At 10 a.m. on the morning of November 7, 1940, Professor F. Bert Farquharson was one of the few people standing on the world's third longest bridge as it bounced and twisted, and he probably knew better than anyone else how she behaved in a gale. But this. "We knew from the night of the day the bridge opened that something was wrong," he said later. Now something was very wrong and with each wave of steel and concrete, it seemed to be getting wronger.
And somewhere out on the twisting span—you can see it in that dream-like Kodachrome footage—a car was sliding across the deck, with Tubby trapped inside.
From afar, the Tacoma Narrows Bridge looked like a long ribbon stretching across Washington's Puget Sound, and on windy days, it acted a lot like one too. Even before it opened to the public, four months earlier in July 1940, the center span, suspended from two massive towers, had a tendency to dance. In a light wind, slow rolling waves would ripple across the concrete and steel deck--with only minor damage, it seemed--sometimes raising and dropping it by as much as ten feet.
Engineers sought a way to stop her swaying, and somebody came up with the nickname “Galloping Gertie,” after a popular saloon piano song, and it stuck. The bridge, officials assured the public, was safe, and within months it became a central part of the local economic and military interests, cutting the 2 and-a-half-hour drive between Tacoma, Washington and the Kitsap Peninusla down to 11 minutes, and connecting Seattle and Tacoma with the Puget Sound Naval Yard.fl
For some courageous motorists and pedestrians, crossing Gertie as she rolled like a coaster was a cheap thrill (the toll was $.75 for cars and just a dime for pedestrians). Her lightweight steel girders and thin layer of concrete permitted a certain unusual flexibility. But no one was quite sure why she flexed in the wind, or what that might lead to.
The Tacoma Narrows Bridge conneted Tacoma, Washington and the Kitsap Peninusla. Via Wikipedia
Enter Farquharson. The 45-year-old engineering professor at the University of Washington was one of the region's most respected authorities on the nature of bridges when he was hired by the state that summer. His job was to find a way to tame Gertie before it was too late. Just days earlier, in fact, he thought he had found a solution.
But at 10 a.m. on November 7, none of that mattered. For about an hour, Gertie had been undulating higher than usual, as the winds reached speeds of 40 mph. This was faster wind than Gertie was used to, but a speed that, her engineers thought, she had been designed for.
And now, for the first time, she wasn't undulating. She was twisting. “It had never done that before,” Farquharson said, according to a history by the Washington State Department of Transportation.
"My knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb."
Half an hour earlier, at around 9:30 a.m., authorities had closed the bridge to traffic, just as one last car was making the crossing. Leonard Coatsworth, news editor for the Tacoma News Tribune, was on his way to his family's summer cottage on the peninsula, with Tubby, his daughter's Cocker Spaniel, in the backseat.
He quickly realized, Gertie's bounce was much bigger than usual. Just past the midpoint, the undulations sent his car toppling over sideways. He climbed out through the window and immediately hit the concrete face first.
"I didn't think of the dog when I first jumped out of the car," he recounted afterwards. "When I did remember and started back, the bridge was bouncing so violently and breaking up so rapidly it was impossible to reach the animal."
"On hands and knees most of the time, I crawled 500 yards or more to the towers," he said. "My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb."
The Elliott footage
It was right around 10 a.m. when Gertie's movement suddenly changed from the vigorous rolling motion to the bizzare new twisting motion. As hundreds of spectators and motorists gathered along both shores amid the howl of wind and screech of steel, Barney Elliott and Harbine Monroe, two owners of a nearby film company, arrived with their brand new Bell & Howell 16mm cameras and several packets of new Kodachrome color film, and began shooting. Monroe stood on a nearby bluff; Elliott was standing on the bridge itself next to Farquharson.
The twisting caused the steel coverings where the cables entered the anchorage to shift, producing a metallic shrieking wail. A workman repeatedly tooted his whistle to try to warn an approaching Coast Guard cutter, Atlanta, which passed under the bridge. "The shrill whistle blasts mixed with the howl of gusting winds and the grinding and screeching of metal and concrete," wrote a historian for the Washington Dept. of Transportation. "The wild noises gave onlookers a sense of dread and impending calamity."
At around 10:30 A.M., a small center span floor panel dropped into the water 195 feet below. By now, Farquharson later estimated, each side of the bridge was tilting by 28 feet on each side and reaching an angle of 30 degrees.
And Tubby was still out on the twisting span. During a lull in the wind, another news photographer, Howard Clifford, decided he would try to save the dog. But he didn't make it past the East Tower, and he scrambled back.
And so, a few minutes before 11, after nearly an hour of twisting, Farquharson—confident enough that the bridge would hold—decided to make his own attempt.
He ran as close to the center line as he could, where the motion was lowest. At the car, he reached for Tubby, but the frightened dog, he said, snapped at him. Amid the wailing and screeching of the bridge, he abandoned his attempt and rushed back to safety, still wearing his tie and trenchcoat and carrying his stopwatch and pipe.
"At least six lamp posts were snapped off while I watched," Farquharson said. "A few minutes later, I saw a side girder bulge out. “I thought she would be able to fight it out. But, that wasn't to be."
