Velocity vs. Distance

[VARIABLE]

Velocity vs. Distance: Theoretical Calculations and Experimental Results

 

As a physicist, I'm always looking at the science behind the sport. So I began working on a program that calculates an airsoft bb’s trajectory. The numbers I kept coming up with didn't seem to jive with the scattered results I've found. Frankly, the initial theoretical calculations I’d came up with bothered me. I knew that bb’s slowed down a lot more that most folks realized, but I wasn’t aware of how quickly they decelerate. So I thought I'd gather some experimental data.

 

I took a slightly upgraded M4 and chrono'd it by firing twenty 0.20g bb's though it. After that, I moved the gun back 5 feet and fired another twenty shots. After that, I moved it back another 5 feet and again with twenty shots. And so on and so forth, recording the results. After I'd recorded the results using 0.20g bb’s, I repeated the test using 0.25 g bb's.

 

Below are the data I recorded. I used the chrono to take measurements from 0-60 feet. Flight duration was calculated using the program, and the vertical drop that the bb's underwent was determined based on the calculated time of flight and assuming that the hop-up is turned off.

 

The airsoft trajectory program I have takes into account air temperature and altitude. For the test, the temperature (indoors) was 68 F (20 C) and the altitude was 35 feet (or, for all practical purposes, sea level).

 

For distances beyond 60 feet (18 meters) the values are taken straight from the program. Given that the drag coefficient is constant (as is the bb size and mass) the theoretical results are accurate. I've tested the calculations using 0.30g bb’s, and also at velocities above 320 fps (though this data isn't posted because it might be over forum limits) and so far the theoretical calculations match the experimental results.

 

The chronometer was a Chrony F-1.

 

Data using KSC 0.20g bb’s.

Dist (ft) . Vel (fps) . Time (s) . Drop(in)

. .. 0 . . . . 320 . . . . 0.00 . . . . 0

. .. 5 . . . . 300 . . . . 0.02 . . . . 0

. . 10 . . . . 286 . . . . 0.03 . . . . 0

. . 15 . . . . 268 . . . . 0.05 . . . . 1

. . 20 . . . . 253 . . . . 0.07 . . . . 1

. . 25 . . . . 241 . . . . 0.09 . . . . 2

. . 30 . . . . 225 . . . . 0.11 . . . . 2

. . 35 . . . . 212 . . . . 0.14 . . . . 4

. . 40 . . . . 201 . . . . 0.16 . . . . 5

. . 45 . . . . 188 . . . . 0.19 . . . . 7

. . 50 . . . . 178 . . . . 0.21 . . . . 9

. . 55 . . . . 167 . . . . 0.24 . . . . 11

. . 60 . . . . 159 . . . . 0.27 . . . . 14

---------------------------------------------

. . 65 . . . . 150 . . . . 0.31 . . . . 18

. . 70 . . . . 142 . . . . 0.34 . . . . 23

. . 75 . . . . 134 . . . . 0.38 . . . . 28

. . 80 . . . . 126 . . . . 0.42 . . . . 34

. . 85 . . . . 119 . . . . 0.46 . . . . 41

. . 90 . . . . 112 . . . . 0.51 . . . . 49

. . 95 . . . . 106 . . . . 0.55 . . . . 59

. .100 . . . . 100 . . . . 0.60 . . . . 70

 

Data using Marushen Maxi 0.25g bb’s.

Dist (ft) . Vel (fps) . Time (s) . Drop(in)

. .. 0 . . . . 286 . . . . 0.00 . . . . 0

. .. 5 . . . . 273 . . . . 0.02 . . . . 0

. . 10 . . . . 261 . . . . 0.04 . . . . 0

. . 15 . . . . 249 . . . . 0.06 . . . . 1

. . 20 . . . . 237 . . . . 0.08 . . . . 1

. . 25 . . . . 226 . . . . 0.10 . . . . 2

. . 30 . . . . 216 . . . . 0.12 . . . . 3

. . 35 . . . . 206 . . . . 0.15 . . . . 4

. . 40 . . . . 197 . . . . 0.17 . . . . 6

. . 45 . . . . 189 . . . . 0.20 . . . . 7

. . 50 . . . . 177 . . . . 0.22 . . . . 10

. . 55 . . . . 172 . . . . 0.25 . . . . 12

. . 60 . . . . 164 . . . . 0.28 . . . . 15

---------------------------------------------

. . 65 . . . . 156 . . . . 0.31 . . . . 19

. . 70 . . . . 149 . . . . 0.35 . . . . 23

. . 75 . . . . 142 . . . . 0.38 . . . . 28

. . 80 . . . . 136 . . . . 0.42 . . . . 33

. . 85 . . . . 130 . . . . 0.45 . . . . 40

. . 90 . . . . 124 . . . . 0.49 . . . . 47

. . 95 . . . . 118 . . . . 0.53 . . . . 55

. .100 . . . . 113 . . . . 0.58 . . . . 64

 

 

 

=============================================

And for fans of the metric system...

 

Data using KSC 0.20g bb’s.

