AMCP 706-285, Elements of Aircraft and Missile Propulsion

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AttC PAMPHLET AMCP 706-285
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» ENGINEERING DESIGN
°° HANDBOOK
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ELEMENTS OF AIRCRAFT
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AND
MISSILE PROPULSION
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STATEMENT #2 UHCMSSIFI-SQ.
This document is subject to sp e ii ol expert controls and esrefr
tra n sm itta l to foreign government , or foreign nation als may be'
made*, oijly y/lth p rio r approval of________________________________________
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# HEMUARTERS, U.S. ARMY MATERIEL COMMAND
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Reproduced by the
CLEARINGHOUSE
lor Federal Scienfiffc & Technical
Information Springfield Va. 22151
HEADQUARTERS
a UNITED STATES ARMY MATERIEL COMMAND
WASHINGTON. D. C. 20315
AMC PAMPHLET
No. 706-285* 29 July 1969
ENGINEERING DESIGN HANDBOOK
ELEMENTS OF AIRCRAFT AND MISSILE PROPULSION
« >
Paragraph Page
LIST OF ILLUSTRATIONS.............................................. xxiii
LIST OF TABLES ............................................................ xxxnr
PREFACE ............................................................................ xxxvii
PART ONE- CHEMICAL ROCKET PROPULSION
CHAPTER 1. CLASSIFICATION AND ESSENTIAL
FEATURES OF ROCKET JET PROPULSION SYSTEMS
1-0 Principal Notation for rhapter 1......................................... 1-1
1-1 Purpose and Scope of handbook......................................... 1-1
4 V
1-2 Scope of the Field of Propulsion......................................... 1-2
<> 1-3 The Reaction Principle ..................................................... 1-3
1-4 The Jet Propulsion Principle ............................................. 1-3
1-5 Classification of Jet Propulsion Systems............................. 1-3
1-5.1 Air-breathing Jet Engines............................................. 1-4
1-5.2 Rocket Jet Propulsion Systems ................................. 1-5
1-5.3 Classification of Rocket Propulsion Systems............. 1-5
1-5.4 Chemical Rocket Propulsion Systems......................... 1-7
1-6 Essential Features of Chemical Rocket Propulsion Systems. 1-7
« V
1-6.1 Classification of Rocket Propulsion Systems ............. 1-10
41 >■ 1-6.2 Liquid Bipropellant Rocket Engine............................. 1-11
1-6.3 Liquid Monopropellant Rocket Engine ..................... 1-11
1-6.4 Solid Propellant Rocket Motor ................................. 1-11
1-6.5 Hybrid Rocket Engine................................................. 1-11
1- 7 Units of Measurement.......................................... 1-11
References ......................................................................... 1-17
CHAPTER 2. MOMENTUM THEORY APPLIED
TO PROPULSION
2- 0 Principal Notation for Chapter 2.......................................... 2-1
2-1 Momentum Theorem of Fluid Mechanics .......................... 2-3
2-1.1 Transport of a Fluid Property Across a
Control Surface .................................................... 2-3
2-1.2 Momentum of a Fluid in Steady Flow......................... 2-4
-V 2-1.3 External Forces Acting on a Flowing Fluid................. 2-6
«> 2-1.4 Steady Flow Momentum Theorem.............................. 2-7
2-2 Application of Momentum Theorem to
Propulsion Systems......................................................... 2-7
2-2.1 General Thrust Equation.............................................. 2-9
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*This pamphlet supersedes AMCP 706-282, Eropulsion and Propellants, August 1963.
