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In a Mach Cone, how fast is the air moving away from the supersonic object?


The details are complicated, but overall your picture’s not quite right. The air doesn’t really move along the shock in the direction you drew.

The head of the bullet creates an obvious shock wave as it pushes the air aside, but notice the blurry bands that connect to the tail of the bullet: this is a “rarefaction wave” created as the air collapses back inward after the bullet passes. It’s the opposite of a shock wave.

In the reference frame of the air, with the bullet moving through it: behind the shock, the air moves in the direction of the bullet and away from it. As the rarefaction wave passes, the air returns to (almost) a stop.

So I’d draw arrow V3 down and to the left. It’s generally much slower than V1 and V2, and it’s only in the region between the two dark lines on the picture.

Usually when we calculate this stuff, we take the perspective of the bullet being stationary and the air moving past it, like in a wind tunnel. In that frame, the air moves to the right, and hits the shock wave, where it slows down and is deflected away from the bullet. Once it hits the rarefaction wave, it speeds back up and its path returns to a straight line. The sites below have some pictures from that perspective, as well as the equations and a calculator.