This paper defines a third dimensionless parameter, i.e., the damping function, besides the impact function and geometry function of a projectile introduced by the author previously, in the penetration/perforation dynamics of a rigid projectile. It only depends on the interaction of projectile and target materials and is independent of projectile geometry. A general penetration resistance, which contains the terms of viscous effect and the dummy mass of a projectile induced by the deceleration effect, is adopted in the formulation. A dimensionless formula of depth of penetration is conducted with only these three parameters for general convex shapes of various rigid projectiles. Accounting for the influence of the damping function, the normal perforations of thick metallic plates struck by sharp nose rigid projectiles are studied further.