Mechanics of snake slithering on deformable substrates.

Elongate, limbless animals like snakes move in both fluid and terrestrial habitats using flexural waves of the body. Little is known about their movement in materials like mud and granular matter (GM) which provide propulsion while yielding but, unlike fluids, may be permanently deformed by the interaction. We studied the ~40 cm long desert-dwelling snake C. occipitalis slithering on the surface of homogeneous GM. The snakes traveled 30-80 cm/s using a stereotyped shape. Surface drag measurements revealed that the ratio of thrust to drag forces, a critical component in undulatory motion, did not depend on speed or depth. We developed a surface resistive force theory (RFT) which revealed their waveform maximized center-of-mass speed given a constraint on peak muscle power. The snakes’ motion was non-inertial, so we explored the performance of a robophysical model, a 10-link 70 cm long robot snake. The waveforms RFT predicted would maximize the speed of the robot instead failed to make progress, largely because the robot would re-encounter previously disturbed material. The snakes’ waveform was in the regime where motion is like that in a frictional fluid; by limiting material yield the animal avoided contending with the memory-dependent effects that stymied the robot.