News in Science

How snakes move on a plane

Serpent locomotion Meeting a snake in the wild might cause you to turn and run, but if you're brave enough to stay put you might get a maths lesson in how they move.

A new study published today has identified the most energy-efficient way snakes move, and could help in the development of serpent-like robots.

"[Previous studies] assumed that the snake is going to move in a basic way and then looked at the properties of how the snake is moving," says Associate Professor Silas Alben, an applied mathematician at the University of Michigan.

"In my study I didn't make many assumptions about how the snake moves. I just wanted to study a wide range of possible friction parameters."

Snakes typically use a side-to-side motion to move themselves forward.

"If you look at waves on water they will move in a certain direction," he says. "And if you look at the snake as it is crawling it is a very similar type of motion, it has these waves on its body."

Alben set about developing a two-dimensional model of this movement across a flat surface, or plane. Across a wide range of choices for the co-efficient of friction of the plane he was able to calculate the most energy efficient way for a snake to move.

"The answer turned out to be pretty simple," says Alben. "It's basically an undulatory wave-like motion, and this has been seen in real snakes and is referred to as transverse undulation."

Backwards to go forwards

In most cases, the movement of the wave through the snake's body is retrograde, meaning the waves on the body go backwards as the snake goes forward.

"It depends on the environment that the snake is moving in. If the snake has a large coefficient of friction in the direction perpendicular to its body axis, then it will do the retrograde motion. If the friction in that direction is much smaller, it will switch to the direct-wave motion," explains Alben.

Alben says his models don't take account for when the snakes lift themselves off the ground, as occurs, for example, in the 'sidewinding' motion.

"That makes the mathematics a lot more complicated and the computations more complicated."

Robotic snakes

As well as better understanding how snakes and other legless animals move through their environment, Alben says his findings could be applied to the field of robotics.

"A lot of researchers are building robotic snakes, which are usually a bunch of linked segments where they control the angles between the links over time. These can be useful for getting robots into tight environments," he says.

"Understanding what kind of motions are optimal can help people design robots that work efficiently."

The study is published today in the journal Proceedings of the Royal Society A.