Shape optimization of impactor penetrating into concrete or limestone targets

The shape of the normally striking impactor that attains the maximum depth of penetration into a concrete or a limestone semi-infinite target for a given impact velocity is found. It is shown that the optimum shape is close to a blunt (in general case) cone and it is independent on the properties of the material of the target in the framework of the employed penetration model. The performance of some other typical shapes of the nose of the impactors (spherical-conic impactors, sharp-conic impactors, truncated-ogive impactors) are analyzed and compared with the optimal impactor.