At around 11, the giant steel cables snapped with a sound like gun shots, flying up into the air "like fishing lines," Farquharson said. Amid a growing cacophony of steel and concrete, he, Elliott and Clifford began to run to safety. Two minutes later, the cracking and wailing of the bridge grew into a yawning rumble, and a mechanical thunder roared. A central, 600-foot section of roadway had broken loose and cascaded nearly 200 feet into the water. A mighty geyser of foam and spray shot over 100 feet high mixing with clouds of concrete dust and sparks from shorting electrical cables, and the sudden release of concrete sent a giant wave rippling across the remainder of the span.
"I saw the suspenders snap off and a whole section caved in," Farquharson said. As he ran from the east tower toward the toll plaza, the bridge rippled up and down in an immense wave that within seconds left Farquharson some 30 feet lower than where he had just been. "The bridge dropped from under me."
"It was bouncing," Clifford told an interviewer in a 2007 documentary, "so I would be going down, [and the deck] was coming back up. It hit me every time and knocked me down." In Elliot's footage from the toll plaza, Clifford can be seen climbing up the roadway to safety and turning back to look for Farquharson, who suddenly appears over the horizon, clutching his cameras.
Over the next eight minutes, people looked on in confusion and horror as the entire center span cracked apart into the waves. “It seemed as though the world was falling apart,” a reporter wrote. Amazingly, while three cars were lost to the collapse, all of their occupants escaped—except Tubby.
One of history’s most well-known bridges—and its spectacular collapse, 75 years ago this year—doesn't actually mean what we tend to think it means.
All that remained were two giant towers, a mess of cables, and a conundrum: why did Gertie gallop—and why did she gallop herself to death? "I'm completely at a loss to explain the collapse," the bridge's lead engineer told the Associated Press that night.
An article two days later in the New York Times, titled "A Great Bridge Falls," seemed to offer an explanation: “Time successive taps correctly and soon the pendulum swings with its maximum amplitude. So with this bridge. What physicists call resonance was established.”
But understanding Gertie would prove trickier than the Times suggested. So tricky, that four decades after the central questions were answered—by Farquharson and his successors—the common explanation taught in physics classrooms, resonance, is inaccurate. So tricky that it was only recently that anyone seemed to notice that some of the eerie, unforgettable footage of the collapse, shown by generations of physics teachers, is also misleading.
Footage of Gertie bouncing vertically, prior to Nov. 7, 1940, and, beginning around :30, footage of it twisting on the day it collapsed
Bridge building has been bedeviling humans for a long time, probably since the 1st century. That may explain why, even when they can't carry lots of people or things, bridges are particularly good at carrying lots of meaning: breaking, burning, going too far, going nowhere; the bridges between cultures, across generations, the ones we’ll cross when we come to them. To this day, however, the meanings of Gertie's collapse and that unforgettable footage—"among the most dramatic and widely known images in science and engineering," wrote one engineer—remain murky.
For physics teachers, the footage of Gertie has proved irresistible as a lesson in wave motion—and, specifically, a textbook example of the power of forced resonance. The image of the undulating bridge left its mark on scores of students (including me) as a demonstration of what one canonical version of the film calls “resonance vibrations." Scores of books and articles, from Encyclopedia Britannica to a Harvard course website, have reported that the Tacoma Narrows was destroyed by resonance.
But it turns out that's not quite right. And yet, while science has known that for years, lots of people apparently didn't get the memo.
The bridge as captured in Monroe’s footage (sped up here)
I realized I had it wrong thanks to a story in November in the Seattle Times that cited a study about the footage of the bridge, published on the recent 75th anniversary of collapse. As the Times article about the collapse noted, resonance occurs when the frequency of an external force matches one of the natural frequencies of a structure that is being excited. A wine glass that is vibrated at its own frequency by the sound waves of an opera singer’s voice, for instance, will absorb more energy than usual until, eventually, it vibrates into pieces.
Due to a series of confusions and misrememberings, this phenomenon became the prevailing explanation for Gertie's failure. While the winds that day over Puget Sound did cause the bridge to oscillate initially, they were not blowing at a frequency equal to that of the bridge (which, by the way, was about 1 Hz). In fact, they were blowing the way winds normally blow—erratically, and at a fairly constant rate (about 40 mph in this case).
After decades of research, physicists have congregated around a more specific explanation, one that's much more nuanced than the resonance theory. That morning, as it had done for months, the bridge undulated in the wind, thanks to a set of aerodynamic forces that moved across the deck in a periodic oscillation—but not at a resonant frequency. At around 10 a.m., this higher-than-usual wave motion led to the snapping of a cable, which caused the bridge to become lopsided and twist out of control. This was the crucial turning point, and when a new set of forces began working on Gertie—her own.
The bridge's downfall was her own peculiar response to the wind, in a phenomenon known as self-excitation, aeroelastic instability, or flutter. In other words, while Gertie was affected by vibrations caused by the wind, those vibrations didn't reach a resonant frequency. Rather, as the wind vibrated her deck both vertically and in a twisting motion, her own response to that movement brought herself down.
The mystery of her collapse “is not a mystery,” Bernard Feldman, a physics professor at the University of Missouri, wrote in 2006. “The real mystery is why the physics community has not taught the correct explanation for all the years since 1950.” He added however, with some optimism: “My experience is that excitement and interest in physics and engineering is generated not only by what is understood but also by what is not.”
