So are two middle-aged mechanical engineers at Princeton.
Jeffrey Aristoff, a post-doctoral researcher, and professor Howard Stone have been researching the physics of jumping rope since last spring, looking specifically at air resistance. In their efforts so far, they have created both a mathematical model and a miniature mechanical jump rope. The researchers presented their initial findings at a physics convention in California in mid-November and are still working on the project.
The idea for the research came as the fluid mechanics specialists were preparing for a pick-up basketball game earlier this year. To warm up his legs before the match, Stone took out his jump rope. It was only natural, Aristoff said, for the pair to ponder the significance of air resistance on the rope.
“We wondered if we could explain factors like the shape, drag and efficiency of rotation of the rope,” explained Aristoff, whose latest publication, “How Cats Lap,” was published in Science magazine last month.
Stone looked through existing literature on jump ropes but found that previous research only examined the ropes in a vacuum, ignoring the effect of air resistance on the shape of the rope.
“Because one interest in my group is currently the interplay of fluid flow phenomena with the shape of elastic objects, the jump rope question seemed quite natural to think about,” Stone said in an e-mail.
Aristoff and Stone then formulated mathematical equations to model the expected effect of air drag on a jump rope. According to their initial predictions, air resistance would be greatest in the middle of the rope and least on the ends.
One challenge for the team was designing a model that both accurately captured the motion and was simple enough to be described in mathematical equations. “You want to meet somewhere in between your model and real life,” Aristoff explained.
To test their hypothesis, the researchers built a mechanical jump rope attached at its ends to a machine that would swing the rope. The model allowed them to vary parameters ranging from the swing diameter to the rope’s speed. After recording many swings under different conditions with their high-speed camera, they analyzed the video with a computer program.
For comparison, they also filmed a person jumping rope so they could examine the motion under realistic conditions.
Preliminary analysis of their videos to date suggests the team’s “main physics are correct,” Aristoff said, showing that drag force is greatest on the middle of the rope and least at its ends.
Stone said the research “has taught us more about problems combining flow and elasticity, and it is always good to build up physical and mathematical intuition and insights.”
The research also has practical implications for jump rope enthusiasts. Because drag force increases with the length of the rope, an ideal jump rope just clears the top of a person’s head.
Aristoff emphasized that the research is still in progress. “We’re still working extensively on the robotic jump rope,” he said.
Asked who the better jump-roper was, Aristoff replied, “[Stone] is technically my boss, so I’d have to say it’s him. He’s more experienced.”
Stone disagreed, explaining that “Jeff is the better jump-roper; he can do a cross-over, and I am still learning that one.”
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