Mathematicians Solve Age-Old Spaghetti Mystery

Noodle twist

In parallel, Patil began to develop a mathematical model to explain how twisting can snap a stick in two. To do this, he generalized previous work by the French scientists Basile Audoly and Sebastien Neukirch, who developed the original theory to describe the “snap-back effect,” in which a secondary wave caused by a stick’s initial break creates additional fractures, causing spaghetti to mostly snap in three or more fragments.

Patil adapted this theory by adding the element of twisting, and looked at how twist should affect any forces and waves propagating through a stick as it is bent. From his model, he found that, if a 10-inch-long spaghetti stick is first twisted by about 270 degrees and then bent, it will snap in two, mainly due to two effects. The snap-back, in which the stick will spring back in the opposite direction from which it was bent, is weakened in the presence of twist. And, the twist-back, where the stick will essentially unwind to its original straightened configuration, releases energy from the rod, preventing additional fractures.

“Once it breaks, you still have a snap-back because the rod wants to be straight,” Dunkel explains. “But it also doesn’t want to be twisted.”

Just as the snap-back will create a bending wave, in which the stick will wobble back and forth, the unwinding generates a “twist wave,” where the stick essentially corkscrews back and forth until it comes to rest. The twist wave travels faster than the bending wave, dissipating energy so that additional critical stress accumulations, which might cause subsequent fractures, do not occur.

“That’s why you never get this second break when you twist hard enough,” Dunkel says.

The team found that the theoretical predictions of when a thin stick would snap in two pieces, versus three or four, matched with their experimental observations.

“Taken together, our experiments and theoretical results advance the general understanding of how twist affects fracture cascades,” Dunkel says.

For now, he says the model is successful at predicting how twisting and bending will break long, thin, cylindrical rods such as spaghetti. As for other pasta types?

“Linguini is different because it’s more like a ribbon,” Dunkel says. “The way the model is constructed it applies to perfectly cylindrical rods. Although spaghetti isn’t perfect, the theory captures its fracture behavior pretty well,”

The research was supported, in part, by the Alfred P. Sloan Foundation and the James S. McDonnell Foundation.

Contacts and sources:
Jennifer Chu
Massachusetts Institute of Technology

Citation: Controlling fracture cascades through twisting and quenching
Ronald H. Heisser, Vishal P. Patil, Norbert Stoop, Emmanuel Villermaux, Jörn Dunkel. . Proceedings of the National Academy of Sciences, 2018; 201802831 DOI: 10.1073/pnas.1802831115