There is a limit to how many times you can fold a crêpe
ResonX /Jasmin Schoenzart
When you fold a disc made of a flexible, possibly tasty material, what keeps it in its folded state? And how often can it be folded before it resists and unfolds?
A French physicist sought to answer these questions and found that a single number holds the key.
Tom Marzin, based at Cornell University in Ithaca, New York, was curious about the folding of crêpes while vacationing in Brittany, France, where these thin pancakes are a local favorite. Folding just a small part of a crêpe often results in it springing back, but a larger fold stays put due to the interplay of friction and gravity. Marzin was intrigued by the rules governing such behavior.
This curiosity led Marzin to develop a research project, which he plans to present on March 20 at the American Physical Society meeting in Denver, Colorado.
Marzin’s research differs from studies of origami-like folds, which are permanent. He explains, “What we’re dealing with here is what I call a soft or smooth fold. And it is just a competition between gravity and elasticity.”
One method to explore this balance is by attaching part of a pancake to a tabletop, letting the other end dangle, and measuring its sag. Marzin identified that this behavior can be predicted using a single number, the elasto-gravity length, which factors in the material’s density, stiffness, and gravitational force. He suspected this number would also apply to other flexible materials, a hypothesis confirmed through computer modeling.
To validate his simulations, Marzin tested various materials, including plastic discs, store-bought tortillas, and crêpes. Initially, he made crêpes himself, but they lacked scientific precision.
“I didn’t control the thickness well,” he admits. “So I asked my mom to perform the experiments over in France. I asked her to buy the calipers and rulers and a bunch of crêpes from a commercial brand. Those were probably made by a machine, [so] that guarantees a good uniform thickness. And she did it really correctly.”
Marzin’s experiments verified that all aspects of crêpe folding depend on the elasto-gravity length. This number dictates how much of a sheet’s surface will form the loop over a fold, determining if enough flat area remains for additional folds.
His calculations accurately predict that a crêpe 26 centimeters in diameter and 0.9 millimeters thick can be folded four times, while a 1.5-mm-thick tortilla of the same size, with an elasto-gravity length 3.4 times larger, permits only two folds. “This length captures all the physics underneath,” Marzin explains.
Topics:
