Techniques
7-7.9 SAMPLE THERMAL DESIGN PROBLEM FOR AERODYNAMIC HEATING
7-7.9.1 General
7-7.9.2 Aerodynamic Heating Calculations
7-8 STRUCTURAL TESTING
7-9 OTHER STRUCTURAL CONSIDERATIONS
REFERENCES

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7-7 7-82 7-84 7-84 7-86 7-86 7-86 7-87 7-87 7-87 7-87 7-93 7-93 7-94 7-94 7-94 7-95 7-95 7-96 7-97 7-98 7-98 7-98 7-9 7-9 7-9 7-102 7-106 7-108 7-108

CHAPTER 8 LAUNCHER CONSIDERATIONS

8-1 INTRODUCTION
8-2 GENERAL
8-2.1 LAUNCHER FUNCTIONS
8-2.1.1 Environmental Protection and Conditioning
8-2.1.2 Test and Checkout
8-2.1.3 Transportation
8-2.1.4 Aiming
8-2.1.5 Ignition, Fuze Setting, and Arming
8-2.1.6 Initial Guidance and Spin
8-2.2 SYSTEM CONSTRAINTS ON LAUNCHER
8-2.3 LAUNCHER CONFIGURATION
8-2.3.1 Tactical Considerations
8-2.3.2 Control of Aiming
8-2.3.3 Research Launchers
8-2.3.4 Tip-Off vs Nontip-Off
8-2.3.5 Supports

8-1 8-1 8-1 8-2 8-2 8-2 8-2 8-3 8-3 8-3 8-3 8-4 8-4 8-4 8-5 8-5

MIL-HDBK-762(MI)

CONTENTS (cont’d)

8-2.3.6 Types of Launchers
8-2.3.7 Air-to-Ground Launchers
8-2.4 LAUNCHER ANALYSIS
8-3 INTERFACE CONSIDERATIONS
8-3.1 MECHANICAL INTERFACES
8-3.2 ELECTRICAL INTERFACES
8-3.3 CONTAINER LAUNCHERS
8-3.4 ROCKET EXHAUST IMPINGEMENT
8-3.4.1 Internal Exhaust Impingement
8-3.4.2 External Exhaust Impingement
8-3.5 ROCKET SPIN TECHNIQUES
8-3.6 LAUNCHER GUIDANCE SCHEMES
8-3.7 ROCKET FIN CONSIDERATIONS
8-4 LAUNCH ACCURACY
8-4.1 MAJOR FACTORS AFFECTING LAUNCH ACCURACY
8.4.2 LAUNCH ACCURACY ESTIMATION

Paragraph 8-4.3 MEASUREMENT OF LAUNCH ACCURACY

8-4.4 FLEXIBLE ROCKET EFFECTS
REFERENCES
BIBLIOGRAPHY
8-5
8-10

Pag e 8-10 8-13 8-13 8-14 8-15 8-16 8-16 8-17 8-17 8-18 8-18 8-20 8-20 8-20 8-21 8-2 8-23 8-24

A-0 LIST OF SYMBOLS
A-1 INTRODUCTION
A-2 ATMOSPHERIC PROPERTIES
A-2.1 BASIC RELATIONSHIPS
A-2.2 SOURCES OF THERMODYNAMIC DATA
A-2.2.1 US Standard Atmosphere, 1976
A-2.2.2 US Standard Atmosphere Supplements. 1966
A-2.2.3 Range Reference Atmosphere Documents
A-2.2.4 Military Standard Climatic Extremes, MIL-STD-210
A-2.2.5 The NASA/MSFC Global Reference Atmoshere Model-Mod 3
A-2.2.6 Other Regional-Seasonal Atmospheric Data
A-3 WIND
A-3.1 WIND SPEED
A-3.1.1 The Surface Layer
A-3.1.2 The Boundary Layer
A-3.1.3 The In-Flight Layer
A-3.2 SOURCES OF WIND SPEED DATA
A-3.3 WIND SHEAR
A-3.4 TURBULANCE
A-4 ENVIRONMENT TEST METHODS
REFERENCES
A-1
A-2
A-2
A-2
A-3
A-3
A-4
A-4
A-5
A-5
A-7
A-7
A-7
A-7
A-8
A-8
A-8
A-8
A-9
A-9
A-9
B-1 DISCUSSIONB-1
B-2 PROGRAMsB-1

xii

MIL-HDBK-762(MI)

Paragraph Page

B-2.1 B-2.2 B-2.3 B-2.4 B-2.5 B-2.6 B-2.7

B-2.8 B-2.9

B-2.10

B-2.1 B-2.12

B-2.13

B-2.14

B-1 B-1 B-2 B-2 B-3 B-3

B-3 B-4

B-4

B-4 B-5

B-5 B-6 B-6

C-0 C-1 C-2

C-3

AERODRAG
AERODSN
NAVYAERO
POINT MASS TRAJECTORY PROGRAMS
AER06D
TRAJ
AERODYNAMIC HEATING ANALYSIS (AERHET)
PROGRAM NAME. FDL/FSI PARABOLIZED NAVIER-STOKES CODE
(S/HABP)

CONTENTS (cont’d) NUMERICAL FLOW FIELD PROGRAM FOR PROGRAM NAME. SUPERSONIC-HYPERSONIC ARBITRARY BODY PROGRAM PROGRAM NAME. COMPUTER PROGRAM FOR CALCULATION OF COMPLEX CHEMICAL EQUILIBRIUM COMPOSITIONS, ROCKET PERFORMANCE, INCIDENT AND REFLECTED SHOCKS, AND CHAPMAN-JOUGET