An Elegant But Flawed Design
On the day of her opening, on June 1, 1940, Gertie was the third longest suspension bridge in the world in terms of main span length (2,800 feet), behind the Golden Gate and the George Washington. At a remarkably low cost of $6.4 million, the nineteen-month construction effort had pioneered new bridge-building approaches, with an emphasis on elegance and cost efficiency.
Opening day of the Tacoma Narrows Bridge, Tacoma, Washington. Via Flickr/ University of Washington Libraries Digital Collections
After an initial review of the budget in 1938, the bridge authority had insisted upon replacing the bridge's original engineer, Clark Eldridge, with Leon Moisseiff, the noted New York bridge engineer who had served as designer and consultant engineer for the Golden Gate and who had become known for his work on nearly every major suspension bridge in the country.
Moisseiff's coup de grace was to substitute Eldridge's original 25-foot deep, open stiffening truss with an eight foot, shallow plate grid. A new aerodynamic principle from Austria known as "deflection theory" had made this approach possible—in theory. It held that the aerodynamic forces on the bridge only push it sideways, not up and down, obviating the need, Moisseiff thought, for a stiffer structure. Some engineers at the Washington State Highway Department however protested the change in design, calling it "fundamentally unsound... in the interests of economy and cheapness."
But there were other, non-engineering arguments in favor of Moisseiff's design. The amount of steel needed would be hundreds of tons less than required by previous practices, which would mean great cost savings. (Moisseiff's proposal was priced at under $6 million, almost half of Eldridge's $11 million approach.) And Gertie's long, slender ribbon of a deck met with a modernist shift at the time, away from the sturdy clunkiness of John Roebling's Brooklyn Bridge and toward the Art Deco ideals of lightness, grace and elegance. Bridges need to be "safe, convenient, economical in cost and maintenance," , Moisseiff wrote, "and at the same time satisfy the sense of beauty of the average man of our time."
Tacoma Narrows Bridge Toll Booth. Image: Washington State DOT
To be fair to Moisseiff and his engineers, the phenomenon of aerodynamic instability wasn't well understood at the time. But it wasn't completely unknown either. The last collapse of a suspension bridge due to its reaction to the wind occurred five decades earlier, when the Niagara-Clifton Bridge fell in 1889. (The heavyset design of the Brooklyn Bridge, which opened five years earlier, in 1883, was meant to withstand the sorts of forces that had affected suspension bridges in previous decades.)
Just four months after Galloping Gertie collapsed, a professor of civil engineering at Columbia University, J. K. Finch, summarized suspension bridge failures in an article in Engineering News Record. "These long-forgotten difficulties with early suspension bridges, clearly show that while to modern engineers, the gyrations of the Tacoma bridge constituted something entirely new and strange, they were not new—they had simply been forgotten."
In its 1941 report on the bridge's behavior and its collapse, a panel of engineers appointed by the Federal Works Administration determined that the cause of the collapse was "random action of turbulent wind." (The panel declined to blame anyone in particular for the bridge's faulty design; Moisseiff would pass away a few years after the collapse, somewhat disgraced, without seeing any more significant work.) It would be another decade before Farquharson could complete landmark wind tunnel tests that offered a richer, more detailed portrait of the physics at play on Gertie.
First, Farquharson pointed to the bridge's unusually large depth-to-width ratio, 1 to 72, and its long, narrow, and shallow stiffening steel girder as cause for its extreme flexibility.
Second, he confirmed that the bridge had been susceptible to instability caused by the wind, and that, in certain cases, this could subsequently cause it to become self-excited and twist apart.
Why Gertie Did The Wave
When wind hits certain non-aerodynamic bodies at a certain speed, these bodies shed eddies of wind along each side. In the wake of each eddy, a small vortex of low pressure forms along the other side of the body. In the GIF below, imagine the wind is blowing from the left, broadside against a long object like a cable, shown here in cross-section:
With each shedding of an eddy along the side of the bridge’s deck, a low pressure vortex followed in its wake on the other side. Because objects will also exhibit a tendency to move toward a low-pressure zone, the deck also came under the influence of the vortices. With each eddy of wind and each subsequent vortex, the bridge came under "lift" and "drag" forces that caused it to bounce up and down.
This sort of oscillation was the result of a phenomenon known as the Karman vortex street effect. You can witness this when, in heavy winds, stoplights strung across streets will oscillate perpendicular to the wind’s direction, and you can hear it sometimes when telephone wires sing in the wind.
You can also see vortex shedding happen in the motion of a sheet of paper when it is dropped to the floor: each sway of the paper represents one vortex being shed.
Caption: In a frame from the film taken by Elliott, you can see a large vortex to the right of the car, outlined by the cement dust from a section of the roadway that was apparently disintegrating. Image via Green, 2004.
When the bridge bounced up and down, as it did for months and earlier in the morning of November 7th, it's thought that the vortex street was causing forced harmonic motion on the bridge. But observations and calculations made by Farquharson about the speed of the wind and the motion of the bridge before it began to twist concluded that as the bridge approached collapse, the vortices were not being shed at the bridge's resonant frequency.
