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.Another interesting fact I didn't know was that some of the footage of the bridge was filmed at a slower speed, making the oscillations of the bridge appear to be faster than they really were. The whole article is worth reading, especially if you are an engineering nerd.
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.
"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."...
The bridge responded to each twist with a slightly larger twist, buffeted by the wind and by new, larger vortices shedding off its edges, all of which were 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.
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.
Thursday, December 17, 2015
The Legend of Galloping Gertie
Alex Pasternack has a fascinating story at Motherboard about how the explanation of resonance causing the collapse of the Tacoma Narrows bridge isn't accurate. And there are a ton of cool videos and GIFs: