A semi-empirical formula based on a modified general penetration resistance for predicting the motion of the rigid projectile

The semi-empirical formula is an effective method for predicting the motion of rigid projectiles in practical applications due to the simplicity of its theory and the convenience of parameter calibration. The commonly used semi-empirical formula is Forrestal's form, combining several specific experimental cases that have been published, we find it exists deficiencies in predicting deceleration histories and the penetration depths of high velocities. To solve this problem, the general penetration resistance is employed to formulate the semi-empirical formula due to the ‘general’ characteristic of the general penetration resistance, and also make an assessment of this semi-empirical through experimental data. The results show that this semi-empirical method, like Forrestal's form, is not good at predicting high-velocity penetration depth. Thus, it propels us to develop a new semi-empirical formula. To this end, the general penetration resistance is modified with the assumption that the additional mass should be increased with the penetrating velocity and the projectile mass, based on which a new semi-empirical formula is developed. Then, the proposed semi-empirical formula is employed in individual published experimental data of different projectiles and striking velocities as well as different targets. The predictions of the proposed semi-empirical formula show good agreement with the experimental data both in penetration depths and deceleration histories, which also demonstrate the reasonableness of the assumption that the additional mass of rigid projectile increases with penetrating velocity and the projectile mass.