There is a limit to how many times you can fold a crêpe
ResonX /Jasmin Schoenzart
If you carefully fold a slice made of a flexible and possibly tasty material, what makes it stay folded? And how many times can you fold it before it struggles and turns back?
A physicist from France, home of the crêpe, decided to find out. He discovered that just one number tells you everything you need to know.
Tom Marzin of Cornell University in Ithaca, New York, wondered about crêpe folding while on vacation in his home region of Brittany, France, where this thin pancake is especially popular. Simply folding a tip of it would cause it to tip back, but with a larger fold, friction and gravity would conspire to keep it still. What rules might govern this behavior?
Marzin turned it into a research project, the results of which he will present March 20 at a meeting of the American Physical Society in Denver, Colorado.
His work is different from the origami-like folds some physicists study, which are permanent. “What we’re dealing with here is what I call a soft or smooth fold. And it’s just a competition between gravity and elasticity,” says Marzin.
One way to observe this competition is to attach part of a pancake to a table top, let the other end hang over the edge and measure how much it sinks. Marzin found that the answer can be predicted by a single number, called the elasto-gravitational length, which combines the material’s density, its stiffness, and the force of gravity. He suspected that this number would also govern the behavior of flexible materials in other situations, and in a computer model it proved to be the case.
To check his simulations in the real world, Marzin experimented with plastic sheets, store-bought tortillas and, of course, crêpes. He began by making the latter himself, but scientifically they were not suitable for the purpose.
“I didn’t control the thickness very well,” he says. “So I asked my mother to do the experiments in France. I told her to buy calipers and rulers and a bunch of crepes from a commercial brand. They were probably made by a machine, (so) that guarantees a good uniform thickness. And she did it right.”
Marzin’s experiments confirmed that all aspects of crêpe folding depend on the elasto-gravitational length. For example, it controls how much of the area of a sheet that is folded will go into the part that goes over. This determines whether there will be enough flat area left for another fold.
His equations correctly predict that a crêpe 26 centimeters in diameter and 0.9 millimeters thick can be folded up to four times, while a 1.5 mm thick tortilla of the same size, with an elasto-gravity length 3.4 times that, will only allow for two folds. “This length captures all the physics underneath,” says Marzin.
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