Improved formulas for velocity, acceleration, and projection angle of explosively driven liners

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Abstract
Improved one‐dimensional formulas for both the direction and magnitude of the velocity of explosively driven liners are developed. First, an analytical formula for the direction of motion of the liner under unsteady conditions is derived. This new formula is compared with both two‐dimensional calculations and experimental data for both shaped‐charge and exploding cylinder geometries. The new formula is more accurate than the classical steady‐state Taylor‐angle formula for these cases.Next, for implosive geometries, a new formula for the fully accelerated liner velocity is given. Since the standard Gurney approach does not apply to imploding geometries, a modified approach was adopted. Results agree well with two‐dimensional code results for a wide range of explosives and geometries. Also, the velocity history is shown to follow an exponential law, and a useful formula for characteristic metal acceleration time was developed.