Physicists create formula for how many times you can fold a crêpe
There is a limit to the number of times you can fold a pancake
ResonX/Jasmin Schoenzart
If you gently bend a disk made of a flexible and possibly tasty material, what makes it stay folded? And how many times can you bend it before it fights and rolls over?
A French physicist, land of pancakes, decided to find out. He discovered that one number tells you everything you need to know.
Tom Marzin of Cornell University in Ithaca, New York, wondered about crepe folding while on vacation in his native Brittany, France, where this thin crepe is particularly popular. Simply bending one tip of it would cause it to flip over, but with a larger bend, friction and gravity would conspire to keep it still. What rules could 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 studied by some physicists, which are permanent. “This 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 stick part of a pancake on a table, let the other end hang over the edge, and measure how much it sags. Marzin found that the answer can be predicted with a single number, called the elasto-gravity length, which combines the density of the material, its stiffness and the force of gravity. He suspected that this number would also govern the behavior of flexible materials in other situations, and this turned out to be the case in a computer model.
To test his simulations in the real world, Marzin experimented with plastic discs, store-bought tortillas and, of course, pancakes. He began making these himself, but scientifically they were not fit for purpose.
“I didn’t control the thickness well,” he says. “So I asked my mother to do the experiments in France. I asked her to buy calipers, rulers and a bunch of pancakes from a commercial brand. These were probably made by a machine, [so] this guarantees a good uniform thickness. And she did it very correctly.
Marzin’s experiments confirmed that all aspects of crepe folding depend on elasto-gravity length. For example, it determines how much of the surface area of a folded sheet will fit into the part that curls. This determines whether there will be enough flat surface left for another fold.
His equations correctly predict that a pancake 26 centimeters in diameter and 0.9 millimeters thick can be folded up to four times, whereas a 1.5 mm thick tortilla of the same size, with an elasto-gravity length 3.4 times greater, will only allow two folds. “This length captures all the physics underneath,” says Marzin.
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