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

Authors: Robert L. McCoy
ISBN-13: 9780764307201, ISBN-10: 0764307207
Format: Hardcover
Publisher: Schiffer Publishing, Ltd.
Date Published: January 1999
Edition: (Non-applicable)

Author Biography: Robert L. McCoy

Book Synopsis

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.

Booknews

This text covers the basic free flight dynamics of symmetric projectiles. It 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, and the development of free flight spark ranges. McCoy, who was an aerospace engineer at the U.S. Army Ballistic Research Laboratory, provides many specific examples of projectile motion illustrating key flight behaviors. In addition, he presents flow field shadow graphs illustrating the entire spectrum of projectile flight from subsonic through transonic and supersonic. Annotation c. Book News, Inc., Portland, OR (booknews.com)

	Preface	9
Chapter 1	A Brief History of Exterior Ballistics	10
1.1	Introduction	10
1.2	Early Beginnings	10
1.3	Exterior Ballistics in the Nineteenth Century	10
1.4	Early Twentieth Century Developments	13
1.5	The First Modern Aerodynamic Force-Moment System for Projectiles	17
1.6	The Beginnings of Computational Aerodynamics	17
1.7	Exterior Ballistics Research During the Second World War	18
1.8	Post-War Progress in Exterior Ballistics	28
1.9	Future Developments	29
Chapter 2	Aerodynamic Forces and Moments Acting on Projectiles	32
2.1	Introduction	32
2.2	Drag Force	33
2.3	Spin Damping Moment	33
2.4	Rolling Moment for Canted Fin Projectiles	34
2.5	Lift and Normal Forces	34
2.6	Overturning Moment	36
2.7	Magnus Force	36
2.8	Magnus Moment	37
2.9	Centers of Pressure of the Normal Force and the Magnus Force	37
2.10	Pitch Damping Force	38
2.11	Pitch Damping Moment	38
2.12	Neglected Forces and Moments	39
2.13	The Effect of Center of Gravity Location on the Aerodynamic Forces and Moments	39
2.14	Modern Aeroballistic and Older Ballistic Nomenclatures	40
2.15	Summary	40
Chapter 3	The Vacuum Trajectory	42
3.1	Introduction	42
3.2	Equations of Motion	42
3.3	Discussion of the Vacuum Trajectory	44
3.4	Firing Uphill and Downhill	47
3.5	Summary	51
Chapter 4	Notes on Aerodynamic Drag	52
4.1	Introduction	52
4.2	Classical Drag Measurements	52
4.3	The Physical Nature of Drag	55
4.4	Airflow Regimes	55
4.5	The Effect of Projectile Shape on Drag	70
4.6	The Effect of a Burning Tracer on Drag	73
4.7	The Effect of Fins on the Drag	74
4.8	The Drag of Smooth Spheres	76
4.9	The Effect of Yaw on Drag	78
4.10	Minimum Drag Projectile Shapes	80
4.11	Summary	84
Chapter 5	The Flat-Fire Point Mass Trajectory	88
5.1	Introduction	88
5.2	Equations of Motion	89
5.3	The Flat-Fire Approximation	90
5.4	Special Analytical Solutions of the Flat-Fire Equations	91
5.5	Constant Drag Coefficient	92
5.6	Drag Coefficient Inversely Proportional to Mach Number	93
5.7	Drag Coefficient Inversely Proportional to the Square Root of Mach Number	94
5.8	Comparison of Flat-Fire Trajectory Approximations	95
5.9	Summary	96
Chapter 6	The Siacci Method for Flat-Fire Trajectories	98
6.1	Introduction	98
6.2	Siacci Assumptions and Approximations	98
6.3	Derivation of the Siacci Functions	98
6.4	The Computation of Siacci Ballistic Tables	101
6.5	The Practical Use of the Ballistic Tables	101
6.6	Form Factors of Typical Small Arms Projectiles	106
6.7	The Effect of Projectile Shape on the Form Factor	106
6.8	Rules for the Use of the Form Factor Charts	111
6.9	Additional Notes on Form Factors	111
Chapter 7	The Effect of Wind on Flat-Fire Trajectories	157
7.1	Introduction	157
7.2	Equations of Motion	157
7.3	The Flat-Fire Approximation	158
7.4	The Effect of a Constant Crosswind on the Flat-Fire Trajectory	158
7.5	The Effect of a Variable Crosswind on the Flat-Fire Trajectory	159
