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Preface	p. 9
A Brief History of Exterior Ballistics	p. 10
Introduction	p. 10
Early Beginnings	p. 10
Exterior Ballistics in the Nineteenth Century	p. 10
Early Twentieth Century Developments	p. 13
The First Modern Aerodynamic Force-Moment System for Projectiles	p. 17
The Beginnings of Computational Aerodynamics	p. 17
Exterior Ballistics Research During the Second World War	p. 18
Post-War Progress in Exterior Ballistics	p. 28
Future Developments	p. 29
Aerodynamic Forces and Moments Acting on Projectiles	p. 32
Introduction	p. 32
Drag Force	p. 33
Spin Damping Moment	p. 33
Rolling Moment for Canted Fin Projectiles	p. 34
Lift and Normal Forces	p. 34
Overturning Moment	p. 36
Magnus Force	p. 36
Magnus Moment	p. 37
Centers of Pressure of the Normal Force and the Magnus Force	p. 37
Pitch Damping Force	p. 38
Pitch Damping Moment	p. 38
Neglected Forces and Moments	p. 39
The Effect of Center of Gravity Location on the Aerodynamic Forces and Moments	p. 39
Modern Aeroballistic and Older Ballistic Nomenclatures	p. 40
Summary	p. 40
The Vacuum Trajectory	p. 42
Introduction	p. 42
Equations of Motion	p. 42
Discussion of the Vacuum Trajectory	p. 44
Firing Uphill and Downhill	p. 47
Summary	p. 51
Notes on Aerodynamic Drag	p. 52
Introduction	p. 52
Classical Drag Measurements	p. 52
The Physical Nature of Drag	p. 55
Airflow Regimes	p. 55
The Effect of Projectile Shape on Drag	p. 70
The Effect of a Burning Tracer on Drag	p. 73
The Effect of Fins on the Drag	p. 74
The Drag of Smooth Spheres	p. 76
The Effect of Yaw on Drag	p. 78
Minimum Drag Projectile Shapes	p. 80
Summary	p. 84
The Flat-Fire Point Mass Trajectory	p. 88
Introduction	p. 88
Equations of Motion	p. 89
The Flat-Fire Approximation	p. 90
Special Analytical Solutions of the Flat-Fire Equations	p. 91
Constant Drag Coefficient	p. 92
Drag Coefficient Inversely Proportional to Mach Number	p. 93
Drag Coefficient Inversely Proportional to the Square Root of Mach Number	p. 94
Comparison of Flat-Fire Trajectory Approximations	p. 95
Summary	p. 96
The Siacci Method for Flat-Fire Trajectories	p. 98
Introduction	p. 98
Siacci Assumptions and Approximations	p. 98
Derivation of the Siacci Functions	p. 98
The Computation of Siacci Ballistic Tables	p. 101
The Practical Use of the Ballistic Tables	p. 101
Form Factors of Typical Small Arms Projectiles	p. 106
The Effect of Projectile Shape on the Form Factor	p. 106
Rules for the Use of the Form Factor Charts	p. 111
Additional Notes on Form Factors	p. 111
The Effect of Wind on Flat-Fire Trajectories	p. 157
Introduction	p. 157
Equations of Motion	p. 157
The Flat-Fire Approximation	p. 158
The Effect of a Constant Crosswind on the Flat-Fire Trajectory	p. 158
The Effect of a Variable Crosswind on the Flat-Fire Trajectory	p. 159
The Effect of Rangewind on the Flat-Fire Trajectory	p. 162
Summary	p. 164
The Point-Mass Trajectory	p. 165
Introduction	p. 165
Equations of Motion	p. 165
Change of Independent Variable from Time to Distance	p. 165
Numerical Solution of the Equations of Motion	p. 166
Standard Atmospheres for Point-Mass Trajectories	p. 166
Examples of Point-Mass Trajectories	p. 169
Comparison of Point-Mass and Siacci Trajectories	p. 172
The Coriolis Effect on Point-Mass Trajectories	p. 178
Summary	p. 183