Why Gertie Collapsed
In 1940, after being hired to tame Gertie, Farquharson and his students quickly assembled two scale models of the bridge to test in wind tunnels. Not only did it bounce, but they noticed, in heavier wind speeds, it had an occasional propensity to twist. "We watched it," the professor later told reporters, "and we said that if that sort of motion ever occurred on the real bridge, it would be the end of the bridge."
A few months after it opened, engineers installed dampers, large shock absorbers often used and in bridges and tall buildings, to dissipate the waves,but these wouldn’t prove effective enough at stopping the undulations. At the beginning of November, just five days before Gertie collapsed, Farquharson had submitted a proposal that promised to quell the bounce once and for all: guide the wind around the bridge better by cutting holes along its sides or add deflectors to make the bridge more aerodynamic. The second option was chosen, and preparations were made to install them.
A cartoon from the Seattle Times, November 8, 1940. Via University of Washington Libraries
The wind on November 7, 1940 was possibly the strongest wind the bridge had ever experienced, and it came at a crucial time: the bracing under the deck was likely weakened during a midnight storm several days prior, according to reports at the time.
Just after 10 a.m., as the bridge's undulations reached new heights, causing each side of the bridge’s suspension cables to alternate between taut and slack, one of those cables snapped into two piece of varying lengths. This created an immediate imbalance. Whereas the deck had earlier exhibited an up-and-down “galloping” motion like a roller coaster, now it was lopsided and capable of twisting along its center axis, which it began to do. As it interacted with the wind in this twisting motion—and with gravity, with the cables, and with its two fixed ends—its twisting movement didn’t dampen the effect of the wind as it continued to nudge the bridge: the twisting increased it.
Each time the bridge twisted, that is, it twisted a little bit more, not less, back in the other direction, in a steady buildup of twisting energy that was reinforced by the wind. After an hour or so of this, it finally twisted itself apart.
Gertie's mechanical suicide was the result of feedback—of a structure entering a self-sustaining vibration as it responds to the steady force of the wind, absorbing more energy than it can dissipate in the process. It's also known as aerodynamically-induced self-excitation, or simply, flutter.
I Can't (Not) Believe It's Not Flutter
"You will find it a challenge to explain!" Donald Olson, a physics professor at Texas State University, warned me. He is the co-author or a new study about the collapse and some problems with the footage that captured it (more on that to come). While he said ninety-nine percent of the physicists reading his study will have been teaching the Tacoma Narrows Bridge as resonance, "subsequent authors have rejected the resonance explanation, and their perspective is gradually spreading to the physics community."
According to the most complete recent research, he and his co-authors write, "the failure of the bridge was related to a wind-driven amplification of the torsional oscillation that, unlike a resonance, increases monotonically with increasing wind speed."
Explaining how that happened requires some unpacking (untwisting?). but I don't think it's that hard to understand.
An animation of a suspension bridge undergoing aeroelastic flutter. In the case of Tacoma Narrows, there was a node (no twisting) exactly at the middle of the center span.
The Tacoma Narrows was already undulating under the force of the wind and the resulting vortices it was shedding. When the cables snapped, that rhythmic up and down movement was suddenly torsional; the rolling motion transformed into a twisting one.
The span, Farquharson observed, had been vibrating in eight or nine segments with a frequency of 36 vibrations per minute and an amplitude of about 3 feet. Suddenly, it began to twist too, and with such extreme violence that, one observer wrote, "the deck appeared to roll completely over."
Its new torsional vibration came in two segments, with a frequency of 14 vibrations per minute. Eventually, the torsional frequency changed to 12 vibrations per minute, with the amplitude of torsional vibration reaching about 35° in each direction from the horizontal.
The bridge responded to each twist with a slightly larger twist, buffeted by the wind and by new, larger vortices shedding off its edges—vibrating the bridge vertically in addition to torsionally. All of this movement was helping to nudge the bridge just a little bit further each time it twisted.
While the earlier vortices—the von Karman vortex street—may have led to the initial oscillations, the bridge's new movement was self induced, its new vortices the result of flutter wake. (If the vortex street was in effect, the bridge would have shed vortices at about 1 hertz, or one vortex per second, but this is out of synch with the .2 hertz torsional vibrations that Farquarson observed when the bridge was twisting.)
Each time the deck of the bridge twisted now, it sought to return to its original position (inertial forces). And as it did so, twisting back with a matching speed and direction (elastic forces), the wind and the vortices caught it each time, pushing the deck just a little bit more in that direction (aerodynamic forces). With each twist and each twist back, the size of the twisting slightly increased.
This is the critical state: Chart via Wind Effects on Cable-Supported Bridges By You-Lin Xu, 2013.
And as the deck flexed slightly higher and higher in its new twisting motion, it released even greater eddies of wind along its sides, which shed larger vortices, further contributing to the deck's instability. You can see another simulation of this effect in this video:
Three forces—inertial, elastic, and aerodynamic—were now acting on the bridge in coordination. While previously the force of the wind and the vortices led the bridge to "gallop," those forces dampened over time. Now, having been pushed into flutter by its new ability to twist, Gertie was no longer significantly affected by the aerodynamics, but largely under the influence of her own forces, and locked in a downward spiral.
