Mathematicians solve age-old spaghetti mystery

August 13, 2018 by Jennifer Chu, Massachusetts Institute of Technology
Credit: CC0 Public Domain

If you happen to have a box of spaghetti in your pantry, try this experiment: Pull out a single spaghetti stick and hold it at both ends. Now bend it until it breaks. How many fragments did you make? If the answer is three or more, pull out another stick and try again. Can you break the noodle in two? If not, you're in very good company.

The spaghetti challenge has flummoxed even the likes of famed physicist Richard Feynman '39, who once spent a good portion of an evening breaking pasta and looking for a theoretical explanation for why the sticks refused to snap in two.

Feynman's kitchen experiment remained unresolved until 2005, when physicists from France pieced together a theory to describe the forces at work when spaghetti—and any long, thin rod—is bent. They found that when a stick is bent evenly from both ends, it will break near the center, where it is most curved. This initial break triggers a "snap-back" effect and a bending wave, or vibration, that further fractures the stick. Their theory, which won the 2006 Ig Nobel Prize, seemed to solve Feynman's puzzle. But a question remained: Could spaghetti ever be coerced to break in two?

The answer, according to a new MIT study, is yes—with a twist. In a paper published this week in the Proceedings of the National Academy of Sciences, researchers report that they have found a way to break spaghetti in two, by both bending and twisting the dry noodles. They carried out experiments with hundreds of spaghetti sticks, bending and twisting them with an apparatus they built specifically for the task. The team found that if a stick is twisted past a certain critical degree, then slowly bent in half, it will, against all odds, break in two.

The researchers say the results may have applications beyond culinary curiosities, such as enhancing the understanding of crack formation and how to control fractures in other rod-like materials such as multifiber structures, engineered nanotubes, or even microtubules in cells.

"It will be interesting to see whether and how twist could similarly be used to control the fracture dynamics of two-dimensional and three-dimensional materials," says co-author Jörn Dunkel, associate professor of physical applied mathematics at MIT. "In any case, this has been a fun interdisciplinary project started and carried out by two brilliant and persistent students—who probably don't want to see, break, or eat spaghetti for a while."

The two students are Ronald Heisser '16, now a graduate student at Cornell University, and Vishal Patil, a mathematics graduate student in Dunkel's group at MIT. Their co-authors are Norbert Stoop, instructor of mathematics at MIT, and Emmanuel Villermaux of Université Aix Marseille.

Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. Credit: Massachusetts Institute of Technology
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.

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.

Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. Credit: Massachusetts Institute of Technology

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 , 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,"

Explore further: Physical Review Letter on Breaking Spaghetti Leads to 2006 Ig Noble Award

More information: Ronald H. Heisser el al., "Controlling fracture cascades through twisting and quenching," PNAS (2018). www.pnas.org/cgi/doi/10.1073/pnas.1802831115

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31 comments

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Whart1984
Aug 13, 2018
This comment has been removed by a moderator.
JongDan
5 / 5 (3) Aug 13, 2018
Isn't it https://phys.org/...#nRlv...

That's for engineers. We're doing pure science here!
Steelwolf
5 / 5 (10) Aug 13, 2018
This may well have very good application with regards to carbon-boron fiber struts in space applications under stress and how such items might fail in extreme situations, how to engineer it to do so in a reasonably safe manner for occupants or equipment.

It even has application with regards to cables in suspension type bridges and how it may affect their failure in extreme, unforeseen conditions.

So, while it may seem like a silly bit of experimentation, it Does supply real world answers to larger questions in engineering.
Cusco
2.3 / 5 (3) Aug 14, 2018
I smell as second IgNobel Award for spaghetti research!
Parsec
5 / 5 (7) Aug 14, 2018
Anyone not recognizing the importance of this work should either take another look or just give up trying to understand anything complicated.

