4th Ed Whole Body Damage from Explosives

[mmartin798]

The physicist in my always knew the game mechanics for whole body damage from explosives was wrong. Until I recently ran some numbers, I did not realize how badly it was broken.

My case study was the effects of an M19 Antitank mine surface explosion on Biff, a resilient test subject who has STR: 30, CON: 30, and MASS: 10. I put him at various distances and looked at the effects on his body. The attached image shows the results.

When I looked for various safe distances from the real world, the Missile Hazard Safe distance for an M19 is 300m. If we treat the M19 as a breaching charge and calculate the minimum Stand-off Distance, which should equate to little or no whole body damage, it comes to 50m.

Comparing the two, Biff being vaporized out to 191m and dying in less than 10 round at 203m using game mechanics seems very broken. There are formulas in the Department of the Army Pamphlet 385-63 that could be used, but I will have to work out a way to simplify it for game play.

[mmartin798]

While waiting on a print job to complete, I ran the Biff versus M19 using the range safety calculations. The assumption for the game mechanics that I made was for 1 DPW at the minimum safe range. This seems reasonable, since that range has a less than 1% chance of bursting an ear drum from the over pressure. The results are in the attached PDF.

I like the numbers, but the math involved pretty much requires a spreadsheet or scientific calculator to determine the damage at an arbitrary range. I can't see a way to nicely simplify it either.

[nuke11]

Those numbers do look more reasonable than the first set. I've been mulling over how to figure out what 1 dPW equals in psi.

I just found these calculators that will help figure out some of this stuff I'm looking for : https://www.un.org/disarmament/un-saferguard/calculators/

[mmartin798]

I had some time to kill today, so I went ahead and just calculated out the whole body damage for just about everything that explodes in the 4th edition and put them all into one PDF, one item per page. There are just a couple things that I need to point out.

I could not find any warhead specs for the Armbrust 300. But since the game has their damage effects virtually identical to the LAW, I assumed the same size warhead.

The M397 40mm HE grenade page is for a successful bounce back into the air. If it fails, just use the M381 40mm HE chart instead.

Hope you find this somewhat useful.

[nuke11]

I had some time to kill today, so I went ahead and just calculated out the whole body damage for just about everything that explodes in the 4th edition and put them all into one PDF, one item per page. There are just a couple things that I need to point out.

I could not find any warhead specs for the Armbrust 300. But since the game has their damage effects virtually identical to the LAW, I assumed the same size warhead.

The M397 40mm HE grenade page is for a successful bounce back into the air. If it fails, just use the M381 40mm HE chart instead.

Hope you find this somewhat useful.

Very nice and helpful! I hope you plan on releasing the excel formula at some point.

For the specs of the Armbrust, I had to dig really deep into the archives, but the projectile is 0.99 kg and the filler is 0.16 kg of RDX (MP RE of 1.20) (it could also be some what closer to 0.19 kg) and it can penetrate 300 mm of rha.

[mmartin798]

Very nice and helpful! I hope you plan on releasing the excel formula at some point.

For the specs of the Armbrust, I had to dig really deep into the archives, but the projectile is 0.99 kg and the filler is 0.16 kg of RDX (MP RE of 1.20) (it could also be some what closer to 0.19 kg) and it can penetrate 300 mm of rha.

I do most of my work at home on my MacBook Pro using Numbers. However, I did export my master as an Excel spreadsheet. There are two sheets. The Explosives Data sheet and the Whole Body Damage sheet. I will explain the assumptions made and the formula used so people can understand where everything came from. If you just want the calculations, you can download the spreadsheet, goto the Explosive Data sheet, enter the weight of the explosive filler in Kg into cell B3, enter the explosive damage number from the game into cell B5 and then goto the Whole Body Damage sheet to see the results.

If you are still reading, I assume you want the math and such behind the sheet. I make two major assumptions in these calculations. The first is that the damage drops off exponentially with distance. The second, the point at which the Department of the Army Pamphlet 385-63 assumes a less than 1% chance of a ruptured eardrum from the over pressure generated by an explosive device, the minimum stand-off distance, is equal to 1 DPW. Using these assumptions, we have two known points with which to solve for the constants a and b in the general exponential function: f(x) = a(b)^x, where f(x) gives the damage at range x from the explosion. The values a and b are calculated on the Explosive Data sheet. When x=0, f(0)=a(b)^0. The term (b)^0 = 1, therefore at range 0 the value of a can be determined to be the full force of the explosion, Ex. To solve for b, we need our second known point. From our assumptions, we know at at the minimum stand-off distance (Msd), damage equals one. The Msd is given by D=23.4*(mass of explosive filler in Kg)^1/3. Therefore, F(Msd)=1. Substituting values we have, 1=Ex(b)^Msd. Dividing both sides by Ex and then taking the Msd-th root of both sides, we end up with b=(1/Ex)^(1/Msd). So our exponential equation is, f(x)=Ex*((1/Ex)^(1/Msd))^x. Easy peasy!

If there are any error in the math or questions about the assumptions, let me know.

[mmartin798]

Those numbers do look more reasonable than the first set. I've been mulling over how to figure out what 1 dPW equals in psi.

I just found these calculators that will help figure out some of this stuff I'm looking for : https://www.un.org/disarmament/un-saferguard/calculators/

I just found a CDC paper on the effects of overpressure on the human body. The rupture of ear drums in 1% of subjects happens at 5 psi.

Here is the whole paper:
https://www.cdc.gov/niosh/docket/archive/pdfs/NIOSH-125/125-ExplosionsandRefugeChambers.pdf