The affect of air resistance on the speed/energy of airsoft bbs

[D.Smitty]

Two things, here:
1) This does not take into account any effect the backspin (hopup) of a bb and it's ability (if any) to reduce drag on the bb - I honestly am not good enough in my fluid dynamics to really know how to calculate that.
2) This data is not measured, it is calculated assuming that the only force acting horizontally on an airsoft bb is the drag of air resistance slowing it down.  Obviously, gravity is also pulling it down, but that will be roughly the same force on each bb - these calculations were time-consuming enough without making them two-dimensional

The following are charts giving information about the velocity and energy of airsoft bbs fired from a DMR which chronos at 550 fps with 0.20 g bbs.

[For those who like math, I basically used Euler's method to estimate the changes to the velocity every 0.05 seconds.  For comparison, I increased the sensitivity 0.005 seconds (10x) and the results were very similar, so I will stick with my initial findings.]

[img width=480 height=360]http://i929.photobucket.com/albums/ad13 ... Slide3.jpg[/img]

[img width=480 height=360]http://i929.photobucket.com/albums/ad13 ... Slide1.jpg[/img]

Notice in these two charts that the 0.40 g bb starts about 175 fps slower than the 0.20, but that at 50 feet, they have nearly the same speed!  At 100 feet, the 0.20 g bb is only going about 130 fps while the 0.40 is still going strong at about 200 fps.

The data ends at 2 seconds.  Notice that, after 2 seconds, the 0.40 g bb HAS ACTUALLY TRAVELED FARTHER THAN THE LIGHTER BB.

[img width=480 height=360]http://i929.photobucket.com/albums/ad13 ... ide4-1.jpg[/img]

[img width=480 height=360]http://i929.photobucket.com/albums/ad13 ... Slide2.jpg[/img]

I include these energy charts here for the purpose of comparing the "stopping power" of the bbs at range.  After a full second flight time, the 0.40 g bb still has about 0.25 Joules left (280 fps w/0.20s is about 1 Joule at Point blank range).  Certainly enough to feel it and hear it, still.

After 1 second in flight, the 0.20 g bb has about 0.04 joules left. 

Can't stop the Signal, Mal!

[D.Smitty]

Now that I have created the Excel spreadsheet that I used in these calculations, I can create graphs of pretty much any combination of factors you want.

I can freely adjust the FPS of the gun, mass of the bb, and even the density of the air (for different temperatures) to see how the velocity of the bbs will react and how far those bbs will travel.

Send me a PM or post a request on this thread and I'll make one up.  Now that I've done all the legwork it's a matter of changing a couple numbers and clicking "create graph."

The next step would be to set up multiple chronos and a well-placed DMR to check and see if my calculations are accurate. 

I have no illusions that there could be other factors more significant than air drag that would completely throw off these results.  I didn't even bother to calculate the Renyold's number to see if the drag equation I used is applicable.  I'm so lazy.

[hombre]

It might be interesting to see the distance that the bb has traveled with respect to time.  A side-by-side comparison of different weight bb's would be cool.  It would be nice to see at what distance/time heavy bb's would pass light bb's if fired simultaneously.

[D.Smitty]

It might be interesting to see the distance that the bb has traveled with respect to time.  A side-by-side comparison of different weight bb's would be cool.  It would be nice to see at what distance/time heavy bb's would pass light bb's if fired simultaneously.

Ask and ye shall receive:

[img width=480 height=360]http://i929.photobucket.com/albums/ad13 ... vstime.jpg[/img]

To answer your question:  in this case (it will be different for every configuration of mass and gun), at about 0.30 seconds both bbs would be about 90 feet away, with the 0.40 traveling faster at that point.

[hombre]

Awesome work!  This is some really helpful stuff, plus you seem to have done a great job of making your program adjustable.  Nice implementation of Euler's Method, gotta love differential equations

[Gabe]

A very similar chart has been on Arnie's and ASR for several years, and I had been using it to quell the (usually new player) mistake that lighter bb's go further just because of their faster initial velocity.  I think I'll start referring the misinformed to this thread instead, it's much less verbose...and honestly, less condescending-sounding than the original, lol.

[Dominum]

Physics FTW.

[Clutch]

Good work Smitt! As reference material for the AOSC, perhaps do a few charts.

1: Distance vs Time for .2, .25, .28, .29, .30, .36, .40, .43

2: FPS Calculator results for the same.

How hard would it be to convert these excel formulas to a web app that would allow people to enter in their own data and get a result?

[Dominum]

Actually, he could just host the Excel files somewhere, and post a link. Then anyone with Excel (everyone) could do whatever they wanted with them.

[Star_folder]

There was a project a few years back, the Airsoft Trajectory Project, or ATP for short. It has alot of data very similar to this, it exists in a few places, but here is the most recent that I have seen:
http://www.northtexasairsoft.org/wiki/index.php/Airsoft_Trajectory_Project

[D.Smitty]

There was a project a few years back, the Airsoft Trajectory Project, or ATP for short. It has alot of data very similar to this, it exists in a few places, but here is the most recent that I have seen:
http://www.northtexasairsoft.org/wiki/index.php/Airsoft_Trajectory_Project

This is really excellent data.  He started from the same ideas I did and actually took the time to go out and test them fully.  He even consulted some physicists and engineers to calculate the Reyonolds numbers, drag coefficients and lift coefficients. 

Kudos to this man.  I only wish I had all the guns and chronos he needed for his full experiment.  As far as I can tell, my rough one-night attempt does match his data as best as can be expected.

His hopup data is also quite impressive, considering that he verified the statement that a hopup which is not turned up high enough can actually cause a bb to FALL FASTER than a bb with no hopup at all!

Check out his headwind/tailwind data.  According to his model, which is verified with multiple rifles, the effective range of an airsoft rifle INCREASES WHEN FIRING AGAINST A LIGHT BREEZE due to hopup affects on the shot. 

...somebody get me a grant!

[Cody C.]

Awesome information Smitty, this parallels the real world experience some of the long range real steel rifle shooters have. Heavier bullets retain their velocity much longer, they also buck the wind better.