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That's the Way the Spaghetti Crumbles

Physicists solve a vexing kitchen puzzle

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11:51am, November 8, 2005
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Great scientists sometimes do silly experiments. The renowned physicist and Nobel prize winner Richard P. Feynman, for instance, once got it into his head to figure out why uncooked spaghetti doesn't snap neatly in two when you bend it far enough to break. Pay attention next time, and you'll notice that the pasta tends to shatter into three or more fragments of unequal lengths.

In the midst of making a spaghetti dinner for themselves one night about 20 years ago, Feynman and a friend—supercomputing innovator W. Daniel Hillis—launched into a brief investigation of this perplexing breaking-pasta performance. "We ended up, at the end of a couple of hours, with broken spaghetti all over the kitchen and no real good theory about why spaghetti breaks in three," Hillis recalls, as quoted in the book No Ordinary Genius by Christopher Sykes (1994, W.W. Norton).

Sometimes, such experiments turn out to be not so silly after all. Recently, French scientists who unwittingly followed in the footsteps of Hillis and Feynman, who died in 1988, finally solved the spaghetti mystery. And a group of physicists and mathematicians conducted a related study that transcends spaghetti. The team examined various kinds of brittle rods under circumstances quite different from ordinary bending.

Besides explaining a quirk of everyday life, the new studies are improving scientists' grasp of fragmentation—the process by which objects shatter. "Fragmentation is a complicated problem that we still don't understand very well," says mechanical engineer and materials scientist Kaliat T. Ramesh of Johns Hopkins University in Baltimore. "Most of us are trying to understand the basic mechanisms involved."

Because spaghetti rods are similar in some ways to a wide variety of brittle objects ranging from industrial cutting tools to body armor, the research may end up elucidating how such structures can fracture and fail. "If we understand how things break, we can build tougher structures," says mathematician Andrew L. Belmonte of Pennsylvania State University in State College.

Shattered science

Fragmentation occurs in nature on many scales, from subatomic-particle collisions to volcanic explosions to the pummeling of planets by asteroids and comets. Disintegration processes are also an important part of the human realm—for instance, the smashing of windows, the pulverizing of ore, and the deadly detonations of bombs, as well as the benign breaking of spaghetti.

The unexpected incomprehensibility of that last example especially perturbs scientists trying to figure out how all this breakage unfolds.

"This is really the kind of simple question that you can't help thinking about over and over until you find the answer," says Sébastien Neukirch of the University of Paris VI, one of the physicists whose new work seems finally to set the bent-spaghetti issue to rest. To illustrate his point, he notes that Feynman isn't the only Nobel laureate to have been captivated by the pasta puzzle. In interviews on French television 14 years ago, after receiving the Nobel Prize in Physics, popular physicist Pierre-Gilles de Gennes of the College of France in Paris repeatedly alluded to the spaghetti mystery as one of the very simple, yet unsolved, problems of science.

Belmonte says that he fell under spaghetti's spell all on his own. An applied mathematician who specializes in fluids and turbulence (SN: 10/31/98, p. 285: References and sources available at http://www.sciencenews.org/pages/sn_arc98/10_31_98/bob2ref.htm), he started experimenting with spaghetti and other types of rods early last year.

Because he was collaborating with some colleagues who had an interest in fragmentation, says Belmonte, "I was inspired to think about breaking things. I actually spent some time one evening breaking spaghetti in my sink because I had always been puzzled by that small piece which flies out of the center."

Belmonte knew of some fragmentation experiments performed in the early 1990s. The researchers had put glass rods inside sturdy steel cases and then dropped those packages onto concrete floors from varying heights. The tests produced an abundance of large and small shards that the researchers could correlate with the energy imparted by each impact.

Fragmentation studies of that type, which go back decades, have revealed an intriguing feature of impacts and explosions. Their debris typically obeys simple mathematical relationships—called power laws—that account for the distribution of fragment sizes (SN: 2/12/05, p. 106: Life on the Scales). Such studies, however, haven't generally been designed to examine what happens during fragmentation, such as what specific forces impinge on various locations in a breaking object.

To uncover those features, Belmonte and his colleagues built a simple apparatus in which they could stand a rod on end and then drop or shoot a metal slug directly onto its top. The team observed the resulting carnage with a high-speed video camera able to record up to 62,000 frames per second.

Among the items that the researchers tested were spaghetti-size rods made of steel, glass, Teflon, and paper, as well as actual pasta—San Giorgio #8 spaghetti and Barilla angel hair.

When smacked on the end by slugs at speeds up to 30 meters per second, all the rods initially responded similarly. First, like a walking cane turning into a snake, the rod would buckle at regular intervals along its length, growing wavy. As the slug pushed in a little farther, the brittle rods, such as those of glass or pasta, suddenly shattered. However, the ductile materials, such as steel and Teflon, just became more sinuous.