DETONATIONS—PACK I
PROGRAM NAME. THE JANNAF STANDARD PLUME FLOW FIELD MODEL (SPF)
ABLATION PROGRAM (CMA3)
COMPUTER PROGRAM (ACE)
WITH KINETICS (BLIMPK)
LIST OF SYMBOLS
INTRODUCTION
THERMAL MODELING
C-2.1 CYLINDRICAL COORDINATE THERMAL MODELING
C-2.1.1 Cylindrical Thermal Storage Model
C-2.1.2 Cylindrical Radial Heat Conduction Model
C-2.1.3 Cylindrical Circumferential Heat Conduction Model
C-2.1.4 Cylindrical Axial Heat Conduction Model
C-2.1.5 Cylindrical Heat Convection Model
C-2.1.6 Cylindrical Heat Radiation Model
C-2.2 SPHERICAL COORDINATE THERMAL MODELING
C-2.2.1 Spherical Thermal Storage Model
C-2.2.2 Spherical Radial Heat Conduction Model
C-2.2.3 Spherical Longitudinal Heat Conduction Model
C-2.2.4 Spherical Latitudinal Heat Conduction Model
C-2.2.5 Spherical Heat Convection Model
C-2.2.6 Spherical Heat Radiation Model
C-2.2.7 Spherical Modeling for Nonhomogeneous Spherical Elements
C-2.2.7.1 General
C-2.2.7.2 Derivation of Area, Volume, and Heat Transfer Equations for a Spherical Slice
FORCED CONVECTION HEAT TRANSFER TO ROCKET MOTOR EXTERNAL SURFACES
C-3.1 SPHERICAL STAGNATION POINT HEATING
C-3.2 LEES’ HEMISPHERICAL DISTRIBUTION, LAMINAR FLOW
C-3.3 DETRA-HIDALGO HEMISPHERICAL DISTRIBUTION, TURBULENT FLOW
C-3.4 ECKERT LAMINAR FLAT PLATE HEATING METHOD

C-1 C-5 C-5 C-5 C-5 C-6 C-8 C-8 C-9 C-9 C-10 C-10 C-1 C-12 C-13 C-14 C-14 C-15 C-15 C-15 C-18 C-19 C-21 C-21 C-2 xiii

MIL-HDBK-762(MI)

CONTENTS (cont’d)

C-3.5 MODIFIED SPALDING-CHI METHOD
C-3.6 LAMINAR CIRCUMFERENTIAL HEATING ON A YAWED CYLINDER
C-3.7 TURBULENT STAGNATION LINES HEATING ON A YAWED CYLINDER
REFERENCES
BIBLIOGRAPHY

Paragraph

Page

C-2 C-24 C-25 C-25 C-27

I-1INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xiv

MIL-HDBK-762(MI)

Figure No.TitlePage

Examples of Midsize Free Flight Rockets
Examples of Small Free Flight Rockets
Examples of Large Free Flight Rockets
Typical Free Flight Rocket Configuration
System Design Phases
Concept Selection Phase Activities
Preliminary Design Phase Activities
System Validation Phase Activities
Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—133-m Rocket
Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—762-m Rocket
Effect of Burnout Ballistic Coefficient and Burnout Velocity on Range—321-m Rocket
Drag Coefficient vs Mach Number—130-m Rocket
Drag Coefficient vs Mach Number—762-m Rocket
Drag Coefficient vs Mach Number—321-m Rocket
Coast Drag Velocity Loss—130-m Indirect Fire Rocket
Boost Drag Velocity Loss—Indirect Fire Rocket
Boost Drag Velocity Loss—Direct Fire Rocket
Coast Drag Velocity Loss—Sounding Rocket
Boost Drag Velocity Loss—Sounding Rocket
Coast Drag Velocity Loss—Surface-to-Air Rocket
Boost Drag Velocity Loss—Surface-to-Air Rocket
Effect of Ideal Burnout Velocity on Booster-Mass Ratio
Effect of Growth Factor on Ideal Burnout Velocity
Elevation
Elevation
Indirect Fire—Boost; Effect of Range on Growth Factor
Boost/Sustain Engine; Variation of Specific Impulse with Thrust
Indirect Fire—Boost/Sustain; Effect of Range on Impulse Ratio
Indirect Fire—Boost/Sustain; Effect of Range on Growth Factor
Indirect Fire—Boost; Effect of Propellant Mass Fraction on Growth Factor
Indirect Fire—Boost; Effect of Ballistic Coefficient on Growth Factor
Direct Fire—Boost/Sustain; Effect of Impulse Ratio on Time to Target
Direct Fire—Boost; Effect of Growth Factor on Time to Target for Various G Values
Direct Fire—Boost; Effect of Ballistic Coefficient on Growth Factor
Direct Fire—Boost; Effect of Propellant Mass Fraction on Growth Factor
Rocket
Sounding Rocket—Boost; Effect of Growth Factor on Summit Altitude
Sounding Rocket—Boost; Effect of Propellant Mass Fraction on Growth Factor-
Sounding Rocket-Boost; Effect of Ballistic Coefficient on Growth Factor
Surface to Air—Boost; Effect of Time to Altitude on Growth Factor
Surface to Air—Boost: Effect of Propellant Mass Fraction on Growth Factor
Surface to Air—Boost; Effect of Ballistic Coefficient on Growth Factor
Effect of Altitude and Flight Path Angle on Maximum Range
Effect of Maximum Range on Growth Factor
Effect of Release Altitude and Flight Path Angle on Air-to-Ground Trajectory
Air to Ground-Boost\ Sustain; Effect of Impulse Ratio on Time to Target
Air to Ground-Boost; Effect of Growth Factor on Time to Target for Various G Values

Indirect Fire—Boost; Effect of Initial Acceleration Level on Optimum Launch Quadrant Indirect Fire—Boost/Sustain; Effect of Impulse Ratio on Optimum Launch Quadrant Effect of Burnout Ballistic Coefficient and Burnout Velocity on Sumit Altitude-133-m xv

1-2
1-3
1-5
1-6
2-2
2-4
2-8
3-6
3-6
3-7
3-8
3-9

2-23 3-10 3-1 3-12 3-13 3-14 3-15 3-16 3-17 3-18 3-20

3-2 3-23 3-23 3-24 3-24 3-25 3-25 3-27 3-28 3-31 3-31

3-32 3-3 3-34 3-34 3-35 3-36 3-36 3-37 3-38 3-39 3-40 3-41

MIL-HDBK-762(MI)

DOD-HDBK-762(Ml) LIST OF ILLUSTRATIONS (cont’d)

Figure No.TitlePage

xvi

Air to Ground-Boost; Effect of Ballistic Coefficient on Growth Factor
Air to Ground-Boost; Effect of Propellant Mass Fraction on Growth Factor
Flow Diagram
Aiming Errors
Thrust Misalignment
Static and Dynamic Imbalance
Effect of Thrust Misalignment on an Aerodynamically Stable Rocket
Effect of Wind on an Aerodynamically Stable Rocket
Static Margin
Variation of Angular Dispersion and Wavelength of Yaw During Flight
Effect of Wind on a Ballistic Free Rocket (After Burnout) (Top View)
Definitions of Sign Conventions for Dispersion Equations of Motion
Angular Dispersion Due to Initial Angular Rate for Various P Values
Angular Dispersion Due to Initial Translational Velocity for Various P Values
Angular Dispersion Due to Wind for Various P Values
Angular Dispersion Due to Thrust Misalignment for Various P Values—Zero Spin
Optimum Wavelength of Yaw for Minimum Total Dispersion
Growth of Angular Dispersion For A Rocket With A Thrust Misalignment and No Spin
Slow Spin
Effect of Spin on Buildup of Angular Dispersion Due to Thrust Misalignment
Effect of Constant Spin on Dispersion Reduction Factor
Constant Spin Rate; Various P Values
Constant Spin Acceleration; Various P Values
Slowly Uniformly Decreasing Spin (SUDS)
Effect of Wavelength of Yaw on Buck Distance for Zero Angular Dispersion
Effect of Buck Distance on Dispersion Reduction
Effect of Static Margin on A Rocket With Thrust Misalignment
Effect of Static Margin on Wind Disturbance
The Inertial Coordinate System and Body-Centered Coordinate System for a Free Rocket
Positive Sign Conventions of the Six-DOF-Equations of Motion
Ratio of CEP to ó/ófor Elliptical Distribution
Ratio of CEP to ófor Elliptical Distribution
Variation of Range Error Probable With Range-Impact Fuze
Variation of Deflection Error Probable With Range-Impact Fuze
Variation of CEP With Range-Impact Fuze
Initial Velocity vs Maximum Range
Unit Effect, Range/Departure Angle vs R/Rfor Various B Values-Impact Fuze
Unit Effect, Range Velocity vs R/R, for Various B Values-Impact Fuze
Unit Effect, Range, Density vs R/Rfor Various B Values-Impact Fuze
Unit Effect, Range/Wind vs R\Rfor Various B Values-Impact Fuze
Unit Effect, Deflection/Wind vs R/Rfor Various B Values-Impact Fuze
QE vs R/Rfor Various B Values-Impact Fuze
Time of Flight vs R/Rfor Various B Values-Impact Fuze
QE vs R/Rfor Various B Values-Time Fuze
Time of Flight vs R/Rfor Various B Values—Time Fuze
Unit Effect, Range/Density vs R/Rfor Various B Values-Time Fuze
Unit Effect, Range Velocity vs R/Rfor Various B Values-Time Fuze
Unit Effect, Range/Wind vs R/R, for Various B Values-Time Fuze
Unit Effect, Range/Departure Angle vs R/Rfor Various B Values—Time Fuze
Unit Effect, Deflection/Wind vs R/Rfor Various B Values—Time Fuze
Unit Effect, Altitude/Density vs R/Rfor Various B Values—Time Fuze

Growth of Angular Dispersion For A Rocket With A Thrust Misalignment and

4-6
4-8
4-8
4-9

3-42 3-42 3-4 4-10 4-1 4-12 4-13 4-15 4-18 4-20 4-23 4-26 4-28 4-28

4-28 4-29 4-31 4-32 4-35 4-37 4-39 4-39 4-4 4-4 4-50 4-50 4-59 4-60 4-61 4-61 4-64 4-65 4-71 4-75 4-78 4-81 4-85 4-8 4-91 4-94 4-97 4-100 4-103 4-106 4-109 4-112

MIL-HDBK-762(MI)

LIST OF ILLUSTRATIONS (cont’d)

Figure No.TitlePage 4-49 4-50

C, Cand vs Total Fineness Ratio

Afterbody Lengths
Unit Effect, Altitude/Velocity vs R/Rfor Various B Values—Time Fuze
Unit Effect, Range/Time vs R/Rfor Various B Values—Time Fuze
Unit Effect, Altitude/Time vs R/Rfor Various B Values—Time Fuze

