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01192013, 04:14 PM  #1 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  External Ballistics, The First Strike Round, and Paintballs
External Ballistics, The First Strike Round, and Paintballs Quote:
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". 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 highend 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:
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: Quote:
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 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
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
 
01192013, 04:16 PM  #2 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  .683, 3g DXS Silver ball Applying the math to a .683, 3g DXS Silver ball that Bryce Larson and Cockerpunk shot in their dual chrono test. I'm only using the 50ft data as the trajectory was likely straighter (less elevation) Testing conditions: 1k ft altitude, 70*f Note: You could use one single shot. I use averages and not just one shot so that I can get a hypothetical average of the ball orientations.Calculated BC: .0060 at above conditions "TrueBC" (adjusted for 70deg f, Sea Level): .0057 I don't need to solve any equations to start making predictions for .683, 3g projectiles. I'm going to solve for the form factor (i) here as it will come in handy when making predictions for .50cal rounds and hypothetical 'large bore' rounds. .0057 = (0.0066lbs/.683^2) / iData and Graphics derived from the exploitation (I use Chairgun Pro, software specifically designed for airgun ballistic calculations): Note: All initial velocities are 300FPS. Maximum Range: 94 YardsVelocity Vs Distance Drop Vs Distance Energy Vs Distance Time Vs Distance Distance Vs Deflection Caused by 3MPH Wind (a wind strong enough to drift smoke but, not strong enough to move a wind vane, you would barely feel it).
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
Last edited by uv_halo; 05242013 at 11:10 AM. Reason: broken picture link  
01192013, 04:17 PM  #3 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  .683, 3.11g Tiberius Arms First Strike Round Applying the math to a .683, 3.11g Tiberius Arms First Strike Round that Punkworks shot in a dual chrono test with a smoothbore barrel (I'll update this comment if we can recover the data or retest). Testing conditions: 1k ft altitude, 70*f I calculated the Ballistic Coefficient demonstrated for each shot and the average, corrected for standard environmental conditions (zero altitude, 70F) is: .0162 I'm going to solve for the form factor here as it will come in handy when making predictions for other virtual First Strike rounds. Numbers rounded for readability. Final Number accurate to four decimal places. .0162 = (0.0069lbs/.683^2) / iData and Graphics derived from exploitation (I use Chairgun Pro, software specifically designed for airgun ballistic calculations): Note: All initial velocities are 300FPS. Maximum Range: 178 YardsVelocity Vs Distance Drop Vs Distance Energy Vs Distance Time Vs Distance Distance Vs Deflection Caused by 3MPH Wind (a wind strong enough to drift smoke but, not strong enough to move a wind vane, you would barely feel it).
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
 
01192013, 04:22 PM  #4 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  a .50, 1.21g G.I. Milsim ball Applying the math to a .50, 1.21g G.I. Milsim ball that Bryce Larson weighed. This is an example of how one could take a known form factor, and determine the BC without using a dual chrono. However, I would like a dual chrono test at some point. BC = SD/iThis BC value is below the lower limit for my ballistic calculator. Until I get dual chrono data for G.I. Milsim rounds, I will use the lowest BC I can (.0050). Know that the actual performance is most likely worse than depicted below. Maximum range: 86 YardsVelocity Vs Distance Drop Vs Distance Energy Vs Distance Time Vs Distance Distance Vs Deflection Caused by 3MPH Wind (a wind strong enough to drift smoke but, not strong enough to move a wind vane, you would barely feel it).
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
 
01192013, 04:46 PM  #5 (permalink) 
Ask me about my Join Date: Oct 2009 
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.
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01192013, 04:59 PM  #6 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  Quote:
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).
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
 
01192013, 09:00 PM  #7 (permalink) 
Your Favorite Minecrafter Join Date: Jul 2011 Location: Panama City, FL 
My head hurts now
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01202013, 06:01 PM  #8 (permalink) 
Brass Monkey Customs 
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 Ty 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
__________________ Brass Monkey Customs If you were doing business with me via text message, please send me a text with your name, as my phone has killed my contact list. Thank you in advance. Brass Freak compatible and Equation inserts in .665, .670, .675, .678, .680 and .685 Still selling brass tubing, with .678 barrel stock now available! My feedback: MCB  eBay  AO Last edited by tymcneer; 01202013 at 10:04 PM. Reason: Source code is available, so I answered my own question 
01212013, 10:47 PM  #9 (permalink)  
12g4L Join Date: Sep 2008 Location: Halifax, NS 
Nice work guys!
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01222013, 03:43 PM  #10 (permalink)  
Paintball Ballistician :P Join Date: Mar 2008  Quote:
I'll PM you about my next meeting availability.
__________________ FN303SD Totmacher 13  SP 'Woodstalker' Ion  1989 Line SI Bushmaster SI Deluxe First Strike Round Field Listing  External Ballistics, FSRs and PBs  My Feedback Quote:
 

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