Abstract: The present paper defines a third dimensionless parameter,i.e., the damping function \xi, besides the impact function I andgeometry function N of a projectile introduced early, in the penetrationdynamics of rigid projectiles. It only depends on the interaction of theprojectile and the target materials and is independent of the projectile geometry. Ageneral penetration drag, which contains the terms of damping effect and thedummy mass of the projectile induced by the deceleration effect, is adopted inthe formulation. Dimensionless formula for the depth of penetration (DOP) isobtained with only three parameters I, N and \xi for generalconvex shapes of various hard projectiles. Different geometry parameters arealso presented for some common shapes of warheads. Theoretical predictionsfor DOP dependent/independent of the damping function \xi, showgood agreement with the published test data for differentprojectiles and impact velocities as well as different targets.