Six-Degrees-of-Freedom (6-DOF) and Modified Point-Mass Trajectories	p. 187
Introduction	p. 187
Equations of Motion for Six-Degrees-of-Freedom Trajectories	p. 187
Initial Conditions for Six-Degrees-of-Freedom Trajectories	p. 191
Numerical Solution of Six-Degrees-of-Freedom Trajectories	p. 193
Examples of Six-Degrees-of-Freedom Trajectories	p. 194
Summary and Comments on Six-Degrees-of-Freedom Trajectories	p. 212
The Modified Point-Mass Trajectory Model	p. 212
Examples of Modified Point-Mass Trajectories	p. 214
Linearized Pitching and Yawing Motion of Rotationally Symmetric Projectiles	p. 221
Introduction	p. 221
Equations of Motion for the Linearized Problem	p. 221
Solution of the Differential Equations for Velocity and Spin	p. 228
Simplified Pitching and Yawing Motion of a Spinning Projectile	p. 229
The Classical Gyroscopic Stability Criterion	p. 230
The Yaw of Repose for Spin-Stabilized Projectiles	p. 231
Initial Conditions for Simplified Epicyclic Motion	p. 231
Complete Linearized Pitching and Yawing Motion of Projectiles	p. 232
Gyroscopic and Dynamic Stability of Symmetric Projectiles	p. 233
Initial Conditions for Damped Epicyclic Motion	p. 234
An Example of the Linearized Pitching and Yawing Motion	p. 235
The Motion of the Rotating [i, j, k] Coordinate System	p. 236
Pitching and Yawing Motion of a Slightly Asymmetric Missile	p. 237
Summary	p. 238
Linearized Swerving Motion of Rotationally Symmetric Projectiles	p. 240
Introduction	p. 240
The Differential Equation of Swerving Motion	p. 240
Solution of the Differential Equation for Swerve	p. 243
Discussion of the Linearized Swerving Motion	p. 244
Lateral Throwoff and Aerodynamic Jump	p. 252
Introduction	p. 252
Derivation of the Lateral Throwoff Effect	p. 254
The Effect of a Slight Mass Asymmetry on the Initial Pitching and Yawing Motion of a Spinning Projectile	p. 255
The Generalized Aerodynamic Jump Effect	p. 259
The Effect of Mass Asymmetry on Lateral Throwoff and Aerodynamic Jump	p. 260
Derivation of Kent's Equation for a Small Mass Asymmetry	p. 264
The Effect of In-Bore Yaw on Lateral Throwoff and Aerodynamic Jump	p. 264
Derivation of Kent's Equation for a Small In-Bore Yaw	p. 266
The Aerodynamic Jump Due to Crosswind	p. 267
Firing Sidewise From an Airplane	p. 270
Summary	p. 272
Nonlinear Aerodynamic Forces and Moments	p. 273
Introduction	p. 273
Analysis of Nonlinear Drag Coefficient Data	p. 273
Quasi-Linear Analysis of a Cubic Pitching Moment	p. 275
The Effect of a Cubic Pitching Moment on Stability	p. 279
Pitching and Yawing Motion With All Nonlinear Moments	p. 280
Bi-Cubic and Tri-Cubic Magnus Moments	p. 284
Nonlinear Magnus Moments and Limit-Cycle Yawing Motion	p. 287
Quasi-Linear Analysis of a Cubic Lift Force	p. 293
Measurement of Aerodynamic Forces and Moments	p. 299
Introduction	p. 299
Wind Tunnel Methods	p. 299
Free-Flight Ballistic Ranges	p. 303
Classical Data Reduction for Spark Photography Ranges	p. 304
Six-Degrees-of-Freedom Data Reduction for Spark Ranges	p. 317
Modern Data Reduction for Yaw-Card Firings	p. 318
Methods of Yaw Induction	p. 320
Yawsonde Testing	p. 323
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Modern Exterior Ballistics : The Launch and Flight Dynamics of Symmetric Projectiles

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