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The Physics of Jumping Rope

November 23, 2010 Leave a comment

63rd Annual Meeting of the APS Division of Fluid Dynamics Volume 55, Number 16 

Abstract: CX.00008 : The aerodynamics of jumping rope

Authors:

  Jeffrey Aristoff
    (Department of Mechanical and Aerospace Engineering, Princeton University)

  Howard Stone
    (Department of Mechanical and Aerospace Engineering, Princeton University)

We present the results of a combined theoretical and experimental investigation of the motion of a rotating string that is held at both ends (i.e. a jump rope). In particular, we determine how the surrounding fluid affects the shape of the string at high Reynolds numbers. We derive a pair of coupled non-linear differential equations that describe the shape, the numerical solution of which compares well with asymptotic approximations and experiments. Implications for successful skipping will be discussed, and a demonstration is possible.

[My comments: The authors built a robot jump rope device and controlled parameters of rope rotation rate, rope density, diameter, length etc. using high speed cameras, they developed equations to describe the motion of the jump rope.

“Our main discovery is how the air-induced drag affects the shape of the rope and the work necessary to rotate it,” says Princeton researcher Jeff Aristoff. “Aerodynamic forces cause the rope to bend in such a way that the total drag is reduced.” (Leaves do this too when they bend out of the wind.) This deflection or twisting is most important in the middle of the rope and the least at the ends. If the rope is too light it might not clear the body of the jumper. (From Physorg.com)

I hope they did a demonstration. My experience is that physics conferences can be a bit stuffy.]