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AMCP 706-285
TABLE OF CONTENTS (Continued)
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2-2.2 Effective Jet Velocity..................................................... 2-12
2-2.3 Exit Velocity of the Propulsive Jet............................. 2-13
2-3 Thrust Equations for Rocket Propulsion............................... 2-13
24 Power Definitions for Propulsion Systems ........................ 2-14
24.1 Thrust Power (Pp) ........................................................ 2-14
24.2 Propulsive Power (P) .................................................... 2-14
24.3 Exit Loss (Fjj£> ............................................................. 2-14
24.4 Jet Power (Pp................................................................. 2-15
2-5 Performance Parameters for Jet Propulsion System ........... 2-15
2-5.1 Specific Thrust .............................................................. 2-15
2-5.2.1 Specific Impulse (I~ )............................................ 2-15
i 2-5.2.2 Specific Impulse ana Jet Power ........................... 2-15
2-5.3 Overall Efficiency (rjQ) ................................................. 2-16
2-5.4 Thermal Efficiency (ij^)................................................. 2-16
2-5.5 Propulsive Efficiency (rjp) ............................................. 2-16
2- 5.6 Ideal Propulsive Efficiency (rjp) .................................... 2-16
References ............................................................................. 2-18
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CHAPTER 3. ELEMENTARY GAS DYNAMICS
3- 0 Principal Notation for Chapter 3 ............................................ 3-1
3-1 Introduction .......................................................................... 3-4
3-2 The Ideal Gas .......................................................................... 3-5
3-2.1 The Thermally Perfect Gas ............................................. 3-5
3-2.2 Specific Heat ................................................................... 3-5
3-2.2.1 Specific Heat at Constant Volume (Cy) .............. 3-6
3-2.2.2 Specific Heat at Constant Pressure (Cp) .............. 3-6
3-2.2.3 Specific Heat Ratio (7) ........................................ 3-6
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3-2.2.4 Specific Enthalpy and Specific Heat ................... 3-6
3-2.3 Calorically Perfect Gas...................................................... 3-6
3-2.4 Specific Heat Relationships....................... 3-6
3-2.5 Acoustic or Sonic Speed in an Ideal Gas ..................... 3-7
3-2.6 Mach Number................................................................... 3-7
3-3 General Steady One-dimensional Flow ............................... 3-7
3-3.1 Continuity Equation ...................................................... 3-7
3-3.2 Momentum Equation ...................................................... 3-8
3-3.2.1 General Form of Momentum Equation ............. 3-8
3-3.2.2 Momentum Equation for Steady, Ohe-
dimensional, Reversible Flow ........................... 3-8
3-3.3 Energy Equation for Steady One-dimensional Flow... 3-8
34 Steady One-dimensional Flow of an IdealG as......................... 3-1 p
34.1 Continuity Equation '...................................................... 3-10
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TABLE OF CONTENTS (Continued)
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■* > 3-4.2.1 Momentum Equations for the Steady One­
dimensional Flow of an Ideal Gas...................... 3-12
3-4.2.2 Momentum Equation for a Reversible, Steady,
One-dimensional Flow ....................................... 3-12
3-4.3 Energy Equation............................................................. 3-12
3-4.3.1 Energy Equation for a Simple Adiabatic Flow... 3-12
3-4.3.2 Energy Equation for the Simple Adiabatic
Flow of an Ideal Gas........................................... 3-13
3-5 Steady One-dimensional Isentropic Flow.............................. 3-13
3-5.1 Energy Equation for the Steady One-dimensional
Isentropic Flow of an Ideal Gas................................... 3-14
, 3-5.2 Stagnation (or Total) Conditions................................... 3-15
3-5.2.1 Stagnation (or Total) Enthalpy (h°) ................... 3-15
■. 3-5.2.2 Stagnation (or Total) Temperature (T°)............. 3-15
^ r 3-5.2.3 Stagnation (or Total) Pressure (P°)...................... 3-15
3-5.2.4 Relationship Between Stagnation Pressure
and Entropy........................................................ 3-17
- *■ 3-5.2.5 Stagnation (orTotal) Density (p°)...................... 3-17
3-5.2.6 Stagnation (orTotal) Acoustic Speed (a0) ......... 3-17
3-5.3 Isentropic Exhaust Velocity ....................................... 3-17
3-5.4 Critical Conditions for the Steady, One-dimensional,
Isentropic Flow of an Ideal Gas.................................. 3-18
' v 3-5.4.1 Definition of Critical Area and Critical
• * Acoustic Speed................................ 3-18
3-5.4.2 Critical Thermodynamic Properties for the
Steady, One-dimensional, Isentropic Flow
of an Ideal Gas ........................................... 3-18
3-5.5 Continuity Equations for Steady, One-dimensional,
Isentropic Flow of an Ideal Gas................................... 3-20
3-5.5.1 Critical Area Ratio (A/A*) ................................... 3-20
3-5.5.2 Critical Area Ratio in Terms of the Flow
Expansion Ratio (P/P°) 3-20
3-5.5.3 Critical Area Ratio in Terms of the Flow
Mach Number .................................................... 3-20
3-5.6 Reference Speeds (a0 ), (a*), and (cQ).......................... 3-20
1-5.6.1 Continuity Equations in T rms of
Stagnation Conditions ....................................... 3-21
3-5.6.2 Critical Mass Flow Density (G*)........................... 3-21
-• *- 3-5.7 Tables of Isentropic Flow Functions for Ideal Gases... 3-2!