Dist (m) .. Vel (m/s) . Time (s) . Drop(cm)

. .. 0 . . . . 98 . . . . 0.00 . . . . 0

. .. 2 . . . . 92 . . . . 0.02 . . . . 0

. .. 3 . . . . 87 . . . . 0.03 . . . . 1

. .. 5 . . . . 82 . . . . 0.05 . . . . 1

. .. 6 . . . . 77 . . . . 0.07 . . . . 2

. .. 8 . . . . 73 . . . . 0.09 . . . . 4

. .. 9 . . . . 69 . . . . 0.11 . . . . 6

. . 11 . . . . 65 . . . . 0.14 . . . . 9

. . 12 . . . . 61 . . . . 0.16 . . . . 13

. . 14 . . . . 58 . . . . 0.19 . . . . 17

. . 15 . . . . 54 . . . . 0.21 . . . . 22

. . 17 . . . . 51 . . . . 0.24 . . . . 29

. . 18 . . . . 49 . . . . 0.27 . . . . 37

--------------------------------------------

. . 20 . . . . 46 . . . . 0.31 . . . . 46

. . 21 . . . . 43 . . . . 0.34 . . . . 57

. . 23 . . . . 41 . . . . 0.38 . . . . 70

. . 24 . . . . 38 . . . . 0.42 . . . . 86

. . 26 . . . . 36 . . . . 0.46 . . . . 104

. . 27 . . . . 34 . . . . 0.51 . . . . 125

. . 29 . . . . 32 . . . . 0.55 . . . . 149

. . 30 . . . . 30 . . . . 0.60 . . . . 178

 

Data using Marushen Maxi 0.25g bb’s.

Dist (m) .. Vel (m/s) . Time (s) . Drop(cm)

. .. 0 . . . . 87 . . . . 0.00 . . . . 0

. .. 2 . . . . 83 . . . . 0.02 . . . . 0

. .. 3 . . . . 79 . . . . 0.04 . . . . 1

. .. 5 . . . . 76 . . . . 0.06 . . . . 2

. .. 6 . . . . 72 . . . . 0.08 . . . . 3

. .. 8 . . . . 69 . . . . 0.10 . . . . 5

. .. 9 . . . . 66 . . . . 0.12 . . . . 7

. . 11 . . . . 63 . . . . 0.15 . . . . 10

. . 12 . . . . 60 . . . . 0.17 . . . . 14

. . 14 . . . . 57 . . . . 0.20 . . . . 19

. . 15 . . . . 55 . . . . 0.22 . . . . 24

. . 17 . . . . 52 . . . . 0.25 . . . . 31

. . 18 . . . . 50 . . . . 0.28 . . . . 39

---------------------------------------------

. . 20 . . . . 48 . . . . 0.31 . . . . 48

. . 21 . . . . 45 . . . . 0.35 . . . . 58

. . 23 . . . . 43 . . . . 0.38 . . . . 70

. . 24 . . . . 41 . . . . 0.42 . . . . 84

. . 26 . . . . 40 . . . . 0.45 . . . . 101

. . 27 . . . . 38 . . . . 0.49 . . . . 119

. . 29 . . . . 36 . . . . 0.53 . . . . 140

. . 30 . . . . 34 . . . . 0.58 . . . . 163

 

 

It's important to realize that bb's have no memory of what kind of gun they've been fired from or what the initial muzzle velocity was. That is to say that if the bb is traveling at 286 fps, 5 feet later it will only be traveling at 268 fps. The bb doesn't care whether that 284 fps was achieved immediately after leaving the barrel or if it was achieved after traveling 10 feet wherein its initial velocity was 320 fps, either way the force of drag at 284 fps for a 0.20g bb is the same.

 

This information could also be useful if your gun only fires at, say 286 fps. If your gun fires at 286 fps, after flying 5 feet the velocity would be 268 fps. After flying 10 feet, it would have a velocity of 253 fps. (However, all of the information for time of flight and vertical drop could not be used.)

 

 

Anyway, these are the results I've noticed and the calculations I've made. I've seen several other caches of data where calculations have been made (though the data were not verified experimentally). If you come across some data, let me know and I'll guess as to why the discrepancy. If you have made similar (or different) observations, please post the results (along with bb's used and chronometer used).

 

Also, although I'm convinced that the calculations are highly accurate, they're certainly not gospel. So if you'd like to point out that your gun, which may shoot at 270 fps is capable of hitting a mailbox 500 feet away, or if you believe that bb's actually get faster after they've left the barrel, then I'm not going to argue with you nor try to disabuse you of such notions. Feel free to disagree.

 

In the mean time, I'll keep working on the program as I'm trying to incorporate lift due to hop-up spin.

 

-Variable

[bigfish312]

that is what i always thorght, is it true that hops hold verlosity better than non-hop?

[Shoot&Loot]

No its not. Hop Up just spins the bb backwards creating high pressure under the bb and low pressure above it.

[VARIABLE]

Here are some graphics to go with the data...

 

 

[Hissing_Sid]

What value were you using for the co-efficient of drag?

 

Also, the BB drop column should be irrelavent since the way gravity acts on a 0.2 or 0.25 BB will be the same according to the flight time.

 

What I mean is that, for example, 0.1 secs after leaving the barrel a 0.2g BB should have dropped the same distance as a 0.25. The difference, of course, is that the 0.2g BB will have travelled further because it's lighter.

 

Your figures don't actually dispute this (I don't think) but because you've tabulated the results by distance it's difficult to see for sure.

