Dynamics of shallow impact cratering

TL;DR

This study investigates the dynamics of shallow impact cratering by analyzing the penetration of wooden spheres into glass bead packings, revealing a longer stopping time than simple models predict and proposing a velocity-dependent stopping force.

Contribution

It introduces a model with a position- and velocity-dependent stopping force that accurately describes impact dynamics and matches previous observations on penetration depth scaling.

Findings

Stopping time is three times longer than simple travel time estimate.

Acceleration decreases monotonically during impact.

A new model with velocity-dependent stopping force fits observed data.

Abstract

We present data for the time-dependence of wooden spheres penetrating into a loose non-cohesive packing of glass beads. The stopping time is a factor of three longer than the time $d/v_\circ$ needed to travel the total penetration distance $d$ at the impact speed $v_\circ$. The acceleration decreases monotonically throughout the impact. These kinematics are modelled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.