Force response of running up a sand dune

Running up a sand dune is challenging because: (1) sand fluidizes when an external force exceeding the material yield stress is applied; and (2) at inclines approaching the angle of repose, the sand pile is increasingly unstable. In this study, we experimentally examined the impact force normal to a flat plate against a bed of poppy seeds, to determine how intrusion kinematics affect force generation. We tested a range of impact speeds (0.01-1.2 m/s), substrate angles, and impact angles. We identified two regimes with distinct force production patterns: 1) the gravity regime (<0.6 m/s) and 2) the inertial regime (>=0.6 m/s). In the gravity regime, the force-depth relation tends to diverge when comparing, for example, (θ_intrusion, θ_substrate)=(40,0) and (0,40). This difference is likely due to the propensity of the angled substrate to avalanche and reduce the material force response. On the other hand, the same set would converge at higher impact speeds, indicating that inertia dominates the system with particle movement instigated by the intruder exceeding that due to avalanching. This insight will help inform how animals and robots may navigate up sand dunes efficiently.