 

Also, while we're at it, care to show the formula and figures you use to arrive at your results?

I ask cos the last guy who did this came up with similar figures which showed that 0.25s were vastly superior to 0.2s.

However, all his data was based on a theoretical 3 second flight time.

Which is, of course, bonkers.

When I do these sums I always get the same curves as you've shown on those graphs but, based on a 0.5 second flight time (sensible for airsoft) the advantage of using o.25s is always marginal IMO.

[VARIABLE]

What value were you using for the co-efficient of drag?

<{POST_SNAPBACK}>

Sorry, I thought I'd included that. The initial Cd I used was 0.50 (which is the normal estimate for spherical objects). The modified Cd is 0.465.

 

 

Also, the BB drop column should be irrelavent since the way gravity acts on a 0.2 or 0.25 BB will be the same according to the flight time.

<{POST_SNAPBACK}>

The drop is in there because it takes a different amount of time for a 0.20g bb to get to 100 feet vs the amount of time it would take a 0.25g bb to get there. So if you look at the amount of drop for a 0.20g bb, you'll notice that it drops 70" (as opposed to 64" for a 0.25g bb). So, yes, it's true that the bb's fall at the same rate, however the time it takes to get to a certain distance changes.

 

 

Also, while we're at it, care to show the formula and figures you use to arrive at your results?

<{POST_SNAPBACK}>

 

Which formulas? All of them?! The spreadsheet uses many different formulas and, frankly, it utilizes over 100,000 cell calculations (in it's current form). I don't mind doing this, Sid, but please keep in mind that it takes a lot of work to provide all of that.

 

If you want the raw experimental data, I can provide that but I won't take the time to retabulate the data for the forum (think about it, 20 measurements x 20 readings x 2 types of bbs -- that's a lot of data to modify and post). Also, keep in mind that data for the first 60 feet was taken experimentally, while data was calculated from 65-100 feet.

 

Probably the main formula you're looking for that I used is the standard drag equation of:

 

Fd = 1/2 * Cd * A * rho * v^2

 

where

Fd is the Force of drag

 

Cd is the drag coefficient (again, 0.465 seems to work the best)

 

A is area in square meters (I took the average size of a bb to be 5.95mm, so the area should be 0.0000278051 m^2 (and area is calculated as A = pi * radius ^2)

 

rho is air density calculated as standard air pressure reduced to ambient air pressure, then accounted for temperature. At 0C and 0m altitude (STP) the pressure is 1.293. Altitude effect is done using an integral table but can be approximated... however I'll skip that one for the time being. More important is temperature, which has a linear effect on air pressure. Probably the best simple formula would be 1.293-0.0045*(temperature in degrees Celsius). (At 68F, you should get 1.203 kg / m^3.)

 

and v is velocity in meters per second.

 

Distance and resultant velocity can be calculated more easily, though because this is a forum and it's hard for me to use symbols here (which is to say that I'm not sure how to) the formulas are harder to post. But I'll try..

 

Distance

x = x0 + v * t + 1/2 * a * t ^2

where

x is the final distance calculated

x0 is the previous distance calculated

v is the average velocity

t is time in seconds

and a is acceleration (where the acceleration is extrapolated from Fd)

 

Now, if you used the equation for a distance at 1s, you'd come up with some totally different from what I did. The reason for this is that the average velocity and acceleration change in a non-linear fashion. Consequently, you have to perform an integral to accurately determine x. For my program, I preformed calculations once every millisecond. You could perform calculations once every 0.1s and be close to my results, however the smaller the time interval, the better (i.e., more accurate).

 

Velocity

v = v0 + a * t

where v is calculated velocity and v0 is initial (previous) velocity

 

 

As I said, I can provide whatever you want. The point I'm trying to make is that it is complicated, and more importantly (to me, anyway) it's very time consuming for me to provide all of the information. Nevertheless, if you want to know more or need more information, please let me know.

[gunfighters]

good stuff

we have done simular tests out here so we could bace ord MEDs on FACTS.

and the faster the BB starts the faster in slows down!!!! with AEGs here in the us we have seen drops of 100FPS!!!!!!!!!! in 20ft

what this data does illastraite is the mimumal efect of upgraded springs on range.

with the difrent on range between a stock (253fps) and a 320fps up grade being only 20ft. tigh bore barrel and a well tuned hop up are way more important the the higher fps.

[VARIABLE]

I ask cos the last guy who did this came up with similar figures which showed that 0.25s were vastly superior to 0.2s.

However, all his data was based on a theoretical 3 second flight time.

Which is, of course, bonkers.

When I do these sums I always get the same curves as you've shown on those graphs but, based on a 0.5 second flight time (sensible for airsoft) the advantage of using o.25s is always marginal IMO.

<{POST_SNAPBACK}>

 

Sorry about that, Sid, I may not have read your post thoroughly. Concerning the previous calculations comparing 0.20g and 0.25g bb's, I spoke with the author and noted a difference in area. Recalculating the results (after accurately calculating area) provided results that matched experimental data. Also, I should admit that the difference in calculation iterations (0.001s vs. 0.1s) is fairly negligible.

