Rolling resistance of shallow granular deformation

Experiments are conducted to measure the resistance experienced by light cylinders rolling over flat beds of granular media. Sand and glass spheres are used for the beds. The trajectories of the rolling cylinders are determined through optical tracking, and velocity and acceleration data are inferred through fits to these trajectories. The rolling resistance is dominated by a velocity-independent component, but a velocity-dependent drag exceeding the expected strength of air drag is also observed. The results are compared to a theoretical model based on a cohesionless Mohr-Coulomb rheology for a granular medium in the presence of gravity. The model idealizes the flow pattern underneath the rolling cylinder as a plastically deforming zone in front of a rigidly rotating plug attached to the cylinder, as proposed previously for cylinders rolling on perfectly cohesive plastic media. The leading-order, rate-independent rolling resistance observed experimentally is well reproduced by the model predictions.