Paintball Ballistics Research Paper


First StrikeEverything first strike related

01-19-2013, 04:14 PM   #1 (permalink)
Paintball Ballistician :P
External Ballistics, The First Strike Round, and Paintballs

External Ballistics, The First Strike Round, and Paintballs

Originally Posted by wikipedia
External ballistics is the part of the science of ballistics that deals with the behavior of a non-powered projectile in flight.
"non-powered projectile" sounds like a paintball to me.

Background: I've been playing since early 1990 and in that time, I've always wanted something that would allow me to make more accurate shots from a further distance away. I was one of those guys, back in the 90s who experienced first hand, the ridiculous amount of hype surrounding paintball products in all price ranges, in every source of information about paintball. Coincidentally, I've also had a very long standing recreational interest in physics.

Early Research and Study: I have faith (maybe misplaced) that over the years, at least a few companies did research on paintball ballistics. However, none of them really shared what they learned. Eventually, Tom Kaye published a lot of his experimental data and fostered a lot of scientific discussion via the Deep Blue forum on Automag Owners (AO). Regrettably, not being an Automag owner, I was oblivious to their discussions at the time.

Gary Dyrkacz ultimately built upon a lot of the discussion on AO and his efforts led to the "Paintball Trajectory Calculator" (page currently down). He presents a very technical and detailed discussion of the Newtonian physics and fluid dynamics (aerodynamics, more specifically) that influence the trajectory of a paintball. Unfortunately, he found himself lacking one key piece of information: the drag profile for a 'mostly spherical, smooth gelatin surfaced, object with a single seam'. Instead, for his calculations he used drag data derived from the testing of smooth spheres. I'm not writing off his calculator as a failure by any means. Given the limitations he faced, his calculator performs very well even by today's standards.

In my own research, I learned about the science/mathematics of external ballistics. I've come to think of it as a mathematical shorthand that allows for tweaking the key variables that influence a projectile's trajectory. At first glance, a lot of individuals dismiss external ballistics as only pertaining to firearm projectiles, velocities, etc. However, I found that airgunners (the guys who shoot high-end pellet guns for hunting small game, and marksmanship competition) also use the mathematics of external ballistics to predict the performance of their projectiles. I conducted a lot of my own research in this area because I was interested in resurrecting the "Safety Paintball". In any case, knowing the math isn't enough. You need the data to run through it. Generally speaking, there are three methods of collecting this data:
  • The weakest method of is to measure how much a projectile drops if fired at a given velocity and distance. The problem we have all seen with this is that paintballs tend to spread (due to inaccuracy) and this can impact your ability to measure the true drop vs, a shot hitting low because of spread.
  • The absolute best method is a doppler radar tracking and measuring the speed of a projectile as it moves through its entire flight path. Yeah, fat chance of that ever happening in this next to cottage industry.
  • Dual Chronograph measurements are the 'standard' method in firearm and airgun communities. The idea here is to measure the speed of a projectile as it moves through two optical chronographs some distance apart. The difference in speed measured between the two chronographs allows for a calculation of the drag the paintball was subjected to. However, nobody I knew owned one optical chronograph, let alone two.

A Breakthrough: Cockerpunk and Bryce of Punkworks got it in their heads to do a "ranged" chronograph test to simply see how much paintballs actually slow down between two points so, they could try to create a curve that would describe how fast a paintball would be going at any point in the curve.. What they didn't seem to realize was that they were conducting a test that would allow one to calculate the drag, if they knew how to apply external ballistics. This is where I came in.

Intro to the math: A key piece of data describing a projectile's performance is the Ballistic Coefficient:

Originally Posted by wikipedia
In ballistics, the ballistic coefficient (BC) of a body is a measure of its ability to overcome air resistance in flight.
So, what is the ballistic coefficient? Well, it is a measure of how aerodynamic a projectile is both in terms of it's shape (i.e. pointy nosed, round nosed, flat tail, boat tail, etc) and it's mass vs. size. Mathematically, it is expressed as:
BC = SD / i
BC: Ballistic Coefficient (how well does it resist drag) You can obtain this value through solving with SD and i, or you can use data gathered through dual chrono testing to determine it with the aid of a BC calculator like this one.
SD: Sectional Density (how heavy is it vs how wide it is)
SD = M/A
M: Mass of the projectile in pounds
A: Square of the Diameter in inches. Yes, I know that this is not the same as the area of a circle. This is a common shortcut in external ballistics used for comparison purposes. This can be gotten away with because the ratio of D^2 to PiR^2 will always be the same.

i: Form Factor (how pointy it is, how the back end is shaped, etc): Drag Coefficient / Drag Coefficient of the G1 model bullet. WTF? Yeah, in external ballistics, everyone is comparing their round to the G1 model bullet which is a projectile that has a Ballistic Coefficient of 1. Think of the "i" as a common point of reference. You express how your projectile performs relative to the standard model and, calculation software can then predict how your round will perform when given other variables (like mass, velocity, etc). If you have the BC (derived from dual chrono test), and the SD (measured and calculated), you can solve for the form factor with i = SD/BC.
So, doing all the math has allowed me to feed data to Chairgun Pro (ballistics software optimized for airguns) and make fairly accurate predictions. The following posts below will apply these techniques.

