A method is established for the calculation of the trajectories of shocks moving upward in the atmosphere, on the basis of the assumption that they are of the self-propagating type. The results of calculations for self-similar motions are given, and these are used to establish a propagation law based upon the concepts of the Chisnell, Chester and Whitham (CCW) approximation. This propagation law enters a characteristics law based upon that proposed by Whitham, but reformulated for the computation of axisymmetric shocks with varying density.

An asymptotic self-preserving shock shape is investigated, and is computed for the case γ = 1·4. A parabolic approximation scheme suggested by the self-preserving solution is developed, in which the solution near the axis is reduced to the solution of a system of ordinary differential equations. Finally, the governing equation for the general case without axial symmetry (but without winds) is presented.