General scaling relations for locomotion in granular media
Name
PhysRevE.95.052901.pdf
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1.62 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Slonaker, James C.
Motley, David Carrington
Zhang, Qiong
Townsend, Stephen C.
Senatore, Carmine
Iagnemma, Karl
Kamrin, Kenneth N
Date Issued
June 2017
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PHYSREVE.95.052901
