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Old 02-13-2010, 03:55   #381
glock20c10mm
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Join Date: Dec 2004
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N/Apower,

The following are the current estimated probabilities of BPW playing a role for humans taking an unobstructed hit to the chest for given pressure wave magantudes:

BPW Probablility
500psi = 15%
700psi = 50%
1000psi = 75%
1300psi = 90%

The probability approaches 100% as BPW continues to increase, but will never really reach 100%. The accuracy in the prediction is roughly 10%.




And, since I have time right now, and in case you and/or others want to know, here is why bullet fragmentation increases the level of peak ballistic pressure wave -

If kinetic energy and penetration depth are equal, bullets that fragment create a larger pressure wave than bullets that retain 100% of their mass. This is because the average penetration depth is shorter than the maximum penetration depth. Recall that the average force with no mass loss is given by [COC06c]

Fave = E/d,

where E is the kinetic energy and d is the maximum penetration depth.

If we consider the case of a bullet with some fraction, f, of mass lost to fragmentation, the fraction of retained mass is (1-f) and the average force is then given by

Fave = (1-f)E/d + f E/df,

where df is depth of the center of mass of the bullet fragments. In other words, df is the average penetration depth of the fragments. Most fragments do not penetrate as deeply as the maximum penetration depth d, so that the average fragment penetration depth df can be expressed as a fraction of the maximum penetration depth

df = d/k,

where k is greater than 1. Consequently, the average force becomes,

Fave = (1-f)E/d + f k E/d.

This can be rewritten as

Fave = [1 + f (k-1)]E/d.

So we see that the enhancement factor for the average force is [1 + f(k 1)], where f is the fraction of lost mass, and k describes the relative penetration depth of the mass lost by fragmentation. If the mass lost by fragmentation penetrates of the maximum penetration depth on average, k = 2, and the enhancement factor for the average force is (1+f). In other words, a 40% loss of mass increases the average force (and thus the pressure wave) by 40%.

If the mass lost by fragmentation penetrates ⅓ of the maximum penetration depth on average, k = 3, and the enhancement factor for the average force is (1+2f). In other words, a 40% loss of mass increases the average force (and thus the pressure wave) by 80%.

Consequently, bullets that fragment can create larger pressure waves than bullets that do not fragment but have the same kinetic energy and penetration depth. Most fragmenting bullets have an average fragment penetration depth of ⅓ to of their maximum penetration depth, so that the pressure wave enhancement factor is between (1+f) and (1+2f).

In other words, a bullet which loses 10% of its original mass has a BPW 10-20% larger than one which retains 100% of its original mass. Likewise , a bullet which loses 30% of its original mass to fragmentation has a BPW 30-60% larger than one which retains 100% of its original mass.



Good Shooting,
Craig
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