3-6 Steady One-dimensional Adiabatic Flow in a Constant
Area Duct With Wall Friction (Fanno Flow)...................... 3-23
4% 3-6.1 Friction Coefficient (f) ................................................. 3-23
•m 3-6.2 Principal Equations for Fanno Flow ........................... 3-23
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AMCP 706-285
TABLE OF CONTENTS (Continued)
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3-6.3 Fanno Line Equation ................................................... 3-23
3-6.4 Fanno Flow With Ideal Gases ...................................... 3-26
3-6.4.1 Principal Equations............................................... 3-26
3-6.4.2 Critical Duct Length for the Fanno Flow of
an Ideal Gas ...................................................... 3-27
3-6.4.3 Duct Length for a Specified Change in
Mach Number .................................................. 3-27
3-6.4.4 General Characteristics of the Fanno Flow
of an Ideal Gas .................................................. 3-28
3-6.5 Equations for Compiling Tables for Fanno Flow
Functions, for Ideal Gases......................................... 3-28
3-7 Steady One-dimensional Frictionless Flow in a Constant
Area Duct With Stagnation Temperature Change
(Rayleigh Flow)................................................................... 3-29
3-7.1 Principal Equations for a Rayleigh Flow..................... 3-29
3-7.2 Rayleigh Line ................................................................ 3-32
3-7.2. i General Characteristics ...................................... 3-32
3-7.2.2 Characteristics of the Rayleigh Line for the
Flow of an Ideal Gas......................................... 3-32
3-7.3 Rayleigh Flow Equations for Ideal Gases.................. 3-34
3-7.4 Equations for Tables of Rayleigh Flow Functions
for Ideal Gases .......................................................... 3-35
3- 7.5 Development of Compression Shock ......................... 3-37
References ......................... 3-39
CHAPTER 4.COMPRESSIBLE FLOW IN NOZZLES
4- 0 Principal Notation for Chapter 4 .......................................... 4-1
4-1 Introduction ............................. 4-3
4-2 Ideal Flow in a Converging Nozzle ...................................... 4-5
4-2.1 Isentropic Exit Velocity for a Converging Nozzle .. 4-5
4-2.2 Isentropic Throat Velocity for the Flow of a Perfect
Gas in a Converging Nozzle ..................................... 4-5
4-2.3 Effect of Varying the Back Pressure Acting on a
Converging Nozzle...................................................... 4-7
4-2.4 Mass Flow Rate for Ideal Nozzle Flow (Converging
and Converging-diverging Nozzles)............................ 4-8
4-3 Ideal Flow in a Converging-diverging (or De Laval) Nozzle. . 4-10
4-3.1 Area Ratio for Complete Expansion of the Gas
Flowing in a Converging-diverging Nozzle............... 4-14
4-3.2 Effect of Varying the Back Pressure Acting on a
Converging-diverging Nozzle..................................... 4-20
4-3.2. i Underexpansion in a Converging-diverging
Nozzle ............................................................... 4-20
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4-3.2.2 Overexpansion in a Converging-diverging Nozzle . 4-21
4-3.3 Effect of Varying the Inlet Total Pressure of a Nozzle... 4-24
4-4 Flow in Real Nozzles .............................................................. 4-26
4-4.1 Losses in Nozzles.................. 4-26
4-4.2 Area Ratio for an Adiabatic Nozzle............................... 4-26
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4-5 Nozzle Performance Coefficients............................................ 4-27
4-5.1 Nozzle Efficiency (»7n)..................................................... 4-27 H
4-5.2 Nozzle Velocity Coefficient (0) .................................... 4-27
4-5.3 Nozzle Discharge Coefficient (C^) ................................ 4-27
4-6 Mass Flow Rate for a Nozzle Operating With Adiabatic
Flow and Wall Friction........................................................ 4-28
4-7 Nozzle Design Principles.......................................................... 4-28
4-8 Nozzle Design Configurations................................................. 4-29
■•i *
4-8.1 Conical Nozzle.................................................................. 4-30
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4-8.1.1 Thrust Equation for a Conical Nozzle................. 4-31
4-8.1.2 Factors for Determining Adequacy of a
Conical Nozzle .................................................... 4-32
4-8.2 Contoured or Bell-shaped Nozzle.................................... 4-34
4-8.3 Annular Nozzie .............................................................. 4-36
4-8.4 Plug Nozzle...................................................................... 4-36
4-8.5 Expansion-deflection or E-D Nozzle ........................... 4-39
•* V References .............................................................................. 4-40
CHAPTER 5. PERFORMANCE CRITERIA FOR
ROCKET PROPULSION
5-0 Principal Notation for Chapter 5 ............................................ 5-1
5-1 Introduction ........................................................................... 5-2
5-2 Effective Jet (or Exhaust) Velocity (c) ............................... 5-2
