## Exterior ballistics calculator

Yes. For the mathematically inclined, Robert McCoy’s Modern __Exterior__ Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles is a great overview of both historical and modern methods. It is not a book for those without a very strong math background. If the words "solve a coupled system of first order ODE’s with a numerical method" don’t at least jog something loose in your memory, you’ll probably not understand most of the book’s math. There is some information to be gained outside of the math as well, but this is really a college text book at its core. If I had to have only one book on the subject, this would be it.

*Bryan Litz*‘s *Applied Ballistics* for Long Range Shooting is a newer and more accessible book for those who don’t want to wade through McCoy’s volume.

It also has extensive measurements of drag data using the G7 drag function, which is the best match for today’s long range bullets. This book is not overly technical, but it’s not simple either. It’s light on math, but heavy on advanced **ballistics** concepts. For the practically minded, this book is tough to beat. I also highly recommend Bryan’s follow on Books for even more intermediate to advanced information.

F. W. Mann’s 1909 classic, The Bullet’s Flight From Powder To Target: The Internal And External Ballistics Of Small Arms , is my favorite shooting book. Like Vaughn’s book, it’s about more than ballistics and has a heavy experimental (as opposed to theoretical) angle. Amazing is too light a term for this book’s content. It was out of print for quite a while, but appears to have resurfaced in 2010 – so buy one while it’s still available.

Most of the data comes straight from the manufacturer’s websites and publications. Additionally, some ballistics data is from taken from the data gathered by Bryan Litz of *Applied Ballistics*, LLC. He’s generously allowed us to use his data in our **calculator**. If you would like to see the data in detail, including test methodologies, G1 & G7 BC’s, form factors, variance, and other test data, we highly recommend purchasing his books. They provide an excellent introduction to *advanced ballistics* topics, but without all the tortuous math.

The equations of motion for even a simple model like the point mass model are painfully difficult to solve analytically. That is, it’s tough to come up with an equation that says at time x, your bullet will be at point y. In the old days, they came up with clever simplifications that allowed them to find workable solutions. One of the most prevalent is the Siacci method, which is a great option if computers are hard to come by. However, there are always compromises. The Siacci method assumes a small angle of fire where the point mass model does not. For sporting firearms, that assumption is a good one. For artillery, not so much. Siacci also makes use of extensive tables of variables that get used in the calculation, which can be a pain.

In modern times with modern computers, we can calculate a very close approximation of the analytical solution without having to actually solve the equations analytically. It’s actually pretty trivial these days to write a program to do this, which is what we’ve done. The result is a pure solution to the equations of motion, which are themselves based on fundamental physical principles.