Twisting induced more twisting, then greater and greater twisting, and so on, in a runaway, exponential fashion, until eventually the bridge could no longer dissipate its energy fast enough. The rest of the suspender cables failed, the deck could not hold, and “Galloping Gertie” was loosed upon Puget Sound.
Photographer Howard Clifford running off the Tacoma Narrows Bridge during collapse. Via University of Washington's Tacoma Narrows Bridge Collection
If resonance is a wine glass that's been shattered by an opera singer's voice, self-excitation is more like the screech of a speaker that's too close to its own microphone
The flutter / self-excitation explanation was developed by Robert Scanlan, an engineering professor at Johns Hopkins who co-authored a canonical 1991 paper about the event with K. Yusuf Bilah of Princeton. Their findings were reinforced by the research of Daniel Green and William Unruh of the University of British Columbia in a 2004 paper. But even now, the explanation for how the wind caused the bridge to gallop to begin with remains a topic of discussion. "The detailed method through which the oscillatory behaviour is established," they write, "may require some further details.”
A Positive Feedback Effect (With Negative Effects)
If resonance is a wine glass that's been shattered by an opera singer's voice as it vibrates at the glass' natural frequency, self-excitation or flutter is more like an amp that shrieks when it gets too close to its own microphone. This feedback effect is used all the time to great and weird effect in rock music, but the closer you bring a live microphone to its speaker—the louder the audio that's fed into the system and fed back out and fed back in and so on—the closer you'll come to blowing the speaker (and maybe nearby eardrums). The bridge behaved in a similar way that morning. It was stuck in its own loop of self-interaction, feeding its own energy back into itself until it fell apart.
The effect of flutter can also be heard in instruments with continuous sound. When a violinist draws a bow steadily across a violin string, the energy of her muscles and the bow feeds the violin string. The frequency of the string’s vibration is affected by its own mass, length, and tension, as well as by the back-and-forth vibration with the bow; the key point is that as the bow moves faster, there is less, not more, friction between it and the violin string, and the oscillations of the string grow exponentially. (Understanding how violins evolved—which is to say, how humans understood the physical principles at work on a violin—is the subject of a recent research project at MIT funded by the U.S. Navy.)
Aerospace engineers use wind tunnels to test the effect of flutter on a wing in slow-motion footage from NASA.
On an airplane wing, self-excitation can occur when the wind causes the rhythm of two structural motions—bending and twisting—to become coupled in such a way that they reinforce each other. Pilots refer to the resulting hum as “buzz,” and it's less annoying than scary: A wing in full flutter will break apart. While aerospace engineers have spent decades designing balancers and dampers and other systems to prevent flutter, and all certified aircraft must be tested for it. But the problem persists, especially in prototype and homemade aircraft.
At an air show in 1997, a loose elevon at the trailing edge of the wing of a U.S. Air Force F-117 fighter jet began vibrating, causing a flutter excitation across the rest of the wing and the rest of the stealthy aircraft, until the vibrations broke the plane apart.
An F-117 fighter breaks apart during an air show. The cause, it was later determined, was flutter
Flutter on airplane wings is significantly different than flutter on bridges, however, aerodynamically speaking. Wings experience much greater air speeds than bridges do, and their flutter behavior arises from the response of the wing to the aerodynamic forces affecting it. In the case of bridges like Gertie, which experience relatively slower wind speeds and slower vortex wakes, aerodynamic forces are not a driving factor for bridge flutter. While these forces can nudge the bridge—making it even harder for it to dampen its vibrations—these aerodynamic forces pale in comparison with the forces of the bridge as it bends and twists. The flutter effect on Gertie that led to catastrophe lasted for about 45 minutes; a wing can shake itself apart in seconds.
But just as feedback can be useful in music, flutter isn't always destructive. Inventor Shawn Frayne has attempted to exploit it for energy. His Windbelt, which debuted in 2007, uses the principles of flutter and negative damping to generate electricity in high wind. The key component is a taut membrane designed to flutter. "That oscillation moves a set of permanent magnets that are on the membrane itself at one of the ends," Frayne told Physics.org, and the motion of these magnets between two copper coils induces an electrical current.
When resonance attacks (and doesn't)
Whereas a quantitative definition of resonance involves an external energy source causing the vibration, flutter, by contrast, is considered a kind of instability in the structure itself, a flaw resulting from the free response of the structure when exposed to air flow. “Aeroelastic flutter is not specifically a resonance because the input is not a periodic force, rather the input is uniform relative velocity of air and some object,” explains Mark Barton, a physicist at the National Astronomical Observatory of Japan, at Quora.
Nevertheless, resonance is no small concern for people who build bridges and buildings and airplanes and anything that shakes. When an opera singer's voice meets a pane of glass at its natural frequency, we not only hear the effects of this resonant vibration, but ultimately see them: the glass shatters.
Play a tone that matches the natural frequency of a wine glass loud enough, and the glass will shatter. GIF via Youtube / Marty33
The glass is exhibiting a tendency common to any moving system: it absorbs the energy of the singer’s oscillating voice. This is known as forced harmonic oscillation. But when the frequency of those oscillations match the glass’ natural frequency of vibration—its resonant frequency—it absorbs dramatically more energy than usual. When it can't absorb any more, it collapses.
