How Flowers Help Us Understand Why Bridges Collapse

How Flowers Help Us Understand Why Bridges Collapse

The catastrophic collapse of Washington State’s Tacoma Narrows Bridge in 1940 launched intensive research into the aerodynamics of bridge design. Now a team of South Korean scientists have identified a geometric structure that can better withstand the complicated aerodynamic forces at play — and they found their inspiration in the shape of a daffodil stem. Daffodils have a unique structure that reduces drag. Image: Sally J. Bensusen/Visual Science Studio, Used with permission.

When wind flows across a long object, like a daffodil stem, it sheds little eddies of wind along each side, with a small vortex of low pressure forming in the wake. The technical term is “von Karman vortex shedding”. Stick your arm out the window of a moving car and you can feel those oscillating side forces in action. You can also see the effect simply by dropping a sheet of paper to the floor. It will sway back and forth as it falls, and each sway is a vortex being shed.

Physicists from Seoul National University and Ajou University in South Korea noticed that daffodil stems have a twisting cross-section shaped a bit like a lemon. Somehow this unique structure enabled the flower to turn away from strong winds, to better protect its petals. Using computer simulations of similar geometric structures, the scientists found that the daffodil shape stopped the vortex shedding, eliminating those nasty side-force fluctuations. This, in turn, reduced overall drag by as much as 23 per cent, compared to a round cylinder. They described their work in a recent paper in Physics of Fluids.

Vortex shedding played a key role in the collapse of the Tacoma Narrows. Perhaps you heard that it had to do with a phenomenon known as forced resonance: The wind matched the bridge’s natural resonant frequency, gaining energy with every undulation until it broke apart. That’s the explanation I heard long ago, too, but scientists have since learned otherwise. (Even the press release for this new paper repeated the myth.)

The vortex shedding is what caused the bridge to “gallop”, undulating up and down in response to high winds — hence its nickname, “Galloping Gertie”. And it’s true the winds were stronger that day in November, and hence the undulations were that much higher. But neither wind nor undulations ever approached the natural resonant frequency of the bridge, according to Frederick Burt Farquharson, an engineer at the University of Washington who was part of the investigation into the collapse.

However, those undulations eventually did cause one of the suspension cables to snap, creating an imbalance. The now-lopsided bridge began to twist along its centre axis, as well as undulate, emitting a shrieking metallic wail in the process. It was this new movement that proved to be its undoing. The real culprit was something called aerodynamically induced self-excitation, or “flutter”. It’s a self-sustaining vibrational feedback loop, in essence.

While forced resonance is best exemplified by an opera singer shattering a wine glass with her voice, Motherboard’s Alex Pasternack likened flutter to an amp that shrieks whenever it gets too close to the microphone. (For anyone interested in all the gory engineering details, Pasternack’s lengthy examination is a must-read.) That kind of feedback can be cool when used in moderation by rock musicians, but let the feedback build up too much, and eventually you’ll blow out your speakers.

That’s essentially what happened to the Tacoma Narrows Bridge: Each time the bridge twisted along its centre axis, it increased the effect of the wind instead of dampening it, with ever-larger vortices shedding off its edges. The feedback kept building and building in energy, until ultimately Galloping Gertie twisted itself apart.

This doesn’t detract from the Korean scientists’ paper’s main takeaway: that you can eliminate vortex shedding and significantly reduce drag by employing a twisty, helical shape when designing an object.

The daffodil’s unusual geometry isn’t especially well-suited for bridge design, and hence would not have saved Galloping Gertie. But co-author Haecheon Choi said he and his colleagues already have a patent for a daffodil-inspired golf club. Similar principles could also be applied to things like antennae, lampposts, chimneys and skyscrapers — all of which could benefit from better aerodynamical design.

[Physics of Fluids]