If you've ever pulled a rolling suitcase through the airport, chances are you've also been annoyed by this common occurrence: the suitcase starts rocking back and forth on each wheel and finally tips over.
"It's a very classic phenomenon in physics." Sylvain Courrech du Pont, a physicist at the University of Paris Diderot. "So if you perturb the system it goes very easily unstable. This is shared by many, many phenomena in nature."
Courrech du Pont and his students wanted to get to the bottom of why luggage tips. So they built what looks like the skeleton of a wheeled suitcase, and then filmed it rolling on a treadmill. Then they modeled what they saw mathematically.
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And here's what they found. Under normal rolling conditions, the forward motion of the suitcase is perpendicular to the wheels' axis of rotation. All good. But when you hit a bump or jerk the handle, one wheel lifts up. All of a sudden the pulling motion is no longer perpendicular to the still-rolling wheel's rotation, and the wheel corrects that by drifting towards the center. But by that time the other wheel's coming down, same thing happens, and now the suitcase is really rocking.
"And the first reaction you will have maybe is to slow down. But actually if you slow down you'll experience very big rocking oscillations." The way back to a smooth ride, he says, is to keep up your speed, or move even faster, once rocking begins. The study is in the Proceedings of the Royal Society A. [G. Facchini et al., The rolling suitcase instability: a coupling between translation and rotation]
There are other solutions to suitcase instability—like doing a better packing job. "If you put heavy stuff close to the axis of symmetry, or close to the wheel axis, then it's stable, too."
And Courrech du Pont has one more piece of advice to avoid rocking in the first place: "If you go slow enough it will always be stable." Keep that in mind, next time you're running to your gate.
—Christopher Intagliata
[The above text is a transcript of this podcast.]
