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This is a proxy for a question from a friend. I'm an aerospace engineer so I have some domain-knowledge on compressible flow but less about missile design and even less about explosives. I also realize that this question is radically underspecified and a lot would probably depend on detailed design.

I was basically asked: if you have a hypersonic missile carrying a high-explosive warhead, how would the shockwaves produced by the high-explosive detonating interact with the shockwaves produced by the hypersonic missile's own movement through the air?

My own expectation is that there's going to be significant lensing or reflection of the high-explosive's shockwave, and that the hypersonic shock will dominate the interaction. I haven't gathered enough data yet to make a solid case for that though.

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For large yield high-explosives, won't the initial blast wave move at hypersonic speeds? The detonation speed of acetone peroxide is over 5000 m/s, which is well within the hypersonic speed range. The substance octanitrocubane has a detonation speed of over 10,000 m/s.

As I explain at https://physics.stackexchange.com/a/242450/59023 and https://physics.stackexchange.com/a/271329/59023, the shock speed from a blast wave (i.e., what is produced by chemical explosives or any type of sufficiently strong, sudden energy release) is proportional to $\left( \tfrac{ E_{o} }{ \rho_{up} } \right)^{1/5} t^{-3/5}$, where $t$ is time from the initial release of energy, $E_{o}$, from a point source and $\rho_{up}$ is the ambient gas mass density. The MOAB, for example, releases ~11 tons of TNT equivalent energy during its explosion. One ton of TNT energy yield is $\sim4.184 \times 10^{9}$ joules. The density of the atmosphere at STP is ~1.2754 kg $m^{-3}$. Then the ratio in the above expression for the MOAB would correspond to ~130 m $s^{-2/5}$. If we take our initial time to be 1 ms then the shock speed will be on the order of ~8000 m/s and the blast wave will have moved ~10 m from the origin (i.e., it will have enveloped the launch vehicle and much of its leading shock wave).

My own expectation is that there's going to be significant lensing or reflection of the high-explosive's shockwave, and that the hypersonic shock will dominate the interaction. I haven't gathered enough data yet to make a solid case for that though.

I think the explosion will likely dominate, if enough energy is released and the explosive material has a high enough detonation velocity (like most modern high explosives do). The incident kinetic energy of the launch vehicle will add to the carnage, of course.

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    $\begingroup$ excellent. thanks for the links to your other answers as well. I obviously underestimated the capabilities of explosives $\endgroup$
    – Erin Anne
    Mar 31, 2022 at 19:03
  • $\begingroup$ in the last sentence: "The incident kinetic energy of the launch vehicle will add to the carnage, of course." Are you referring to the LV striking the target, or is the additional kinetic energy making the blast wave more destructive? $\endgroup$
    – Erin Anne
    Mar 31, 2022 at 19:37
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    $\begingroup$ @ErinAnne - Both $\endgroup$ Mar 31, 2022 at 22:13

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