In one analysis, Belmonte and his coworkers measured thousands of fragments of spaghetti and angel hair from separate experiments, then tallied the fragments of each particular length. They found that two sizes were by far the most abundant—one approximately equal to the distance from a peak to a valley of the wavy buckling pattern that preceded the breakup, and another that was roughly half that long.

From the longer fragments and from the videos, the scientists concluded that fractures occurred nearly simultaneously at every location where the rods had become intensely curved—that is, roughly, at each peak and valley of those undulations. The shorter dominant fragments had snapped from the ends of the rods and represented half of the peak-valley distance.

Belmonte and his colleagues reported their findings in the Jan. 28 Physical Review Letters.

It's rare to find any size that dominates the debris of fragmentation events, says Hans J. Herrmann of the University of Stuttgart in Germany, who has studied disintegrations of eggshells and hollow glass spheres. Indeed, the absence of a predominant trait is typical of phenomena that obey power laws, he notes.

The spaghetti findings probably don't actually contradict power-law models, Belmonte says. He expects that the results represent a low-energy breakage pattern that would change into a power-law pattern were the researchers to crank up the speed of the metal slugs.

The team had refrained from higher-energy experiments because of worries about flying projectiles. "We're just in a math department," Belmonte notes. "It was getting a little dangerous."

Snappy answer

For Neukirch and his University of Paris colleague Basile Audoly, the spectacle of Belmonte's buckling pasta rods brought to mind the puzzle that de Gennes had discussed long ago. "To our great surprise, the question of why bent spaghetti breaks into many pieces was still unsolved," Neukirch recalls. That's because in the kitchen, people don't break spaghetti by pushing in on the ends.

So, Neukirch and Audoly set out to rigorously test kitchen-style spaghetti breakage. Rather than bending a spaghetti rod until it broke, they reasoned they could simply pretend that their bent spaghetti rod was the remainder of a hypothetical longer strand that had just snapped and hadn't yet straightened out.

To achieve that, they clamped one end of a rod in place and then bent the rod short of causing breakage. Then, by letting the unclamped end go, much as if releasing a catapult, they duplicated what would happen if a hypothetical strand had broken and its still-clamped portion were then free to unbend. In that manner, they could observe any further breakage of the rebounding rod.

In their setup, which they dubbed "the equivalent catapult experiment," the researchers recorded the action with a digital camera that took 1,000 images per second. Those images, along with computer simulations, showed that a released spaghetti rod behaves in surprising ways.

It doesn't act as a diving board would, springing back to its resting position and then cycling up and down with diminishing amplitude. Instead, each rod's sudden release triggered ripples that whipped along its length and bounced back from the clamped end, locally increasing the rod's curvature. At some locations where the crests of the initial waves and crests reflected momentarily added together, the curvature tripled from what it had been before the rod was released, the scientists calculate.

It's all too much for the spaghetti, which spontaneously snaps where the curvature is greatest, Audoly says. What's more, the process repeats itself in the remaining stretch of spaghetti each time a fracture occurs.

Consequently, each freshly severed remnant undergoes its own burst of ripples, causing further breaks. The process is a cascade that yields many fragments, Audoly says. He and Neukirch describe this process in the Aug. 26 Physical Review Letters.

The physicists are surprised by their result. "You would expect that by releasing stresses on a material, you would make it less likely to break," Neukirch says.

Thomas A. Witten of the University of Chicago says that the buildup of curvature observed in the spaghetti is a previously unrecognized way to focus energy. "New mechanisms of energy concentration are of great value," he says. Like cracking a whip, it puts the energy at a specific location.

Noodling along

Audoly and Neukirch's revelations do seem to finally answer the long-standing question of why spaghetti breaks the way it does. "The combination of theory and experiment makes for a very elegant story," comments Howard A. Stone of Harvard University.

However, the Parisians' study also raises a new question. If the pasta-fragmentation process does follow the described cascade, why does a laboratory chef typically generate only no more than 10 pasta shards?

"We explain that it should break into many, many pieces," Audoly says. "What we really miss is how it stops."

He and Neukirch plan to look into not only that still-hidden part of the process but also at other aspects of spaghetti breaking. For instance, the researchers can't yet predict exactly where a spaghetti rod rattled by waves will break. In some cases, fractures probably occur where peaks of extra curvature coincide with weaknesses of the rod, perhaps caused by small, preexisting cracks or voids.

The mechanisms of fragmentation uncovered by the pasta investigations "are both astonishing and are examples of how everyday effects still contain a lot of novel physics," Herrmann says.

Such fragmentation mechanisms probably also have relevance outside the kitchen, says Ramesh. For instance, the spaghetti findings may illuminate failures of brittle structures such as cutting bits for machining high-strength alloys and strong, light, ceramic blades found in some engine turbochargers.

Whether or not such implications hold up under further study, one thing's for certain: Even everyday phenomena have secrets worth cracking.


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