A bouncy foot bridge is charming — until it isn’t.
This was the case for Brooklyn’s Squibb Park Bridge in 2014, London’s Millennium Bridge in 2000 and a long list of other bridges throughout history that became worrisomely wobbly when large crowds crossed over them. Authorities temporarily closed the Squibb Park and Millennium bridges and spent millions of dollars on repairs.
Engineers expect all bridges to move a little with cars, people and wind. But when things get dangerous, like during the Millennium Bridge opening, you can blame it on the interactions between moving crowds and bridges, scientists suggest in a study published Friday in the journal Science Advances.
Movements of bridges and people feed off one another, Igor Belykh, an applied mathematician at Georgia State University, who led the study, explained. You step on a bridge, it moves a little bit; you adjust to steady yourself. And on and on. “However when the bridge starts wobbling significantly, I, as a pedestrian, have to adjust my gait,” he said. And when a critical number of people try to find balance at the same time and their movements sync up, they can align with the sway of the bridge. And that’s when things get scary.
Researchers had attributed the wobbly Millennium Bridge to this phenomenon, which they call phase-locking. The new study confirmed that and challenged a popular belief that the sway gradually grew with crowd size. They found that the wobble starts suddenly, after the crowd exceeds a critical threshold. For the Millennium Bridge, that was about 165 people.
Dr. Belykh and his colleagues described these dynamic relationships using complex mathematical models — which they jokingly call “crash test dummies” — that they hope will become part of industry standards. Using these models, engineers and designers may be able to plug in all the details about a bridge and its potential pedestrians and figure out how big a crowd must get before a bridge starts to wobble.
What exactly causes the initial wobbling, though, is something the researchers are still trying to figure out. It may have something to do with how you might switch your gait to find balance, taking wider steps, moving from side to side and lifting your legs more. They describe pedestrians moving in this manner as non-smooth oscillators in their models.
Every time you step, you push the ground one way, then the other. If you’re on a bridge, you push it too. This causes it to sway. You respond. It sways. And so on. Now imagine a whole bunch of you in a crowd — hundreds of non-smooth oscillators. The timing of your steps, and the force they put on the bridge are important to what happens with wobbliness.
This might also explain cases of wobbly bridges that didn’t show visual signs of crowds syncing up steps, like the Clifton Suspension Bridge in Bristol, England, where authorities limited pedestrian traffic during the city’s busy annual Balloon Fiesta. The researchers are currently collaborating with scientists in England and the United States to see if this is the case and if visual signals could help orchestrate crowd movements to prevent or stop bridges from wobbling.
But until then, we all may think twice when crossing a bridge. “Unfortunately, the more I study and know about the bridges, the more uncomfortable I become when I cross,” said Dr. Belykh.