On certain bridges, oscillations can be caused by the periodic force of people moving across it. In April 1850, a battalion of French soldiers was crossing the Angers Bridge when it collapsed, killing over 200 of them. The culprit, it was theorized, was the lockstep march of the soldiers, creating enough of a periodic force to match that of the bridge. Since then, it has been standard practice for soldiers to break step when crossing bridges.
On opening day in 2000, London’s Millennium Bridge felt the resonant effects of pedestrians swaying in time to its own sway
Something similar happened on June 12, 2000, the opening day of London’s Millennium Bridge. As a mass of pedestrians crossed the short steel suspension span, they created a different kind of oscillation: not up and down but sideways. According to a study by Steven Strogatz, a mathematics professor at Cornell University, the bridge was moving in lockstep with the slight lateral motion of all the people crossing the bridge who were themselves inadvertently swaying as they walked. As the bridge began to sway ever so slightly in one direction due to winds, the pedestrians naturally leaned slightly in the other direction to keep their balance, and, not unlike soldiers moving in lockstep, they did this at exactly the same time. Eventually their swaying reinforced the movement of the bridge as it swayed. Officials quickly ordered the bridge closed, which is how it stayed for two years, until stabilizers and dampers could be added, at a cost of £5M. Still, the nickname “The Wobbly Bridge” stuck.
On May 21, 2010, home video captured the nearly 3 km-long Volgograd Bridge oscillating over Russia's Volga River. The authorities closed the bridge and later that year installed tuned mass dampers to prevent future oscillations. Shortly afterward, officials speculated that strong river currents caused by melting snow upstream had loosened one of the bridge's vertical supports. The most likely culprit, physicists suspect, were the sort of aeroelastic forces that had caused Gertie to gallop—but not collapse—in a gale.
To avoid so-called “resonance disasters,” engineers of machines with engines must ensure that the frequencies of the component parts do not match each other. Like bridges, buildings and trains and other large spans use shock mounts to absorb resonant frequencies and dissipate the absorbed energy. At buildings like Taipei 101, which is located on an active seismic zone, a 660-ton pendulum—a tuned mass damper—is designed to absorb the effects of resonant frequencies.
In 2011, a 39-story building in Seoul had to be evacuated after vertical tremors began shaking it violently for about ten minutes. At first this puzzled engineers. “Eliminating earthquake and windstorms,” wrote Motherboard’s Kurt Poropatich, “the culprit they landed on was bizarre to say the least: an aerobics class of 23 people on a mid-level floor. Their Tae Bo workout was apparently twice as intense that day, making their fancy footwork synch up with the building’s structural resonance.”
In describing other examples of resonance, the Motherboard article regurgitated the fallacy that Galloping Gertie was wrecked by resonant frequencies. A correction has been issued. But there are possibly thousands of other un-corrected articles and books, including in some from very large and seemingly reputable sources, including Encylopedia Britannica and the Harvard math department.
But even in the years following the collapse, the Federal Works Agency Commission report of the ensuing investigation found that it is
very improbable that the resonance with alternating vortices plays an important role in the oscillations of suspension bridges. It was found that there is no sharp correlation between wind velocity and oscillation frequency such as is required in case of resonance with vortices whose frequency depends on the wind velocity.
At a glance of the edited footage, it's tempting to think that Gertie was brought down by resonance, given the vivid visual evidence of a bridge that undulates before it collapses, not unlike the wine glass that shatters under the vibrations of a singer's voice. In fact, resonance is a similar phenomenon to flutter, to the extent that it involves the "reinforcement" of existing oscillations and can lead to a dramatic and possibly destructive amplification of energy.
Bilah and Scanlan write that the phenomenon acting on the bridge "would appear not to contradict the qualitative definition of resonance... if we now identify the source of the periodic impulses as self-induced [rather than external], the wind supplying the power, and the motion supplying the power-tapping mechanism." The key term there is self-induced. That is not how forced resonance is typically described (the matching of an external force's oscillations with that of another object), or what is implied when people blame only the force of the wind for the bridge's collapse.
But the resonance explanation has persisted, thanks to repeated mistakes by physics teachers and textbook writers and science journalists, and buttressed by the convenience of the video evidence. The bridge's engineers had forgotten many lessons from the early days of suspension bridges. Somehow, the media, teachers, and scientists misremembered the new lessons.
How We Got It Twisted
How did the incorrect explanation persist for so long? In their paper about the event, Bilah and Scanlan cite 30 sources that mention resonance as a cause of the bridge's failure. Ultimately, they point their fingers at a mix of rough, semi-empirical guess work and the "telephone" effect. "The primary reason for all this, we believe, is that many post facto accounts or investigations were speculative or reviews of still other accounts," they write.
It's easy to see why: the math and physics involved can seem complicated. And the unforgettable image—a bridge undergoing large periodic motion as an external force applies energy to it until it collapses—is, to physics teachers and textbook writers, an irresistible scientific example, an eye-popping way to wake up the kids at the back of the classroom.
"While it is understandable how so many textbooks have, over the years, oversimplified the physics involved," wrote Bilah and Scanlan, "it is probably time... to offer the next generation of students subtler, more complex and correct explanations." That was in 1991.