 

Concerning 0.20g vs. 0.25, yes, the charts do show that you'll only have a marginal advantage by switching to the heavier weight bb's. Above about 45 feet, 0.25g bb's work better but the advantage is slight. For me, what I use comes down to the price difference between 0.20's and 0.25's (if 0.25's are only slightly, slightly, more expensive, I'll get them. (And I've stocked up with about 50,000 of the 0.25's, so I'll continue using them.) In terms of the effect of wind on the two different weights of bb's, again the gain is there, but it is very, very slight.

 

I've also done calculations comparing many different bb's (in terms of weight) as well as different velocities. I'll post a link to that information later (I'm still tweaking the program).

 

Seriously, I don't mind discussing this ad infinitum. If you have any questions, let me know. And, if you disagree with me, let me know. I'll probably stick by my results but my goal is to get it right in the end (as opoosed to calculating it once and sticking by it regardless of accuracy).

 

Variable

[Shao14]

I suppose the data above were averaged over multiple shots at each distance? Did you turn the hop up off when you did the experiment? The initial energy for the .25g BB recorded is roughly 1% lower than that of the .20g BB, is that because of the hop up since hop up for heavier BBs is turned slightly more?

 

In any case, this is excellent work, so it confirms all the theoretical "speculations" out there that .25g will out-range .2g at a reasonable range.

[VARIABLE]

I suppose the data above were averaged over multiple shots at each distance?  Did you turn the hop up off when you did the experiment?  The initial energy for the .25g BB recorded is roughly 1% lower than that of the .20g BB, is that because of the hop up since hop up for heavier BBs is turned slightly more?

 

In any case, this is excellent work, so it confirms all the theoretical "speculations" out there that .25g will out-range .2g at a reasonable range.

<{POST_SNAPBACK}>

 

Yes, each batch of 20 shots was averaged. The standard deviation for each batch was typically 1.7-2.5 fps. Even so, the specific difference was 320.0 fps for 0.20's, and 285.8 fps for 0.25, which yield energies of .9518 and .9490 respectively (or roughly a 0.2% difference).

 

For the tests, the hop-up was turned as low as it would go (read: off). Adding hop-up causes the muzzle velocity to decrease. I also did tests with hop-up turned up all the way and found the average velocity was around 300. For the hop-up tests, the standard deviation was higher (closer to 3.5). However, had hop-up been enabled, the energy should not have changed (at least not noticeably). While the heavier bb's have more inertia and should be less affected by the collision with the hop-up (adding to the energy), they should also grip the rubber a little more securely since it would be harder for a heavier bb to overcome rotational inertia (therefore more resistant to the friction induced by the hop-up) and thus counteract / reduce the energy. That's my analytical assessment anyway. I'm not sure how much of a difference you should see between 0.20 and 0.25g bb's, but it shouldn't change much. One thing that is certain is that the effects of hop-up should be more consistent with heavier weight bb's because the bb will spend more time in contact with the hop-up rubber as well as the fact that heavier bb's (which require more force to induce spin) would be less affected by the random velocity difference of each shot.

 

0.25g bb's will certainly outrange 0.20g, however for energy below .95J, the effects are negligible. As muzzle velocity progresses to higher energies than 0.95J, the effects are much more noticable.

 

As gunfighters pointed out, for higher velocities, the corresponding drag will be exponentially higher. At low velocities, the change in velocity is very low. One of the charts I'm working on now (for posting on another site per forum energy limits) shows that drag is very significant for velocities above 0.95J.

 

If anyone knows their specific muzzle velocity and would like for me to do a quick calculation with a couple different bb weights, feel free to PM me.

 

-Variable

[Hissing_Sid]

Thanks for the info.

 

I must admit, I DO find all this stuff very interesting.

 

The fundamental thing that I've learned is that there IS something of a "half second barrier" in airsoft. Basically, you're always limited to a half-second flight time before things start to work badly against you. Maybe it's BB drop or power dissipation or maybe the effects of wind but, basically, I've found that you pretty much hit a brick wall after half a second.

Which I reckon is interesting cos "in the field" 40-50m is about the longest shot I've ever reliably made.

I always enjoy reading about people making 100m+ shots with a stock Marui PSG1 (cos it "rulez!!!111") and I just know that the physics make it impossible. At that range the BB would be rolling along the ground at about 2fps and, if the ground wasn't there to stop it, it would have fallen about 20m!

 

The other thing I find interesting is that it always seems, to me, that the effects of hop-up are overestimated. I know hop-up works and I know how it works but it always seems that real-world performance using guns with hop-up is usually comparable with theoretical data which doesn't take hop-up into account.

 

Without doing the sums, I'm guessing that there's a swings-and-roundabouts thing going on whereby you're using a certain amount of energy to keep the BB aloft and, thus, that energy isn't going toward driving it forward.

 

Whatever the reason, it always seems that the theoretical figures calculated based on muzzle velocity will be very close to real-life but no amount of hop-up will extend the accuracy or range of a BB beyond the theoretical range.

 

Except in the minds of AEP owners, who seem to believe that the gun has a magical hop-up which can "float" a BB for 100m even though it only has muzzle energy of about 0.6J.

[VARIABLE]

The fundamental thing that I've learned is that there IS something of a "half second barrier" in airsoft. Basically, you're always limited to a half-second flight time before things start to work badly against you. Maybe it's BB drop or power dissipation or maybe the effects of wind but, basically, I've found that you pretty much hit a brick wall after half a second.

