Light BB vs Heavy BB with Mathmatic Proof

[The Acer]

Here is the Mathmatic Proof that shows that using heavier bb hurts more

Lets say you have a 1 joule spring, same size bb, neglect friction and wind resistance, to keep this simple as possible


the formula of Kinetic Energy is as following
E = 1/2 * m * s ^2
E is in Joules
M is in KG
S is in m/s

two situations, .2g bb and .3g bb

With .2g bb
1 J = 1/2 * 0.0002 KG * s^2
s = 100m/s or 328fps

With .3g bb
1J = 1/2 * 0.0003 KG * s^2
s = 81.7m/s or 268fps


According to the Taylor Knockdown Formula
TKO value = m * s * caliper / k
m is in G
s is in m/s
caliper is in mm
k is constant, 3507

With .2g bb
TKO = .2 * 100 * 6 / 3507
TKO = 0.0342

With .3g bb
TKO = .3 * 81.7 * 6 / 3507
TKO = 0.0419

As you can see the heavier bb has a bigger TKO value, hense more "penitration power" or would just hurt more.

or instead of Taylor Knockdown Value, you can use Momentum formula

P = M * V
P is the momentum
M is mass in KG
V is in m/s

with .2g bb
P = .0002kg * 100m/s
P = .02 kg m/s

with .3g bb
P = .0003kg * 81.6m/s
P = .02448 kg m/s

.3g has more momentum than the .2g, even though same amount of energy was applied


Hope this helps

[BlackRain]

You have way too much spare time on your hands.... you need to get out and play more...lol.

:smile:

[Qlong]

If I had a .20 gram bb made of a hard non-elastic material say glass, and a .21 gram bb made of jello, the heavier bb would hurt less.

There, I disproved you. MUHAHAHAH!

[coach]

Originally Posted by Qlong

If I had a .20 gram bb made of a hard non-elastic material say glass, and a .21 gram bb made of jello, the heavier bb would hurt less.

There, I disproved you. MUHAHAHAH!

yes and no. that .21gm jello BB would disintegrate upon impact, thus dissipating it's kinetic energy.

[FOX_111]

Since pain is not a constant value from one individual to an other, your theory must be re-written. (o:

But yeah, heavier object retain their energy longer wich result in more pain potential.

[The Acer]

Originally Posted by Qlong

If I had a .20 gram bb made of a hard non-elastic material say glass, and a .21 gram bb made of jello, the heavier bb would hurt less.

There, I disproved you. MUHAHAHAH!

not true, as in the Taylor Knockdown Value as stated, K is constant, and K changes as you change the material, therefore non elastic glass would have more "penitration" just because of the K value

(i sorta cheated and gave the constant of a metal bullet, also still wouldnt change the ratio between the two of them, as K would be the same in both)

[Tankdude]

What conversion table did you use to go from joules to pain?

[Styrak]

Originally Posted by Tankdude

What conversion table did you use to go from joules to pain?

You aren't familiar with the Acer-Pain standard formula?

[The Acer]

kinetic energy is not in 100% in relation to pain, as there is other factors, also i gave the taylor knockdown value, not pain,
but it can be said in airsoft that pain is in relation to this value,

[The Acer]

Originally Posted by Styrak

You aren't familiar with the Acer-Pain standard formula?

must higher tolarance than the styrak-pain convertion

[Brian McIlmoyle]

I may take pleasure in...

Depending on what side of the trigger one is on.

I have seen some people mosty immune the the pain of BB hits.. they end the night with multiple bleeders.. and could care less.

And others knocked down and squirming with a flank shot.

All with .2 bbs

Althoug I'll agree that heavier BBs hurt more... did we need math to prove that? should be self evident from childhood.. based on random stone pelting

[The Acer]

well the question was asked in an another thread,
http://www.airsoftcanada.com/showthread.php?t=70343
as DonP prove it with his experiment, i got bored in Engineering class, and i thought i should prove it, did a little research, an hour later, i proved it with math, just thought you guys would be interested, as this is a forum that is about sharing one's knowledge

[Azuki]

Why are we still arguing this? o_O... who cares what hurts more as long as I'm not getting BBs imbeded in my skin I don't really mind... -_-.

The thing is all those calculations are done with muzzle velocities...(even then you are assuming that over the length of the barrel 100% of the energy in the spring is transferred to the BB etc. etc.) Over a distance wind resistance does matter, and you must remeber at (practically) no point does a BB maintain constant velocity. It is always (except for maybe one point, which is not 'constant') either accelerating or decelerating. What you proved is true for one situation and mathematically its 100% true. IRL though, I think the penetration tests were closer to reality although not perfect.

The question was too vague to begin with IMO... *sigh*... we should stop debating or we should get a bunch of AEGs, a couple of test subjects, a few bags of BBs, and start firing to end this once and for all. Last resort: we call up the Mythbusters.

[LyquidFyre]

Originally Posted by Azuki

Last resort: we call up the Mythbusters.

Do it!

[FOX_111]

Adam is so getting shot if they try this!