The Bison Ballistics ballistics calculator is a fully-featured modern ballsitics calculator for sportsmen. To use it, just pick a bullet from our library, fill in the appropriate information and click "Calculate Trajectory". It's free to use, so use it as much as you like - you may learn a thing or two about ballistics along the way.
Important: Do not rely on results generated by this software for any purpose whatsoever. It is a demonstration of ballistic theory, not a predictive tool for real-world use.
Just select a bullet, and then enter the remaining variables:
Yes. For the mathematically inclined, Robert McCoy's Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles
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.
Sierra includes a section in their Sierra - 5th Edition Manual
that gives a good, but basic, introduction to some of the concepts of exterior ballistics. It's a great place to get started.
Rifle Accuracy Facts by Harold Vaughn is not strictly a ballistics book, but it includes a section or two on the topic, and is a fantastic book for other reasons. A simply fascinating book all around. You will learn something if you read this book - guaranteed.
F. W. Mann's 1909 classic, The Bullet's Flight From Powder To Target: The Internal And External Ballistics Of Small Arms
For almost all of the bullets in our library, the G7 drag function is used. For long-ogive boat tails, G7 is simply a better fit than G1 (which is what most bullet makers publish). For flat based, blunt bullets, G1 can be better. We've chosen the best drag function for each bullet so you don't have to worry about it.
The BC data is from Applied Ballistics for Long Range Shooting by Bryan Litz. 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 book. It's an excellent introduction to advanced ballistics topics, but without all the tortuous math.
We'll be continually be working on the ballistics engine that drives the calculator. It's capable of much more than is exposed here, but we wanted to keep it simple. There are plenty of calculators out there with dozens of inputs. If we get enough requests for a certain feature, we will be happy to add it.
We use the point mass method. That means that the projectile is modeled as a point in space and affected by drag and gravity. The projectile's spin is not modeled, so drift effects are not reflected in the calculation. Coriolis is also not modeled.
The equations of motion turn out to be a system of coupled ordinary differential equations, which we solve numerically with a 4th order Runge-Kutta method. If a specific zero is required, we find those via a secant method root-finding algorithm.
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.