Dynamics of a projectile penetrating in granular systems

The impact of a sphere with velocity u(0) on a fine, loose granular system under the acceleration due to gravity has been studied by fast video photography. The behavior of the granular bed is found to be similar to a fluid during initial impact, followed by a cavity drag during projectile penetration. From the trajectory of the projectile it is found that the drag on the projectile can be well described by adding a bulk frictional force f to the hydrostatic force kappa z where kappa is a constant and z denotes the penetration depth. Both kappa and f are u(0) dependent. This form of the drag force suggests that fluidlike viscous dissipations in the bed can be neglected in these three-dimensional (3D) experiments. However, due to the imposed boundary this hydrodynamic term of the drag force is found to be not negligible in quasi-2D granular beds.