Engineers Give The Jump Rope A Spin

When they both worked at Princeton, Howard Stone and Jeff Aristoff used to play basketball at lunchtime. One day, when Dr. Stone was warming up with his jump rope, the two wondered if anyone had mathematically modeled the shape of the rope. The two researchers decided to give it a whirl.

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JOE PALCA, HOST:

Aha. I see someone in the studio, the mists are clearing. It's Flora, Flora Lichtman.

FLORA LICHTMAN, BYLINE: Hi, Joe.

PALCA: Time for the Video Pick. What have you got for us, Flora?

LICHTMAN: This week, the video is - was inspired by a pickup basketball game between two researches at Princeton. They were Princeton at that time, Dr. Howard Stone and Jeff Aristoff. And they, apparently, frequently play basketball lunch. Dr. Stone would warm up with a jump rope. And like curious scientists, they wondered themselves - no, this is not something that I had ever wondered - they wondered, could you mathematically model the shape of that jump rope?

PALCA: But wait a minute. I mean, you swing the jump rope, it's like a parabola or something like that.

LICHTMAN: Yeah. So I've thought this too. And actually, in our Video Pick of the Week this week, which is on our website at sciencefriday.com, we have the daughters of Dr. Stone because they're real jump rope experts. And they, too, are sort of like, what are you talking about with the shape?

PALCA: Right.

LICHTMAN: But apparently, it's more complicated than that. You have to take into account centrifugal course and tension and air drag. That was sort of the big contribution of their paper, is looking at the air drags effect on the shape of that jump rope. So if you imagine a jump rope, you - it's not all in one plane, if you look at, say, with a high-speed video camera, which is what they did. It bends backwards, away from the direction that you're actually spinning and that's drag.

PALCA: So you could model it with a rope that was not subject to wind resistance. But if you model it with a real rope, you can - and then you can say, well, it's a different picture if you're at ground level or sea level than if you're up in Denver or something like that?

LICHTMAN: Well, this was the question that I had. You know, does that mean that it takes less twirling force to jump rope at - in a high altitude place where the air is thinner? And, you know, of course, it's a very complicated model. So it's hard to predict. But, yes, it does seem that you will see less drag on your jump rope if you're jump roping at high altitudes. But Jeffrey Aristoff pointed out that that may not make it easier because there's also less oxygen.

PALCA: Less oxygen, right. Right, right.

(SOUNDBITE OF LAUGHTER)

LICHTMAN: Yeah. Yeah.

PALCA: You're not thinking about moving on to something like jacks or pick-up sticks or something that for (unintelligible)?

Ah, probably, actually, if you know of any jacks research, I'd, of course, be interested.

I see.

LICHTMAN: But, you know, the thing that Dr. Stone said about this work is that these types of questions are things that he thinks about all the time because he's into modeling slender things in flow, like in air or water. So this is, you know, jump roping was a good exercise.

PALCA: Well, there's a lot - yeah, I get it.

(SOUNDBITE OF LAUGHTER)

PALCA: Where's my rim shot? OK. Exactly. All right. Flora, thanks very much. And I guess that brings us just about to the close. But before we go, I wanted to remind people that last fall, I ate smoked eel with James Prosek, and I'm sure that's something that everybody remembers. Well, if it's not, you can relive that moment, or take a look at Prosek's latest work by surfing over to our site, Art's page on sciencefriday.com. There's a new story there on James Prosek's paintings and a link back to our eel chat of some time ago. It was - he's a very interesting painter, and it's worth taking a look if you have the chance. In New York, I'm Joe Palca.

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