Penetration depth for shallow impact cratering

TL;DR

This study investigates how the penetration depth of spheres into granular media depends on sphere size, density, and drop height, providing more precise data to support scaling laws for impact cratering.

Contribution

The paper offers improved experimental data and analysis on the scaling laws governing penetration depth in shallow impact cratering, refining previous findings.

Findings

Penetration depth scales with the square root of sphere density.

Penetration depth scales with the two-thirds power of sphere diameter.

Penetration depth scales with the one-third power of drop height.

Abstract

We present data for the penetration of a variety of spheres, dropped from rest, into a level non-cohesive granular medium. We improve upon our earlier work [Uehara {\it et al.} Phys. Rev. Lett. {\bf 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 our 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.