<{POST_SNAPBACK}>

That’s a pretty astute observation. In all of the data that I’ve plotted, a half-second time of flight seems to be the best indicator of effective range. I think that it’s possible to accurately make a shot in the 0.75-1.00s range but a shooter would have to know their trajectory fairly well and wind would nullify any margin of accuracy.

 

 

The other thing I find interesting is that it always seems, to me, that the effects of hop-up are overestimated. I know hop-up works and I know how it works but it always seems that real-world performance using guns with hop-up is usually comparable with theoretical data which doesn't take hop-up into account.

 

Whatever the reason, it always seems that the theoretical figures calculated based on muzzle velocity will be very close to real-life but no amount of hop-up will extend the accuracy or range of a BB beyond the theoretical range.

<{POST_SNAPBACK}>

Ditto that. I’ve modeled hop-up and found that while it does provide a flatter trajectory, it doesn’t extend range by very much. The trajectory program seems to match experimental evidence, yet I’m still testing it. While hop-up does provide backspin, it also lowers the muzzle velocity and incurs additional drag through the duration of flight.

 

I’ve came across a lot of reports of people making shots at 100+ meters. It’s just not possible. If someone turns their hop-up up all the way and arcs the trajectory, they might get some distance out of it, making the bb’s rain down on the target. But the shooter wouldn’t be accurate. And from my point of view, it’s no fun to shoot someone this way and definitely no fun to be taken out by someone who simply sprayed a rainstorm of bb’s.

 

 

 

 

One thing I’ve noticed is that people tend to estimate range very poorly. I’m as much a victim of this as anyone else. After a day of shooting, some of the guys where I do milsim were saying that they made long distance shots. We got a few guys together and asked one of them to stand downrange. We then all estimated how far away he was. We all guessed somewhere between 140-200 feet (with most people guess around 175 feet). Then we took out the steel tape and measured it: it was about 115 feet.

 

Then we had the guy downrange pick a different spot (and different range). This time we had to estimate range while looking at the guy through our rifle sights. Again, most people figured it was in the 150-200 foot range. When we measured it, we found that he was less than 100’ downrange. To me, this makes sense. Most people’s ability to accurately gauge distance just isn’t that great. Furthermore, most people find the distance exaggerated when they’re looking through sights (not sure why, maybe it’s because sighting a target makes it much more apparent as to just how small the target really is).

 

 

 

 

 

 

Below are some different graphics that look at the calculations. I did calculations for muzzle velocities of 200, 280, 300, and 328 fps using 0.20g bb’s.

 

Here is the standard non-hop-up plot. Nothing too surprising...

 

 

 

 

 

Here’s a plot with modeled hop-up data. For hop-up, I set the maximum height that a bb can make above the horizon as 4”. This is one of the functions that I’m still testing but it’s matching the data I’ve taken so far. The lift generated by the hop-up is dependent upon the instantaneous velocity and is a more straight-forward calculation (both in terms of physics equations and in terms of computer coding).

 

One thing that one notices is that the range doesn’t increase that much. Furthermore, at greater distances the trajectory has such a strong downward component that accuracy becomes non-existent. Think about it: if a shot is 60” above the ground at 130’ and it hits the ground at 135’, being able to hit a target relies less so with the shooter’s ability to line up a target and more so with his or her ability to accurately gauge the target’s distance.

 

(Keep in mind that height has been greatly exaggerated in this plot... 4" above the horizon would appear pretty flat to the shooter.)

 

 

 

 

 

This shows the velocity breakdown among the different muzzle velocities. Notice that at higher velocities, the force of drag is higher and consequently the bb decelerates at a much higher rate.

 

 

 

 

 

This shows the bb’s time of flight. I think that effective range can be best estimated, as Sid mentions, by looking at the distance reached after 0.5s of flight. Keep in mind that, at this distance, a bb that has no backspin (i.e., hop-up not used) will have dropped 48” below the aimpoint.

 

I find the time of flight charts to be pretty handy. Most people estimate the range for 0.5s by multiplying the muzzle velocity by the elapsed time. For instance, for a 300 fps gun, multiplying it by 0.5s would mean that the bb would travel 150 feet. While this is a quick way of calculating distance, it fails to take into account the fact that the bb’s velocity is constantly changing. In the case of the 300 fps gun, after 0.5 seconds the bb would only go about 85 feet, which is a far cry from 150 feet.

 

 

 

 

 

Lastly, we see a plot of energy. This is very useful as it’s not the velocity of the bb that hurts, but the energy it has. After all, a 0.12g bb shot at 387 fps would hurt less than a 0.20g bb shot at 320 fps. Why, because the energy of the former would be 0.84 joules while the latter would be 0.95 joules.

 

Personally, I find shots that impact below 0.25 joules to not hurt much at all. This corresponds to a range of 60’ with a 328 fps (1 Joule) gun.

 

 

 

 

 

The article I’m working on will be published on a vendor’s website in the US. Hopefully it’ll dispel a lot of the myths out there. I’ll let folks know when it hits the web.

 

-V

[Zero_DgZ]

This is good stuff.

