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10-05-2017, 12:36 PM   #3
Ulzgoroth

Join Date: Jul 2008
Re: Flexible ballistics armor: right through or totally stopped

Quote:
 Originally Posted by Varyon Flexible ballistic armor in GURPS functionally gets a multiplier against cutting and piercing damage - removing this multiplier to determine injury may be appropriate. Interestingly, from what I understand of realistic armor behavior, roughly dividing by 3 any time armor is penetrated (removing the multiplier would be on top of this) is fairly realistic. This is because realistic armor penetration would follow a difference of squares approach - that is, you square damage to get rough kinetic energy and square DR to get a rough value of how armor resists KE (which is linear with the square of thickness, rather than linear with thickness as in GURPS DR), take the difference, then take the square root of that to determine actual penetrating damage. As luck would have it, dividing DR by 3 actually gets you very close to the same result, with much less math.
This is a puzzling statement, since obviously there's only going to be a limited range where that's true...

Letting R be the DR value and R+x be the damage value, the indicated relation is:

-ε < (R + x)^2 - R^2 - (R + x -R/3)^2 < ε
-ε < -4/9 * R^2 + 2/3 * x * R < ε
-ε < 2/3 * R * (x - 2/3 * R) < ε

So, basically, it's accurate while the damage is close to 5/3s of the DR. Perhaps you don't care about the error increasing without bound on the high end (on the theory that at that point the target is dead either way). But on the low end it can over-estimate damage by as much as:
2/3 * R + 1 - sqrt(2R+1)
Which is, for instance, about 24 damage at R=50.
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