# How would high-explosives interact with the shockwaves around a hypersonic weapon?

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.

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).