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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 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 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.
The noteworthy findings and innovative methods of predicting projectile trajectory, introduced in my books Exterior Ballistics: A New Approach (EBNA), Xlibris, 2010; and Exterior Ballistics with Applications (EBA3e), Xlibris, third edition, December 2011, require a methodical approach and further development. As result, the amateurs and professionals interested in exterior ballistics of firearms, and especially in long-range shooting with small arms, have a new book, Exterior Ballistics: The Remarkable Methods (EBRM), that aims to enrich the foundations of modern exterior ballistics and to lessen the complexity of physics and mathematics techniques in use. Exterior Ballistics: The Remarkable Methods is a book that combines and develops further the methods introduced in EBA3e, EBNA, and in the Exterior Ballistics of Small Arms (EBSA, Xlibris 2009). The foundations of the book are mainly the findings and the innovative ballistics methods presented in EBA3e and EBNA. The remarkable methods of exterior ballistics presented in this new book include: • The methods of determining the function of resistance G(v) of a given bullet (i=1) using range tables, or the experimental data measurements of three or four coordinates at the points of projectile impact. • The model of “Tangent Law of Trajectory Refraction” and the related set of formulas that we use to study the trajectories of projectiles in nonstandard atmosphere. • Series expansion method and the techniques of (second to sixth order) parabolas we employ to predict with great accuracy the projectile trajectory. • The exceptional Siacci’s methods that we apply as well for the projectile trajectory in nonstandard atmosphere and in inclined shooting combined with the tangent law of trajectory refraction. It is important to note that using the similarity laws of fluid dynamics we have obtained the “tangent law of projectile refraction,” which represents a progress with respect to “Newton–Snell’s law” on projectile refraction. For better understanding of the information presented in the book, the reader should refer to my three preceding books on exterior ballistics, already published by Xlibris, although most of the material is self-contained and clear enough to be accessed and assimilated by a wide range of readers. The system of units used in the book is the International System (SI). For readers that are unfamiliar with the SI system it is not difficult to become accustomed and use the materials presented in the book to benefit from the simple illustrations, exercises, and PC programs that, at the same time, give answers to many problems encountered in practice. My studies and writing work in exterior ballistics intend to find new and simple mathematical models and methods to predict the elements of the projectile trajectory. I believe that I have achieved some good results, which need to be further developed. George Klimi, PhD New York, December 2012 [email protected] [email protected] [email protected]
Exterior Ballistics with Applications Skydiving, Parachute Fall, Flying Fragments presents a modern approach to introduce the basics of exterior ballistics and its methods from the simple ideal model of projectile motion to the automatic solution of the differential equations of projectile flight using PC programs. The book uses different approaches to solve the differential equations of projectile motion among them the Siacci method and the numerical methods. The results obtained through the integration of differential equations of projectile flight are mostly analytical formulas that describe the projectile trajectory and make the exterior ballistics a comprehensible science. The Differential Equations of Projectile Flight are also integrated numerically using some original PC programs that can be easily modified to be used in similar scenarios or other new ones and give the reader the possibility to solve a great variety of Exterior Ballistics problem. Exterior Ballistics with Applications can be considered as an interdisciplinary applied mathematics and physics manuscript for the vast mathematics and physics models and techniques employed. It is a great source for applications in physics, calculus, differential equations, numerical methods, and PC programming as well. The book is illustrated with about 140 solved examples related to different artillery and infantry firearms that demonstrate the use of formulas and the solution methods of ballistics to find the elements of projectile trajectories. Exterior Ballistics with Applications includes as well two interesting topics that can be considered as applications of exterior ballistics: 1. Skydiving and parachute falling related with the trajectory of a parachutist launched from a horizontally flying airplane with un-deployed parachute, in different meteorological conditions, and in presence of air resistance and wind. 2. The ballistics of projectile fragments that is an important element of Terminal Ballistics necessary to study the effectiveness of fragmentation ammunitions on the personnel and objects, and other problems related with the construction of fragmentation ammunitions, or with Forensic Sciences. Exterior Ballistics with Applications is comprehensive and serves as reference material to provide answers to problems encountered in the practice of motion of unguided projectiles, skydiving and flying fragments of antipersonnel ammunitions.
"Elements of Exterior Ballistics: Long Range Shooting" is a concise but comprehensive instructive book on exterior ballistics applied into long-range shooting with small arms. The foundations of the book are innovatively related to the exterior ballistics of point-mass projectile as well as to the new findings and contemporary ballistics methods presented in my preceding books. The book is designed for exterior ballistics professionals, amateurs, and competitive shooters interested in long-range shooting and, in general, in exterior ballistics. Though the exterior ballistics applications are related to long-range shootings with small arms, the reader can easily extend the ballistics techniques to the artillery fire. The book has a large number of illustration examples to demonstrate the exterior ballistics solving techniques and to help the readers understand the ballistics concepts and principles as well as the challenging theoretical and practical applications.
With new chapters, homework problems, case studies, figures, and examples, Ballistics: Theory and Design of Guns and Ammunition, Third Edition encourages superior design and innovative applications in the field of ballistics. It examines the analytical and computational tools for predicting a weapon’s behavior in terms of pressure, stress, and velocity, demonstrating their applications in ammunition and weapons design. New coverage in the Third Edition includes gas-powered guns, and naval ordinance. With its thorough coverage of interior, exterior and terminal ballistics, this new edition continues to be the standard resource for those studying the technology of guns and ammunition.