Rocket Axes—Showing Direction and Sense of Forces, Moments, and Angular

Quantities
Relationships
Normal Force Coefficient Gradient for Tangent Ogive-Cylinder Configurations
Center of Pressure for Tangent Ogive-Cylinder Configurations
Normal Force Coefficient Gradient for Cone-Cylinder Configurations
Center of Pressure for Cone-Cylinder Configurations
With Varying Afterbody Lengths

Normal Force Coefficient Gradient and Center of Pressure—4-cal Tangent Ogive

Afterbody Lengths

Normal Force Coefficient Gradient and Center of Pressure—7.125-deg Cone With Varying Normal Force Coefficient Gradient and Center of Pressure—l/2-Power Nose With Varying

Lengths With Constant Afterbody Length of 6 cal
With Constant Afterbody Length of 6 cal
With Constant Afterbody Length of 6 cal
for 2-cal Ogive Cylinders
cal Ogive Cylinders
of Pressure
Some Aerodynamic Characteristics of a Spike-Nosed Rocket
Boattail Normal Force Correlation Coefficient
Ratio of Boattail Center of Pressure to Boattail Length
Effect of Afterbody Diameter to Head Diameter Ratio on Aerodynamic Parameters
2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Center of Pressure vs Boattail Length to Afterbody Diameter Ratio at2.2 . . . . . . . . .
Rocket With Necked-Down Center Body
Aerodynamic Characteristics of Necked-Down Center Body With and Without Shroud
Mach Number for Family of Nose-Cylinder Configurations—4-cal Nose
Number for Family of Nose Cylinder Configurations-3-cal Tangent Ogive Nose
Typical Free Rocket Stabilizing Devices
Nomenclature of Some Typical Rocket Components
tion
Subsonic Fin Normal Force Coefficient Gradient
sonic Speeds
Center of Pressure for Rectangular Fins at Transonic Speeds
Linear Theory Normal Force Gradient of Rectangular Fins vs Mach Number
Linear Theory Normal Force Gradient of Delta Fins vs Mach Number

Normal Force Coefficient Gradient and Center of Pressure—Varying Tangent Ogive Nose Normal Force Coefficient Gradient and Center of Pressure—Varying Conical Nose Angle Normal Force Coefficient Gradient and Center of Pressure—Varying n-Power Nose Shape Variation of Normal Force Coefficient Gradient and Center of Pressure vs Mach Number Variation of Normal Force Curve Gradient and Center of Pressure vs Mach Number for 3- Effect of Nose Blunting of a 4-cal Ogive on Normal Force Coefficient Gradient and Center Normal Force Coefficient Gradient vs Boattail Length to Afterbody Diameter Ratio at Normal Force Coefficient Gradient and Center of Pressure Over Rocket Diameter Ratio vs Normal Force Coefficient Gradient and Center of Pressure Over Rocket Diameter vs Mach Illustration of Exposed Fin-Body and Isolated Wing Geometry, and Accompanying Nota- Summary Curves of the Generalized Normal Force Gradient for Electangular Fins at Tran-

5-81 5-81 5-82 5-82 5-83 5-83 5-84

5-85 5-86 5-87 5-8 5-89 5-90 5-91 5-92

5-93 5-94 5-95 5-96 5-97

5-98 5-98 5-9 5-9

xvii

MIL-HDBK-762(MI)

LIST OF ILLUSTRATIONS (cont’d)

Figure No.TitlePage 5-35

Taper Ratios
Ratio of Fin Center of Pressure to Fin Root Chord Length for Various Fin Taper Ratios
Normal Force Coefficient Gradient and Center of Pressure for Rectangular- Fins
Theory and Faired Curves for Rectangular Fins
Fin Geometry
Variation of Normal Force Coefficient Gradient With Aspect Ratio
(Center of pressure is measured from the leading edge of the root chord.)
Stabilizing Effectiveness Of Tangential Fins and WAF

Fin Normal Force Coefficient Gradient at Supersonic Mach Numbers for Various Fin Center of Pressure for Clipped-Delta Wings for Various Aspect and Thickness Ratios

Comparison of Flat and WAF Static Stability Derivatives for a Typical Rocket Variation of Roll Moment Coefficient With Mach Number for Tangent Fins Having 0-deg

and—5-deg Sweepback
Ratio Tangent Fins
WAF Roll Moment {coefficients at Zero Angle of Attack
t/Cr= 3%
Ratio of WAF Lift Effectiveness at Closing Angles
Effects of Opening AngleWAF Roll Moment at Zero Angle of Attack Cr/d = 1.75,
b/(2d) = 0.665
Combinations With Differential Incidence of the Horizontal Surfaces
WAF Roll-Moment Coefficient With Varying Fin Cant Angles
Incremental Normal Force Coefficient Gradient for a Flare
Incremental Normal Force Coefficient Gradient for a Flared Afterbody for= 1.5 and
2.0
Incremental Normal Force Coefficient Gradient for a Flared Afterbody for= 3.0...........
Incremental Normal Force Coefficient Gradient for a Flared Afterbody for= 4.0...........
Incremental Normal Force Coefficient Gradient for a Flared Afterbody for= 5.0. . . .
Ringtail Geometry,= 4-deg Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ratio of Ringtail to Equivalent Planar Fin Normal Force Coefficient Coefficient
Effect of Ringtail Geometry and Longitudinal Position on the Variation ofWith
Mach Number, 4-deg inter-nal Expansion Angle
Effects of Chord, Diameter, and Longitudinal Position onon Ringtails, 4-deg
Internal Expansion Angle
Five Typical Configurations of Longitudinal Strut-Supported Ringtails

Effect of Sweepback Angle and Roll Position on Roll Moment Coefficient on High Aspect WAF Roll Moment Coefficient vs Mach Number, Effect of Modifying WAF Root and Tip Chord Cross Section on Roll Moment, Roll Moment Effectiveness Coefficient Gradient for Cruciform and Planar Wing-Body

