When you fold a flexible material, such as a pancake or a crepe, its behavior depends on a dispute between gravity and elasticity.
If we gently bend a disk made of a flexible (and possibly tasty) material, what causes it to stay bent? AND how many times o can we bend before starting to resist and return to the starting position?
The French physicist Tom Marzincoming from the country of crepes, decided to find out the answer. And concluded that just a single number to explain everything you need to know.
Marzin, a researcher at Cornell University in Ithaca, New York, started thinking about folding crepes when he was on holiday in his home region of Brittany, France, where this thin pancake is particularly popular.
If I bent just one corner, it would go back; but, with a greater fold, the friction and gravity combined to keep her still. What rules could explain this behavior?
Marzin turned the issue into a research projectwhose results he will present on March 20th, at a meeting of the American Physical Societyin Denver, Colorado.
His work addresses different aspects of permanent folds, similar to those of , that some physicists study. “What we are dealing with here is what I call a soft, or gentle fold. And it’s just a competition between gravity and elasticity”, says Marzin, quoted by .
One way to observe this dispute is fix part of a pancake to a table, let the other end hang over the edge and measure how much it bends.
Marzin concluded that the answer may be predicted with a single numberwhich he called elastogravitational lengthl, which combines the density of the material, its rigidity and the force of gravity.
The investigator suspected that this number would also govern the behavior of flexible materials. in other situations — and that is exactly what he verified in a computational model.
To confirm the simulations in the real world, Marzin experimented with plastic discs, store-bought pancakes and, of course, crepes. In a first phase, tried to make the crepes himselfbut, from a scientific point of view, they were not useful for this purpose.
“Didn’t control the thickness well“, he explains. “Therefore, I asked my mother to carry out the experiments in France. I asked him to buy a caliper, rulers and a set of trademark crepes. These will probably have been made by machine, which ensures good thickness uniformity. And she did everything impeccably.”
Marzin’s experiments confirmed that all aspects of crepe folding depend on the elastogravitational length. For example, it is he who determines which part of the area of a folded sheet becomes part of the arched section. This defines whether enough flat area remains to make another fold.
Their equations correctly predict that a crepe 26 centimeters in diameter and 0.9 millimeters thick can be folded up to four timeswhereas a pancake 1.5 millimeters thick and the same size, with an elastogravitational length 3.4 times greater, only allows two folds.
“This length captures all the underlying physics”, says Marzin.
