Try breaking spaghetti into two pieces.
It’s not as easy as it sounds.
If you take two ends of a strand of spaghetti and bring them together, the noodle will almost always break into three or more pieces.
This counterintuitive phenomenon has perplexed scientists for decades, stumping even American theoretical physicist and Nobel laureate Richard Feynman, who sought to explain why.
It wasn’t until 2005 that French scientists Basile Audoly and Sebastien Neukirch cracked the code and discovered the underlying forces that occur when spaghetti – or any long, thin rod – is bent.
Typically, the noodle will break at the point of highest curvature, after which it wants to straighten itself out.
This subsequently creates a so-called snap-back effect, which sends a vibrating wave down the noodle and causes multiple fractures – a fracture cascade.
In 2006, Audoly and Neukirch were awarded the Ig Nobel Prize – a parody of the original Nobel that celebrates unusual achievements in science – for their ingenuity in solving this age-old puzzle.
But their findings still begged the question: can spaghetti ever break into two pieces?
Fast forward to 2018. Following months of breaking spaghetti with a specially designed noodle-breaking apparatus, a team of MIT researchers said, yes – but with a twist.
In a paper published in Proceedings of the National Academy of Sciences, MIT researchers found that spaghetti can be broken into halves by either twisting the noodle or compressing it very slowly.
Via the first method, the spaghetti strand must be twisted by nearly 300 degrees in order to break into two.
“In order to get anything to break, you must apply supercritical stress. This can be achieved through bending or twisting,” said Jörn Dunkel, co-author of the project and Associate Professor of Physical Applied Mathematics at MIT.
When a noodle is bent or twisted past its neutral straight position, it wants to correct itself accordingly.
The correction creates waves that result in additional fractures.
Dunkel’s students Ronald Heisser and Vishal Patil discovered that simultaneouslyapplying bending and twisting stresses to a noodle coerces it to break into two pieces.
When the noodle snaps, “The bending and twisting waves are propagated at different speeds, so you never get supercritical stress at some other location in the rod,” Dunkel said.
The two processes essentially distribute and dissipate the energy needed to fracture spaghetti a third time. Hence, supercritical stress is never attained, and a fracture never occurs.
The researchers also found a second way to break the spaghetti into two through a process called quenching, or compressing the noodle.
If done at a very slow velocity, the noodle breaks into two. On the other hand, if compressed quickly, the noodle shatters into multiple fragments.
Dunkel likens the process of quenching to that of a vibrating string on an instrument. When a low pitch is played, the wavelength of the sound wave is high and the frequency is low.
This situation parallels the large waves that result from slow compression of a noodle.
The low frequency and high wavelength of compression divides the noodle at fewer points, which results in fewer points of supercritical stress.
Higher speeds of compression induce waves with higher frequencies, which creates more areas of supercritical stress, and, thus, more fracture points.
While the practical applications of this research are currently unclear, Dunkel and his team’s research provides us with a better understanding of how elongated rods behave under stresses of bending, twisting, and quenching and paints a clearer picture of how fractures work.
After all, examples of fractures are everywhere around us, like in broken bones and fracturing plate tectonics.
The results of this research may even provide a glimpse into how the microtubules in our cells behave under duress, as Dunkel’s mathematical models can fit rods made of different materials, elasticities, lengths, and radii.
For now, Dunkel reminds us to appreciate the scientific and mathematical theories underlying even the most mundane of phenomena.
“We like to connect with the broader public, but one should also remain aware of the broader theoretical implications that reach beyond breaking spaghetti!” The next time you snap spaghetti, just remember that there’s more than meets the eye.
A deep dish dive
Heisser, together with project partner Edgar Gridello, originally took up the challenge of breaking spaghetti in the spring of 2015, as a final project for 18.354 (Nonlinear Dynamics: Continuum Systems), a course taught by Dunkel.
They had read about Feynman’s kitchen experiment, and wondered whether spaghetti could somehow be broken in two and whether this split could be controlled.
“They did some manual tests, tried various things, and came up with an idea that when he twisted the spaghetti really hard and brought the ends together, it seemed to work and it broke into two pieces,” Dunkel says.
“But you have to twist really strongly. And Ronald wanted to investigate more deeply.”
So Heisser built a mechanical fracture device to controllably twist and bend sticks of spaghetti.
Two clamps on either end of the device hold a stick of spaghetti in place.
A clamp at one end can be rotated to twist the dry noodle by various degrees, while the other clamp slides toward the twisting clamp to bring the two ends of the spaghetti together, bending the stick.
Heisser and Patil used the device to bend and twist hundreds of spaghetti sticks, and recorded the entire fragmentation process with a camera, at up to a million frames per second. In the end, they found that by first twisting the spaghetti at almost 360 degrees, then slowly bringing the two clamps together to bend it, the stick snapped exactly in two. The findings were consistent across two types of spaghetti: Barilla No. 5 and Barilla No. 7, which have slightly different diameters.
Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending.
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.
