Shape of shock wave produced by a concentrated impact on a surface

An approximate similarity solution, derived by Raizer, of a concentrated impact (or intense explosion) at the boundary of a semi-infinite volume of a perfect gas is used to determine the propagation velocity of the shock front as a function of its position. This velocity function is then used to obtain the shape of the propagating shock wave. It is shown that dish-shaped shock fronts are formed when the movement of the gas at the surface is into the gas region and that cup-shaped shock fronts are formed when the movement is out of the gas region. Comparison of these results with the shapes of explosions and meteorite craters are discussed