Re-visiting 1-D hypervelocity penetration

Classical, one-dimensional theory of hydrodynamic penetration is used as the basis of establishing simplified analytical relationships describing energy, momentum, and power deposition during hypervelocity impact events. A concise overview of the 1-D model is given followed by a select grouping of terms into relationships that offer first-order criteria for making engineering design considerations on relevant applications and assist in the analysis of experimental observations. Momentum, energy, and power deposition are found to be proportional to second, third and fourth power exponents, respectively. These analytical terms are presented for constant velocity gradient, i.e. fixed length, rods as well as linear velocity gradient rods, such as shaped charge jets. The role of penetrator-to-target density ratio is then examined in terms of the backflow, or reverse flow of 1-D penetration. Again, the non-dimensional ratio of penetrator-to-target mass density is used to compare the relative velocity of material flow during penetration. The relationship highlights the role of penetrator materials for achieving desired effects in these hypervelocity, terminal ballistics events. Albeit the relationships are derived on the assumptions for hydrodynamic processes, their generality of form and ease of implementation make them a useful first-order description for engineering insight and application over a broad range of velocities.