An article in the New York Times on November 9, 1940.
An early assertion that resonance was to blame appeared in that New York Times story two days after the collapse. (Resonance has been named by the Times as a culprit in the Tacoma Narrows collapse three times since that 1940 story.) But strangely, a story published on page 1 the previous day included a more accurate account of the collapse that had nothing to do with resonance. C.E. Andrews, one of the bridge's engineers, pointed to the closed stiffening trusses along the sides of the bridge's deck. The wind hitting them "caused the bridge to flutter, more or less as a leaf does, in the wind. That set up a vibration that built up until the failure occurred."
In mainstream and science media, however, that idea got drowned out by resonance. The textbooks written by David Halliday and Robert Resnick in the early 1960s included photographs of the Tacoma Narrows Bridge in its section on resonance, and concluded that the “wind produced a fluctuating resultant force in resonance with a natural frequency of the structure.” Bilah and Scanlan lay specific blame at the feet of Lee Edson, in his 1963 biography of Harman von Karman, the aerodynamic theoretician for whom the vortex street is named, and who sat on the commission that investigated the bridge collapse. "The culprit in the Tacoma disaster was the Karman vortex Street," Edson wrote, not quite correctly.
The professors speculate that Edson mistook the vortices that induced the earlier rolling motion with the ones that began to form as the bridge twisted higher and higher: "We see the flutter vortex trail as a consequence, not a primary cause."
In this version of the bridge film originally published by Franklin Miller, the first caption erroneously describes its “resonance vibration”
Meanwhile, in a 1998 report to accompany an educational videodisc, the American Association of Physics Teachers points a finger at Franklin Miller, who published and distributed the first and most famous footage of the collapse for use in classrooms around the country. The term “resonance vibration,” notes the AAPT, was “indeed erroneously used in one of the captions in the film first edited in 1962."
Not So Fast
There is a crucial irony in the AAPT's paper. Its authors failed to note that the footage contained in the accompanying DVD is itself erroneous.
While Monroe shot at 24 frames per second, Elliot had switched his camera to run at 16 frames per second, possibly to preserve film. According to a study published last month in Physics Today by Donald Olson and colleagues at Texas State University and East Carolina University, the films were converted to early film reels for classrooms as if they both ran at 24 frames per second. This led to a pair of innocent but crucial conversion errors that have since been immortalized on the AAPT's DVD and on other film reels, videotapes and websites.
The film shot from the shore is roughly accurate, showing the bridge's slow swaying and twisting and eventual collapse. But in many versions, the footage Elliot shot on the bridge makes the movement look about 40 percent faster than it really was. (In the footage, the oscillations of the bridge appear to be about 18 cycles per minute, but Farquharson’s own stopwatch that day measured a torsional frequency of 12 cycles per minute.)
At 2:00 the footage of the bridge appears accelerated
The first conversion mistake happened in the early 1960s, when the film was converted for use by Franklin Miller in a series of physics classroom film loops that played at 18 fps in 8mm projectors. The second error happened in 1982, when three scientists used Miller's loops to produce the AAPT's videodisc, The Puzzle of the Tacoma Narrows Bridge Collapse, which contains Miller's film, additional archival film footage, and interactive material.
Due to the conventions of US and other TV signals at the time, the format operated at 30 fps. "The technicians making the conversion from film to videodisc assumed that all of the 16mm cameras were running at 24fps, and they knew that videodisc players would operate at 30 fps," writes Olson.
The Monroe footage:
The Elliott footage at normal speed:
The Elliott footage at or close to normal speed
The Elliott footage sped up:
The Elliott footage sped up
The Elliott footage sped up even more:
The Elliott footage sped up more
By examining every frame of the videodisc sequences, he and his colleagues observed that the technicians made the leap from 24 to 30 fps by "stretching" every 4 frames into 5 frames through a technique known as telecine, which aims to make the converted video appear natural and at normal speed. They later confirmed this theory with one of the video’s producers. As a result, they write, “viewers of the modern video formats see the torsional oscillations significantly sped up (18 cycles per minute), compared to... the more majestic and lower frequency oscillations (12 cycles per minute) measured by eyewitnesses on Nov. 7, 1940."
The powerful video evidence coincides with a particular tendency of ours, I think: to interpret what we see according to what we expect to see. This phenomenon, sometimes described as “the observer effect,” is so feared by scientists that various methods have been developed to prevent it. And yet it lingers, influencing experiments and everything else.
After the collapse, authorities pledged to rebuild the bridge immediately. But the war effort changed all that: the bridge's side spans were melted down for steel, a valuable commodity for the country's military machine. The remains of its once-undulating deck were left under the waves of Puget Sound, where they now form a giant artificial reef. In 1992, "Galloping Gertie" was placed on the National Register of Historic Places, in part to deter scavengers, and in part to part to memorialize an event that has been misremembered if not forgotten. "As is common in much of human history," notes its registration form, "we often learn more from our failures than from our successes."
In general, for scientists and engineers, Gertie's failure represents progress. And understanding the other failures—how for so long so many failed to accurately describe or depict why she collapsed—yields yet more lessons. "In science, revision is a victory," says Stuart Firestein, professor of biology at Columbia University and author of a new book on that couinterintuitive idea, Failure. "We're always revising."
