Drag force scaling for penetration into granular media

TL;DR

This study investigates how spherical and cylindrical projectiles of various densities penetrate granular media, revealing that inertial and frictional drag forces depend on material properties and scale differently, explaining penetration depth behavior.

Contribution

It introduces a new scaling analysis of inertial and frictional drag forces in granular impact, highlighting their dependence on material properties and providing insights into penetration depth scaling.

Findings

Inertial drag scales with internal friction coefficient, similar to fluids.

Frictional drag scales with the square root of the medium and projectile density.

Results explain previously observed penetration depth scaling.

Abstract

Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure and Coulomb friction law. The combined results provide an explanation for the previously-observed penetration depth scaling.