Snake walk: The physics of slithering

By Jonathan Webb Science reporter, BBC News

"This is the Mojave shovel-nosed snake," says Perrin Schiebel as she hands me a 40cm reptile. It is vibrantly patterned, apparently harmless, and quickly wraps itself around my fingers.

"They're native to deserts of the American south-west. This is a full-grown adult."
Ms Schiebel is studying for a PhD in physics at the Georgia Institute of Technology in Atlanta, US. She has spent many months putting 10 of these snakes through their slippery paces in a sand-filled aquarium.
Why is a team of physicists playing with snakes in a custom-built sand pit? Because, I am told, the way they move is a marvel. (The snakes, not the physicists.)
Innumerable critters have evolved superb ways to scuttle and slither - or even burrow and "swim" - across the most unhelpful of terrains: those that flow.
If you've ever tried to walk up a sand dune, then you are familiar with the problem: unstable ground makes a mission out of locomotion. Now, imagine doing it on your belly.
"One of the things that's really interesting about snakes is that their entire body is, in this type of locomotion, in sliding contact with the ground," Ms Schiebel explains.

"So they have to be able to push off things in their terrain effectively, to overcome the fact that they've got these frictional drag forces on their stomach all the time."

And these denizens of the desert - including my new shovel-nosed friend - make it look easy.
In fact, as soon as this particular snake lands back in the glass tank, it vanishes.
"They can travel fairly substantial distances completely submerged," Ms Schiebel says. "We think this body shape is an adaptation to that."
Some of her colleagues have used X-rays to peer beneath the sand and study the snake's swimming in detail. But she is more interested in how they get around on the surface.

Ms Schiebel has "tens of thousands of frames" of high-speed video showing the shovel-nosed snake navigating the tank, both with and without obstacles.
"That's what I'm interested in - how they can use these this flowing sand and these obstacles, and push off them to travel."

All in the wave

This laboratory has sand-based experiments down to a fine art. For one thing, the snake is not slithering on any old sand.
"These are 300-micron (0.3mm) glass beads," says Ms Schiebel. "So it's sort of a laboratory physics version of desert sand. That's very similar to the size and composition in their natural habitat."
Also in the name of precision, a remarkable routine unfolds in between trials. A pump blasts air through a mesh beneath the sand, to "fluidise" it; the artificial dune bursts into roiling movement.

"If you want to do controlled, repeatable experiments… you need some way to control the initial state of the media.
"With a fluidised bed you're guaranteed that the entire bed will be in the exact same state. And it lets you control things like the compaction very precisely."
One thing these controlled experiments have revealed is a surprising simplicity in the snake's slither. It arranges its body into a very regular, flat "S" shape - no matter what.
"I've studied 10 of these snakes and they always make the same shape," Ms Schiebel says. "That was somewhat surprising. With their long body, they're very flexible - you can imagine they could make all sorts of shapes.
"But there's this very specific, stereotyped waveform that they all seem to use."

This observation was in stark contrast to what the team expected - which was, in short, tortuous complexity.
"What I've found... is that the snake is using a waveform that is beneficial for travelling quickly at the surface - and that all of these complex things, like the grains flowing away, or the tracks the snake makes, may not be important."
It also marks out the Mohave shovel-nosed snake as rather different from other species, which the team has observed in a nearby zoo adopting much more irregular and complicated shapes.

Wiggle and wind

One such snake with a famously baffling way of getting around is the sidewinder rattlesnake. Another member of the lab, Henry Astley, has been unravelling its secrets for some time.
"Sidewinding is famously confusing," he tells me as we look through some videos of real and simulated sidewinders in action. "There's actually a saying in herpetology, that if you want to go mad, watch sidewinders."
I can see his point. The hypnotic ripples of movement that propel these snakes - sideways - flow up-and-down along their bodies, as well as side-to-side.

 

That way madness lies: Sidewinder movement is notoriously complex

"During sidewinding, portions of the snake are lifted and lowered cyclically, in order to allow them to lift themselves over the sand and place their body in a new location," Dr Astley explains.
Working with a lab at Carnegie Mellon University in Pittsburgh, he and colleagues have already unpicked how the sidewinder climbs steep, sandy slopes by copying its movement with a robotic replica.
"Sidewinders are fantastic at locomoting - they're the real deal, they've got sensory systems and brains and muscles. But with that come the consequences of behaviour; they do what they want to do.
"With the robot, we can program it to do what we want it to do."
Using a similar approach - combining video footage of real snakes at Zoo Atlanta, with the programmable Pittsburgh robot - Dr Astley recently reported, for the first time, how sidewinders turn corners. He discovered two contrasting techniques.
First, there is the lazy "differential" turn, which works much like a car.
"One side of snake - or one set of wheels on the car - moves further than the other, and as a result, the whole animal rotates and you get this large, gradual turn over many, many cycles," he says.
The second option is more of a handbrake turn: the snake instantly reverses its body wiggle and jack-knifes its overall progress by anywhere from 70 to 180 degrees.

"The key is that in differential turning, the sidewinder continues with its head on the left or the right, throughout the turn," Dr Astley says.
"However in reversals, they instantaneously switch from head-on-the-right to head-on-the-left, or vice versa, allowing them to rapidly change and take off in a whole new direction."

Better bots?

When the team applied these findings to the sidewinder robot, which is ultimately aimed at search-and-rescue missions in tricky terrains, they managed to navigate a small maze with a combination of these turns.
But the research is not all about building better robots - though negotiating sandy landscapes will be crucial, for example, as humans continue to explore Mars.
Dan Goldman, who runs the lab at Georgia Tech, says he is most powerfully driven by pure intellectual curiosity.

"I'm interested in how nature works, in how living systems manage to do such beautiful and seemingly elegant behaviours in their natural environments."
The robots fill a gap, Prof Goldman explains, between mathematical simulations and real-world animal actions. Both the animals themselves and natural terrain - from leaf litter to sand dunes - are difficult to model accurately with computers.
"We don't have all the mathematics. There's a lot of parameters and it's also not clear how the biological subsystems are put together to effect interesting locomotor feats."
So a robot is a "physical model" that recreates certain elements of the interaction, in a programmable way.
"It's certainly not a faithful reproduction of an organism - but at least the leg of a robot, or the body of a snake robot, is interacting with a somewhat realistic material.

And therein, Prof Goldman concludes, lies a fruitful two-way street between his team of biology-focused physicists and the robotics engineers with whom they collaborate.
"It just turns out that the animals we study, and the physics we study... turn out to have some relevance for making better robots."
He and nearly 10,000 other physicists will be presenting their latest findings next week as the 2016 March Meeting of the American Physical Society.
You can hear an interview with Perrin Schiebel on Thursday's BBC Inside Science on Radio 4, or Science in Action on the BBC World Service.
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