5-3 Specific Impulse (Igp).............................................................. 5-3
5-3.1 Specific PropeUant Consumption (wjp) ....................... 5-4
5-3.2 Weight-flow Coefficient (Cw) ......................................... 5-4
5-3.3 Mass-flow Coefficient (Cm) ............................................. 5-4
5-4.1 Thrust Coefficient (Cp) ................................................. 5-4
5-4.2 Relationship Between ISp, Cw, and Cp ....................... 5-5
5-5 Characteristic Velocity (c*)..................................................... 5-5
5-6 Jet Power (Pp.......................................................................... 5-5
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5-7 Total Impulse (If) .................................................................. 5-5
* I* 5-8 Weight and Mass Ratios .......................................................... 5-6
5-8.1 Propulsion System Weight (Wpg).................................... 5-6
5-8.2 Specific Engine Weight (r) ............................................. 5-7
I 5-8.3 Payload Ratio (Wpay/W0) ............................................. 5-7
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5-8.4 Propellant Weight (Wp) ................................................. 5-7
5-8.5 Propellant Mass Ratio (£)................................................. 5-7
5-8.6 Veliicle Mass Ratio (A) ................................................. 5-7
5-8.7 Relationship Between the Propellant Mass Ratio (£)
and the Vehicle Mass Ratio (A)................................... 5-8
5-8.8 Propellant Loading Density (Sp).................................... 5-8
5-8.9 Impulse-weight Ratio for a Rocket Engine ................... 5J8
5-9 Vehicle Performance Criteria ................................................. 5-8
5-9.1 Linear Motion With Drag and Gravity.............................. 5-9
5-9.1.1 Thrust of Rocket Engine With Linear Motion
of Vehicle............................................................. 5-9
5-9.1.2 Aerodynamic Drag ................................................. 5-11
5-9.1.3 Approximate Solution of Differential Equation
for Linear Motion With Drag and Gravity......... 5-11
5-9.2 Burnout Velocity (Vfc) ................................................. 5-13
5-9.2.1 Burnout Altitude (z^)............................................. 5-14
5-9.2.2 Coasting Altitude After Burnout (zc) ................... 5-14
S-9.2.3 Maximum Drag-free Altitude (zmax) ................... 5-14
5- 9.3 Ideal Burnout Velocity (V^j) ........................................ 5-14
References ............................................................................. 54 6
CHAPTER 6. THERMODYNAMIC RELATIONSHIPS FOR
CHEMICAL ROCKET PROPULSION
6- 0 Principal Notation for Chapter 6 ............................................. 6-1
6-1 Introduction ........................................................................... 6-3
6-2 Assumptions in Thermochemical and Gas Dynamic
Calculations .......................................................................... 6-4
6-2.1 Exothermic and Endothermic Chemical Reactions.... 6-5
6-2.2 Conditions for Thermochemical Equilibrium .............. 6-6
6-2.’3 Dissociation and Reassociation Reactions ................... 6-6
6-3 Thermodynamic Equations for Rocket Performance Criteria . 6-6
6-3.1 Isentropic Exit Velocity (ua) ........................................ 6-7
6-3.2 Actual or Adiabatic Exit Velocity (ue) ....................... 6-9
6-3.3 Propellant Flow Coefficients ........................................ 6-11
6-3.3.1 Mass Flow Rate of Propellant Gas (m)................... 6-11
6-3.3.2 Weight Flow Coefficient (Cw) ............................... 6-11
6-3.4 Thrust (F) ...................................................................... 6-11
6-3.4.1 Effective Jet (or Exhaust) Velocity (c) ............... 6-13
6-3.4.2 Thrust Coefficient (Cp) ........................................ 6-13
6-3.5 Nozzle Area Ratio for Complete Expansion .............. 6-13
6-3.6 Characteristic Velocity (c*)............................................ 6-18
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TABLE OF CONTENTS (Continued)
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6-3.7 Theoretical Specific Impulse (1^,) ............................... 6-20
6-3.7.1 Reduced Specific Impulse .................................... 6-20
6- 3.7.2 Density Specific Impulse (I<j) ................................ 6-23
References .............................................................................. 6-26
CHAPTER 7 .PROPERTIES AND CHARACTERISTICS OF
SOLID PROPELLANTS
7- 1 Classification of Solid Propellants ........................................ 7-1
7-2 Homogeneous Propellants ..................................................... 7-1
7-2.1 Polymers for Homogeneous Propellants....................... 7-2
7-2.2 Oxidizer-plasticizers for Homogeneous Propellants ... 7-2
7-2.3 Fuel-plasticizers for Homogeneous Propellants .......... 7-2
7-2.4 Additives to Double-base Propellants ........................... 7-2
•*v 7-2.5 General Characteristics and Applications of Double­
base Solid Propellants ................................................ 7-2
7-3 Heterogeneous or Composite Propellants................................ 7-4
