GURPS Damage in Joules?

[DrTemp]

Originally Posted by whswhs

That's bad physics. Energy and momentum are NOT equivalent. It's momentum of the bullet and momentum of the rifle against your shoulder that are equal.
[,,,[

I'd rather assume that it is a misunderstanding of the expressions "momentum" and "impulse", in a way that I have misunderstood them, too. To me, it looks as if he wanted to say exactly what you said.

[Akahige]

My head hurts.

[vitruvian]

My head hurts.

It's not actually that bad.

Momentum scales linearly with both mass and velocity.

Kinetic energy scales linearly with mass and as the square of velocity.

Big, slow objects may have significant momentum and relatively little kinetic energy. Small, fast objects like bullets may have relatively little momentum and quite a bit of kinetic energy.

An assumption has been made from the way the DR of armor scales with thickness, and from old 3e Vehicle rules, that GURPS damage scales roughly as the square root of kinetic energy. It is recognized that no such relationship will actually be a smooth one, there being discontinuities and the factor of impact cross-section probably taking a part.

However, this may be inconsistent with the one solid datum point we have on the meaning of GURPS damage in physical terms - the collision damage formula.

Damage dice equals HP x velocity over 100.

HP for large animals and such scales as the cube root of mass.

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...

[lwcamp]

Originally Posted by Akahige

For a long time I've wondered how a weapon's energy is distributed to a target, and due to the lack of any discussions to the contrary, I presumed GURPS must've had it right (albeit in a very generalized form). Now I don't know what to believe.

Not to unduly invoke the name of Kromm, but we seriously need a qualified physicist to explain in simple and concise terms how such energies affect targets, and whether or not GURPS is at least generically accurate in this matter.

It depends on what sort of material is being penetrated. This gets complicated, but the short answer is that for materials that respond elastically, the depth of penetration is roughly proportional to the square root of the energy. For non-elastic materials that can simply be "crushed" out of the way, penetration is proportional to the energy. For materials that primarily interact with a projectile though viscosity, penetration is proportional to the momentum, and for materials that are non-viscous fluids penetration is formally infinite, but the energy and velocity of the projectile decrease exponentially with distance until you reach a velocity regime where non-hydrodynamic forces dominate.

Things used for armor tend to be elastic solids. This means when exposed to a force, they will deform to distribute the strain of the force over a significant part of the volume of the solid. The thicker it is, the more the "layers" behind the first "layer" can butress the first layer, helping it to resist deformation and failure (there are not really layers, since the material is uniform). For this reason, the GURPS formulas for damage where damage is roughly proportional to the kinetic energy and DR is roughly proportional to armor thickness tends to reflect real life trends. Now, things get more complicated when the armor gets thicker than the typical radius of elastic response, or when the projectile is travelling supersonically in the armor medium, so it simply does not have time to respond elastically (in either of these cases, penetration is going to be roughly linear with energy). Things also get complicated when the projectile itself can deform - in an extreme case you would treat it as a fluid plume interacting hydrodynamically with the armor medium (shaped charge explosive jets fall into this regime).

I hope that helped you get a grip on things. If any of this is confusing, let me know and I'll try to explain in clearer terms when I have a bit more time to post.

Luke

[lwcamp]

Originally Posted by Ian Wright

Unfortunately, a qualified physician will tell you that 'how such energies affect targets' is not a simple question. It's easy to calculate how much potential energy the projectile is carrying, but even for a target of uniform material and density the calculations of how that energy is deposited are pretty complex. Shockwave propogation through a solid isn't easy material. And the usual target - A person - is a messy bag of meat, squishy organs, and crunchy bones that can send a bullet bouncing at odd angles through the victim.

Just a quibble, but modern bullets from hand held weapons do not travel fast enough to produce shock waves in most kinds of tissue. They may be supersonic in air, but they are subsonic in tissue (and water, and very subsonic in steel). The shocks transmitted from the air through the air-tissue interface are negligible.

Luke

[Akahige]

I've printed posts 33 and 34 for later contemplation. :D

[elustran]

Sorry for the long post (hopefully not too many spelling/grammar errors), but check out the last bit of data at least.

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...

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

[crox]

I use this table to convert real weapons to GURPS's one.

NIJ
Threat Energy (J) DMG
Level
I.......100-125.........1d-1
I.......125-150.........1d
I.......150-175.........1d+1
I.......175-200.........1d+2
II-A...200-250.........2d-1
II-A...250-300.........2d
II-A...300-350.........2d+1
II-A...350-400.........2d+2
II......400-450.........3d-1
II......450-500.........3d
II......500-550.........3d+1
I.......550-600.........3d+2
III-A..600-700.........4d-1
III-A..700-800.........4d
III-A..800-900.........4d+1
III-A..900-1000.......4d+2
III.....1000-1250......5d-1
III.....1250-1500......5d
III.....1500-1750......5d+1
III.....1750-2000......5d+2
IV.....2000-2500......6d-1
IV.....2500-3000......6d
IV.....3000-3500......6d+1
IV.....3500-4000......6d+2
IV+...4000-5000......7d
IV+...5000-6000......8d
IV+...6000-7000......9d
IV+...7000-8000.....10d
IV+...8000-10000....11d
IV+...10000-12000..12d
IV+...12000-14000..13d
IV+...14000-16000..14d
IV+...16000-20000..15d
IV+...20000-24000..16d
IV+...24000-28000..17d
IV+...28000-32000..18d