The mechanics of slithering locomotion

1. What they did

Snakes have long been thought to slither by pushing the sides of their bodies against rocks, branches and other bumps on the ground. But snakes can also slither over fairly smooth ground, such as sand or bare rock, where there is little to push against. The authors set out to explain how, combining laboratory experiments with a mathematical model.

• The snakes. Ten juvenile Pueblan milk snakes, weighing about 15 g and about 36 cm long, kept in a university animal care facility.
• Measuring belly friction. Snakes were briefly put under general anaesthesia, laid straight on a tilting board in nine different directions, and the board was raised by hand until they began to slide. This gave the friction of their belly scales when sliding forward, backward and sideways, on rough cloth and on smooth fiberboard (90 measurements).
• Filming slithering. Awake snakes were filmed slithering on cloth or fiberboard, on flat boards and on slopes from 20 degrees downhill to 20 degrees uphill. Movement of the body’s centre was measured from the video (70 films analysed).
• Modelling. They built a model snake that moves only through friction with the ground and its own changing body shape, and compared its predicted speeds and paths with the real snakes.

2. What they found

Belly scales and friction

• The wide, overlapping belly scales snag on small bumps in the surface; this snagging could be heard during the experiments.
• On rough cloth, friction was lowest when sliding forward (0.11), in between when sliding tailward (0.14) and highest when sliding sideways (0.20). On smooth fiberboard, friction was nearly the same in every direction.
• As the anaesthetised snakes woke up, they began twitching individual scales, which fits with each scale having its own muscle attachment.

Slithering on flat ground

• On the smooth surface, snakes tried to slither but made little progress. On the rough cloth they moved forward with no difficulty.
• Although the body moves in waves, the body’s centre moved almost straight ahead at a nearly steady speed (about a fifth of a body length per wave cycle of about 2 seconds), with almost no sideways drift. Snakes could also make short bursts at nearly double this speed.
• Friction forces were about ten times larger than the forces from the body’s momentum, so unlike most land animals of this size, momentum plays little part in slithering.

Slithering on slopes

• Below a critical uphill slope of about 7 degrees (plus or minus 2), snakes slithered forward. At about 7 degrees they slithered in place, and on steeper uphill slopes they slid backward even while trying to move forward.

The model

• With equal friction in all directions, the model snake hardly moved, as on the smooth surface. With the measured, direction-dependent friction, its path matched the real snakes fairly well, though it was somewhat slower.
• Real snakes lift the curved parts of their bodies and press down where the body is straightest between bends (points of zero curvature). When the model did the same, its speed rose by 35% and its mechanical efficiency by nearly 50%, closer to what was observed.

3. What they concluded

• Slithering on flat ground, and possibly in general, depends on the belly scales gripping better in some directions than others, not only on pushing against rocks and branches.
• How a snake spreads its weight matters. By lifting parts of the body and loading others, snakes can slither faster and more efficiently. The authors see the ability to redistribute weight as important in limbless as well as legged movement.
• The model does not explain the full range of speeds. Possible reasons include the tapering tail and the snake’s ability to change the angle of its scales and so its grip; snakes may change their friction when moving up and down slopes.
• The findings may help in designing snake robots that slither over flat surfaces without wheels.

6. Other technologies, skills or innovations

• An inclined plane to measure the friction of snakeskin, with the snakes under anaesthesia.
• Video filming (Sony camera) and digital image analysis in MATLAB to follow the centre of the body.
• A mirrored surface to see which parts of a slithering snake’s belly touch the ground.
• A mathematical model and numerical simulation of slithering.