7-3.1 Binders for Composite Propellants ............................... 7-4
7-3.2 Oxidizers for Composite Propellants ........................... 7-5
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7-3.3 Additives to Composite Propellants............................... 7-6
7-4 Factors Governing the Selection of a Solid Propellant........... 7-7
7-4.1 Specific Impulse (Isp)..................................................... 7-7
7-4.2 Density of Propellant (pp) ............................................ 7-7
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7-4.3 Hygroscopicity ............................................................. 7-7
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7-4.4 Controllable Linear Burning Rate (rQ) ........................... 7-7
7-4.5 Coefficient of Thermal Expansion ............................... 7-7
7-4.6 Thermal Conductivity..................................................... 7-7
7-4.7 Chemical Stability ......................................................... 7-7
7-4.8 Toxicity .......................................................................... 7-8
7-4.9 Shock Sensitivity................................ 7-8
7-4.10 Explosive Hazard............................................................. 7-8
7-4.11 Smoke in Exhaust ......................................................... 7-8
7-4.12 Attenuation of Electromagnetic Signals...................... 7-8
7-4.13 Availability of Raw Materials ........................................ 7-9
7-4.14 Fabrication and Process Control................................... 7-9
7-4.15 Cost................................................................................... 7-9
7-5 Mechanical Properties of Solid Propellants............................ 7-9
< V 7-5.1 Ultimate Tensile Strength ............................................ 7-9
7-5.2 Elongation in Tension..................................................... 7-10
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7-5.3 Modulus in Tension......................................................... 7-10
7-5.4 Stress Relaxation............................................................. 7-10
7-5.5 Creep .............................................................................. 7-10
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7-5.6 Compressive Strength .................................................... 7-10
7-5.6.1 Deformation At Rupture in Compression ........... 7-10
7-5.6.2 Modulus in Compression....................................... 7-10
7-5.7 Shear Properties ............................................................. 7-11
7- 5.8 Brittle Temperature........................................................ 7-11
References ............................................................................. 7-12
CHAPTER 8 SOLID PROPELLANT ROCKET MOTORS
8- 0 Principal Notation for Chapter 8 ........................................... 8-1
8-1 Internal Ballistics of Solid Propellant Rocket Motors......... 8-3
8-1.1 Burning of a Solid Propellant (Piobert’s Law).............. 8-3
8-1.2 Combustion Temperature ............................................ 8-3
8-1.3 General Characteristics of the Combustion Process ... 8-4
i 8-1.4 Combustion Characteristics of Double-base
: Solid Propellants ......................................................... 8-5
i 8-1.5 The Flame Reaction Zone for a Double-base Solid
: Propellant...................................................................... 8-7
\ 8-1.6 Combustion Characteristics of Composite (Non-
■ homogeneous) Solid Propellants ............................... 8-7
< 8-1.7 Linear Burning Rate (Saint-Robert’s Law) .................. 8-7
i 8-1.8 Weight Rate of Propellant Consumption (wp) ............. 8-9
; 8-1.9 Volumetric Fate of Propellant Consumption (Qp) ... 8-9
| 8-1.10 Equilibrium Combustion Pressure and Its Stability ... 8-11
j 8-1.11 Effect of Propellant Area Ratio (K„) ........................... 8-11
! 8-1.12 Stability of the Shape of the Burning Surface.............. 8-12
8-1.13 Pressure Deflagration Limit and Pressure Limit .......... 8-12
8*1.14 Effect of the Temperature of a Solid Propellant.......... 8-12
8-1.14.1 General Effects of Temperature ........................... 8-12
8-1.14.2 Temperature Sensitivity .................................. 8-13
8-1.15 Erosive Burning ............................................................. 8-13
8-2 Combustion Pressure Oscillations in Solid Propellant
> Rocket Motors (Unstable Burning) .................................. 8-14
! 8-2.1 Terminology Employed in Unstable Burning of
( Solid Propellant Rocket Motors............................... 8-14
j 8-2.2 Acoustic Instability in Solid Propellant Rocket
i Motors .......................................................................... 8-14
| 8-3 Ignition of Propellant Grain ................................................. 8-19
j 8-4 Solid Propellant Grain Configurations.................................... 8-20
I 8-5 Port-to-ithroat Area Ratio (1/J) ............................................ 8-23
j 8-6 Heat Transfer in Solid Propellant Rocket Motors .............. 8-23
8-6.1 Aerodynamic Heating..................................................... 8-24
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