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Why Theories Fall Down

Winter 1993 | Volume 8 |  Issue 3

NEW YORK, N.Y. : Why did the Tacoma Narrows Bridge collapse? The famous fiasco is a staple of introductory physics classes. Few students can forget seeing the grainy black-and-white film of the 1940 incident: the bridge ripples gently at first, then starts heaving and twisting with fearsome amplitude until finally, shockingly, it breaks apart.


Classroom demonstrations in physics tend to be dull, generally involving nothing more exciting than a top or a pendulum. Certainly there is little to rival the chemistry teacher’s arsenal of explosions and fancy colors, or the biologist’s gross-out potential. The Tacoma Narrows Bridge is a rare opportunity for physics teachers to steal the spotlight. The only problem is that exciting as the incident is, no one is quite sure what it illustrates.

One thing today’s scholars agree on is that the explanation most students get is wrong. Every object has a set of resonant frequencies, it is said; in the case of the unfortunate bridge, the wind was blowing at just the right speed to excite one of them. The oscillations kept getting stronger until the bridge’s structure could no longer handle the strain, and it collapsed.

This forced-resonator explanation has always seemed a little fishy. Could the wind possibly have been blowing at exactly the right speed the whole time? And besides, there were two different types of oscillation: an up-and-down, roller-coaster motion and a torsional, out-of-horizontal twisting. Wouldn’t that require two different winds?

With questions like these in mind, researchers are coming up with evermore-complicated explanations of why the bridge fell down. A recent paper in the SIAM Review by a pair of applied mathematicians, A. C. Lazer of the University of Miami and P. J. McKenna of the University of Connecticut, points out one problem with the traditional view: it assumes that cable stays, the vertical cords on which the roadbed hangs, act like springs. Yet clearly they do not. Springs work in both directions; if you compress them they push, and if you expand them they pull. Cable stays, on the other hand, resist expansion just like springs, but can be compressed with little or no resistance; they simply bend. (Other scientists have contested this point.)

Lazer and McKenna use this nonlinearity to derive a set of gnarly differential equations that remind your correspondent why he ended up in publishing. After suitable assumptions and simplifications they stick the equations into a computer, and though they stress that their research is still very much in progress, they do manage to come up with periodic solutions that resemble fairly closely what actually happened.

K. Yusuf Billah of Princeton University and Robert H. Scanlan of Johns Hopkins, in a paper in the American Journal of Physics , approach the matter from a different perspective—that of fluid dynamics. Their target is the notion that oscillations were caused by wind currents that formed a series of vortices along the length of the bridge. Actual wind conditions were way off for that, they say; the bridge’s oscillation caused whatever vortices there were, instead of vice versa.

In place of resonance Billah and Scanlan blame a similar but distinct phenomenon called self-excitation. At low amplitudes the bridge damped oscillations; when it twisted or bent out of shape, structural forces pushed it back in line. At certain higher amplitudes, however, the damping coefficient changed sign and the bridge actually reinforced oscillations. The effect is much the same as forced resonance, but the equations giving rise to it are quite different.

Billah and Scanlan do not claim to have just discovered this phenomenon; their work is based on wind-tunnel tests and calculations by various researchers going back to the early 1950s. The truth has been available for quite some time, they say; in fact, not even the official report on the disaster blamed wind vortices. But simple explanations always have enormous appeal, and it is no surprise that the somewhat complicated truth has remained obscure.

Neither paper explains exactly how the particular wind conditions in effect at the time caused oscillations; rather, they explain how those oscillations were able to propagate once they’d been started. It’s clear that the full story, if it is ever discovered, will be far beyond the understanding of most students of elementary physics. Meanwhile, the disagreement between Lazer/McKenna and Billah/Scanlan has turned into the sort of genteel professorial catfight that the popular press loves. Yet sentimentalists need not fear that the Tacoma Narrows Bridge, having already collapsed once, will now suffer a second demise, this time as a teaching tool. Jettison the simplistic physical explanations, and it still remains a useful reminder of several important points.

It took only an hour for the Tacoma Narrows Bridge to collapse. For the next fifty years scientists have been trying to explain why it did.

