A new penetration equation for ballistic limit analysis

Abstract

A new penetration equation for ballistic limit analysis (BLA) of a projectile–target pair is developed and presented. A critical review of the classic BLA (CBLA) has identified that the CBLA penetration equations do not satisfy the conservation of momentum and energy principles simultaneously and completely. It has also been found that the classic definition of residual velocity of the projectile does not quantify the instantaneous rigid body velocity of the projectile at ballistic limit. A new definition of the projectile relative velocity with respect to the target in contact (and in motion) is defined, and this new definition is used to define the projectile instantaneous velocity at ballistic limit. With this new definition of the projectile instantaneous velocity, the new penetration equation is derived satisfying both the conservation of momentum and energy principles simultaneously. A general functional form of the new penetration equation is used in analyzing experimental data and the results are found to match well with the experiments. The new equation is shown to be able to explain projectile residual velocity at and around ballistic limit, can predict the jump velocity at ballistic limit (if any), and is applicable to experimental ballistic data of a wide range of thin and thick targets. The present work sets the background for further development of theoretical penetration models incorporating material properties and parameters of the projectile–target pair.