Steady state equation of motion of a linear shaped charges liner

The sweeping detonation effect creates a unique turning angle of plates upon detonation. This effect was addressed by G. I. Taylor and opens a broad range of applications in many different engineering regimes. In case of linear shaped charges (LSCs), because of the unique geometrical shape, which are comprised of long, flat liners and multiple flat claddings, an approach to understand the performance of LSCs must be analyzed under the Taylor turning angle, motivating this research. In this paper, an analytical approach to describe the unique liner motion of LSCs upon detonation is addressed first. Subsequent modification of the original Birkhoff theory is addressed in order to build a steady state analytical equation of motion of LSCs liner based on the Taylor turning angle. The analytical model is then compared to the numerical simulation results created from Autodyn™ in terms of M/C ratio and apex angles in reasonable sized LSCs, and it exhibits favorable results in a limited range.