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Researchers Solve Mystery Of How Flying Snakes Move
July 9, 2020

For decades, scientists have wondered about what functional role the wiggling motion a flying snake makes as it glides from one tall tree branch to another serves. That movement, known as aerial undulation, happens in each glide made by members of the Chrysopelea family, the only known limbless vertebrates capable of flight.

Now, according to information provided by Virginia Polytechnic Institute and State University (Virginia Tech), an interdisciplinary team of researchers have developed the first continuous, anatomically-accurate 3D mathematical model of the paradise tree snake, Chrysopelea paradisi, in flight. The results of their study, Undulation enables gliding in flying snakes, were published recently by Nature Physics.

Led by Jake Socha, a professor in the Department of Biomedical Engineering and Mechanics at Virginia Tech, the team, which included Shane Ross, a professor in the Kevin T. Crofton Department of Aerospace and Ocean Engineering, and Isaac Yeaton, a recent mechanical engineering doctoral graduate and the paper’s lead author, developed the 3D model after measuring more than 100 live snake glides. The model factors in frequencies of undulating waves, their direction, forces acting on the body, and mass distribution. With it, the researchers have run virtual experiments to investigate aerial undulation.

In one set of those experiments, to learn why undulation is a part of each glide, they simulated what would happen if it wasn’t — by turning it off. When their virtual flying snake could no longer aerially undulate, its body began to tumble. The test, paired with simulated glides that kept the waves of undulation going, confirmed the team’s hypothesis: aerial undulation enhances rotational stability in flying snakes.

“We know that snakes undulate for all kinds of reasons and in all kinds of locomotor contexts,” noted Prof. Socha. “That’s their basal program. By program, I mean their neural, muscular program? — they’re receiving specific instructions: fire this muscle now, fire that muscle, fire this muscle. It’s ancient. It goes beyond snakes. That pattern of creating undulations is an old one. It’s quite possible that a snake gets into the air, then it goes, ‘What do I do? I’m a snake. I undulate.’”

At the outset of the study, Prof. Socha proposed a theory for aerial undulation based on a comparison of two types of aircraft: jumbo jets versus fighter jets. Jumbo jets are Designed for stability, jumbo jets start to level back out on their own when perturbed, he said, whereas fighter jets roll out of control. Of the two, which did the paradise tree snake most resemble?

“Is it like a big jumbo jet, or is it naturally unstable?” Prof. Socha pondered. “Is this undulation potentially a way of it dealing with stability?”

Upon reflection, he reached the conclusion that the snake would be more like a fighter jet.

To run tests investigating undulation’s importance to stability, the team set out to develop a 3D mathematical model that could produce simulated glides. But first, they needed to measure and analyze what real snakes do when gliding.

In 2015, the researchers collected motion capture data from 131 live glides made by paradise tree snakes. They turned The Cube, a four-story black-box theater at the Moss Arts Center, into an indoor glide arena and used its 23 high-speed cameras to capture the snakes’ motion as they jumped from 27 feet up — from an oak tree branch atop a scissor lift — and glided down to an artificial tree below, or onto the surrounding soft foam padding the team set out in sheets to cushion their landings.

The cameras put out infrared light, so the snakes were marked with infrared-reflective tape on 11 to 17 points along their bodies, allowing the motion capture system to detect their changing position over time.

“With this number, we could get a smooth representation of the snake, and an accurate one,” noted Prof. Socha.

The researchers went on to build the 3D model by digitizing and reproducing the snake’s motion while folding in measurements they had previously collected on mass distribution and aerodynamics. An expert in dynamic modeling, Prof. Ross guided Yeaton’s work on a continuous model by drawing inspiration from work in spacecraft motion.

In virtual experiments, the model showed that aerial undulation not only kept the snake from tipping over during glides, but it increased the horizontal and vertical distances traveled.

According to Prof. Ross, by undulating the snake is able to balance out the lift and drag forces its flattened body produces, rather than being overwhelmed by them and toppling, and it’s able to go further.

The experiments also revealed to the team details they hadn’t previously been able to visualize. They saw that the snake employed two waves when undulating: a large-amplitude horizontal wave and a newly discovered, smaller-amplitude vertical wave. The waves went side to side and up and down at the same time, and the data showed that the vertical wave went at twice the rate of the horizontal one. “This is really, really freaky,” said Prof. Socha. These double waves have only been discovered in one other snake, a sidewinder, but its waves go at the same frequency.

“What really makes this study powerful is that we were able to dramatically advance both our understanding of glide kinematics and our ability to model the system,” said Yeaton. “Snake flight is complicated, and it’s often tricky to get the snakes to cooperate. And there are many intricacies to make the computational model accurate. But it’s satisfying to put all of the pieces together.”

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