Ce site est une copie mise en place provisoirement car le site original http://cybersloth.org/airsoft/trajectory/index.htm est indisponible.
 The ATP is undergoing a major rework.  As of such, some links many not work.  If you come across incomplete or misdirecting links, please notify me and I will fix them as soon as possible.  Thank you.

Introduction

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

- altitude

- temperature

- 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."

In terms of usefulness, those using upgraded guns or guns that tend to have a high degree of accuracy will benefit most from the data.  If your gun's muzzle velocity varies by 20-30 fps per shot or if, for a variety of reasons, your gun is incapable of reproducing the same trajectory shot after shot (and frankly some of mine fit that description) then the data may be less useful.  Ultimately the usefulness of the data will be determined by the end user and will still be dependent upon how familiar the user is with their gun.  For me, I think that it is very handy to have.  But of course, I am biased.

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.)

If you have a question or comments about the data, or would like to see some additional analysis or data plots, feel free to contact me.  Particularly if you want advice or graphics depicting recommended Minimum Engagement Distances, drop me a line and I'll try to help make some tailor-made plots for use at your airsoft site.

Lastly, while I consider the hop-up trajectories to be close, they're not perfect; if you have an opinion or have observational information concerning trajectory, by all means drop me a line.  Doing so will help to modify some of the coefficients that affect hop-up calculations.  I hope to eventually post a program online for people to download so that they can calculate trajectory for their own rifles, however given the lack of copious spare time, it may be another year or so before I can develop the online calculator.

Nathan

December, 2006

 I.      Physics Principles and Equations A.      Physical Characteristics of BB's, Pellets, Paintballs, Etc. 1.    Diameter 2.    Volume / Density and Terminal Velocity B.      Air Density C.      Kinetic Energy D.     Forces Governing Trajectory 1.     Drag Force 2.     Velocity 3.     Distance 4.     Magnus Force 5.     Terminal Velocity 6.     Spin Decay 7.     Drag Coefficient 8.     Lift Coefficient 9.     Gravity II.      Testing and Model Validation A.      Verifying Velocity Calculations III.     Effects of Hop-Up IV.     Effective and Maximum Range for 6mm BB's A.      Definitions of Effective and Maximum Range B.      Effective Range and Recommended BB Weight C.      Effective Range Observations V.      Environmental Effects A.      Effect of Wind on Trajectory 1.     Headwind / Tailwind Component B.      Effect of Altitude on Trajectory C.      Effect of Temperature on Trajectory VI.    Minimum Engagement Distance A.      Determining Muzzle Energy B.      Safe Impact Energy C.      Recommended Universal MED's VII.  Modeled Data A.      Velocity Comparisons Using BB's of Equal Masses 1.     Velocity Comparison Using 0.20 Gram BB's 2.     Velocity Comparison Using 0.25 Gram BB's 3.     Velocity Comparison Using 0.28 Gram BB's 4.     Velocity Comparison Using 0.29 Gram BB's 5.     Velocity Comparison Using 0.30 Gram BB's 6.     Velocity Comparison Using 0.36 Gram BB's 7.     Velocity Comparison Using 0.43 Gram BB's 8.     Velocity Comparison Using 0.88 Gram BB's 9.     Velocity Comparison Using 0.34 Gram 8mm BB's 10.     Velocity Comparison Using 0.45 Gram 8mm BB's B.      Mass Comparisons of Projectiles Fired at Equal Energies 1.     Effects of Different BB Masses Fired at 0.37 Joules (200 fps Using 0.20g) 2.     Effects of Different BB Masses Fired at 0.47 Joules (225 fps Using 0.20g) 3.     Effects of Different BB Masses Fired at 0.58 Joules (250 fps Using 0.20g) 4.     Effects of Different BB Masses Fired at 0.70 Joules (275 fps Using 0.20g) 5.     Effects of Different BB Masses Fired at 0.84 Joules (300 fps Using 0.20g) 6.     Effects of Different BB Masses Fired at 0.98 Joules (325 fps Using 0.20g) 7.     Effects of Different BB Masses Fired at 1.14 Joules (350 fps Using 0.20g) 8.     Effects of Different BB Masses Fired at 1.49 Joules (400 fps Using 0.20g) 9.     Effects of Different BB Masses Fired at 1.88 Joules (450 fps Using 0.20g) 10.     Effects of Different BB Masses Fired at 2.32 Joules (500 fps Using 0.20g) 11.     Effects of Different BB Masses Fired at 2.81 Joules (550 fps Using 0.20g) 13.     Effects of Different BB Masses Fired at 3.93 Joules (650 fps Using 0.20g) 14.     Effects of Different BB Masses Fired at 4.55 Joules (700 fps Using 0.20g) VIII. Closing Remarks IX.    References X.     Online Calculators A.      MilDot Scope Calculator B.      Relative Energy / Minimum Engagement Distance Calculator