Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles

Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles

by Robert L. McCoy

Hardcover

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Overview

Modern Exterior Ballistics is a comprehensive text covering the basic free flight dynamics of symmetric projectiles. The book provides a historical perspective of early developments in the 19th century, the technology leading to World War I and that through World War II into the modern post-war era. Historical topics include the first ballistic firing tables, early wind tunnel experiments, the development of free flight spark ranges and the first supercomputer, ENIAC, which was designed to compute artillery trajectories for the U.S. Army Ballistic Research Laboratory. The level of the text requires an undergraduate education in mathematics, physics, and mechanical or aerospace engineering. The basic principles of ballistic science are developed from a comprehensive definition of the aerodynamic forces that control the flight dynamics of symmetric projectiles. The author carefully starts with the basic vacuum point mass trajectory, adds the effects of drag, discusses the action of winds, simple flat fire approximations, Coriolis effects and concludes with the classic modified point mass trajectories. Included in the discussion are analytical methods, change of variables from time to distance, numerical solutions and a chapter on the Siacci Method. The Siacci Method provides a historical perspective for computing flat fire trajectories by simple quadrature and is used in the sporting arms industy. The final six chapters of the book present an extensive physical and mathematical analysis of the motion of symmetric projectiles. The linearized equations of angular and swerving motion are derived in detail. The effects of mass asymmetry, in-bore yaw, cross wind and launch in a slipstream arediscussed. Special consideration is given to the derivation and explanation of aerodynamic jump. These subjects are then expanded to include a complete chapter on nonlinear aerodynamic forces and moments. The final chapter in the book presents an overview of experimental methods for measuring the flight dynamics of projectiles. The great forte of Modern Exterior Ballistics is the author's effort to provide many fine specific examples of projectile motion illustrating key flight behaviors. The extensive collection of data on projectiles from small arms to artillery used to substantiate calculations and examples is alone a valuable reference. The ultimate joy of the book is the incomparable comprehensive set of flow field shadow graphs illustrating the entire spectrum of projectile flight from subsonic, through transonic and supersonic. The volume is a necessary addition to any undergraduate or graduate course in flight dynamics.

Product Details

ISBN-13: 9780764307201
Publisher: Schiffer Publishing, Ltd.
Publication date: 01/01/1999
Pages: 328
Product dimensions: 20.04(w) x 20.45(h) x 0.45(d)

