Differences between shockwaves

[Traab]

Anyone out there with the knowledge to help on this? When breaking the sound barrier, what kind of difference, if any, in size, power, and distance traveled of the shockwave would you see with say, a person sized object in a straight line horizontal pose, versus a cannonball large enough to hold 7 people both traveling at the same speed? Also, does speed come into play on the disruption? Like, is the shockwave of an object traveling at mach 1 different than at mach 2? 3? 13?

If it helps, the question is coming up in regards to a superhero comic where they are fighting what amounts to a sentient sandstorm, and I was wondering if said cannonball would provide any significant disruption to the sand doing a bit of boom and zoom through it at upwards of mach 4. Like, would the shockwave propagate far enough to be at all useful, with enough power to accomplish anything or would it be fairly small scale. I was thinking going at multiples of the speed of sound with such a large object would make for a more powerful shockwave, but realized that I have no idea if speed past the speed of sound matters in such things.

[halfeye]

Anyone out there with the knowledge to help on this? When breaking the sound barrier, what kind of difference, if any, in size, power, and distance traveled of the shockwave would you see with say, a person sized object in a straight line horizontal pose, versus a cannonball large enough to hold 7 people both traveling at the same speed? Also, does speed come into play on the disruption? Like, is the shockwave of an object traveling at mach 1 different than at mach 2? 3? 13?

If it helps, the question is coming up in regards to a superhero comic where they are fighting what amounts to a sentient sandstorm, and I was wondering if said cannonball would provide any significant disruption to the sand doing a bit of boom and zoom through it at upwards of mach 4. Like, would the shockwave propagate far enough to be at all useful, with enough power to accomplish anything or would it be fairly small scale. I was thinking going at multiples of the speed of sound with such a large object would make for a more powerful shockwave, but realized that I have no idea if speed past the speed of sound matters in such things.

The size of the object wouldn't make a significant difference to the shape of the shockwave once shockwave left the object, the energy would affect the loudness, and breaking the sound barrier with a bigger object would require more energy. Higher mach numbers make the shockwave more steeply conical, at mach 1.01 the wave is more or less hemi-spherical, at mach 2 it is more or less a cone, as speed goes up from there the cone gets narrower, and louder.

[Lord Torath]

halfeye covered the basics pretty well.

Naturally, a larger object will produce a larger shockwave. I don't remember for certain, but I think that the energy dissipated by the shock is proportional to the cross-sectional area of the of supersonic object. Double the cross-section, double the energy. A person has maybe a couple square feet of cross-sectional area. A sphere that can hold seven people would be what, 15 feet or so across (depending on how the people are packed in there)? It's cross-sectional area would be 56.25 pi square feet ~175 square feet. So the cannonball's shockwave would be roughly 10-15 times more powerful that the individual shockwaves generated by 7 people.

Blunt objects will tend to produce a blunt or "normal" shock (so called because the shockwave is perpendicular or normal to the air flow). Sharp, pointed objects will produce oblique, cone-shaped shocks. There is generally more energy lost across a normal shock than an oblique one (you can still have supersonic flow behind an oblique shock, while a normal shock always has subsonic airflow behind it - keep in mind that the abrupt changes in temperature and density behind a shock will change the speed of sound behind it).

As far as how the energy varies by mach number, I don't remember what the relationship is (my compressible fluid dynamics class is further behind me than I want to contemplate), but I'm pretty sure it's exponential by velocity.

[Traab]

I need to apologize, im sorry, I came here and read these replies, thank you very much for them the both of you. I cant believe I forgot to reply!