The optimal nose shape of a projectile penetrating into targets described by a locked hydrostat and a linear shear failure relationship

The present paper analyzes the optimal nose shape of an axisymmetric rigid projectile which penetrates into a thick target. The optimal projectile nose shape is defined as the shape on which the minimum resistive force is developed in its interaction with the target. This resistive force sums up the contributions of the contact interaction pressures acting on the projectile nose envelope. The interaction pressure between the projectile and the target depends on the projectile total mass, on the target material properties, the projectile motion characteristics and the projectile geometrical parameters and especially on the unknown nose shape function and its derivatives. A variational analysis, aiming at minimization of the resistive force functional using the Euler-Poisson equation is carried out. In the general case, the problem of the optimal nose shape of an axisymmetric rigid projectile which penetrates into a semi-infinite target can be solved only by numerical methods. Using simplified constitutive relationships may allow a closed form solution of the optimal nose shape. This paper considers a locked hydrostat and a linear shear failure-pressure relationship that may enable a simplified representation of targets like soil and concrete, and allow a closed form solution of the optimal nose shape. It is confirmed that the Euler-Poisson equation is only a necessary condition for the existence of an extremum of the functional and therefore the obtained solution should be examined whether it actually yields a minimum resistive force and maximal penetration depth. To verify the optimal solution, the calculated deceleration and penetration depth time histories of the optimal nose shape projectiles are compared with calculated and experimental results of similar projectiles with an ogive nose, and the efficiency of the optimal nose is confirmed. (C) 2020 Elsevier Ltd. All rights reserved.