Table of Contents

Preface9
Chapter 1A Brief History of Exterior Ballistics10
1.1Introduction10
1.2Early Beginnings10
1.3Exterior Ballistics in the Nineteenth Century10
1.4Early Twentieth Century Developments13
1.5The First Modern Aerodynamic Force-Moment System for Projectiles17
1.6The Beginnings of Computational Aerodynamics17
1.7Exterior Ballistics Research During the Second World War18
1.8Post-War Progress in Exterior Ballistics28
1.9Future Developments29
Chapter 2Aerodynamic Forces and Moments Acting on Projectiles32
2.1Introduction32
2.2Drag Force33
2.3Spin Damping Moment33
2.4Rolling Moment for Canted Fin Projectiles34
2.5Lift and Normal Forces34
2.6Overturning Moment36
2.7Magnus Force36
2.8Magnus Moment37
2.9Centers of Pressure of the Normal Force and the Magnus Force37
2.10Pitch Damping Force38
2.11Pitch Damping Moment38
2.12Neglected Forces and Moments39
2.13The Effect of Center of Gravity Location on the Aerodynamic Forces and Moments39
2.14Modern Aeroballistic and Older Ballistic Nomenclatures40
2.15Summary40
Chapter 3The Vacuum Trajectory42
3.1Introduction42
3.2Equations of Motion42
3.3Discussion of the Vacuum Trajectory44
3.4Firing Uphill and Downhill47
3.5Summary51
Chapter 4Notes on Aerodynamic Drag52
4.1Introduction52
4.2Classical Drag Measurements52
4.3The Physical Nature of Drag55
4.4Airflow Regimes55
4.5The Effect of Projectile Shape on Drag70
4.6The Effect of a Burning Tracer on Drag73
4.7The Effect of Fins on the Drag74
4.8The Drag of Smooth Spheres76
4.9The Effect of Yaw on Drag78
4.10Minimum Drag Projectile Shapes80
4.11Summary84
Chapter 5The Flat-Fire Point Mass Trajectory88
5.1Introduction88
5.2Equations of Motion89
5.3The Flat-Fire Approximation90
5.4Special Analytical Solutions of the Flat-Fire Equations91
5.5Constant Drag Coefficient92
5.6Drag Coefficient Inversely Proportional to Mach Number93
5.7Drag Coefficient Inversely Proportional to the Square Root of Mach Number94
5.8Comparison of Flat-Fire Trajectory Approximations95
5.9Summary96
Chapter 6The Siacci Method for Flat-Fire Trajectories98
6.1Introduction98
6.2Siacci Assumptions and Approximations98
6.3Derivation of the Siacci Functions98
6.4The Computation of Siacci Ballistic Tables101
6.5The Practical Use of the Ballistic Tables101
6.6Form Factors of Typical Small Arms Projectiles106
6.7The Effect of Projectile Shape on the Form Factor106
6.8Rules for the Use of the Form Factor Charts111
6.9Additional Notes on Form Factors111
Chapter 7The Effect of Wind on Flat-Fire Trajectories157
7.1Introduction157
7.2Equations of Motion157
7.3The Flat-Fire Approximation158
7.4The Effect of a Constant Crosswind on the Flat-Fire Trajectory158
7.5The Effect of a Variable Crosswind on the Flat-Fire Trajectory159
7.6The Effect of Rangewind on the Flat-Fire Trajectory162
7.7Summary164
Chapter 8The Point-Mass Trajectory165
8.1Introduction165
8.2Equations of Motion165
8.3Change of Independent Variable from Time to Distance165
8.4Numerical Solution of the Equations of Motion166
8.5Standard Atmospheres for Point-Mass Trajectories166
8.6Examples of Point-Mass Trajectories169
8.7Comparison of Point-Mass and Siacci Trajectories172
8.8The Coriolis Effect on Point-Mass Trajectories178
8.9Summary183
Chapter 9Six-Degrees-of-Freedom (6-DOF) and Modified Point-Mass Trajectories187
9.1Introduction187
9.2Equations of Motion for Six-Degrees-of-Freedom Trajectories187
9.3Initial Conditions for Six-Degrees-of-Freedom Trajectories191
9.4Numerical Solution of Six-Degrees-of-Freedom Trajectories193
9.5Examples of Six-Degrees-of-Freedom Trajectories194
9.6Summary and Comments on Six-Degrees-of-Freedom Trajectories212
9.7The Modified Point-Mass Trajectory Model212
9.8Examples of Modified Point-Mass Trajectories214
Chapter 10Linearized Pitching and Yawing Motion of Rotationally Symmetric Projectiles221
10.1Introduction221
10.2Equations of Motion for the Linearized Problem221
10.3Solution of the Differential Equations for Velocity and Spin228
10.4Simplified Pitching and Yawing Motion of a Spinning Projectile229
10.5The Classical Gyroscopic Stability Criterion230
10.6The Yaw of Repose for Spin-Stabilized Projectiles231
10.7Initial Conditions for Simplified Epicyclic Motion231
10.8Complete Linearized Pitching and Yawing Motion of Projectiles232
10.9Gyroscopic and Dynamic Stability of Symmetric Projectiles233
10.10Initial Conditions for Damped Epicyclic Motion234
10.11An Example of the Linearized Pitching and Yawing Motion235
10.12The Motion of the Rotating [i, j, k] Coordinate System236
10.13Pitching and Yawing Motion of a Slightly Asymmetric Missile237
10.14Summary238
Chapter 11Linearized Swerving Motion of Rotationally Symmetric Projectiles240
11.1Introduction240
11.2The Differential Equation of Swerving Motion240
11.3Solution of the Differential Equation for Swerve243
11.4Discussion of the Linearized Swerving Motion244
Chapter 12Lateral Throwoff and Aerodynamic Jump252
12.1Introduction252
12.2Derivation of the Lateral Throwoff Effect254
12.3The Effect of a Slight Mass Asymmetry on the Initial Pitching and Yawing Motion of a Spinning Projectile255
12.4The Generalized Aerodynamic Jump Effect259
12.5The Effect of Mass Asymmetry on Lateral Throwoff and Aerodynamic Jump260
12.6Derivation of Kent's Equation for a Small Mass Asymmetry264
12.7The Effect of In-Bore Yaw on Lateral Throwoff and Aerodynamic Jump264
12.8Derivation of Kent's Equation for a Small In-Bore Yaw266
12.9The Aerodynamic Jump Due to Crosswind267
12.10Firing Sidewise From an Airplane270
12.11Summary272
Chapter 13Nonlinear Aerodynamic Forces and Moments273
13.1Introduction273
13.2Analysis of Nonlinear Drag Coefficient Data273
13.3Quasi-Linear Analysis of a Cubic Pitching Moment275
13.4The Effect of a Cubic Pitching Moment on Stability279
13.5Pitching and Yawing Motion With All Nonlinear Moments280
13.6Bi-Cubic and Tri-Cubic Magnus Moments284
13.7Nonlinear Magnus Moments and Limit-Cycle Yawing Motion287
13.8Quasi-Linear Analysis of a Cubic Lift Force293
Chapter 14Measurement of Aerodynamic Forces and Moments299
14.1Introduction299
14.2Wind Tunnel Methods299
14.3Free-Flight Ballistic Ranges303
14.4Classical Data Reduction for Spark Photography Ranges304
14.5Six-Degrees-of-Freedom Data Reduction for Spark Ranges317
14.6Modern Data Reduction for Yaw-Card Firings318
14.7Methods of Yaw Induction320
14.8Yawsonde Testing323

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