Shock Wave Energy: Explosions in Air, Ground, and Water

Abstract

The Shock Wave Energy is a measurable parameter for detonation generated shock waves in air, ground and water. For a medium where the characteristic impedance is quite “constant” (such as geological materials) the energy flux measurement is readily performed by applying the following equation: $E = \left(\rho c/2\right)\int {u}^2\mathrm{d} t$. Where ρc is the characteristic impedance and u is the particle velocity. For water and air, the energy flux equation is quite similar: $E = \int {\left(\rho c\right)}^{-1}{P}^2\mathrm{d} t$,where P is the varying pressure along the pressure versus time curve. In air, as compared to water, the technique of measuring the energy flux is complicated by the fact that the characteristic impedance, (ρc), of air varies considerably with pressure. In the body of this paper, the varying values of impedance used while performing this integration as a function of P ² are included. It is now possible to perform computer assisted energy flux measurements for all three of the above media.

The energy flux for summarized blast wave data from surface bursts in air taken from the literature have been analyzed employing the Modified Friedlander equation based on the parameters of peak pressure and positive duration. The total shock wave energy in blast waves can now be compared with the total available detonation energy. Values of the shock energy as well as its variation with distance from the detonation point in various media are presented. Suggested applications of the now available Shock Wave Energy parameter in air are presented for safety considerations as well as for evaluating protective construction.