General scaling relations for locomotion in granular media
Author(s)
Slonaker, James C.; Motley, David Carrington; Zhang, Qiong; Townsend, Stephen C.; Senatore, Carmine; Iagnemma, Karl; Kamrin, Kenneth N; ... Show more Show less
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Inspired by dynamic similarity in fluid systems, we have derived a general dimensionless form for locomotion in granular materials, which is validated in experiments and discrete element method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from resistive force theory or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extraplanetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.
Date issued
2017-06Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
Physical Review E
Publisher
American Physical Society (APS)
Citation
Slonaker, James et al. “General Scaling Relations for Locomotion in Granular Media.” Physical Review E 95, 5 (May 2017): 052901 © 2017 American Physical Society
Version: Final published version
ISSN
2470-0045
2470-0053