The kickback effect from the traveling wave is an entirely new mechanism for propagating material flaws, generating cracks, and ultimately equipment failure. I am simply astonished that anyone at all doesn't realize the vast sums of money our civilization spends replacing machines that fail prematurely. Even recovering 1% of that money amounts to hundreds of billions or even trillions of worldwide savings per year.
Captain Skip
not rated yet Aug 14, 2018
Pretty clear why the spaghetti breaks in many pieces .. the entire piece is under bending stress. when it lets go there are segments along the way that relax in the other direction, rapidly and they snap and others snap too.
twisting them adds an additional vector which in certain conditions will dissipate the stress axially
and actually strengthen the filament.
any fisherman can tell you this.
the applications for composite fiber construction using this info will make for stronger materiel configurations, and actually some have been doing it all along .
Captain Stumpy
2.3 / 5 (3) Aug 14, 2018
@zeph
Isn't it researched again and again?
https://en.wikipe...c_method
Beeble
5 / 5 (3) Aug 14, 2018
I'm just an average person whose brain surface resembles a peach rather than a prune. I think of donuts a lot and like cartoons. I also like to cook and love spaghetti. And yes, a spaghetti noodle or lots of spaghetti noodles can be broken into two pieces simply by holding them near the noodle center rather than the ends. But that's rather logical and obvious and works for cooks.

Although many of us may be quite content to sit in a cave while watching cartoons, eating spaghetti, and thinking of donuts for dessert, I'm grateful for those (often misunderstood) individuals who can think beyond their bellies and apply their imagination and creativity.
Whart1984
Aug 15, 2018
This comment has been removed by a moderator.
JuergenMichele
not rated yet Aug 16, 2018
The stress level for breaking of a brittle material (spaghetti is such a material) is at certain torsional stress value (shear fracture).
By adding torsion to the bending the total stress is increased.
That means that not so much bending is necessary for the rupture to occur.
The dynamic action after breaking is reduced.
So the rupture may not be in multiple pieces.
antialias_physorg
2.3 / 5 (3) Aug 16, 2018
The dynamic action after breaking is reduced.

Not really since the amount of stress that needs to be relieved is the same. How I understand it is that the snap-back effect is decoupled into two components: a rotational and a longitudinal one.
The two components travel at different speeds down the fiber so that at no point the stress for breaking it again is locally achieved.

I wonder if an inhomogeneous structure (e.g. a multi-mode fiber optic with a different core density) shows a similar effect. In this case it wouldn't be twist and longitudinal wave but two longitudinal waves that travel at different speeds.
JuergenMichele
5 / 5 (1) Aug 16, 2018
You are correct!
The bending action is reduced!
Anonym385793
not rated yet Aug 16, 2018
Whew! Finally, I will be able to sleep tonight...
Anonym927599
not rated yet Aug 16, 2018
This symbolic. Somethings, such as divorce, when you break apart, more pieces result, than just 2.
Anonym523449
not rated yet Aug 16, 2018
Perhaps this may explain in part why DNA is twisted? Less likelihood of multiple fractures?
YellerKitty
not rated yet Aug 16, 2018
Some people never notice the anomalies that lead to discoveries. Others may briefly wonder why things occur as they do, but then shrug it off. Those with scientific minds wonder why, and then go on to pursue the answers, and THAT is the behavior that has moved human enterprises forward since the first person wondered why sticks got hot when they were rubbed together and decided to see just how hot they could get. Who knows what significant applications this may ultimately have, but I'm intensely grateful to those who bother to pay attention to their "Hmmmmm..." impulse.
Poolbum1111
not rated yet Aug 16, 2018
That's why i break them under the water in the pot. They break in halves. Send me the Nobel Prize now. Thanks.
Poolbum1111
not rated yet Aug 16, 2018
Perhaps this may explain in part why DNA is twisted? Less likelihood of multiple fractures?

No. It's twisted so it can pack in smaller space or shorter length. Sperm sacs are the same way.:)
AngryPirate
not rated yet Aug 16, 2018
At the quantum level, isn't it really breaking into thousands of pieces, making the point moot?
Whart1984
Aug 17, 2018
This comment has been removed by a moderator.
Whart1984
Aug 17, 2018
This comment has been removed by a moderator.
antialias_physorg
2.3 / 5 (3) Aug 17, 2018
At the quantum level, isn't it really breaking into thousands of pieces

What is that even supposed to mean?

