The Theory of the Ideal Armor Plate. Energy Regularities of the High-Speed Body Impact on an Armor Plate

Abstract

This study analyzes the optimal energy characteristics of a flying body (FB) impacting an armor plate (AP). The considered energy characteristics include momentum, kinetic energy, and the power of both bodies. It is shown that only a small fraction of the FB momentum is transferred to the AP, whereas nearly all of the FB kinetic energy is converted into the internal energy of the AP. This internal energy consists of the energy of mechanical oscillations of the plate and the energy associated with material displacement within it. The energy of the natural oscillations of the AP, modeled as a rectangular parallelepiped with dimensions a, b,  (with a ⁓ b) and thickness c, is estimated. The frequencies of bending oscillations perpendicular to and along the plate surface are calculated. It is shown that the energy of bending oscillations along the surface with the largest area exceeds that of oscillations perpendicular to the surface by a factor of a²/c². The transfer of the FB kinetic energy is assumed to occur in a cylindrical channel of base area S₀. It is shown that the maximum power transferred from the FB to the AP is equal to 16/27 ≈ 0.5926 of the initial FB power and is accompanied by a reduction of the FB velocity by a factor of three. The characteristic penetration length corresponding to maximum power loss is proportional to the FB length h. The multilayer AP configuration is also considered. It is shown that in subsequent layers with lower material density, conditions for maximum power loss are preserved. The thickness of each layer is determined by the distance over which maximum power loss occurs. The results indicate that properly designed multilayer APs can significantly reduce overall dimensions and weight while maintaining high protective efficiency. It should be noted that the present analysis is qualitative and does not aim at quantitative agreement with experimental data, as some secondary effects are neglected. The results provide a physical basis for understanding energy dissipation mechanisms and suggest directions for further optimization using numerical methods.