Sorry for the long post (hopefully not too many spelling/grammar errors), but check out the last bit of data at least.
Quote:
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Originally Posted by vitruvian
Damage dice equals HP x velocity over 100
Ergo, GURPS damage is linear in velocity and scales as the cube root of mass. The velocity part is consistent with saying it scales as the square root of kinetic energy, but the mass part doesn't jibe...
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That actually seems to be very similar to the gun formula in Gurps Vehicles, and if anyone hasn't noticed, the damage for guns in G4e seems unchanged compared to the damage for guns in G3e. The Vehicles formula was bore size times various constants for barrel length and TL. Mass of a bullet is based on the cube of bore size, therefore, you could say damage scales with the cube root of projectile mass times variables that would seem to indicate projectile speed, which is essentially the same as with 4e collision rules.
Sorry, apparently my statement that, "Energy or momentum dissipated into a target, therefore does not equal damage," was a bit out of place and needs a bit of clarification - I was referring to earlier discussions on energy doing damage. If you look up ballistic damage calculators, (I found a few here:
http://www.beartoothbullets.com/rescources/) you'll find that there's a lot of argument as to how to calculate bullet damage or stopping power.
I've assembled some information I put together from data on WWII Brit and US canon rounds and one German gun that I found that this site:
http://www.freeweb.hu/gva/. They're not stats for small arms, but they'll do.
@457m vs. RHA
P = 1000 kgm/s (momentum)
Round: mass, muzzle velocity = energy, momentum (penetrated RHA), penetration per unit energy, penetration per unit momentum
40mm APCBC: 1.22kg 792m/s = .383MJ, .966P (57.5mm) 150mm/MJ, 59.5mm/P
57mm APCBC: 3.23kg 831m/s = 1.12MJ, 2.68P (81mm) 72.3mm/MJ, 30.2mm/P
76mm APCBC: 7.00kg 792m/s = 2.20MJ, 5.54P (93mm) 42.3mm/MJ, 16.8mm/P
76mm APCR : 4.26kg 1036m/s = 2.29MJ, 4.41P (157mm) 68.6mm/MJ, 35.6mm/P
90mm APCBC: 10.94kg 808m/s = 3.57MJ, 8.84P (120mm) 33.6mm/MJ, 13.6mm/P
90mm APCR : 7.62kg 1021m/s = 3.97MJ, 7.78P (221mm) 55.7mm/MJ, 28.4mm/P
(for this gun, penetration is at range of 500m, difference is within acceptable tolerance, only a few mm of difference in penetration between 100m, and 500m)
128mm APCBC: 28.3kg 845m/s = 10.1MJ, 23.9P (178mm) 17.6mm/MJ 7.45mm/P
possible faults in data:
muzzle velocity isn't a measure of impact velocity, and cross-section, specific construction, and round profile aren't taken into account. APCBC rounds contained some explosive filler - there may be some skewing from the shell content.
Cross section may be easy to correct for simply by comparing the rounds based on relative cross section. Corrected for cross-section (APCBC rounds only):
cross section of 128mm round = 16384sqmm
cross section of other rounds based on fraction of 128mm, followed by previous energy and momentum penetration results multiplied by the ratio:
128mm = 1:1 17.6mm/MJa, 7.45mm/Pa
90mm = 0.494:1 16.6mm/MJa, 6.72mm/Pa
76mm = 0.343:1 14.5mm/MJa, 5.76mm/Pa
57mm = 0.198:1 14.3mm/MJa, 5.98mm/Pa
40mm = .0977:1 14.7mm/MJa, 5.81mm/Pa
% difference between highest and lowest: 18.8% for MJ, and 22.7% for P. Of course, that's not surprising, considering most of these rounds had similar
Okay, so now here's some data that should be pretty easy to interpret: two variations on the same round to determine whether it's energy or momentum that makes the difference.
90mm APBC(1): 10.91kg, 853m/s = 3.97MJ, 9.31P (119mm) 30.0mm/MJ, 12.8 mm/P
90mm APBC(2): 10.91kg, 975m/s = 5.19MJ, 10.6P (132mm) 25.4mm/MJ, 12.5mm/P
While two entries isn't exactly a great data set, it seems that it's momentum that makes the difference here since damage per MJ decreased with the more penetrating round. To further clarify (possibly), here's some data from a variety of Russian guns firing the same APBC 76mm round out of different guns:
6.3kg
370 m/s .431MJ, 2.33P (31mm), 71.9mm/MJ, 13.3mm/P
558 m/s .981MJ, 3.52P (61mm), 62.1mm/MJ, 17.3mm/P
612 m/s 1.18MJ, 3.86P (62mm), 52.5mm/MJ, 16.1mm/P
655 m/s 1.35MJ, 4.13P (69mm), 51.1mm/MJ, 16.7mm/P
680 m/s 1.46MJ, 4.28P (75mm), 51.4mm/MJ, 17.5mm/P
It's starting to seem like it's difficult to relate any one factor directly to damage in the real world, especially considering all of the variables that enter into ballistics - current air pressure, wind speed, manufacturing variables, specific losses from gun design, etc.
Now, here's a test of the gurps formula.... using the cube root of round weight times velocity, we'll see how well each round from the first example penetrates, using G = (Mass^(.3333)*velocity)/100. For APCBC rounds, I'll compare the relative penetration per G with relative penetration per MJarea and Parea.
40mm APCBC: 8.46G (57.5mm) 14.7mm/MJa, 5.81mm/Pa, 6.80mm/G
57mm APCBC: 12.3G (81mm) 14.3mm/MJa, 5.98mm/Pa, 6.59mm/G
76mm APCBC: 15.1G (93mm) 14.5mm/MJa, 5.76mm/Pa, 6.16mm/G
76mm APCR : 16.8G (157mm) 9.35mm/G (this is 1.52x as much as the APCBC)
90mm APCBC: 17.9G (120mm) 16.6mm/MJa, 6.72mm/Pa, 6.70mm/G
90mm APCR : 20.1G (221mm) 11.0mm/G (this is 1.64x as much as the APCBC)
128mm APCBC: 25.7G( 178mm) 17.6mm/MJa, 7.45mm/Pa, 6.93mm/G
% difference between highest G value and lowest amongst APCBC rounds: 5.3%
So, it actually appears that Gurps damage formulas are fairly accurate for real-world armor penetration capability - they're more accurate than a raw comparison between KE or momentum and more accurate than a KE or momentum comparison that's been adjusted for cross-sectional area. The Gurps damage formula appears to be a momentum comparison that's beem adjusted for projectile diameter. You'll notice an interesting case with the APCR rounds - they penetrate a little more than 1.5x as much as the APCBC rounds. Gurps has also accounted for this: APCR rounds do a little extra damage (like the +1/ die that APDS rounds get), and would have an armor divisor of some sort, perhaps (2) or (1.5) and APCBC rounds would have a divisor of perhaps (1.5) or (1), maybe with follow-up explosive damage, which isn't reflected here because either the round wouldn't penetrate, and it would have little effect or the round would penetrate and damage would be applied to the interior