# Would conventional explosives work differently under denser atmosphere?

Would conventional explosives work differently under denser atmosphere? (If yes in any noticeable way, then how to roughly calculate the difference)

Possible clarifications:

• normal, conventional explosives, like ex. dynamite, grenade or aerial bomb - not thermobaric weapon
• roughly the same partial pressure of oxygen, just total atmospheric pressure is 3 times higher thanks to nitrogen
• I'm just interested in pressure wave, I assume that with shrapnels it is easy as they simply lose energy faster by going through denser medium (but please correct me if I am wrong)

Modern explosives self produce the oxygen needed for their functioning (this is why you can fire them underwater), so the oxygen content of the atmosphere has negligible effect.

With 3 times higher pressure you have approximately 3 times higher density. Density is important because the energy transferred by the shock wave increases by decreasing the difference in acoustic impedance of the carrying media. I.e. all other being the same, firing a bomb underwater deals more damage to a structure a bigger damage than firing the bomb in air, because the acoustic impedance of water is closer to the acoustic impedance of any solid.

The thing is, air is about 3 order of magnitude less dense than solids or liquids, or to put it in layman terms, it is a factor 1000 less dense. Thus, even multiplying the density by 3, you are barely scratching that 1000: the pressure wave will produce roughly the same damage.

If you want to go the math way, given two media, 1 and 2, the Transmitted acoustic power when going from 2 to 1 is given by $$T=1-Z_1-Z_2 \over {Z_1 + Z_2}=2Z_2 \over {Z_1 + Z_2}$$, where Z is the acoustic impedance.

As you can see, if you triple $$Z_2$$ you are slightly increasing the transmitted power.

To have a ballpark figure, let's say that $$Z_1=1000$$, $$Z_2=1$$ and $$Z^*_2=3$$.

$$T=2Z_2 \over {Z_1 + Z_2}=2 \over 1001=0.1\%$$

$$T^*=2Z^*_2 \over {Z_1 + Z^*_2}=6 \over 1003=0.59\%$$

Incidentally, this is why one get spread with gel before getting an echo scan: to make some ultrasound reach the inner of the body.

• I don't think that acoustic impedance isn't quite the thing you care about here; a powerful shockwave reflecting off an object still imparts a considerable impulse to it, no? Jul 2, 2019 at 12:58
• (a little further investigation suggests that shockwaves behave somewhat differently to vanilla acoustic waves at interfaces, but I suspect that most of the useful research on this matter is not public, military research being what it is) Jul 2, 2019 at 13:01
• Your math shows 6 times the effect of the denser atmosphere. While the energy transfer of neither is very efficient, one is substantially less efficient. Jul 2, 2019 at 13:23
• I think you simply truncated your calculations instead of rounding. Your first answer should be 0.1998%, your second be 0.5982%. Rounding both to the first sig digit to match the numerator, you should get 0.2% and 0.6%. Which is much more sensible when you recall your Z2's are in the ration of 3. Jul 2, 2019 at 13:56
• I don't want to dive deep into math, but effect of air pressure/density is actually much more pronounced than a fraction of 1%. This article suggests that blast pressure should differentiate by 10-100% Jul 2, 2019 at 17:14