Projectile impact and penetration in loose granular bed

Dynamics of a projectile impacting on a loose granular bed under the acceleration due to gravity g has been studied by fast video photograph. Granular jet formation and projectile penetration are observed in 3D and quasi-2D experiments. It is found that the penetration velocity u can be described by mdu/dt=-γu-κz+mg′, where γ and κ are the parameters which characterize the viscous damping and hydrostatic drag forces of the bed, respectively, z is the penetration distance of the projectile, and g′ is a modified gravity term. The viscous damping term is found important in quasi-2D experiments. For 3D, the damping term is only important at the beginning of the impact, and can be neglected during penetration.