Pages: 226

No chapter abstract available.

Pages: 3

The subject of ballistics is defined for the reader. The differences between interior, exterior, and terminal ballistics are described. Interior ballistics concerns itself with phenomena occurring inside the gun tube. Exterior ballistics is the science of examining the flight of a projectile. Terminal ballistics deals with the interaction of the projectile and the target. A fourth category called intermediate ballistics is sometimes considered a separate field of study. This concerns itself with the behavior of the projectile after it has left the gun but while still under the influence of the propellant gases. The unique terminology describing a gun is explained. A description of the units used in this text is provided.

Pages: 60

The energy generated in the transformation of propellant from solid to gas is an important principle in gun launch. Gas behavior is described through various mathematical models called gas laws. The gas laws are described from the simplest (ideal gas) to more complex. Thermochemistry and thermophysics are described. The basic laws of thermodynamics and how they relate to the combustion of propellants are explained. Combustion is the process through which chemical energy is transformed into the kinetic energy of the projectile. Combustion of solid propellants is physically described. An introduction to fluid mechanics is provided as this too plays a part in the physics of a gun launch.

Pages: 44

The goal of performing calculations of the behavior of the propellant and projectile in a gun is described. This goal is to be able to predict the pressures of the propellant gases and the velocity of the projectile, among other things. The principle of the Lagrange Gradient is derived and explained. This is fundamental to analytic ballistic calculations and assumes a space-wise, though not time-wise, invariance of gas density (i.e., a zero-dimensional model). This simplification allows for many useful calculations to be performed and provides useful insight into system design. The effects of propellant geometries are discussed as is the chambrage gradient assumption. Some discussion of rudimentary numerical techniques is provided. A discussion of sensitivities to the various parameters is developed.

Pages: 52

The design of guns and ammunition requires the application of both machine design principles and solid mechanics. Some solid mechanics fundamentals are reviewed such as stress and strain, particularly applied to cylinders. Failure criteria for various types of materials are discussed. The different methods by which ammunition can be constructed are described. Some of the intricacies associated with propellant ignition are discussed as well as the dynamics of events that occur within the chamber of a weapon. The design of cartridge cases is discussed, and a simple method for calculating whether a cartridge case will stick or not is examined. The design of projectiles such that they survive the stresses of gun launch is described as well as some rudimentary tips for using finite element analysis to perform analysis. Since buttress threads are used quite often in the design of both projectiles and guns, a method for their analysis is provided. Finally, some of the nuances of sabot design are described.

Pages: 34

This chapter builds on the previous and includes descriptions and techniques for designing structures to withstand fatigue. The application of machine design principles to gun tubes is expounded upon. The dynamics of gun tubes, focusing on recoil and recoil reduction, is described. Muzzle devices are used for many different purposes. Muzzle device geometry and how they achieve their purposes are discussed. A section on an analytic technique to model gas-operated guns is presented. This analytic approach allows for rapid design analysis of gas-operated guns.

Pages: 9

Recoilless guns are described. These systems may completely eliminate or just reduce recoil. As platforms that guns are mounted on get progressively lighter, the reduction of recoil without transmitting large forces to the platform itself becomes critical. Even though physics tells us that the recoil energy has to go somewhere, by clever design of the system this has been and can be achieved. The recoil discussion of the previous chapter is expanded. The interior ballistics of weapons where there is a flow out of the rear of the weapon as well as that following the projectile is discussed.

Pages: 22

Determination of propellant burn rates is important for the weapon designer. The concept of the closed bomb is explained and described in more detail than the earlier chapters. Procedures for closed bomb testing and the analysis of the data are discussed. The dynamic vivacity and the methods by which it is calculated are described. Finally, the analysis of the burn rate of propellant grains of varying configurations is laid out.

Pages: 166

No chapter abstract available.

Pages: 14

Exterior ballistics is the study of projectile flight from the time it leaves the muzzle (or more properly, the influence of the muzzle gases) and when it performs its mission at the target. Since exterior ballistics is a combination of fluid mechanics and dynamics, a review of important concepts is in order. Most important is the definition of coordinate systems as well as clear definitions of the symbols and terms. Visualizing some of the forces we encounter in three dimensions is important so significant energy is devoted to explaining these opening concepts.

Pages: 16

A full understanding of rigid body dynamics is essential to the study of exterior ballistics. Unlike aerodynamics, where reactions are relatively slow, projectile flight is dominated by the dynamic behavior of bodies. Definitions and fundamentals of vector mechanics are reviewed. The derivations of relative velocity and acceleration are performed using vectors.

Pages: 81

Different models for the ballistic behavior of projectiles can be used by a ballistician depending on the fidelity of the answer required and/or the amount of data available. Four models are examined: vacuum trajectory, flat fire trajectory, modified point mass trajectory, and six degree-of-freedom trajectory. These models vary in complexity, and some need to be handled through the use of computer programs, but in all cases they are limited by the data available to the ballistician. Even though a 6-DOF model may be very accurate, if the data is not available in the form of coefficients, a simpler model must be used. These issues and nuances are discussed. The chapter concludes with some general statements about first round hit probability.