Compared to Solid Body
Values of Lift Ratios Based on Slender Body Theory
Interference Effects of Fin on Body
Lift Factors—Influence of Fin on Body
Total Fin-Body Interference Factor for Various a/m Ratios
Normal Force of Fin-Body Combinations for Various Values of (AR)and 2r/b
2r/b
Effect of Roll Angle on Cruciform Fins at
Normal Force Coefficient of Multiple Fins at Various Supersonic Speeds

Aerodynamic Stability Coefficients for Various Longitudinally Supported Ring Shapes Center of Pressure for Fins With Fin-Body Interference for Various Values of (AR)and Effect of Roll Angle on 8-Fin Configuration at xviii

MIL-HDBK-762(MI)

LIST OF ILLUSTRATIONS (cont’d)

Interference Parameters I and I’, and Fin Geometry
Correlation of Data with I’ for Various Aspect Ratios
Multiple Fin Model Geometry
Faired Center of Pressure vs Interference Parameter I
Fin Effectiveness With Gaps as a Function of Mach Number
Mach Number of a Typical Rocket With and Without Thrust
Effect of Downwash Generators and Fin-Body Gaps on Static Stability
Body Data—Sample Calculation
Fin-Afterbody Configuration and Design Parameters for Sample Stability Calculation
Configuration and Aerodynamic Coefficients—Sample Calculation
Variation ofWith Cfor Various Values of (Cylindrical Afterbody, d/d= 0.8,
Air Nozzles Having Similar Plume Shapes)

Normal Force Coefficient Gradient and Ratio of Center of Pressure to Rocket Diameter vs Variation of Base Pressure With Cfor Various Nozzles at Variation of Base Pressure With Cfor Various Nozzles at Effect of Thrust on Body Surface Pressure Distribution on Cylindrical Afterbody at

Effect of Thrust on Body Pressure X/d = 0.225, Cylindrical Sonic Nozzle, d/d= 0.45)
Plume Effects on Configuration Stability Characteristics at= 1.0 (Ogive-Cylinder Body
= 10.2, Moment Center 5.1d Aft of Nose). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ratio of Radial Thrust To Axial Thrust Required for Same Plume Effect

Effect of Thrust on Base and Body Surface Pressure Distribution on Cylindrical Afterbody Effect of Plume on Normal Force Characteristics of Fins Located at Three Different

Effect of Radial Thrust Coefficient on Longitudinal Derivatives
2.0, and 2.3)
Position= 0.2, 0.4, 1.0, 1.25 and 1.5)
Plume Effects on Afterbody Static Stability
Normal Force Coefficient vs Angle of Attack
Crosswind in Nonlinear Aerodynamic Environment
Comparison of Pitch Damping Coefficient Estimate to Experiment
General Army Free Flight Rocket Configuration
Thrust Effects on Total Pitch Damping Coefficient
Combinations With Differential Incidence of Horizontal Surfaces
Coefficient of Damping in Roll for Cruciform and Planar Wing-Body Combinations
Re = 0.71 X 10
Re = 0.65 X 10
Re = 0.65 X 10
Re = 0.65 X 10
of Attack and Fin Cant Angle
Drag Coefficients Due to Pressures on Noses at

Longitudinal Positions Along Body at Effect on Fin Number 2 Normal Force Characteristics in Forward Position Thrust Effects on Horizontal Fin Panel Normal Force Characteristics—Fin in Forward Coefficient of Roll Moment Effectiveness for Cruciform and Planar Wing-Body Magnus Characteristics of Finned and Nonfinned Rockets at Magnus Characteristics of Finned and Nonfinned Rockets at Magnus Characteristics of Finned and Nonfinned Rockets at Magnus Characteristics of Finned and Nonfinned Rockets at Variations of Side Force Coefficient and Yawing Moment Coefficient With Angle Pressure Drag of Noses of Fineness Ratio 3, Total Fineness Ratio

Wave-Drag Coefficient of Optimum Secant Ogive Cylinder at Transonic Speed

xix

MIL-HDBK-762(MI)

DOD-HDBK-762(MI) LIST OF ILLUSTRATIONS (cont’d)

Figure No.TitlePage 5-113

Wave-Drag Coefficient of Slender Ogives at Transonic Speeds
Wave-Drag Coefficient of Cones and Ogives at Supersonic Speeds
Sketch Depicting Development of Tangent Ogive (2 cal in this case) and “Given” Ogive
Profiles of Nose Shapes
Nose Fineness Ratios
otherwise indicated)
Zero Lift Dragon Three Special Nose Configurations
Variance of Boattail Base Diameter on Total Drag vsfor Complete Body
Configuration
Length-to-Diameter Ratios
Wave-Drag Coefficient of Conical Boattails at Supersonic Speeds
Wave-Drag Coefficient of Parabolic Boattails at Supersonic Speeds
Wave-Drag Coefficient of Conical Flare at Various Mach Numbers
Drag of Slender Conical Afterbodies or Forebodies
Sketch Showing Diameters to be Used in Eq. 5-39
Comparison of Drag of Flare, Split Flare, and Split Flare With Shroud
Double-Wedge Shapes for Various c/cRatios
Wave-Drag Coefficient of Fins of Various Sectional Shapes
Wave-Drag Coefficient of Rectangular Fins at Subsonic and Transonic Speeds
Wave-Drag Coefficient of Delta Fins at Subsonic and Transonic Speeds
Wave-Drag Coefficient of a Double-Wedge Fin at Transonic Speeds
Effect of Internal Expansion Angleand Longitudinal Positioning E/d on
Ringtail Drag
Flat Plate Average Skin-Friction Coefficient
Reynolds Number as a Function of Flight Mach Number and Altitude
Typical Variation of Base Pressure With Thrust
Base Flow Geometry