 

Some thoughts of mine to consider: Given the smooth surface of an airsoft BB (by nature, in fact) the effects of spin on the air around the BB are slight because there's not much surface there to 'grab' and move the air.

 

A good example of something that's designed to take advantage of backspin to generate lift is the surface of a golf ball, which is dimpled for that precise purpose. Another useless tidbit is the fact that the pattern of dimpling on a golf ball is standardized for tournament play to keep players from engineering custom balls and having an advantage. I don't rightly know what that advantage would be (probably pretty damn small), but there it is.

 

More than anything else, I find, the backspin on an airsoft BB aids in horizontal accuracy. Back in the civil war days when lots of muskets still weren't rifled there was a saying about the safest place to be when someone's shooting at you is right in front of the gun. Figure that without some form of external input the spin on a round shot leaving an unrifled round barrel is very random, as inconsistiencies in the barrel, the muzzle, and the projectile could result in the shot taking off with all kinds of funky spin on it. This held true especially in the case of round musket balls that were crudely cast and not actually very round at all; However, try shooting your AEG around sideways and you'll get a pretty good illustration of what I'm thinking about.

 

A known vertical spin is better than an unknown and potentially horiontal spin.

 

Unless you're a trick shot and like to shoot around corners...

[Ledpocket]

I'd be very interested to see the full article, please do post that link when it becomes available.

 

And all the stuff in this thread is very interesting (even if I'm not quite a physics major I can still seem to follow much of it)

 

Good job.

[MooCow]

1

[bronney]

VARIABLE,

 

I am sorry for being a noob but I need to hear this from YOU and you only.

 

1. Hop-up OFF, will a .20g bb travel further than a .25g bb? If yes, theoretically, will a .05g bb goes even further?

 

2. Hop-up set to "optimal" +/- 1 inch of horizon, will a .20g bb travel further than a .25g bb in this setting?

 

Thanks a lot mate I need to know this once and for all because from your graph on post #4, http://www.arniesairsoft.co.uk/forums/inde...ndpost&p=502663, it seems that the .25g line is going to end more to the right, what does that mean?

[Hissing_Sid]

1. Hop-up OFF, will a .20g bb travel further than a .25g bb?  If yes, theoretically, will a .05g bb goes even further?

A 0.25g BB should travel further than a 0.2g BB.

Take a ping-pong ball and a golf ball. Which could you throw further?

The golf ball, right?

It would be much easier to throw the ping-pong ball a short distance, and it'd fly faster, but beyond about 20ft the ping-pong ball would drop out of the air no matter how hard you threw it.

By contrast, you couldn't throw the golf ball as fast but it'd, untimately, travel much further.

 

As for a 0.5g BB going further the answer is no. It wouldn't.

There are all sorts of variables which make 0.25g BBs slightly "better" than o.2g BBs. If you increased the power of a gun to 2J you might find that a0.3g BB had greater range than 0.25g, for example.

 

2. Hop-up set to "optimal" +/- 1 inch of horizon, will a .20g bb travel further than a .25g bb in this setting?

That depends on a whole bunch of things.

 

In theory, the hop-up should impart slightly more spin to a 0.2g BB cos it's launched at a higher velocity.

Even this isn't a sure thing, though, cos the BB will probably be launched faster out of a gun with a vented cylinder than one without.

 

So, assuming the lift is equal, or greater, on a 0.2g BB then that lift can do more to keep the BB in the air than the same amount of lift could do to keep a 0.25g BB in the air.

However, it's quite possible that this will simply result in longer flight time rather than increased range.

Aside from that, having a BB which can just "float" downrange doesn't mean it's going to be more accurate when it gets there. Again, 0.25g BBs are the more sensible option cos their additinal mass means they aren't affected by wind.

 

So, 0.2g BBs are junk, right?

Well, no.

 

You need to look at all these graphs in conjunction with a decent airsoft power calculator, such as the one Visionviper produced.

If you have a stock marui gun, for example, you can use VVs program to work out what sort of BB drop you can expect, what sort of ultimate range you can achieve and also what flight time you can expect from a BB.

 

For example, it is normally assumed that a 1m drop is as much as you can accurately compensate for when shooting an airsoft gun.

If it turns out that that a 0.2g BB will drop 1m when fired out of your Marui gun after 120ft then it's no good looking at the graph and thinking "Ooooh! after 150ft a 0.25g BB has more power remaining." cos, by that time, either a 0.25g or 0.2g BB will be rolling along the floor when fired out of your gun.

 

As a rule of thumb, for anything up to 100ft you're better off using 0.2g BBs simply cos they're cheaper and the difference in performance is negligable.

If you're engagement distance if further than this then go for 0.25s. It's only at longer ranges, when shot by a suitable gun, that they'll earn their keep.

 

Hope you don't mind me replying to this even though I'm not VARIABLE.

[3vi1-D4n]

Well done VARIABLE for doing these tests, it repeats the findings a study that was done on a Japanese website about this.

 

However, these results (along with the ones done on the Japanese website) does not have results beyond 1J, and that is where it becomes of concern for many airsofters around the world.

 

Problem is that finding an indoor testing area is difficult. There are not many warehouses over 100m in length, and a slight draft can affect testing results. Else I would've done the tests.