Note: Later in this thread you will see me making references to projectiles weighed in grains, 7000grains = 1 pound

Last edited by uv_halo; 02-03-2016 at 12:59 AM. Reason: Gary's site is down
01-19-2013, 04:16 PM   #2 (permalink)
Paintball Ballistician :P

Last edited by uv_halo; 03-23-2015 at 08:00 PM. Reason: broken picture link
01-19-2013, 04:17 PM   #3 (permalink)
Paintball Ballistician :P
.683, 3.11g Tiberius Arms First Strike Round

Last edited by uv_halo; 03-23-2015 at 10:32 PM. Reason: Re-Linked Graphics
01-19-2013, 04:22 PM   #4 (permalink)
Paintball Ballistician :P
a .50, 1.21g G.I. Milsim ball

Last edited by uv_halo; 03-23-2015 at 08:12 PM. Reason: Re-Linked Graphics
01-19-2013, 04:59 PM   #6 (permalink)
Paintball Ballistician :P
Originally Posted by Skibbo
Great info UV. What would be interesting is to determine how much energy it would take to get a break of the round, spreading at least enough fill that a player would be called out. Then you could look at that energy and see what the maximum effective distance for each projectile (.68, FS, .50) would theoretically be.
You could then use this data plus the angles needed to reach that distance and make up a ballistics chart, in the same vein that military marksmen/snipers use. Then using a known distance to a target, you could formulate how to hit the target given a straight flight path.

I agree to an extent.

In regards to reliable markings, the problem I've experienced is that the probability of marking is based on impact angle, and 'squishiness' of the impact point. In other words, I've whacked someone, the shell broke but, most of the paint went off of them rather than on. If one wanted to assume 90deg impact angles and a solid target this would be somewhat easy to do either by direct testing or, a crush test of the shell.

In regards to taking the data and converting to an angle / distance chart, I've run into a wall. None of the calculation software can account for degrees of change (they usually work in "Minutes of Angle which is too fine for our purposes).
01-20-2013, 06:01 PM   #8 (permalink)

We need to talk... If the software is open source, I can "fix" it for you. If not, we can rewrite it the way you want it to work


Edit: Software is open source and written in Java. I am working to convert it to a language I prefer. As he made it open source, so will I.

Uv_halo... What do we need to change? Better yet, let's get together and you can point while I code

Last edited by tymcneer; 01-20-2013 at 10:04 PM. Reason: Source code is available, so I answered my own question
01-21-2013, 10:47 PM   #9 (permalink)


Originally Posted by Usagi Tetsu
Velcor is within all of us, you need not go looking for him. He sayeth, "wherever two or more of you are gathered, there shall I be." He is my solid bunker for me to hide behind from the incoming fire of mine enemies, He is the functioning regulator which keepeth my shots consistent, and He is my keen eye guiding my fire towards my hidden enemies. Yea, whosoever shall believeth in Him shall be guided by His right hand towards the flag, and whosoever denieth Him shall reside for all eternity in the Deadbox of Life.
01-22-2013, 03:43 PM   #10 (permalink)
Paintball Ballistician :P
Originally Posted by tymcneer
We need to talk... If the software is open source, I can "fix" it for you. If not, we can rewrite it the way you want it to work


Edit: Software is open source and written in Java. I am working to convert it to a language I prefer. As he made it open source, so will I.

Uv_halo... What do we need to change? Better yet, let's get together and you can point while I code
I don't have the software in front of me right now (on travel) but, IIRC, there's a field for adjusting how many clicks per MOA. I dunno enough about the math behind the UI to be sure but, I suspect that the UI could be adjusted for clicks per degree, or, an another field added for clicks per degree and clicks per minute, summing them before calculation.

I'll PM you about my next meeting availability.



Thousands of hours of expert ballistics performance research, compiled & freely offered to the firearms community

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In order for a rifle to shoot accurately, the number one rule is that everything needs to be the same with each shot. There are several variables to rifle accuracy and each variable must be addressed. The shooter needs to be in the same position for each shot, each cartridge must be the same as the one before it, and the scope must hold the same zero while the rifle needs to produce the same results each and every time.

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The rifle... read more


Mark. Thanks a bunch for the links. I had been focusing mostly on the 1885 up to now so it's good to have a couple of No. 1 resources to go to. I think the biggest question I'll have about the No. 1 is: Even if I can get it to 1 MOA or better on the bench, what happens when I sling it up in a prone or sitting position and start putting more pressure on that fore-end? I'll do some searching on those forums and see what I can find. Nathan. Thanks for the info. That is a curious...
I knew 2 guys with this very rifle in .308,both shot tight wee loved the set trigger and the other hated it one had set trigger the other std curved jobbie so they swapped them over. as said they both shot tiny wee groups. you say barrel is stuffed......have you given it a really good clean and tried it???? you might be supprised and find it will still do the job you want,cant hurt really can it.


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