Penetration Depth for Shallow Impact Cratering

We present data for the penetration of a variety of spheres, dropped from rest, into a loose noncohesive granular medium. We improve upon earlier work [J. S. Uehara et al., Phys. Rev. Lett. 90, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support the previous conclusion that the penetration depth is proportional to the 1 ∕ 2 power of sphere density, the 2 ∕ 3 power of sphere diameter, and the 1 ∕ 3 power of total drop distance.