 

Using a laser range finder, and a custom 450fps spring rifle, PSG tightbore and 0.36g BBs, I have consistently hit a dinner plate sized chimney cover from 45m away. The longest shot I have measured of a hit was using a TW KAR98K, Green gas, 580fps on 0.2g (hop up on), on 0.36g BB at a fence post 120m away. These were outdoors and on some of the calmest days possible.

 

But yes, what I intend to say is that, the tests are good, but we do need more tests done, particularly in the higher power trajectories, and heavier ammo.

[FUmiYAsu]

How can you say hop up doesn't give a lot more range?

 

According to your graph, it almost doubles the range. At 280 fps it reaches 50ft when dropped 12 feet which is about as much drop as you can shoot accurately. then with hop, it travels to abt 105 ft before dropped 12 ft... So it doubles the range....

[bronney]

Hope you don't mind me replying to this even though I'm not VARIABLE.

There're people I respect most on this board and that includes you (teh Omniscience™), Sledge (lol/hour), R22Master (super noob saviour), and Shao14 cuz he likes kimbers. And recently VARIABLE for taking the time to show us his findings.

 

So no I don't mind. And that explains why I see my crude results on my end with .30's on the VSR beyond the limits; while it acts all weird on a 1J MP5. Thanks.

[Hissing_Sid]

How can you say hop up doesn't give a lot more range?

 

According to your graph, it almost doubles the range. At 280 fps it reaches 50ft when dropped 12 feet which is about as much drop as you can shoot accurately. then with hop, it travels to abt 105 ft before dropped 12 ft... So it doubles the range....

<{POST_SNAPBACK}>

Hop-up doesn't add a great deal to range cos it imparts lift by causing the BB to spin backwards. This in turn, reduces the forward velocity of the BB.

 

A BB fired without hop-up (off a high place) would travel further although it would drop as it flew.

Another BB fired with hop-up would travel a flatter trajectory but actually come to a stop sooner.

 

In the real world, of course, hop-up is usefull cos you're only ever going to be, at most, a couple of metres above the target so ultimate range isn't ever an issue. It's getting the longest possible distance which is still accurate that's important.

[VARIABLE]

VARIABLE,

 

I am sorry for being a noob but I need to hear this from YOU and you only.

 

1. Hop-up OFF, will a .20g bb travel further than a .25g bb?  If yes, theoretically, will a .05g bb goes even further?

 

2. Hop-up set to "optimal" +/- 1 inch of horizon, will a .20g bb travel further than a .25g bb in this setting?

 

Thanks a lot mate I need to know this once and for all because from your graph on post #4, http://www.arniesairsoft.co.uk/forums/inde...ndpost&p=502663, it seems that the .25g line is going to end more to the right, what does that mean?

<{POST_SNAPBACK}>

 

 

Ditto everything Hissing Sid said (and thanks for your response, Sid... couldn't have said it better myself). I think that 0.20g BB's are the way to go (cost-wise, certainly) for most situations. As Sid points out, if you're anticipating engagement ranges beyond 100', 0.25g BB's would help.

 

It has been a while since I posted this. Since then I've been incredibly busy and haven't had a chance to resume the testing necessary for posting the final article. The main hold up is that I'm having to collect a lot of data to determine the spin decay a BB encounters when hop-up is applied (i.e., how quickly the BB's spin is reduced). This may seem trivial but it makes a huge difference in determining the terminal trajectory of the BB. That, and the spin imparted upon a BB is pretty phenomenal. Again, I haven't ironed out the calculations because I need more data but the estimates are that the BB experiences spin in excess of 100,000 rpm (which jives with data collected by other researchers doing similar experiments with ping-pong balls, golf balls, tennis balls, baseballs, and every other sphere you could think of).

 

Spin also gets pretty tricky because it changes the coefficient of drag (and lift, for that matter) as the rotational velocity changes with respect of the forward velocity. Again, I hope to have it ironed out before too long...

 

I get e-mails from time to time concerning the effect the wind has on a BB's flight. Because of this, I went ahead and published one of the sections from the article that deals with crosswind. It's from the fifth section of the article and deals with wind effects. I haven't published the section on how a head- or tail-wind would affect the BB (still waiting on the hop-up data). But the crosswind information is pretty handy and a lot of folks have found it useful.

Here's the link:

http://www.cybersloth.org/temp/index.htm

 

If you have any questions about it, I'd rather that you PM me or e-mail me at airsoft@cybersloth.org. I say this simply because I don't want to junk up this topic with wind efffects. Maybe it would be better if I simply created a new post for wind effects.

 

------------------------------

 

Well done VARIABLE for doing these tests, it repeats the findings a study that was done on a Japanese website about this.

 

However, these results (along with the ones done on the Japanese website) does not have results beyond 1J, and that is where it becomes of concern for many airsofters around the world.

 

...

 

But yes, what I intend to say is that, the tests are good, but we do need more tests done, particularly in the higher power trajectories, and heavier ammo.

<{POST_SNAPBACK}>

 

Thanks for the feedback, 3vi1-D4n.

 

The calculations I'm making will take into account a multitude of different energies, however 1J is the limit that can be regularly discussed on Arnies (per forum regulations). Because of forum regulations, I've shied away from discussing anything above 1J on the forum. When I'm through with the article, I will probably converse with some of the moderators about what can be discussed, and be signed off on anything before actually posting it here. In the interim, please do not discuss > 1J energies (i.e., > 328 fps using 0.20g BB's).

