Thanks to impressive athleticism, high-speed video and clever computer modeling, two researchers have unraveled the hidden aerodynamics behind the playful task of skipping over a speeding rope.

“Fewer than 10 people have published studies on jump ropes, but no one considered the influence of air. They simplified the problem by jumping rope in a vacuum,” said applied mathematician Jeffrey Aristoff of Numerica Corp.  “That’s a nice first step, but it doesn’t capture the full dynamics.”

The idea to dissect jump rope fluid dynamics,  described in a study published Nov. 1 in Proceedings of the Royal Society A, came to Aristoff while a graduate student at Princeton University. Colleague and study co-author Howard Stone told Aristoff that Jiang Li, a student visiting from jump-rope-obsessed China, was especially good.

“She turned out to be the best at Princeton, and then we wondered if anyone had studied the fluid dynamics [of jumping rope],” Aristoff said. “We realized no one had.”

To begin exploring the problem, the researchers filmed Li hopping in front of a high-speed camera. From this ideal example, the researchers constructed a rope-twirling robot to capture more detailed high-speed video and see how the rope interacted with the air.

They realized the U-shaped tip of jump ropes — the fastest-moving parts of the rope — bent away from the direction of motion. From there, they crafted a computer model able to deform a virtual rope’s end based on its aerodynamic drag.

“Now we can say what’s a good or fast jump rope: one that’s lightweight, has a small diameter and is short. That gives you the lowest drag and highest speed,” Aristoff said.

Beyond satisfying curiosity, the research may lend engineers a hand in designing objects that more through the air quicker or are more resistant to breaking.

“Things outside are always moving in response to fluid flow, including branches, water, flags, everything,” Aristoff said. “The ability to understand these fluid interactions, including those of a jump rope, can allow you to design better man-made objects and structures.”

Image: A rope-twirling machine, imaged several times with a strobe light, reveals a distinctive bend in the end of the moving rope. (Jeffrey Aristoff and Howard Stone/Proceedings of the Royal Society A)

Video: In the first sequence, Jiang Li jump ropes in front of a 500 fps video camera. In the second sequence, a machine recreates the bend in a twirling loop of a jump rope. The final clips show a computer model of a virtual jump rope accounting for aerodynamics. (Jeffrey Aristoff and Howard Stone)

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