A Progressing-Wave Approach to the Theory of Blast Shock

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Abstract
This paper deals with a theoretical description of the motion of a spherical shock wave in a homogeneous medium, such as a blast shock in free air. In order to facilitate such a treatment, a simple assumption concerning the flow is made. The concept of a “progressing wave” as used in this paper is explained and compared with that used by other authors. A simple assumption is made about the motion of the progressing wave, and on its basis an ordinary second-order differential equation for the shock front is derived. Conservation of energy in the shock sphere reduces this to an ordinary first-order differential equation. Examination of the asymptotic behavior of the wave reveals that the original assumption in its simplest form contradicts conservation of energy. The original assumption is then suitably modified and the resulting new equations derived, including asymptotic values. Values for the high-pressure approximation, i.e., near the center of the explosion, are derived, and finally asymptotic as well as high-pressure values are derived for the pressure decay behind the shock front.

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