Guys. Seriously. If you don't know what certain words mean, don't use them. OK?
Nerfhammer
not rated yet Aug 17, 2018
At the quantum level, isn't it really breaking into thousands of pieces

" What is that even supposed to mean?

Guys. Seriously. If you don't know what certain words mean, don't use them. OK"

Well, if a quantum is defined as the minimum amount of a physical entity that's involved in a given interaction, I'd say that he's questioning how clean the break really is. He's nitpicking but his use of the word quantum is OK. Ironically, it's his point that's essentially mute as the experiment involved predicting and controlling the localized failures of a piece of spaghetti when it's bent, not necessarily the nature of those failures at a microscopic level. Nonetheless, it is a stupid experiment as all this knowledge has already been in practice in the engineering and material science fields for ages. Using torsion to control a beams failure is nothing new.
BruceH
not rated yet Aug 18, 2018
When Jorn says, "It will be interesting to see whether and how twist could similarly be used to control the fracture dynamics of two-dimensional and three-dimensional materials," he's got a REAL problem: There is *NO* such THING as a two-dimensional material. It's not possible in our Universe. Two Dimensions exist ONLY on paper, i.e., in theory, not in reality. (Even paper is 3 dimensional, regardless of how thin you make it.) Think about it....

catrov
not rated yet Aug 18, 2018
that scientific community has very small motivation for utilitarian prioritizing of its research: its incentives are actually perverse in this respect: they actively pushing the scientists into research of the most abstract and least useful things possible

You fundamentally misunderstand how scientific and engineering progress is made. All current work is built from the pieces discovered in the past, which were discovered as part of such "abstract" and "useless" research. They did not know at the time that their work would become a piece of something greater -- how could they, since they would not know what was to be discovered in the future. If you knew in advance exactly what steps would lead to a given development you would just go ahead and implement it directly, no research needed. Deeming some research "utilitarian" and others "abstract" is to dictate that the answer is known before it has been figured out. Such "research" programs never yield breakthroughs.
Whart1984
Aug 19, 2018
This comment has been removed by a moderator.
Whart1984
Aug 19, 2018
This comment has been removed by a moderator.
antialias_physorg
2.3 / 5 (3) Aug 19, 2018
When Jorn says, "It will be interesting to see whether and how twist could similarly be used to control the fracture dynamics of two-dimensional and three-dimensional materials," he's got a REAL problem: There is *NO* such THING as a two-dimensional material.

Why are you even posting this. You know full well what he means by a two dimensional material (Graphene, phosphorene, etc.)

It's completely asinine to redefine words to suit you and then attack your own (false) definition.
Strawman fallacy:
https://www.logic...-Fallacy
Whart1984
Aug 19, 2018
This comment has been removed by a moderator.
jpdemers
not rated yet Aug 20, 2018
Somebody, somewhere, is going, "Hmmm .... I wonder how it affects the strength of fiber-reinforced composites if I twist the fibers before curing the material?"
Maybe it'll be an insignificant academic paper. Maybe it will revolutionize a couple of industries and make the inventor fabulously rich.
Asking questions, and getting the answers, is never a bad idea.
ricknkenosha
not rated yet Aug 24, 2018
Someone should take the Nobel prize away from them because it's a no brainer that success in bridge suspension is due to twisted cable. Mistaking the twist in a cable suspension bridge as merely being reinforced strength. Clearly the twisted cable allowing wind to swing the bridge without it snapping is beyond mere strength, or wire reinforcing wire reinforcing wire with the ability to separate stress as 200 wires instead of solid mass. The twist itself unveils that strength by taking in the shock that prevents 2 or 3 or 4 breaks. Therefore you act as if this is new when instead the suspension bride inventor is the true Nobel winner. These idiots is why knowledge gets lost and then new bridges fail and collapse killing people. Unil someone else is praised and worshipped as if they discovered new what was never shared in a non-copyright world

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