New study questions popular explanation of London’s infamous ‘Wobbly Bridge’

Enlarge / London’s Millennium Bridge had problems with excessive shaking and swaying when it opened in June 2000.

Alberto Pezzali / NurPhoto / Getty Images

London’s Millennium Bridge is known for its “sway” when it opened in June 2000, as thousands of pedestrians poured in. Londoners have nicknamed it “Wobbly Bridge”. The accepted explanation was that the sway was due to a strange synchronicity between the lateral (lateral) sway of the bridge and the pedestrian gaits – an example of an emerging collective phenomenon.

But this explanation turns out to be a little more complicated, according to a recent article published in the journal Nature Communications. “This [old] the explanation was so popular, it was part of the scientific trend “, said co-author Igor Belykh, mathematician at Georgia State University. “Our work shows that very small vibrations of each walking person can be greatly amplified.” People adjust their strides to keep their balance in response to the oscillation, which only makes matters worse. Eventually the bridge becomes unstable.

As we noted earlier, this phenomenon is not limited to the Millennium Bridge. There is a sign dating from 1873 on the Albert Bridge in London warning military troops to break their usual locking movement when crossing, as the bridge tends to shake and wobble, hence its nickname “The Lady trembling “. Other similar ‘unstable’ bridges include the Clifton Suspension Bridge in Bristol, UK; the Squibb Park Bridge in Brooklyn, New York; and the Changi Mezzanine Bridge at Singapore Airport.

Many different approaches to studying these fascinating dynamics have been taken over the years, including a recreation on treadmill in laboratory of people walking over the Millennium Bridge by Cambridge University engineer Allan McRobie. (McRobie is co-author of the new article.) Cornell University mathematician Steven Strogatz co-authored a 2005 Nature Paper with McRobie and two others who modeled the dynamics of the Millennium Bridge as a weakly cushioned and driven bridge harmonic oscillator.

The Albert Bridge between Chelsea and Battersea in London, circa 1885. It has been nicknamed
Enlarge / The Albert Bridge between Chelsea and Battersea in London, circa 1885. It has been nicknamed “The Trembling Lady” because of its tendency to shake when soldiers crossed it.

Hulton Archives / Getty Image

According to Strogatz, the bridge was caused to swing sideways by pedestrians as they crossed it. Their periodic steps pumped energy into the bridge and caused it to move side to side, causing people to adjust their gaits to conform to the movement of the bridge. Over time, the pedestrians inadvertently synchronized with each other causing the bridge to wobble even more. The spontaneous crowd synchrony was similar to what happens with the highly synchronized flashing of fireflies or the triggering of neurons in the brain.

But this original explanation was incomplete. “The initial impulse that many researchers got when looking at this problem was that it was collective behavior,” said Ars Varun Joshi, a biomechanical engineer at the University of Michigan. “This was based on the presence of multiple pedestrians and the apparent synchronization between them, as observed in the videos. However, data collected from real bridges has shown a lack of synchronization in many cases. This has led to much experimental work studying the individual human response to shaken treadmills, looking for a “negative damping effect” in individuals. The hope was that the large-scale effect of negative damping (even without any adaptation to the presence of other people) would explain the phenomenon. “

The simulated figures demonstrate the fundamental mechanism underlying a negative damping effect.
Enlarge / The simulated figures demonstrate the fundamental mechanism underlying a negative damping effect.

Igor Belykh et al., 2021

When Joshi was at Ohio State University, he and his co-author, Manoj Srinivasan, simulated the biomechanics of large crowds of people walking across a bridge, resulting in a improved model of how people adjust their gait when walking on a wobbly surface. Their suggested conclusions that you may not even need synchronization to cause the tremor. The improved model correctly predicted certain phenomena that the 2005 model could not explain, such as the wobbling of walkways even in the absence of crowd synchrony. In addition, the start of crowd synchronization and the start of bridge wobble are not simultaneous. They occur at different numbers of pedestrians.

This latest study is based on Research 2017 by Belykh et al., using models inspired by biomechanics based on an inverted pendulum to mimic the lateral movement of people, as well as the forward movement. This revealed a “threshold effect” or a tipping point. While the common opinion was that the more pedestrians there were on the bridge, the more the bridge would wobble, they found that more pedestrians produced wilder swings, but only for crowds above a critical size. For example, 164 people on the Millennium Bridge won’t cause tremors, but adding one more person will tip the scales.

They also devised a mathematical formula that could be used to estimate the critical size of the crowd at which a given bridge would begin to wobble. The new document further refines this formula, based on data collected from 30 different bridges. Belykh and his colleagues concluded that the synchronized movement of pedestrian feet was not necessarily the main cause of the onset of bridge vibrations. Bridges can start to wobble even if there is no synchronization between pedestrians. Pedestrian synchronization exacerbates, but does not cause, oscillations.