Models and experiments of normal penetration of polygon cross-section rigid projectiles

We address the normal penetration problem for projectiles having an arc-shaped head and a polygonal cross-section with an axis at the center of the circle inscribed in the polygon. We put forward an analytical model to determine the resistance and depth of rigid normal penetration for this class of projectiles and prove that it shares the mathematical form and the physical implications with models for circular cross-section projectiles, thus providing a unifying model for both types. We also prove that for normal penetration, the lateral force on such polygon cross-section projectiles and the torque around the projectile axis are both zero, thus providing a design methodology for polygon cross-section projectiles without lateral forces and torques. Our analysis indicates that at the fixed cross-sectional area and projectile head length, projectiles having a regular polygonal cross-section with fewer sides show better penetration depth. On the other hand, for projectiles with non-regular polygon cross-section, the smaller is the radius of the inscribed circle, the better is the penetration depth. We validate our theoretical results with experiments of normal penetration on concrete mortar targets performed using five types of regular polygon cross-section projectiles. The test results confirm that the penetration depth of regular triangular and quadrilateral cross-section projectiles is superior to that of regular pentagonal, hexagonal, and circular cross-section projectiles, with the penetration depth of the latter three being relatively close. Our model provides excellent predictions for the penetration depth of projectiles with (regular) pentagonal, hexagonal, and circular cross-section, while the predictions for regular triangles and quadrilaterals are relatively low. The main reason for this discrepancy is that the model involves a one-dimensional cavity expansion resistance model and does not account for the potential shear damage and weakening effects caused by the edges of the polygonal projectile on the target material.