Millennium Bridge wobble finally explained

Posted by Derek Mason

29th March 2022

Photo credit: Johan Mouchet on Unsplash

Engineers and mathematicians finally explained why the Millennium Bridge moved from side-to-side – and it’s not “walking in step” that caused the wobble

Those of us with long memories might remember that back in the early noughties, when the Millennium Bridge first opened, it was forced to close three days later due to a disturbing sideways movement.

In the years since the wobble was fixed by adding 91 shock absorbers, it was thought that pedestrians inadvertently “walking in step” had been causing the bridge to wobble. But some 20 years later this has been dispelled by an international team of engineers and mathematicians.

The theory was that once the bridge had a certain number of people crossing, those people spontaneously and involuntarily began to coordinate their behaviour. With their footsteps falling in line with the bridge’s natural frequency – the frequency at which the bridge oscillates – this created the swaying effect that led to the bridge’s closure for safety reasons.

This phenomenon is called “spontaneous emergence of synchronous behaviour from incoherent agents”. The Millennium Bridge has regularly been quoted as an example of this, along with the flashing of fireflies in a coordinated manner, or the sudden onset of clapping after a speech.

However, there is a simpler explanation. The Millennium Bridge became unstable as pedestrians tried not to fall over.

In a new paper, published in the journal, Nature Communications, a team led by Georgia State University in the United States and the University of Bristol here in the UK, the synchronisation myth has been put to bed.

The team found that many other bridges have displayed large amplitude lateral oscillations when carrying large numbers of pedestrians and there is little or no evidence for footstep synchronisation.

What does happen – which is consistent with all the evidence – is that in trying not to fall over, pedestrians walk randomly and provide ‘negative damping’. This is a positive feedback effect that means energy is transferred from pedestrian wobbles to bridge movement.

Any footstep synchronisation that may be seen is as a result of the bridge motion, rather than a cause of it.

The team came to this conclusion after reviewing existing evidence, conducting detailed computer simulation and mathematical analysis, and combining knowledge and expertise across multiple disciplines in engineering, mathematics and physics.

These findings will be important for bridge engineers. We know that long, slender structures like pedestrian bridges can get ‘excited’ quite easily and further knowledge and understanding in this area is a positive outcome. After all, moving bridges tend to frighten people!

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