Wave Drag of Secant Ogives in Terms of Ogive Radius for Several Mach Numbers and Percent Change in Drag Coefficient vs Me’plat Diameter (Flat unless Subsonic/Transonic Boattail Wave Drag vs Mach Number for Various Wave-Drag Coefficient of Fins at Supersonic Speeds for Parabolic Arc and

= 1.5 and 2.0, Turbulent Boundary Layer

Measured and Correlated Base Pressure for Several Configurations,

Effects of Mach Number and Reynolds Number on Base Pressure
Cylinder to Boattail Base Pressure Ratio as a Function of Base Area Ratio (Power-Off)
at free-stream Mach numbers of 1.65 and 2.21. )
Plume-Off Boattail and Flare Base Pressure Coefficients
Diameter Ratio
Base Pressure for Various Split Petal Configurations (Jet-Off)
Effect of Rocket Jet Plume on Base Pressure at= 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Base Pressure Variation With Jet Momentum Flux Ratio
Effect of Conical Afterbody Geometry on Base Pressure Ratio
Effects of Nozzle Position on Base Pressure

Base Pressure Coefficient for Finless Bodies of Revolution in Terms of Local Pressure and Local Mach Number Ahead of Base, Effect of Boattailed and Flared Afterbodies on Jet-Off Pressures (Flare data were obtained Variation of Conical Boattail Wave and Base Drag With Base Diameter to Cylinder

Effect of Multiple Nozzles on Base Pressure
Airplane With Theory

Base Pressure Variation With Thrust for Cylindrical Afterbody With Nozzle Flush With Comparison of Two-Dimensional Base Pressures From Upper Vertical Fin of X-15

5-179 5-180 5-181 5-182

5-183 5-184

5-186 5-187 5-187 5-188 5-191 5-191 5-192

5-193 5-201 5-202 5-202 5-203

5-204 5-205 5-205 5-206 5-206

5-208 5-209 5-210

5-210 5-211

5-212 5-213 5-214 5-214 5-215 5-217

5-218 5-219

MIL-HDBK-762(MI)

LIST OF ILLUSTRATIONS (cont’d)

Figure No. 5-153

5-157 With Cylindrical Afterbody at

6-7

6-20 6-21 6-21 6-2 6-2 6-27 6-29

7-8

6-30 6-31 6-3 6-37 6-40 6-41 7-12 7-15 7-16 7-17 7-18 7-19 7-20 7-21 7-23 7-24

Comparison ol Lengths ov Various Types of Nozzle for

Base Pressure Coefficient of Fins at Transonic Speeds
Revolution Having a d/d
Configuration and Design Parameters for Sample Drag Calculation
Sample Total and Component Drag Coefficients vs Mach Number
= 2.0

Title Effect of Ringtail Longitudinal Location on Base Pressure Characteristics of Body Local Normal Force Coefficient Gradient Ratio Distribution for Tangent Ogive

Cylinder-Boattail, and Cone-Cylinder-Flare Configurations at= 2.0 . . . . . . . . . . . . .
Distribution of Local Axial Force Coefficients
Distribution of Local Pressure Coefficients
Comparison of Test Results on Full-Size and Scale Model Artillery Rocket
Arnold Engineering Center
Aerodynamic Force Components
Typical Normal Jet Plume Simulator
Case Bonded Solid Propellant Rocket Motor
Motor Performance and Temperature Effect
Two Basic Types of Nozzles Employed in Rocket Motors
p/pfor Different Values of= c/c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Distributed Normal Force Coefficient Gradient on Cone-Cylinder, Cone- Axial Force Distributions on Conical Flare and Boattail Following a Relationship Between Maximum Allowable Model Dimensions and Test Section Dimension in Tunnel A and 12X12-in. Tunnel at Von Karman Gas Dynamics Facility at Area Ratio A/A* for Complete Expansion as a Function of the Nozzle Pressure Ratio

Conditions
Design Thrust Ratio as Function of Nozzle Divergence Angle
Schematic Cross Sections of Plug and Expansion-Deflection Nozzles
Off-Design Thrust Coefficients of Conventional and Plug Nozzles
Grain Asymmetries Considered
Flow Chart of Motor Design Sequence Showing Major Iteration Loops

Pressure Distributions in a Converging-Diverging Nozzle Under Different Operating

Ratios
Typical Characteristic Curves for a Solid Propellant
Influence of Pressure and Gas Flow Velocity on Burning Rate
Typical Variation of Erosive Constant With Burning Rate
Illustration of Basic Nozzle Configurations and Nozzle Nomenclature
Nozzle for PERSHING First Stage
Analysis Cycle for Free Flight Rockets
Illustration of Symbols Used in Nose Shape Defining Equations
Volume of Nose Shapes
Ratio of Secant Ogive Volumes to Cone Volume
Ratio of Ogival Volumes to Cone Volume
Surface Area of Nose Shapes
Ratio of Secant Ogive Surface Areas to Cone Area
Ratio of Ogival Surface Areas to Cone Area
CG Location of Ogival Shapes
Secant Ogive Pitch Inertia vs Fineness Ratio
Secant Ogive Roll Inertia vs Fineness Ratio

Specific Impulse Parameter as a Function of Pressure Ratio for Different Specific Heat xxi

MIL-HDBK-762(MI)

Page Figure No.

