One of the reasons I wanted to do some book reviews was to highlight books like this one. This is a treasure trove of information for someone who is deeply interested in exterior ballistics. However, reader be warned, it is written more for a technical audience. As my mentor, and boss, told me, “This is a good book, I know you are not fluent in calculus but this will teach you the moments and forces that act on a projectile in flight. Do not get lost in the math.”
He was right, the math is well beyond my level of expertise. However I studied this book from cover to cover and found it to be one of the most interesting, and informative books on the subject. The book is laid out to provide value to both the layman and the engineer looking to gain an in-depth insight into the field of ballistics. The first edition was published in 1998 and the Second Edition was published in 2012.
The first chapter of the book provides the reader with a pretty complete summery of the history of the study of ballistics including a summery of the Gâvre Resistance Function commonly referred to as the G# Drag Function used for determining Ballistic Coefficient. (We typically use the G1 or G7 model for B.C.). You will learn a bit about spark ranges, which were the early means for photographing projectiles in flight. The book has many, many, shadowgraph’s of bullets inflight.
These shadowgraphs are simpler then the more modern Schlieren photo’s we may be used to seeing but accomplish much the same thing. The photo’s cover the same bullet at different velocities which give a clear visualization of how pressure waves change with velocity and how they dissipate as the bullet decelerates. While there are several places which showcase these shadow graphs, Chapter 4 which discusses Aerodynamic Drag has the most impressive collection.
Perhaps one of the most important chapters in the book is Chapter 2, which covers the aerodynamic forces and moments that influence a projectile in flight. When we think of anything flying through the air, the first thing most people think about is the drag force. After all is the force of drag that gives us the Drag Coefficient, which is translated into an Ballistic Coefficient. However there are other forces that act on a bullet, which can influence how it flies through the air. This chapter covers them in detail and will provide the mathematical expressions behind them.
Unless you are someone who is a serious student of ballistics, this book may be a bit much. It is priced like a text book, and in my opinion the information it contains makes it worth it. However it is not a casual read, and while it is informative, you are unlikely to use the equations or some of the technical information unless you work in the field. I can give a few examples where we did use the information in this book to help us develop better small arms bullets.
The first example comes from Chapter 10.5 which discusses the spin stability and yawing motion of axial symmetric projectiles (Read Bullets). Based on the equations and a machine typically used to balance dental rotors we would spin bullets to evaluate the balance. Similar to how we spin a car tire to balance it. We could take a lot of bullets and spin them and then plot the predicted dispersion on an excel chart. Now, this was predicted dispersion based on bullet balance alone, which is one of about a dozen difference factors that determine group size. The theory behind this was simple, if we could hand pick a lot of bullets that would shoot the tightest group we want the bullets that demonstrate they are as close to perfectly balanced as possible.
The second example comes from the same chapter, and concerns the yawing of a bullet. Indirectly this deals a bit with the term “Go to Sleep”. If you have been around long distant shooters you may have heard this magical term. It is often misunderstood, or it is not explained correctly. This chapter does not use the shooters jargon, rather the technical term yaw. When a bullet leaves the muzzle of a gun it typically flutters. Meaning it will yaw up and down, side to side for a distance. This yawing motion can either dampen out, or it can get worse the further down range it goes. These motions occur at a frequency and can be calculated and observed if witness cards are placed at the correct distance from the muzzle.
A bullet that has considerable yaw exposes a larger cross sectional area to the wind and conversely has more drag, and lower’s the Ballistic Coefficient. If the yaw does not dampen out, it can get worse and worse. A bullet can still maintain spin stability and exhibit small amounts of yaw. We saw this when testing a overbore cartridge. For some reason, one that I never got to the bottom of, an occasional bullet would become a major flier. Sometimes the shot would land 30 inches from the main group. This stumped us for awhile as the bullet would shoot fine out of lesser, magnum cartridges. After placing the witness cards at the calculated moments of maximum yaw we began to see what was going on. The bullet was yawing out of the muzzle, and sometimes that yawing motion would not dampen out and determined the trajectory of the bullet.
It is true that bullets “Go to sleep” meaning yawing motion stops, but it happens pretty darn quickly within feet of the muzzle. If it does not, then the yawing motion will adversely affect down range trajectory. This may include opening up group sizes, or erratic fliers as we saw in the lab. Some how this term has been elevated to mythical magic, something beyond what it actually is. Books like this, help the shooter to understand the forces at play, and not only provide an explanation but provide the math and the testing data behind it.
One last useful thing, is the tables the book has. They are extremely useful when doing computational fluid dynamics with Solid Works. Sometimes you need to check to make sure everything is set up correctly, and when you want to get an idea of what a bullet design might do at 2,600fps, running your inputs on the models published in this book can be helpful in checking the outputs. If you are off by 5% or 10% in the results that may give you an indication on how to adjust the results when the model is run on your bullet design.
As I said, it is not a book that you read your son before putting him down for bed. While there are some very fun bits, it is also a pretty dry read. If you enjoy the technical, and you enjoy the theory and math behind exterior ballistics, this book will fit well on your book shelf. However if you are like most shooters and would like a high level book that really breaks things down into layman’s terms without overwhelming the reader with technical mumbo-jumbo this book probably is not for you. Especially will the widespread accessibility of trajectory calculators out there (Ballistic AE being my favorite), it’s hard to make an argument that the hobby shooter is going to benefit from this book on his shelf. I will say though, the pictures are pretty phenomenal.