Pages: 24

The dynamic motion of a projectile is complex with many factors affecting it. Simplification of the equations of motion is necessary to allow us to solve the equations in analytic form. This is done through the process of linearization whereby higher-order and less significant terms are dropped, resulting in equations which can be solved by hand or with a computer. The process of linearization is described. The application of these linearized equations to projectile stability is discussed—both static and dynamic stability. We formally define yaw of repose. An example of instability in the form of roll resonance is examined.

Pages: 3

The mathematics and even the visualization of projectile motion become more complicated when the realities of production are accounted for. No projectile is ever made perfectly. The equations of motion introduced earlier assumed this away. In this chapter the differences between a “real” projectile and an idealized one are discussed. Some of the concepts are illustrated; however, no new math is introduced as this is reserved for the following chapters.

Pages: 10

Mass asymmetries are common in projectiles. The geometry and effects of mass asymmetries are examined. These asymmetries manifest themselves in a phenomenon known as lateral throwoff. The equations that describe this phenomenon are introduced through the use of a vacuum trajectory so as not to confuse the physics. The inclusion of these aerodynamic effects is examined in an introductory manner, and, from this, the reader can infer that it is a topic that deserves its own book. The reader is directed to the references for further details.

Pages: 7

Projectile swerve motion is described. Aerodynamic jump is defined, and some equations are introduced for its calculation. The phenomenon of epicyclic swerve is discussed, and equations are introduced to quantify it. Finally, projectile drift is described.

Pages: 9

Nonlinear aeroballistics is the study of the behavior of projectiles where the coefficients themselves vary. In particular, the coefficients governing the stability of a projectile will dominate the flight, sometimes giving rise to what is known as limit-cycle motion or, as commonly referred to in the general literature, coning. Some mathematical concepts are developed, and the effect of these nonlinear forces and moments is discussed.

Pages: 241

No chapter abstract available.

Pages: 3

Terminal ballistics is the study of the interactions of a projectile with the target. Key concepts such as the V 50 concept are introduced. Since small variations in parameters such as mechanical properties of both the projectile and the target, hardness, and toughness make a difference in whether a projectile will penetrate to a certain depth, statistical descriptors are required. How these descriptors are obtained is described in this chapter.

Pages: 45

Methods of predicting penetration depth in various materials are presented. The physics of these different materials is quite pronounced, and different techniques are required to analyze the penetration event, sometimes requiring computer assistance. In all cases there are relatively simple analytic approaches to even very complex situations which provide reasonable estimates prior to performing extensive computational studies.

Pages: 58

Steel is a common target material. Many methods for determining the penetration of steel targets were developed in the late nineteenth and early twentieth centuries and still work today. We discuss the development of these formulas along with the characteristics of target materials. The testing that was performed to develop these formulas is described. A more detailed description of the physics of the penetration event, as pertains to steel is discussed, as well as the influence of impact obliquity and nose shapes.

Pages: 84

Shock physics is important to understand when dealing with explosive behavior as well as penetration mechanics. Shock Hugoniots are introduced, and their use in describing both the impact and detonations of explosives is described. Rarefaction waves are described as nature’s way of restoring shocked objects back to their unshocked state. These rarefaction waves also give rise to a phenomenon known as spalling or scabbing. A method for calculating spallation is presented using simple mechanical principles. Detonation physics and the equations of state necessary to predict sustained detonation are introduced.

Pages: 15

Many projectiles deliver their effect through explosive events. The use of an explosive to drive metal is the primary focus of this chapter. The Gurney method is introduced to calculate the velocity at which a given explosive will drive a given metal. Different geometries are examined. The Taylor angle is described as a means by which one can calculate the direction an explosive will drive the metal. Different behaviors of metals based on material properties are described, and the Mott formula for the determination of the number and mass of the fragments is discussed.

Pages: 23

The invention of shaped charges as a means to defeat heavy armor revolutionized anti-armor weapons and gave an individual soldier a cheap, effective means to defeat a heavily armored vehicle. The explosive effects described in the previous chapter are tailored to the design of these shaped charge weapons. Although complex computer codes are necessary for the design of these systems, hand calculations provide reasonable estimates of performance. The use of the Gurney formula and applications of the Taylor angle are described in predicting jet and slug velocities, and some rudimentary penetration calculations are described.

Pages: 11

Wound ballistics is a complex topic that is provided here as an introduction for completeness. While penetration into “simple” steel structures is complex in its own right, the diversity of materials and behavior of living tissue makes analytic treatments nearly (more likely completely) impossible. Though hundreds of extremely smart researchers have tried their hand at generating criteria to describe wounding, it appears to be a science of exceptions rather than rules. In cases where rules are postulated, they are usually valid in only a limited set of circumstances. For the student interested in this extremely interesting and complex topic, this chapter is but the pinhead-sized tip of the proverbial iceberg.