Wiggling Through the World: The mechanics of slithering locomotion depend on the surroundings

1. What they did

Many animals move without legs: snakes, worms, slugs and some lizards. The authors, a physicist (Goldman) and a mathematician and engineer (Hu), asked how such animals move so effectively in two very different settings: snakes slithering over the ground, and the sandfish lizard “swimming” beneath the surface of desert sand.

• Snakes above ground. Working with juvenile milk and corn snakes, Hu and colleagues measured how the friction of the belly scales changes with direction, by briefly anaesthetizing snakes and laying them straight on tilted planes covered in cloth. They dressed snakes in a snug fabric “jacket” to stop the scales gripping, filmed snakes on mirrors and on light-transmitting gelatin to see which parts of the body touched the ground, and built a mathematical model to predict slithering speed.
• The sandfish below ground. Goldman’s group filmed the sandfish with high-speed x-ray video as it dived into and swam through a bed of tiny glass beads. Air blown up through the bed let them set the sand to loosely or tightly packed. They measured drag on small rods pulled through the sand, then modelled the lizard’s swimming with a resistive force model, a computer simulation of individual grains, and a robot sandfish.

2. What they found

Snakes

• A snake’s belly scales overlap like roof shingles. On cloth, milk snakes slid most easily forwards (friction coefficient 0.10), less easily tailwards (0.14) and least easily sideways (0.20). This difference with direction is what lets a snake move forward on flat ground with no obvious push points.
• Snakes in the fabric jacket, or on very smooth surfaces, slithered in place without moving forward.
• A model assuming the snake’s weight is spread evenly along its body predicted only half the speed seen in the laboratory (8 cm per second, or 0.2 body lengths per second).
• Mirror and gelatin experiments showed that snakes lift parts of their body while slithering. In the model, lifting the curves of the body and putting weight elsewhere increased speed by 35% and efficiency by 50%.

The sandfish

• The 10 cm lizard runs on the surface using its legs, but when startled dives into the sand within about half a second, using its legs and body together.
• Once under the sand, it holds its legs against its sides and swims by sending a wave down its body from head to tail, at nearly two body lengths per second, faster than milk snakes move on flat ground. It went to a depth of about 4 cm and then stopped.
• Drag in tightly packed sand was nearly double that in loose sand, yet the lizard moved the same way in both and was, on average, faster in tightly packed sand, by raising its wave frequency (up to four undulations per second).
• Its wave efficiency (forward speed divided by the speed of the body wave) was about 0.5, nearly twice that of nematode worms in fluids (about 0.2) and more than snakes on surfaces (about 0.3), and did not change with how tightly the sand was packed.
• The resistive force model predicted a wave efficiency of 0.4 to 0.7 and a best body-wave height of about 0.2 of the wavelength. The lizards’ movements clustered at this best value.
• The grain simulation and the robot (seven motor segments in a fabric skin, swimming in 6 mm plastic beads) agreed with each other within 5%, and both swam fastest using the sandfish’s own movement pattern.

3. What they concluded

• Above ground, the direction-dependent friction of snake belly scales produces thrust; below ground, the sandfish uses the fluid-like but frictional behaviour of sand. Although the forces differ, resistive force models first made for swimmers in water work for animals on and within dry land.
• Snakes lifting their bodies suggests that movement in three dimensions improves performance, and the sandfish dives at a shallow angle rather than swimming flat, so 3D effects need further study.
• Questions remain, such as whether speed or efficiency leads limbless animals to switch from slithering to sidewinding, and how animals move through wet material.
• These models could help design limbless robots that move through complex terrain faster and more efficiently than animals.

6. Other technologies, skills or innovations

• High-speed x-ray video to watch an animal moving inside sand.
• A fluidized bed: air blown up through the sand sets it to repeatable loose or tight packing.
• Photoelastic gelatin between crossed polarizing filters, which lights up where a snake presses hardest, and mirrored surfaces to show when the belly lifts.
• Molecular dynamics simulation, which follows the motion of every grain, and a seven-segment robot sandfish built from hobby servo motors.