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 post-graduate student at Princeton University. Colleague and study co-author Howard Stone told Aristoff that Jiang Li, a professor 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” and smooth, Aristoff said. “That gives you the lowest drag and highest speed.”
Beyond satisfying curiosity, the research may lend engineers a hand in designing objects that move through the air quicker or are more resistant to breaking.
“Things outside are always moving in response to fluid flow, including branches, [suspension bridges] … 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.”
Updated: Nov. 2, 2011; 9:30 a.m. EDT
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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