wobbly — why the Millennium Bridge moved

Plan view, looking down at the 144 m centre span. Blue dots are people walking; orange ones have grabbed the handrail and stopped feeding the deck. Watch the phase ring on the left while you add people.

sway, mid-span

0 mm

lateral accel

0 g

synchrony r

0.00

still walking

0 of 0

crowd

0 / N_L 41

bridge time

0 s

What you are looking for. Push the crowd past about 41 people with negative damping selected and the deck runs away — while the phase ring stays a smear. Nobody is marching in step. Each person is just leaning into a floor that is already moving, and a crowd doing that is a shock absorber wired backwards. That was the surprise of the 2000s: for years the story was that pedestrians synchronise, and the measurements say they mostly don't have to.

Switch to phase locking and turn the spread of pacing rates down to zero: now twenty-five people are enough, the ring collapses to a clump first, and the deck follows. Two different ways to shake a bridge, one dial apart. Turn the spread back up and the locking route needs a crowd again — and needs a lot, unreliably: at ninety people it depends on the crowd you happen to get, and only around a hundred and twenty does it lock every time. It has to beat the disagreement between people's own walking rates before it can beat the structure.

Numbers are the London Millennium Bridge centre span as measured by Arup after it closed: first lateral mode 0.49 Hz, damping 0.7% of critical, 300 N·s/m of pedestrian negative damping per person. The modal mass and the phase-pull strength are mine, not theirs — see the README. This is a toy, not an engineering tool: it has one mode, a flat deck and no wind.