Physicists create a formula for how many times you can fold a crepe

If you gently fold a disc made of some flexible and possibly tasty material, why does it stay folded? And how many times can you fold it before it struggles and flips back over?

A physicist from France, the home of the pancake, decided to find out. He found that a single number tells you everything you need to know.

Tom Marzin at Cornell University in Ithaca, N.Y., thought about folding crêpes while on vacation in his native Brittany, France, where the thin crêpe is particularly popular. Simply bending its tip would cause it to topple back over, but with more of a bend, friction and gravity would combine to keep it still. What rules might govern this behavior?

Marzin turned it into a research project, the results of which he will present on March 20 at the meeting of the American Physical Society in Denver, Colorado.

His work differs from the origami-like folds studied by some physicists, which are permanent. “We’re dealing here with 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 tape part of a pancake to a table top, let the other end hang over the edge, and measure how much it sags. Marzin figured out that the answer could be predicted by a single number called the elastogravitational length, which combines a 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 the computer model showed it.

To test his simulations in the real world, Marzin experimented with plastic discs, store-bought tortillas, and, of course, pancakes. He started making the latter himself, but they were scientifically unfit for the purpose.

“I didn’t control the thickness well,” he says. “So I asked my mom to do the experiments in France. I asked her to buy calipers and rulers and a lot of commercial brand pancakes. They were probably made by machine.” [so] which guarantees a good uniform thickness. And she did it really right.”

Marzin’s experiments confirmed that all aspects of crepe folding depend on the elastogravity length. For example, it determines how much of the folded sheet’s area goes into the part that loops. This determines whether there is enough flat surface left for the next fold.

His equations correctly predict that a 26-centimeter-diameter, 0.9-millimeter-thick crepe can be folded up to four times, while a 1.5-mm-thick tortilla of the same size, with an elastogravity length 3.4 times greater, will allow only two folds. “That length captures all the physics underneath,” says Marzin.

topics: