Welcome to the BB Bastard hosted version of the Airsoft Trajectory Project and the Minimum Safe Engagement Distance Calculator.
We feel it is important to keep this information online and available to the global airsoft community, which is why after our corporate website overhaul, we decided to give it a dedicated place under our domain so it can be crawled/spidered properly by search engines.
Every effort has been made to get in touch with Nathan. He seems to have dropped off the face of the earth. Considering the science here, he's probably been recruited by the CIA.
We are not trying to present this as "our" science. Heck, we don't understand 90% of it, but it DOES, in our opinion, have immense value to the sport, and thus we present it here in its entirety. Full credit is due to Nathan for his efforts. Note that I have updated Nathan's note here a little to reflect the fact that he did complete certain work - this initial introductory section is a little dated.
NOTE - PLEASE USE INTERNET EXPLORER TO NAVIGATE THE LINK IN THE AT PROJECT FILES THEMSELVES. We are looking at upgrading the site and data, but right now the code is old HTML and the links do not work in Firefox or Safari.
What is the AT Project?
I’m always trying to figure out the science behind the sport. Whether it's golf, football, tennis, or airsoft, I like to get into the details of what happens in terms of physics. Taking this approach to airsoft, I decided to set out to estimate trajectories based on experiments and the myriad equations for calculating trajectory. In the end, I had compiled the equations necessary to calculate the many forces acting upon airsoft BB's, coupled that with a little know-how and developed a program in MATLAB to ultimately calculate projectile trajectory. Basically, the program can be used for paintball, regular 0.177 BB’s, as well as airsoft BB's. It is designed to account for:
- muzzle velocity
- mass of projectile
- diameter of projectile
- air density / pressure
- wind and wind direction
- crosswind component
- amount of hop-up applied
The gun the BB is fired from is irrelevant. Once the BB leaves the barrel, it has no memory of the gun it was fired from. It has a magnitude (several, technically) and a vector, and in terms of physics, that's all that matters. Consequently, I needed to model the data knowing the initial velocity of the BB, the direction of the BB, and the spin that the BB incurs from hop-up. Granted, different guns will have a slightly different directional component when the BB exits the barrel (and we're talking VERY SLIGHT), and hop-up varies from unit to unit, however the program assumes that the BB is following the path dictated by the direction of the barrel, that the muzzle velocity is, at worst, +/- 2% of it's average muzzle velocity, and that the hop-up is capable of putting a consistent amount of backspin on the BB (i.e., it has been "broken in").
Before publishing calculated results, I went to great lengths to make sure that the calculations were accurate in terms of describing the actual trajectory. I spent several months performing tests, gathering data, contacting other scientists in the know, reading a plethora of theses, collecting information from others who had collected data, staying up late at night jotting down equations (and scratching through yet more equations), testing algorithms, performing tests AGAIN to ensure that I hadn't made errors in my methods, and of course many hours of the standard vitriolic spewing that occurs when you just can't get the programs to work.
Ultimately, all of the testing verified the final calculations. For more information on testing methods and validation, consult Section II: Testing and Model Validation.
Having verified the data, the next thing I wanted to do was calculate standard trajectory, hop-up trajectory, energy dissipation, velocity reduction, time of flight, minimum engagement distances, and the effects of altitude and temperature for a wide variety of muzzle velocities and BB weights and post the results online. Hopefully it will answer many of the questions people are putting forth about airsoft rifles, questions such as:
- What is the terminal velocity of a 0.20g BB?
- Is it worth upgrading a gun from x fps to y fps to get more range?
- For equal muzzle energies, which BB goes further, 0.20g or 0.25g?
- Which mass BB gets to the target the quickest for the given velocity?
- Do heavier mass BB's have more energy than lighter one down range?
- Is it necessary to restrict a rifle with a 600 fps muzzle velocity to a minimum engagement
distance of 100 feet?
- What MED's are recommended to ensure both safety and fairness to all shooters?
- Will lower temperatures increase or decrease range?
- Does altitude really affect trajectory and minimum engagement distances?
- Do 0.43 gram BB's negate the effects of wind that much better than 0.20 gram BB's?
- Do 8mm BB's resist the effects wind better than 6mm BB's?
- Do high-velocity BB's resist wind better than low-velocity BB's?
- What's the effective range on my rifle?
- What's the absolute maximum range on my rifle?
- Are people really able to achieve ranges out to 300 feet?
- Do 8mm BB's provide better range than 6mm BB's?
Those are all good questions. Unfortunately, I've seen many answers out there that are, at best, just guesses. And more often than not, I've seen answers that simply disagree with the laws of physics. Hopefully all of the data will provide people with some answers to these and other questions. If you find yourself in disbelief over what the calculations depict, spend some time looking at the equations; they're the standard equations used for this sort of thing and are universal when it comes to ballistics. Even if you're still not convinced, spend some additional time reading about the methodology used to verify the equations. If you're not convinced after that, I encourage you to do some testing and see how your results compare.
Additionally, I realize that airsoft is an inexact science. Air pockets, surface bumps, diameter inconsistencies, shifting winds, muzzle velocities inconsistencies... these things and others lead to erratic behavior in a BB's trajectory down range. Even so, I think that it is better to have a rough idea of what the "ideal BB" would do in flight, and allow the shooter to factor in their own "fudge factor."
Anyway, here are the data. It's divided up into many sections as it's all a little overwhelming (with around 270 charts and graphs). It's designed to be read from start to finish so if you can't figure out something in a later section, chances are that the explanation was provided in an earlier section. (And, if you're still trying to make sense of all of the questions above, they're answered concisely in Section VIII: Closing Remarks.)
Lastly, while I consider the hop-up trajectories to be close, they're not perfect; so there is some hop-up fudge factor. This site has an online calculator that enables you to apply the theory explained in this document as a solid calculable result. See this page for the MSED.
Nathan (modified slightly by the Head Bastard)
December, 2006 / August 2009