LIST OF ILLUSTRATIONS (cont’d)

Axial Loads on Free Flight Rocket
Circumferential Loads on Motor Case
Concentrated Loads on Free Flight Rockets
Nozzle Structural Configuration
Representative Solid Propellant Grain Geometries
Payload Structure Configuration
Payload Nose Fairing
Thin-Plate Fin Concepts
Superposed Shear Diagram
Methods of Mass Distribution Approximation
Coordinates for Moment-of-Inertia CalCulations
Lumped Mass Model of a Typical Rocket
Compontents of Total Normal Acceleration
Example Problem to Illustrate Shears and Bending Moments on a Typical Rocket
Shear Load Diagram for Inertial Load Sample Problem
Bending Moment Diagram for Inertial Load Sample Problem
Typical Axial Load Diagram During Powered Flight
Motor Case Discontinuity Stress
Motor Case Thermally Induced Strain
Filament Wound Motor Case
Modeling Y-Ring Structure by Shell Elements
Geometry of Plane-Strain Analysis Model
Fin and Airload
Fin Shear Carrying Members
Equivalent Two-Flange Beam Fin
Relative Motor Case Cost vs Case Thickness
Relaxation Modulus Spectrum for a Typical Double-Base Propellant
Probability of Kill vs Warhead Diameter
Propellant Volumetric Loading Efficiency
Propellant Mass vs Motor Case Fineness Ratio
Rocket Sizing Trade-Off Summary
Degrees of Freedom in Local Coordinate System
Two-Mass Rocket Model
Beam Displacement Model
Finite Element Mode] of a Typical Nozzle
Magnified (50X) Deformed Outline
Maximum Shear Stress Contours
Hoop Stress Contours
Maximum Principal Stress Contours
Minimum Principal Stress Contours
Case Wall
Physical Situation for Sacrificial Ablative Insulation
Motor Case Internal Heat Environment
Nozzle Internal Heating
Analysis Procedure Flowchart
Heating
Ballistic Trajectory Input for Aerodynamic Heating Analysis
Heat Transfer Output From Aerodynamic Heating Calculations
Heating

Title Typical Motor Case Wall Heating Before and After Propellant Is Consumed Adjacent to Sketch of a Hypothetical Free Flight Rocket Showing Geometry Pertinent to External Hot Wall Heat Flux and Motor Case Temperature Calculated From Aerodynamic

7-26 7-27 7-28 7-31 7-32 7-36 7-37 7-37 7-39 7-40 7-41 7-41 7-43 7-45 7-47 7-48 7-49 7-50 7-52 7-52 7-53 7-5 7-57 7-58 7-58 7-65 7-67 7-71 7-72 7-74 7-75 7-78 7-79 7-79 7-83 7-83 7-85 7-85 7-85 7-85

7-8 7-89 7-90 7-91 7-100

7-101 7-103 7-104

MIL-HDBK-762(MI)

LIST OF ILLUSTRATIONS (cont’d)

Figure No.TitlePage 7-61

8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 8-10 8-1 A-1 A-2 A-3 A-4 A-5 A-6 C-1 C-2 C-3 C-4 C-5 C-6 C-7 C-8 C-9 C-l0 C-1 C-12

Heating for Various Flight Times
Examples of Tip-Off and Nontip-Off From Tubes and Rails
Airborne, Multiple-Round Launcher
Examples of Launcher Types
Typical Aircraft Flow Fields
Considerations in the Launcher Analysis Process
Two-Degree-of-Freedom Launcher Analog
Examples of Mechanical Interfaces
Elements of Rocket Plume Interaction With Launch Tube
Rocket Exhaust Interaction in a Constrictive, Nontip-Off Tube
Fin Deloyment Schemes
Rocket Bending Due to Thrust Misalignment

Temperature Gradient Into Motor Case and Internal Insulation From Aerodynamic

8-2 Density Deviations from the US Atmospheric Model of 1962 at 15°N Latitude

Density Deviations from the US Atmospheric Model of 1962 at 30°N Latitude Density Deviations from the US Atmospheric Model of 1962 at 45°N Latitude Density Deviations from the US Atmospheric Model of 1962 at 60°N Latitude Density Deviations from the US Atmospheric Model of 1962 at 75°N Latitude

Cylindrical Heat Storage Model for Node 1
Cylindrical Radial Heat Conduction Model for Node 1 to Node 2
Cylindrical Circumferential Heat Conduction Model For Node 1 to Node 2
A-6
A-6
A-6
A-6
A-7
A-9
C-6
C-7
C-9
Cylindrical Axial Heat Conduction Model
Cylindrical Heat Convection and Radiation Model
Spherical Heat Storage Model
Spherical Radial Heat Conduction Model
Spherical Longitudinal Heat Conduction Model
Spherical Latitudinal Heat Conduction Model
Spherical Heat Convection and Radiation Model
Spherical Slice Model
Spherical Slice Coordinate System

Steady-State Scalar Wind Speed vs Altitude for Two Risk Levels for All Locations

C-9 C-10 C-1 C-12 C-13 C-14 C-15 C-16 C-17

MIL-HDBK-762(MI)

Table No.

