The dynamics of granular impact cratering

Granular media can exhibit both solid- and liquid-like behavior. This is familiar in everyday life, and underlies a wealth of applications and geophysical phenomena. One simple laboratory experiment to quantify this is to drop a ball into a bucket of sand, and to study the scaling of penetration vs system parameters. Earlier we discovered that the penetration is proportional to the one-third power of drop distance and the two-thirds power of ball diameter. This connects directly to the depth-average force acting between medium and ball. To tease apart separate position- and speed-dependent contributions to the instantaneous stopping force, we now report on high-resolution measurements of impact dynamics using a novel apparatus. We find that the force grows with depth, independent of speed, and that it grows with the square of speed, independent of depth. We also find that seemingly-contradictory results of prior researchers can all be accounted for by various limits of such a force law. This granular mechanics must ultimately account for other behavior such as jetting and crater morphology.