First, it demonstrates the ever-present role of failure in engineering, a valuable lesson for all students. Second, it illustrates the interplay between technology and “pure” science; bridge builders have made great strides since 1940 in preventing wind-induced oscillations, while mathematicians and physicists are still trying to figure out what happened. And finally, it emphasizes the importance of making use of experience and taking every contingency into account.

As Eugene S. Ferguson writes elsewhere in this issue, computers and high-powered analytical tools are an enormous boon to engineers, but they can be relied on too heavily. The image of a suddenly flimsy-looking bridge swaying, twisting, and then flying apart should serve to remind students that the power of nature must always be respected, and that a theory, no matter how learned and detailed, must always be accompanied by a healthy measure of practice.

BUFFALO, N.Y. : The Society for Industrial Archeology (SIA) met last June in Buffalo, a city whose history encapsulates the development of America’s industry. Buffalo got its first big boost in 1825, with the completion of the Erie Canal. Railroads eventually took much of the canal’s traffic, but in the 1890s Buffalo’s location near Niagara Falls, with its cheap hydroelectricity, attracted a whole new set of industries. Today many of them have moved away, and Buffalo is facing yet another transformation. The SIA convention dwelt mostly on the past, but the city’s (and the nation’s) difficult present and uncertain future were inescapable.

The convention’s first day was devoted to “process tours"—visits to local industrial sites. One led by Tom Leary, chairman of the local chapter of SIA, amounted to (in his words) “a long, funereal procession through what’s left of Bethlehem Steel.” Gloom did indeed prevail during the first part of the bus trip, which was mostly spent listening to Mr. Leary point out derelict grain elevators along the way. As the bus passed one old building with a nice stone facade, he said of its current owners, “They’re letting it deteriorate to the point where they hope the city will give them a demolition permit as a hazard.”

The bus pulled into a large rubblestrewn site in nearby Lackawanna that was dotted with anonymous dilapidated buildings. As the group waited for its escort from Bethlehem to arrive, members tossed around statistics from the old days. “There used to be five trains daily from Cleveland direct to this site,” one said, staring at an ancient set of tracks now overgrown with weeds.

“Twenty thousand people worked here once,” said another, gesturing toward the emptiness. “You’d come out here during a shift change… .” He looked out over the vast space, now populated by a few lonely security guards and a couple of men driving pickup trucks, and let out a sigh.

But the gloom lifted when Joseph Murphy, supervisor of BethEnergy’s very much active coke division, boarded the bus. Murphy, a local product, told of his long association with Bethlehem, how the company had paid his college tuition and hired him right after graduation. “My relatives almost exclusively worked here,” he said, and as he discussed the history of coke production, his love for the old Buffalo and what remains of it today was palpable.

Coke is the residue left after heating bituminous coal to drive off the volatile matter. It is nearly pure carbon, which makes it ideal for reducing iron ore. A coke oven looks like a gigantic hundred-slice toaster, a bank of slots eighteen inches wide by about twenty feet tall and deep. Loose coal is poured in the top and baked until it has become a single red-hot block. Watching a specially designed car the size of a house roll up and push the glowing slab out a side door, it was easy to see why people can be so zealous about the grandeur of heavy industry.

As the bus crawled through the coke plant, it seemed that every piece of equipment Murphy mentioned had been the first, or the biggest, of its kind in the country. (The scale on which the division operates is shown by a set of recycling vessels for used oil, each about twenty feet tall, which Murphy offhandedly referred to as “the little tanks.”) When Murphy ticked off a list of the various forces that make his job interesting—OSHA, EPA, the Clean Air Act, the U.S.-Canada freetrade agreement, Australia, Japan, and now even Eastern Europe—his dauntless enthusiasm about the future was a welcome antidote to the melancholy past-tense narration that had prevailed through most of the tour.

Buffalo’s past geographical advantages don’t count for as much in today’s economy. Now the city’s strength lies in committed residents like Joseph Murphy and the members of SIA. Despite all the shut-down plants and the talk of what used to be, it’s hard to avoid feeling that Buffalo’s future is nonetheless in good hands.

We hope you enjoyed this essay.

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