Ballistic Wave from Projectiles and Vehicles of Simple Geometry

The ballistic wave is a shock wave generated by a solid body moving at supersonic speed in the atmosphere. It sounds like the crack of a whip for small projectiles and like a detonation (sonic boom) for large-sized objects. Their common signature is a N-shaped pressure profile, the formalism of which is well known but presents a practical difficulty, namely, the calculation of the shape factor, which characterizes the aerodynamic behavior of the object flying at supersonic speed. In the present Paper, we present that calculation for simple geometric shapes defined by their algebraic equations, by using both numerical and analytical approaches. The results do not seem realistic in some cases of round-tipped shapes, which leads us to adopt, in general, a simplified form for the shape factor, different from what is sometimes used in the literature. On the other hand, such an approach suggests to us to take into account separately the ogival length and the overall length of the body. To compare classic and im...