On the Break-Up of Shaped Charge Jets

It is shown from dimensional arguments that the semi-empirical jet break-up formula of Hirsch⁽¹⁾ is consistent with physical models characterized by ideal plasticity (yield stress σ₀), the material initial density (ϱ₀), strain rate (η₀), and jet radius (r₀). Similar arguments applied to a one-dimensional jet stretching model yields the existence of a maximum unstable perturbation wavelength, and fixes its value to within a numerical constant. Within the class of physical models considered the plastic velocity appearing in the Hirsch formula, the incremental velocity between successive fragments of a particulated jet, and the velocity (σ₀/ϱ₀)^1/2 are all related, as originally conjectured by Hirsch.