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by Robert L. McCoy

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 throu
Download Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles epub
ISBN: 0764307207
ISBN13: 978-0764307201
Category: Engineering
Subcategory: Engineering
Author: Robert L. McCoy
Language: English
Publisher: Schiffer Publishing, Ltd. (January 1, 2004)
Pages: 328 pages
ePUB size: 1687 kb
FB2 size: 1343 kb
Rating: 4.6
Votes: 801
Other Formats: lrf txt rtf lrf

Math & Physics

First of all, I think it is important to identify exactly what is meant by some reviews indicating that the book is heavy on the mathematics and physics because it depends on your background. I'm a graduate student in Aerospace Engineering with an undergraduate bachelor's degree in Applied Mathematics. Much of my academic work in drag and aerodynamics is done on a calculus or partial differential equations level. The mathematics in this book do not exceed the high school or undergraduate calculus level, and most of it being accessible to someone with an Algebra II / Math Analysis education. Only some of the more advanced stuff is presented in integral calculus, but I think it could still be enjoyed by the curious shooter or ballistician with an algebra-level math background, although it may be challenging.

How to Use this Book

As far as uses, I approached this book for two reasons. First of all, it caught my eye as a shooter and enthusiast in ballistics several months before I bought it. I have yet to check out the sections on dynamics and spin and trajectories in great detail, but let me say this - it doesn't look like you should expect to be able to buy this book and calculate exact trajectories of your favorite .270 or .30-06 loads to get a leg up for next deer season. Unfortunately, just about no analysis or numerical solution can beat time and lead spent on the range for that.

Engineering Students

Secondly, I actually bought the book for research project I was doing on supersonic boundary layers for a graduate course.

Anyone seeking a resource on that level should probably look to more mathematical material as noted below; however, "Exterior Ballistics" IS a great resource for the mathematically inclined shooter, amateur ballistician or undergraduate mechanical or aerospace engineer seeking a more broad and fine-grained understanding of what all goes into a projectile's flight. It is a great resource for anyone being introduced to compressible flow who is interested in practical examples of drag profiles of actual projectiles in flight. However, the caveat with many of the figures and graphs in this book is that because they are empirically derived, many of them do not provide a lot of insight with respect to specific physical phenomena that are going on. For instance, in some of the graphs depicting zero-yaw drag coefficient as a function of varying headshape for a range of Mach numbers - it is not possible to tell what exactly is causing net drag to drop - whether viscous drag is dropping in the boundary layer due to delayed separation, or whether changes in the shock geometry or wake behavior are lowering pressure drag. So there are some physical ambiguities there that require these figures be studied carefully.

As a preliminary let me just say that this book says NOTHING about boundary layers or compressible shock behavior; in fact, the author specifically disclaims this responsibility near the beginning of "Chapter 4: Notes on Aerodynamic Drag", citing:

"No attempt is made in this chapter to discuss the basic fluid dynamic and thermodynamic processes involved in the formation of boundary layers and shock waves. This book is about exterior ballistics, and space does not permit even a cursory review of the modern science of aerodynamics. References 9 through 12 are recommended to the reader who is interested in a more complete understanding of compressible flow, shock waves, and boundary layer theory."

I have no doubt that given McCoy's CV and background that he was extremely well versed in BLs, compressible flow and fluid dynamics; however this book doesn't attack those subjects academically. While this was admittedly frustrating to me, the resources cited in References 9 - 12 ARE excellent choices - specifically Shapiro's "Dynamics and Thermodynamics of Compressible Fluid Flow" (1953) and Schlichting's "Boundary Layer Theory" (1955) which I cited in my own research. Anyone seeking a graduate level discussion of compressible boundary layer theory should seek out these two resources.

Typographical Erorrs (da dun *TSH*)

Quite a bit has been made of the errors and typos in the text. All I can say is that while I did not read the book from cover to cover or go over it with a fine toothed comb, I only noticed one typo in my research and it was not substantial. Unfortunately, Bob McCoy died just about a month after the final print was sent to the publisher, and they have decided not to publish corrections at this point.

I did some research and discovered a web page where friends and family of the author have published corrections to the text:


It's too bad the book is so pricey because it's just in a strange spot, conceptually speaking. It's a little too heady for the casual shooter, a little light on the math and fluid dynamics to be useful to the graduate student, and a little too expensive to be something you pick up just for fun. However, the material is solid and insightful.
Modern Exterior Ballistics
The Launch and Flight Dynamics of Symmetric Projectiles.

I Want to Keep This Book. Thanks to the auspices of interlibrary loan, it's mine for three weeks. That's not enough. This book really has said everything there is to say about the subject, except for the classified data you would need to calculate trajectories of actual projectiles in the inventory.

Chap 1. A Brief History of Exterior Ballistics - nice shadowgrahs of near sonic and super sonic projectiles. Large drawings of several shell types showing how they are dimensioned.

Chap 2. Aerodynamic Forces and Moments Acting on Projectiles - you have to read this chapter if you are going to understand the symbols.

Chap 3. The Vacuum Trajectory-high school math with interesting examination of the effects of firing up hill or down hill.

Chap 4. Notes on Aerodynamic Drag - just what it says. There is a nice set of shadowgraphs showing a shell at successive mach numbers from sub sonic to transsonic to supersonic. Discussion of ogives, Meplats, burning tracer (provides a little thrust and more range), fins, and yaw.

Chap 5. The Flat-Fire Point Mass Trajectory-if you assume that the trajectory is fairly flat (such as with all small arms, rifles, and tank to tank combat), the effect of verticle motion on the down range motion can be neglected. Approximate the drag function by a simple (and useful) analytic function and you get some managable equations.

Chap 6. The Siacci Method for Flat-Fire Trajectories - More of the above, only the integrals are tabulated for several standard drag functions (about five pages for each drag function). Those tables plus pencil and paper and you too can calculate how far the 0.308 bullet travels and how fast it is going when it hits and at what angle it strikes.

Chap 7. The Effect of Wind on Flat-Fire Trajectories - head winds, tail winds, cross winds: pretty much what you would expect.

Chap 8. The Point-Mass Trajectory - the point mass doesn't yaw or pitch so we only have to worry about its three linear velocities. It only has to contend with the zero yaw drag function, air density, gravity and the Coriolis force. (These last three data sets are not classified). A 417 line basic program is included. With this you can calculate your rifle shots better than you can aim.

Chap 9. Six-Degrees-of-Freedom (6-DOF) and Modified Point-Mass Trajectories - The whole enchilada. Three linear velocities and three rotational velocities are considered. They are all coupled to each other by nonlinear functions, and the (ten or so) coefficients are functions of velocity and air density. Fascinating graphs of gyrating pitch and yaw of a 105mm projectile as it goes down range are included. Then come the modified point mass trajectories. This simplification reduces the degrees of freedom from six to four which allows some of the coefficients to be set to zero while still revealing considerable interesting behavior. The forth degree of freedom is angular velocity of the bullet along its long axis.

Chap 10. Linearized Pitching and Yawing Motion of Rotationally Symmetric Projectiles - ok, another simplification: assume that the pitching and yawing motions are small and linearize the functions. There is still a nasty differential equation, but you can (sort of) solve it and predict such things as the stability of the bullet as it goes down range without a numerical integration.

Chap 11. Linearized Swerving Motion of Rotationally Symmetric Projectiles - same idea as chapter 10, but applied to the position of the projectile's center of mass.

Chap 12. Lateral Throwoff and Aerodynamic Jump - what to do about unbalanced projectiles.

Chap 13. Nonlinear Aerodynamic Forces and Moments. - I don't know; I ran out of time.