McCoy R.L. Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles

Atglen, PA: Schiffer Publishing Ltd., 2012. — 328 p. — (Technology & Engineering). — ISBN: 978-0-7643-3825-0.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 industry. The final six chapters of the book present an extensive physical and mathematical analysis of the motion of symmetric projectiles. The linearised 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 are discussed. 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 behaviours. 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.A Brief History of Exterior BallisticsEarly Beginnings
Exterior Ballistics in the Nineteenth Centuiy
Early Twentieth Century Developments
The First Modem Aerodynamic Force-Moment System for Projectiles
The Beginnings of Computational Aerodynamics
Exterior Ballistics Research During the Second World War
Post-War Progress in Exterior Ballistics
Future DevelopmentsAerodynamic Forces and Moments Acting on ProjectilesDrag Force
Spin Damping Moment
Rolling Moment for Canted Fin Projectiles
Lift and Normal Forces
Overturning Moment
Magnus Force
Magnus Moment
Centers of Pressure of the Normal Force and the Magnus Force
Pitch Damping Force
Pitch Damping Moment
Neglected Forces and Moments
The Effect of Center of Gravity Location on the Aerodynamic Forces and Moments
Modem Aeroballistic and Older Ballistic NomenclaturesThe Vacuum TrajectoryEquations of Motion
Discussion of the Vacuum Trajectory
Firing Uphill and DownhillNotes on Aerodynamic DragClassical Drag Measurements
The Physical Nature of Drag
Airflow Regimes
The Effect of Projectile Shape on Drag The Effect of a Burning Tracer on Drag
The Effect of Fins on the Drag
The Drag of Smooth Spheres
The Effect of Yaw on Drag
Minimum Drag Projectile ShapesThe Rat-Fire Point Mass TYajectoryEquations of Motion
The Flat-Fire Approximation
Special Analytical Solutions of the Flat-Fire Equations
Constant Drag Coefficient
Drag Coefficient Inversely Proportional to Mach Number
Drag Coefficient Inversely Proportional to the Square Root of Mach Number
Comparison of Flat-Fire Trajectory ApproximationsThe Siacci Method for Flat-Fire TrajectoriesSiacci Assumptions and Approximations
Derivation of the Siacci Functions
The Computation of Siacci Ballistic Tables
The Practical Use of the Ballistic Tables
Form Factors of Typical Small Arms Projectiles
The Effect of Projectile Shape on the Form Factor
Rules for the Use of the Form Factor Charts
Additional Notes on Form FactorsThe Effect of Wind on Flat-Fire TrajectoriesEquations of Motion
The Flat-Fire Approximation
The Effect of a Constant Crosswind on the Flat-Fire Trajectory The Effect of a Variable Crosswind on the Flat-Fire Trajectory
The Effect of Rangewind on the Flat-Fire TrajectoryThe Point-Mass TrajectoryEquations of Motion
Change of Independent Variable from Time to Distance
Numerical Solution of the Equations of Motion
Standard Atmospheres for Point-Mass Trajectories
Examples of Point-Mass Trajectories
Comparison of Point-Mass and Siacci Trajectories
The Coriolis Effect on Point-Mass TrajectoriesSix-Degrees-of-Freedom (6-DOF) and Modified Point-Mass TrajectoriesEquations of Motion for Six-Degrees-of-Freedom Trajectories
Initial Conditions for Six-Degrees-of-Freedom Trajectories
Numerical Solution of Six-Degrees-of-Freedom Trajectories
Examples of Six-Degrees-of-Freedom Trajectories
Summary and Comments on Six-Degrees-of-Freedom Trajectories
The Modified Point-Mass Trajectory Model
Examples of Modified Point-Mass TrajectoriesLinearized Pitching and Yawing Motion of Rotationally Symmetric ProjectilesEquations of Motion for the Linearized Problem
Solution of the Differential Equations for Velocity and Spin
Simplified Pitching and Yawing Motion of a Spinning Projectile
The Classical Gyroscopic Stability Criterion
The Yaw of Repose for Spin-Stabilized Projectiles
Initial Conditions for Simplified Epicyclic Motion
Complete Linearized Pitching and Yawing Motion of Projectiles
Gyroscopic and Dynamic Stability of Symmetric Projectiles
Initial Conditions for Damped Epicyclic Motion
An Example of the Linearized Pitching and Yawing Motion
The Motion of the Rotating [i, j, k] Coordinate System
Pitching and Yawing Motion of a Slightly Asymmetric MissileLinearized Swerving Motion of Rotationally Symmetric ProjectilesThe Differential Equation of Swerving Motion
Solution of the Differential Equation for Swerve
Discussion of the Linearized Swerving MotionLateral Throwoff and Aerodynamic JumpDerivation of the Lateral Throwoff Effect
The Effect of a Slight Mass Asymmetry on the Initial Pitching and Yawing Motion of a Spinning Projectile
The Generalized Aerodynamic Jump Effect
The Effect of Mass Asymmetry on Lateral Throwoff and Aerodynamic Jump
Derivation of Kent’s Equation for a Small Mass Asymmetry
The Effect of In-Bore Yaw on Lateral Throwoff and Aerodynamic Jump
Derivation of Kent’s Equation for a Small In-Bore Yaw
The Aerodynamic Jump Due to Cross wind
Firing Sidewise From an AirplaneNonlinear Aerodynamic Forces and MomentsAnalysis of Nonlinear Drag Coefficient Data
Quasi-Linear Analysis of a Cubic Pitching Moment
The Effect of a Cubic Pitching Moment on Stability
Pitching and Yawing Motion With All Nonlinear Moments
Bi-Cubic and Tri-Cubic Magnus Moments
Nonlinear Magnus Moments and Limit-Cycle Yawing Motion
Quasi-Linear Analysis of a Cubic Lift ForceMeasurement of Aerodynamic Forces and MomentsWind Tunnel Methods
Free-Flight Ballistic Ranges
Classical Data Reduction for Spark Photography Ranges
Six-Degrees-of-Freedom Data Reduction for Spark Ranges
Modem Dqta Reduction for Yaw-Card Firings
Methods of Yaw Induction
Yawsonde Testing