7.6	The Effect of Rangewind on the Flat-Fire Trajectory	162
7.7	Summary	164
Chapter 8	The Point-Mass Trajectory	165
8.1	Introduction	165
8.2	Equations of Motion	165
8.3	Change of Independent Variable from Time to Distance	165
8.4	Numerical Solution of the Equations of Motion	166
8.5	Standard Atmospheres for Point-Mass Trajectories	166
8.6	Examples of Point-Mass Trajectories	169
8.7	Comparison of Point-Mass and Siacci Trajectories	172
8.8	The Coriolis Effect on Point-Mass Trajectories	178
8.9	Summary	183
Chapter 9	Six-Degrees-of-Freedom (6-DOF) and Modified Point-Mass Trajectories	187
9.1	Introduction	187
9.2	Equations of Motion for Six-Degrees-of-Freedom Trajectories	187
9.3	Initial Conditions for Six-Degrees-of-Freedom Trajectories	191
9.4	Numerical Solution of Six-Degrees-of-Freedom Trajectories	193
9.5	Examples of Six-Degrees-of-Freedom Trajectories	194
9.6	Summary and Comments on Six-Degrees-of-Freedom Trajectories	212
9.7	The Modified Point-Mass Trajectory Model	212
9.8	Examples of Modified Point-Mass Trajectories	214
Chapter 10	Linearized Pitching and Yawing Motion of Rotationally Symmetric Projectiles	221
10.1	Introduction	221
10.2	Equations of Motion for the Linearized Problem	221
10.3	Solution of the Differential Equations for Velocity and Spin	228
10.4	Simplified Pitching and Yawing Motion of a Spinning Projectile	229
10.5	The Classical Gyroscopic Stability Criterion	230
10.6	The Yaw of Repose for Spin-Stabilized Projectiles	231
10.7	Initial Conditions for Simplified Epicyclic Motion	231
10.8	Complete Linearized Pitching and Yawing Motion of Projectiles	232
10.9	Gyroscopic and Dynamic Stability of Symmetric Projectiles	233
10.10	Initial Conditions for Damped Epicyclic Motion	234
10.11	An Example of the Linearized Pitching and Yawing Motion	235
10.12	The Motion of the Rotating [i, j, k] Coordinate System	236
10.13	Pitching and Yawing Motion of a Slightly Asymmetric Missile	237
10.14	Summary	238
Chapter 11	Linearized Swerving Motion of Rotationally Symmetric Projectiles	240
11.1	Introduction	240
11.2	The Differential Equation of Swerving Motion	240
11.3	Solution of the Differential Equation for Swerve	243
11.4	Discussion of the Linearized Swerving Motion	244
Chapter 12	Lateral Throwoff and Aerodynamic Jump	252
12.1	Introduction	252
12.2	Derivation of the Lateral Throwoff Effect	254
12.3	The Effect of a Slight Mass Asymmetry on the Initial Pitching and Yawing Motion of a Spinning Projectile	255
12.4	The Generalized Aerodynamic Jump Effect	259
12.5	The Effect of Mass Asymmetry on Lateral Throwoff and Aerodynamic Jump	260
12.6	Derivation of Kent's Equation for a Small Mass Asymmetry	264
12.7	The Effect of In-Bore Yaw on Lateral Throwoff and Aerodynamic Jump	264
12.8	Derivation of Kent's Equation for a Small In-Bore Yaw	266
12.9	The Aerodynamic Jump Due to Crosswind	267
12.10	Firing Sidewise From an Airplane	270
12.11	Summary	272
Chapter 13	Nonlinear Aerodynamic Forces and Moments	273
13.1	Introduction	273
13.2	Analysis of Nonlinear Drag Coefficient Data	273
13.3	Quasi-Linear Analysis of a Cubic Pitching Moment	275
13.4	The Effect of a Cubic Pitching Moment on Stability	279
13.5	Pitching and Yawing Motion With All Nonlinear Moments	280
13.6	Bi-Cubic and Tri-Cubic Magnus Moments	284
13.7	Nonlinear Magnus Moments and Limit-Cycle Yawing Motion	287
13.8	Quasi-Linear Analysis of a Cubic Lift Force	293
Chapter 14	Measurement of Aerodynamic Forces and Moments	299
14.1	Introduction	299
14.2	Wind Tunnel Methods	299
14.3	Free-Flight Ballistic Ranges	303
14.4	Classical Data Reduction for Spark Photography Ranges	304
14.5	Six-Degrees-of-Freedom Data Reduction for Spark Ranges	317
14.6	Modern Data Reduction for Yaw-Card Firings	318
14.7	Methods of Yaw Induction	320
14.8	Yawsonde Testing	323

Subjects

History

Military History

Strategy & Weapons of War
Nonfiction