Analysis of the size effect on the penetration depth of earth-penetrating weapons and practical calculating formula

Scaled testing is an important method to study the penetration law. The size effect between the model test results and the prototype is a problem that must be solved to establish the calculation method of penetration. The penetration depth of the earth-penetrating projectile is a basic problem in the design of protection engineering. Based on the existing basic theory, the stress and strain state evolution of the rock-like target medium subjected to the penetration of earth-penetrating weapons and the penetration resistance function of the projectiles are derived. The formula for the caliber coefficient characterizing the size effect is obtained, and a simplified analysis of the nose shape coefficient and caliber coefficient is conducted within the penetration velocity range of the conventional earth-penetrating weapons. A practical calculation formula for the penetration depth of conventional earth-penetrating weapons into rock-like media is proposed, whose coefficients can be directly determined by parameters of target and projectiles. The results show that the main influencing factor of projectile impedance is target wave impedance. The source of the size effect is that the ranges of the target damage zones do not satisfy the geometric similarity law. The nose shape coefficient can be simplified as a linear function of warhead aspect ratio, and the nose shape coefficient of a flat-nosed projectile is 0.57. The caliber coefficient of the projectile is determined by the ratio of the cavity radius of the penetration to the radius of the fracture zone and can be taken as 1.2~1.4 for conventional earth-penetrating weapons. The theoretical calculation formula of penetration depth is in good agreement with experimental results, and thus has high reliability.