When you watch the footage, it turns out that what’s really going on is hard to see. And it's made even harder when you're told--perhaps against your own intuition--that resonance was to blame. Vibrations helped break apart the bridge, that's clear. But being vague about how those vibrations originated—or being sloppy about how they are represented on film—can easily lead to inaccuracies and misrepresentations and the loss of important details, however tiny they may be.
But the engineers examining the collapse weren't swayed by how the collapse looked or by what they heard. They eventually tested a scale model of the bridge in a wind tunnel and took measurements; their analysis of bridge flutter would spawn a new field of engineering, bridge aerodynamics-aeroelastics, which has informed the designs of all the world's great long-span bridges built since then, from New York's epic Verrazano Narrows Bridge to today's longest suspension bridge, the Akashi Kaikyō Bridge over Japan's Akashi Strait.
The Tacoma Narrows' replacement, completed in 1950, was a major on advance on its predecessor, with open 33-foot stiffening trusses (compared with Gertie's 8-foot trusses), wind grates and hydraulic shock absorbers (nickname: "Sturdy Gertie.") In 2007, the state opened another suspension bridge right alongside the other to meet increased demand. Today the two bridges are now the 38th longest bridges in the world. (Speaking of engineering concerns, in general, Washington is now emblematic of the U.S. as a whole when it comes to the conditions of its bridges: 26% either require significant repair or can't handle today's traffic, according to the U.S. Department of Transportation, a problem that a new $300 billion highway bill is intended to help fix.)
What it’s like to drive across one of the Tacoma Narrows Bridges today
A year after the collapse, David L. Glenn, the PWA's field engineer, revealed that he had not signed off on the bridge when it was completed in July 1940. He had submitted a report warning of faults in design and refused to recommend acceptance of the structure. But the PWA accepted the bridge, as did the Washington State Toll Bridge Authority. (The PWA fired David Glenn two weeks after the story made headlines.)
The situation that gave rise to the original bridge's risky design echoes patterns that existed prior to the explosion of the Space Shuttle Challenger and the GM ignition switch debacle. Cultures of groupthink discourage dissent, stepping up, speaking out, admitting fault, and making redesigns even when they are essential.
Those institutional problems are all the more scary because the big new things institutions produce often come with flaws that are unexpected and can be hard to fix. You can design for what you know, but you might not design for what you don't. Not just the unknown knowns, to borrow a burdened phrase but the unknown unknowns. Another innovative marvel of gargantuan but lightweight engineering were the Twin Towers. When they were erected in the 1960s, they were built to withstand the brunt of an airplane slamming head-on into their facades, and on the morning of September 11, they did. But they weren't designed to withstand jet-fueled-fires, which were capable of weakening their lightweight steel structures. Starting in 2000, the Port Authority undertook a new fire-proofing of the towers, a process that was ongoing on the morning of September 11.
In other words, there are problems we know how to address, but there are also problems we don't know how to address yet, because we don't know they exist yet. At that point, the best tool we have is probably our imagination.
From the National Register of Historic Places registration form for "Galloping Gertie"
We also have our memory. But as the process of designing the Tacoma Narrows demonstrated, we don't always remember. Henry Petroski, an engineer and scholar of failure, observes that major bridge failures occur roughly every thirty years, which may be the time that it takes for a new generation of engineers to forget the lessons of their predecessors. "The essential lesson of the Tacoma Narrows Bridge," he writes, "is not that it fell but that it fell in an atmosphere of confidence that it would not, in a manner that was not anticipated."
Of course, when we undertake big new things, we also learn, hopefully, to accept a certain amount of risk and uncertainty. Othmar Ammann, another leading bridge designer and member of the Tacoma Narrows investigating commission, wrote that the collapse "has shown [that] every new structure [that] projects into new fields of magnitude involves new problems for the solution of which neither theory nor practical experience furnish an adequate guide. It is then that we must rely largely on judgment and if, as a result, errors, or failures occur, we must accept them as a price for human progress."
Farquharson during wind tunnel tests to determine why Gertie collapsed. Image via University of Washington Archives
Perhaps. Perhaps an inaccurate explanation and distorted evidence is another price we pay for human progress: the progress that comes from getting generations of kids excited about physics. Of course, it didn’t have to be that way: the mistakes surrounding Galloping Gertie’s collapse were understandable but avoidable. This bridge collapse has always been a useful lesson in physics, just not about the concept we thought it was about. It became an ironic symbol for the limits of our understanding. Now the unforgettable, eerie image of the twisting, collapsing bridge stands for not one but many kinds of failures.
Sometimes a bridge means progress and hope, or a challenge to be dealt with when we get to it. If a bridge stands for failure, maybe it’s also a warning for what happens when we don’t prepare for our future crossings in advance. Look at her collapse for what it seemed to be and what it actually was, and Gertie reminds that when we design things we often don’t fully understand how they work or how they’ll be used—or we do, and we manage to forget. She also sneaks in other warnings to us, ones that should resonate among engineers and scientists and writers and everybody really: don’t accept everything you're told and don't believe everything you see.