Inertial Phenomena and Resistive Force Theory in Wheeled Locomotion on Dry Granular Media

We use an automated testbed to systematically conduct single-wheel (20 cm diam.) locomotion experiments in dry granular media (~1 mm poppy seeds) at angular velocities ω (0.7-6.4 rad/s) where substrate-based inertial effects emerge. In contrast to Resistive Force Theory based predictions for which translation speed is proportional to angular velocity, as ω increases, the translation speed plateaus to a speed dependent on wheel geometry and the system’s force distributions. A frictional plasticity model shows similar phenomena despite lacking a rate-dependent constitutive model. This effect can be explained through a force-momentum balance which accounts for the inertial effects caused by changes in substrate inflow/outflow in the system’s local volume. This force balance creates a net force loss that increases with translational velocity, creating a material-enforced speed limit for wheeled locomotion. Current RFT models describe quasistatic kinematic bodies, but an inertial correction to the RFT forces shows promise in extending RFT into capturing speed-dependent scenarios as well.