How Many People Does It Take to Make a Bridge Wobble?

Millions of dollars and nearly two years of repairs were required to correct an unaccounted for 'wobble' caused by pedestrian foot traffic on London's Millennium Bridge. (Photo: Rob Swatski/Flickr)

When London's Millennium Bridge, a 320-meter-long lateral suspension bridge connecting the city's financial district to Bankside, opened on June 10, 2000, it wasn't quite the charming experience many pedestrians expected. As the video below shows, the footfalls of thousands of people crossing the bridge began to induce a dangerous and completely unexpected wobble.

Two days later, the bridge was closed for repairs that lasted two years and cost millions of dollars.

"The phenomenon was that people who were walking at random, at their own favorite speed, not organized in any way spontaneously synchronized," Steven Strogatz of Cornell University, who published a study on The Millennium Bridge's wobble in 2005, told RedOrbit. "That's the phenomenon. Why did they all start moving in step? They did it unconsciously. That is what nobody had thought about and engineers did not anticipate."

The phenomenon, called "synchronous lateral excitation" or "phase-locking," occurs when the natural sway of a walking crowd matches the frequency of a bridge with lateral sway. As the people attempt to adjust their gait to counter the growing wobble of the bridge, they unintentionally exacerbate the sway. For the Millennium Bridge, the critical threshold for causing a frequency match was discovered to be only 165 pedestrians. On opening day, an average of 2,000 crossed the bridge every hour.

Math to the rescue

In an effort to better gauge foot traffic stress on bridge designs, researchers at Georgia State University have devised complex mathematical models to accurately determine the amount of people it takes to make a bridge wobble. The new simulations, which take into account not only the length, width and materials making up the bridge, but also the timing of the footfalls and the force of each step, are the most accurate measurement yet of crowd behavior impact on pedestrian crossings.

The study, published in the journal Science Advances, could help to significantly improve building code for pedestrian bridges.

"The U.S. code for designing pedestrian bridges does not have explicit guidelines which account for pedestrian or crowd dynamics," researcher Igor Belykh, who led the study, said earlier this year. "That’s the gap we’re trying to fill."

Belykh hopes that his team's research could one day be integrated into the many shared computer programs engineers use to devise pedestrian crossings.

“What we want to do is better help engineers understand the role of pedestrians in the initial formation of a bridge formula and avoid the range of dangerous frequencies, which cannot be identified through conventional linear calculations, to eventually design robust bridges,” he said.