Rolling resistance of a spherical pod on a granular bed

• DOI: 10.1007/s10035-016-0696-z
• Publication Date: 2017-01-24T10:23:34Z
• Authors: Stefaan Van wal; Simon Tardivel; Paul Sánchez; Darius Djafari-Ro...; Daniel Scheeres
• Keywords: Rolling resistance; Slipping; Ball (mathematics); Moment of inertia; Coefficient of restitution

The motion of a spherical ball rolling without slipping or plowing on a granular bed is studied. We propose a definition of the rolling resistance force and torque, and carry out experiments with a basketball and medicine ball rolling on a bed of gravel to measure the corresponding rolling resistance coefficients. These experiments reveal, in good agreement with literature, coefficients that are velocity-independent, and show that little to no plowing of the spheres into the granular substrate occurs. This indicates a regime of motion distinctly different from those treated in previous works. A simplified model correctly predicts the velocity independence and suggests an inverse dependence of the rolling resistance coefficient on the reduced inertia of the ball. These predictions match the experimentally observed behavior. Numerical simulations based on soft-sphere DEM shed more light on the mechanics of energy dissipation that occur in this no-plowing regime, and reveal a mass dependency that is not captured by the model. Our results provide insight into an unstudied regime of motion, and are of interest to the mission design of spacecraft to explore the surfaces of asteroids and comets.