Shotgun Ballistics

A while back, I wrote a ballistics program for round balls fired from a muzzleloader. Except for the source, a pellet from a shot gun behaves identically to a muzzle loader's round ball, so I put together this web application particularly tailored for shotgtunners.

CLICK HERE to open the web application!

Simulating reality

This ballistics program is a computer simulation which calculates the flight of a single shotgun pellet. A round ball (a shot pellet) is unique among projectiles in that its ballistic characteristics are solely dependant upon its diameter and its weight. This allows a (reasonably) simple physics model to calculate how it will behave. In the first decade of the 20th Century, British artillerymen made extensive measurements on the "retardation" of a 'reference' round-nosed one to three pound projectile over a wide range of velocities. These retardation (rearward forces) caused it to lose velocity over time, and this information could then be used to calculate ballistic tables. Of course, this reference projectile bears little resemblance to either a round ball or to almost any type of actual bullet, but it does tell us the relative forces as the velocity changes.

Since the forces retarding the projectile depend almost entirely upon the shape of its forward face, any relatively round-fronted projectile will have at least the same relative resistance as its velocity changes. The trick is then to find (or guess) the relationship of the bullet you are interested in to the reference projectile, and this is referred to as the 'ballistic coefficient', or BC. Unfortunately, the BC is largely mythical, as even small changes in bullet design prevent any exact correspondance between it and the reference, but for our purposes, a round ball is close enough that we can use this British data with a proper 'fudge factor'. I performed a number of real-world measurements to come up with this factor, and the output of this simulator is reasonably accurate. This calculator is implemented as a web application (more about this below) and can be used on any device that has a browser.

The Window

When the app starts, there is a list of all the variables you can change:

You will notice that as you change shot size or type, the shot weight is automatically calculated. If you want to change the weight, just do it, although the value will change back again if you change the caliber. Also, if you change altitude, the temperature will change to reflect the normal reduction in ambient temperature as you go higher. As with the weight, the temperature can be changed as you wish. Note that all entries have some built-in limits, and if you exceed them you will get an error message in the window.

After you have made your changes, clicking the 'PULL!' button will start the simulation. The results are shown in tabular form in the output window. If they get jumbled up, just increase the window size a little. Here is what it shows:

These calculations have some 'simplifying' assumptions. First, it assumes the pellet in question is not deformed, and next, we assume the shot leaves the gun horizontally. Small deviations from horizontal, such as seen in skeet shooting, won't affect the drop all that much, but high shots at birds will show less drop.

The Winds Do Blow

When there is a cross wind, a portion of the speed of the wind is added to the velocity of the projectile (the vector sum), so the shot feels like it is going a little faster than it actually is. Because the forces on the shot rise sharply with velocity, this extra forward resistance from what the shot would normally feel is translated to a side push which accelerates the shot to the side. This means that the most 'damage' done by a cross wind occurs in the early part of the flight. The shot slows down, but the sideways velocity doesn't, so the path of the shot curves ever more as it travels down range. This is why shooting in a variable cross wind is one of the most frustrating things you can imagine.

Leading The Target

Every shotgunner knows about leading the target, but the question is often "How Much?". This program can offer at least some assistance. The time-of-flight calculation shows how long it takes the shot to get to the target, so let's take the example of a duck flying across your position at 30 yards out. If we are using #6 chilled lead shot, we see the time-of-flight as 0.091 seconds, and if the duck is flying at 30 MPH (44 fps), we need a lead of 44 X 0.091 = 4 feet!

Of Interest To Programmers

This web application was written in Dart - a new language specially designed for advanced web applications. The computer code was then automatically translated into JavaScript, which the page actually runs. Those interested in the source code can get it through the webmaster.

Hope this helps everybody's shooting!