Page 2-16 4-51 4-51

6-9
6-9

4-52 4-53 4-54 4-63 5-29 5-3 5-57 5-58 6-15 6-38 7-10 7-14 7-38 7-45 7-46 7-48 7-62 7-63 7-63

7-64 7-6 7-68 7-69 7-75 7-81 7-95 7-101 A-3 A-4

A-5 C-2 2 C-2 4

A-2 A-3

C-1 C-2

Error Budget Example
Six-Degree-of-Freedom Rotational Equations of Motion
Six-Degree-of-Freedom Translational Equations of Motion

Title Euler Transformation Relating the Inertia] Coordinate System and Body-Centered

Coordinate System
Point-Mass Equations of Motion
Pitch Plane Equations of Motion
Error Budget at Warhead Event for Indirect Fire Rocket with Impact Fuze
Fin Selection and Calculation of Supersonic Stability Coefficients
Calculation of Subsonic and Transonic Stability Coefficients
Variation of Reynolds Number and Dynamic pressure With Altitude
Drag Calculation Sheets
Binders for Composite Propellants
Inorganic Oxidizers for Composite Propellants
Nozzle Material Erosion Characteristics
Typical Propellant Burning Rates
Mass Properties of Simple Geometric Shapes
Normalized Coordinates of Several Nose Shapes
Fin Structural Concept Comparisons
Example 7-3 Property Table
Example 7-3 Shear Table
Example 7-3 Bending Moments Table
Properties of Metallic Structural Materials at Room Temperature
Comparison of Some Aerospace Steels at Room Temperature
Properties of Composite Materials at Room Temperature
Temperature
Effect of Case Material Selection on Motor Mass and Cost
Selected Thermal and Physical Properties of Typical Propellants
Safety Factors For Rocket Components
Sample Problem Payload Volume Summary
Frequency Constants and Node Locations of Uniform Beams
Typical Insulation Thermal Properties (Room Temperature Values)
Input Parameters Required for Thermal Analysis of Chamber and Nozzle Insulation
Representative Values of g'and R'
Constants Used in Calculation of US Standard Atmosphere, 1976
Standard Atmosphere, 1976
Coefficients of Expansion for
Coefficients for the Modified Spalding-Chi Method

Typical Composite Material Tensile Properties,Compared with Metals at Room Temperature, Pressure, Density, and Speed of Sound vs Geopotential Altitude: US xxiv

0938-9, RTI, File 0938-01B, Disk 838, A-Times Roman, C-Times Roman Math, JHP MIL-HDBK-762(MI)

AFRPL = Air Force Rocket Propulsion Laboratory

AP = ammonium perchlorate

ARDC = Air Research and Development Command

BF = biaxial improvement factors cal = calibers CEP = circular error probable CG = center of gravity CI = configuration item

COESA = Committee on Extension of the Standard Atmosphere

COSPAR = Committee on Space Research

CP = center of pressure = circular port

CTPB = carboxy terminated polybutadiene

DEP = deflection error probable DoD = Department of Defense DOF = degrees of freedom

FAMAS = Field Artillery Meteorological Acquisition System

FE = finite element FS = factor of safety

HEAT = high explosive antitank

HTPB = hydroxyl-terminated polybutadiene

IR = infrared

IRIG = Inter-Range Instrumentation Group

JMSNS = Justification of Major System New Starts KP = potassium perchlorate

LOA = Letter of Agreement MEOP = maximum expected operational pressure

MHX = cyclotetramethylene tetranitramine

MIL-STD = Military Standard

MLRS =Multiple Launch Rocket System MOC = method of characteristics

MS = margin of safety

MSFC = Marshall Space Flight Center NASA = National Aeronautics and Space Administration

NC = cellulose hexanitrate NG = glycerol trinitrate

PADA = prespin automatic dynamic alignment PBAA = butadiene acrylic acid copolymers

PE = probable error QE = quadrant elevation

RDX = cyclotrimethylene trinitramine

REP = range error probable ROC = Required Operational Capability rps= revolutions per second

SOSR = spin on straight rail

SUDS = slowly uniformly decreasing spin

TE = trailing edge

TMO = transition metal oxide WAF = wraparound fins xxv

MIL-HDBK-762(MI)

CHAPTER 1 INTRODUCTIO N

This chapter introduces the handbook. Rocket systems are presented in two broad classes: military rocket systems and research rocket systems. Military rocket systems are discussed in terms of their application in a battle environment. Research rocket systems are discussed in terms of the application to provide the means of placing data gathering equipment into a desired environment. Operational modes for the rocket systems are described. Finally, brief descriptions of the remaining chapters and the appendices are given.

1-1 PURPOSE OF HANDBOOK

Aerodynamically stabilized free rockets offer relatively simple, reliable, small, low-cost means for delivering payloads and, when great accuracy is not required, are often the optimum systems. This handbook provides engineering design information and data for such rockets. Primarily, this handbook is intended to cover the conceptual and preliminary design phases; however, reference is made to the technical approaches and computer programs required for the system development phase. The material includes operational and interface requirements as they influence the design of the total weapon system. The handbook provides

1. The preliminary design engineer with specific design information and data useful in the rapid response situations required of preliminary design activities

2. The specialist in each technical area an introduction to the other disciplines in terms of data requirements and trade-off studies that must be performed.

Free flight rockets are those rockets that do not have an in-flight guidance system; they are aimed, guided, or directed by the launching device. These launchers usually have a launching rail or tube to provide initial direction to the rocket. Free flight rockets are of two basic kinds—spin stabilized and aerodynamically stabilized. The spin stabilized rocket, as the name implies, depends upon a high rate of spin and resulting gyroscopic moments to oppose disturbances.The aerodynamically stabilized rocket depends upon aerodynamic forces on the body and fins to oppose disturbing forces. The aero- dynamically stabilized rocket generally employs some spin to minimize dispersion caused by nonsymmetrical body characteristics (body asymmetries, fin misalignment, thrust misalignment, etc.). The data and concepts presented in this handbook are limited to aerodynamically stabilized free flight rockets.

(Parte 1 de 6)

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