About the Calculator
How do I use the ballistics calculator?
Just select a bullet, and then enter the remaining variables:
- Muzzle Velocity: The muzzle velocity of the bullet. You can measure this with a chronograph, or look it up in a reloading manual (feet per second).
- Zero Range: The range at which the bullet's path will intersect with your line of sight. This does not have to be a multiple of 100 yards.
- Wind Speed: The wind speed between the muzzle and the target.
- Wind Heading: The direction of the wind. 90 degrees is a left to right wind from the shooter's perspective. 180 degrees is a head wind.
- Sight Height: The vertical distance between the centerline of the bore and the centerline of your scope. Strictly speaking, this is at the muzzle, but measuring the actual scope with a ruler should be close enough.
- Sight Units: The units that your scope's adjustments are in - Minute of Angle (MOA), Inches Per Hundred Yards (IPHY), or Milliradians (mil). This doesn't change the trajectory, it just formats the output in the most convenient units.
- Temperature: The temperature of the air in degrees Fahrenheit.
- Pressure: The absolute (station) pressure at the firing site. This is not the same as the barometric pressure reported by the local news, which has been corrected to the equivalent sea level pressure.
- Relative Humidity: The relative humidity in precent.
- Maximum Range: The maximum range at which the calculation stops.
- Output Interval: The range interval at which the results are printed in the trajectory table.
I want to learn more about ballistics. Can you recommend some books?
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.
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. Unfortunately, it's out of print. Buy it if you see it.
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.
Which drag function should I use and why?
For almost every long range boat tail bullet, G7 is a better fit than G1. For short, flat based bullets, a G1 may be a better fit. In either case, there isn't much difference until you get out past 600 yards or so.
Where did you get your ballistic coefficients?
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 book. It's an excellent introduction to advanced ballistics topics, but without all the tortuous math.
Why won't the ballistics calculator let me input [blank]?
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.
How does the math work?
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.
My reloading manual uses the Siacci method. Why don't you use that?
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.