 

The reason I'm going to such lengths in calculating all of this is to give people a better idea (and hopefully more definitive answer) as to whether it's worth upgrading their airsoft rifle from, say 285 fps to anything higher. Additionally, the trajectory article will hopefully help people determine what distance they should expect and what trajectory it will follow. For instance, if you've ever had to aim a few feet above your target for a long distance shot, the trajectory article should help you to determine how far above your target you're having to aim (again, barring accurate calculations and the inherent accuracy of your rifle). If you subscribe to the "spray-n-pray" philosophy, then it won't be very helpful but if you're firing a bolt-action rifle, it might prove useful. Lastly, it should help tremendously in determining minimum engagement distances (and explain the concept more scientifically).

 

------------------------------

 

How can you say hop up doesn't give a lot more range?

 

According to your graph, it almost doubles the range. At 280 fps it reaches 50ft when dropped 12 feet which is about as much drop as you can shoot accurately. then with hop, it travels to abt 105 ft before dropped 12 ft... So it doubles the range....

<{POST_SNAPBACK}>

 

Keep in mind that the vertical distance listed is in "inches" (unlike the horizontal, which is in "feet").

 

The reason I suggested that hop-up didn't make a huge difference was because I was looking at how far the BB travels before dropping 3 feet, or 36 inches. With no hop-up applied, the distance is about 75 feet. With hop-up applied, it's 115 feet. So, in hindsight, it does add an extra 50% to the total distance. But, the problem here is that the calculations I'd performed were inaccurate depictions of actual trajectories -- I apologize for that and, again, once I've collected more data I should be able to depict trajectory due to hop-up much more accurately. Either way, hop-up does add to the range but it's not quite what some people claim it does (i.e., 60 feet w/o hop-up, 200 feet w/ hop-up... yeah right). For one thing, you see a loss in muzzle velocity as some of the BB's departing energy is absorbed when it collides with the hop-up bucking. That is to say that the charts are not a fair comparison of one another (even if the hop-up were accurately calculated).

 

No need to debate it, though, as it boils down to whether or not someone thinks that a 30-50% increase is substantial (I think that it's certainly significant, but many might not).

 

------------------------------

 

Thanks again for the replies (and thanks again, Sid, for fielding the 0.20g v 0.25g question). For those who have waited patiently (or rather, are waiting patiently) I'll work on finishing the article as soon as I can... but I'd rather make sure I'm correct in all of the theoretical calculations before leading anyone astray.

 

-VARIABLE

[Blazer]

[snipping for clarity]

It has been a while since I posted this... That, and the spin imparted upon a BB is pretty phenomenal.  Again, I haven't ironed out the calculations because I need more data but the estimates are that the BB experiences spin in excess of 100,000 rpm (which jives with data collected by other researchers doing similar experiments with ping-pong balls, golf balls, tennis balls, baseballs, and every other sphere you could think of). 

 

Spin also gets pretty tricky because it changes the coefficient of drag (and lift, for that matter) as the rotational velocity changes with respect of the forward velocity.  Again, I hope to have it ironed out before too long... I get e-mails from time to time concerning the effect the wind has on a BB's flight... I say this simply because I don't want to junk up this topic with wind efffects.  Maybe it would be better if I simply created a new post for wind effects.

[snipping]

No need to debate it, though, as it boils down to whether or not someone thinks that a 30-50% increase is substantial (I think that it's certainly significant, but many might not). 

 

-VARIABLE

<{POST_SNAPBACK}>

 

Well I've done the decent thing and repped you for all the hard work that you have done in posting this information to this forum. Outstanding.

 

You information allowed me to compare my mental notes of gun performance and put it all into some sort of context that reduced some of the variables that were confusing the issue.

 

Personally, I think this thread should be required reading for all airsoft players. I would like to see the wind effect results in this thread, for the reason that it provides a seamless presentation of the data and the confounding variables.

 

Also, have you thought about sending this to NAM and get it into print? I know that is a bit retro, but there are lots of people who do airsoft who do not do the web.

 

Thank you.

[3vi1-D4n]

VARIABLE, just a a few questions to clarify. The graphs are part experimental and part calculated? Shouldn't it first be testing experimentally and then try to fit a model over it?

 

Aside from the governing equations drag, and kinematics, how did you account for hop up? Thats something I am unsure on how to model. I know that we can take a lifting body as an assumption on how the BB acts, and its velocity is directly associated with the lift it has.

[Docv400]

Tell me, you write that you chronoed the BBs at distances up to 60', have I read that correctly?

I took a slightly upgraded M4 and chrono'd it by firing twenty 0.20g bb's though it. After that, I moved the gun back 5 feet and fired another twenty shots. After that, I moved it back another 5 feet and again with twenty shots. And so on and so forth, recording the results. After I'd recorded the results using 0.20g bb’s, I repeated the test using 0.25 g bb's.....Below are the data I recorded. I used the chrono to take measurements from 0-60 feet.....

 

How do you chrono' a BB in flight when more than a few feet from the gun or am I missing something here?

I thought chrono's were extremely sensitive to alignment and even when placed at the barrel/muzzle end were prone to false readings and light interference.