THE BRIDGE
Flexible, by design
The 320-metre bridge was flexible, and its natural frequency was close to that of human walking. It met standards for weight and wind; crowds were the untested part.
Read the storyA PLAIN-ENGLISH GUIDE TO SYNCHRONY
Nobody meant
to walk in step.
On 10 June 2000, thousands of people walked onto a new bridge over the Thames.
See how it happened
IN SYNCby accident
Within moments it began to sway, and people started walking left, right, left, right, in near-perfect unison, planting their feet wide like tentative ice skaters. Nobody planned it. The bridge and the crowd had fallen into sync.
At a glance
- A small sway
- Walkers adjust
- The sway grows
- A feedback loop
≈ 160 people
Walkers needed to start the wobble
Because the bridge's natural frequency was close to walking pace, a relatively small crowd was enough: if a few people fell into step by chance, the bridge became unstable.
CROWD SIZE · CORNELL / NATURE, 2005
91 dampers
Dampers fitted before reopening in 2002
Engineers fitted 91 dampers to absorb both sideways and vertical movement. Cornell reported the modifications cost about $8.9 million.
THE FIX · CORNELL, 2005
TWO NUMBERS WORTH KNOWING
A small crowd,
a big fix.
One figure for the cause,
one for the cure.
The bridge closed almost immediately after opening and reopened in 2002.
HOW MANY WALKERS?
When does a crowd
start the wobble?
Pick a crowd size. The model says nothing much happens until a critical number is reached, then wobbling and synchrony appear together. The bar shows crowd size.
Figures from Cornell University and the 2005 Nature paper, with a 2017 Science Advances study for comparison.
THE SHORT ANSWER
A bouncy bridge
and a crowd.
Two ingredients,
and a feedback loop between them.
THE CROWD
Falling into step
Once it swayed a little, walkers adjusted their steps to keep balance, which pushed it further. Past a critical crowd size, wobbling and synchrony erupt together.
How many walkers?
THE SCIENCE
Clocks on a beam
Christiaan Huygens saw two pendulum clocks on one wooden beam fall into step some 350 years ago. The bridge maths borrows ideas used for fireflies and neurons.
Lessons learned
LESSONS FROM THE WOBBLE
What engineers
took away.
The wobble changed how people think about crowds on footbridges. These points come from the studies that followed.
Crowds are part of the load
The bridge passed tests for weight and wind. The problem was crowd behaviour, which a 2017 study notes design codes still do not explicitly address.
Soldiers already knew
Troops break step on bridges because marching in step can create large vertical forces. The Millennium Bridge sway was sideways, and unintended.
Sideways counts too
A US design guide sets lower limits on a footbridge's natural frequency of 3.0 Hz vertically and 1.3 Hz sideways.
Design for damping
The 2005 model lets engineers estimate the damping needed to keep very crowded footbridges stable.
NOT THE ONLY ONE
Other bridges
that danced.
The Millennium Bridge is the best-known lively footbridge, but not the only one. Studies list the Solférino Bridge in Paris, which vibrated on opening in 1999, and the Clifton Suspension Bridge in Bristol among the well-known cases of unstable pedestrian bridges.
In Brooklyn, the Squibb Park Bridge began bouncing and swaying more than intended. Arup, the engineers of the Millennium Bridge, added a truss and large mass dampers that greatly reduced the bouncing, and it reopened in April 2017.
Questions
Questions people ask
Why did the Millennium Bridge wobble?
It was flexible and its natural frequency was close to that of human walking. A small sway made walkers adjust their steps, which pushed the bridge further, until many people were walking in step without meaning to.
How many people does it take?
Cornell reported the critical number as low as 160. A 2017 study cites about 165. Below that, the bridge stayed steady.
How was it fixed?
It closed almost immediately and reopened in 2002 after engineers fitted 91 dampers to absorb sideways and vertical movement.
Why do soldiers break step on bridges?
Troops marching in step can create enough vertical force to damage a bridge, so it is standard practice to break step when crossing.
What does this have to do with fireflies?
The 2005 Nature model adapted ideas first developed to describe how biological oscillators such as neurons and fireflies fall into sync.
Sources
Where the facts come from
- Cornell Chronicle: Explaining why the Millennium Bridge wobbled (2005)
- Strogatz, Abrams, McRobie, Eckhardt and Ott: Crowd synchrony on the Millennium Bridge, Nature (2005)
- Belykh, Jeter and Belykh: Foot force models of crowd dynamics on a wobbly bridge, Science Advances (2017)
- ScienceDaily: Explaining why the Millennium Bridge wobbled (Cornell University release)
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