Theoretical mechanics: Crowd synchrony on the Millennium Bridge

  title={Theoretical mechanics: Crowd synchrony on the Millennium Bridge},
  author={Steven H. Strogatz and Daniel M. Abrams and Allan McRobie and Bruno Eckhardt and Edward Ott},
Soon after the crowd streamed on to London's Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridge's vibrations, inadvertently amplifying them. Here we model this unexpected and now notorious phenomenon — which was not due to the bridge's innovative design as was first thought — by adapting ideas originally developed to describe the collective synchronization of biological oscillators such as neurons… 

Emergence of the London Millennium Bridge instability without synchronisation.

An alternative to Kuramoto theory for emergence of coherent oscillations in nature is described; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony

A simple biped model capable of walking stably in three dimensions is used, showing that they naturally synchronize under certain conditions, but that synchronization is not required to shake the bridge.

Parallels between wind and crowd loading of bridges

Parallels between the dynamic response of flexible bridges under the action of wind and under the forces induced by crowds allow each field to inform the other. Wind-induced behaviour has been

Visualization of crowd synchronization on footbridges

A current mathematical model of crowd synchronization on footbridges is extended to include human walking model and crowd simulation techniques and the influence of these extensions on synchronization is evaluated.

Lateral excitation of bridges by balancing pedestrians

  • J. Macdonald
  • Engineering
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian–structure interaction has since been

Foot force models of crowd dynamics on a wobbly bridge

This study develops “crash test dummies” to help designers avoid their footbridges oscillating or bouncing alarmingly, and develops foot force models of pedestrians’ response to bridge motion and detailed, yet analytically tractable, models of crowd phase locking.

Paper : Synchronization Proposal : Synchronization of Three Dimensional Oscillators

In 1665, the Dutch scientist Christiaan Huygens discovered that two pendulum clocks mounted on the same wall synchronize with one another—the bobs swing with the same frequency but exactly out of

Experimental demonstration of crowd synchrony and first-order transition with lasers

Crowd synchrony, which corresponds to the synchronization of different and independent oscillators that interact with each other via a common intermediate, is ubiquitous in many fields. Here, we

Pedestrian-structure synchronisation : application to swaying footbridges

A continuous crowd-structure model is proposed which allows for the modelling of the lateral oscillations of the bridge and the behaviour of the crowd, taking into account the synchronization, and application to real footbridges allows for a better understanding and a correct representation of pedestrians behaviour.

Contrarians Synchronize beyond the Limit of Pairwise Interactions

We give evidence that a population of pure contrarians globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the



From Clocks to Chaos: The Rhythms of Life

One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions.


It was observed on a pedestrian cable-stayed bridge that the girder vibrated laterally with a frequency of about 0.9 Hz, the natural frequency of the first lateral mode, when a large number of people

The geometry of biological time

The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways is presented.

The ionic channels in excitable membranes.

  • R. Keynes
  • Biology
    Ciba Foundation symposium
  • 1975
Comparisons can now be made between the kinetics of the ionic conductances as described by Hodgkin & Huxley, and the steady-state distribution and kinetic changes of the charged controlling particles, which should lead to useful conclusions about the intramolecular organization of the sodium channels and the conformational changes that take place under the influence of the electric field.

First and second law performance variations of a coal gasification fuel-cell-based combined cogeneration plant with varying load

Abstract An advanced combined cogeneration plant based on a solid oxide fuel cell (SOFC) stack, fuelled by synthetic gas by coal gasification, upstream of a gas turbine and heat recovery steam

Chemical Oscillations, Waves, and Turbulence


The London Millennium Footbridge is located across the Thames River in Central London. At its opening on June 10, 2000, the bridge experienced pedestrian-induced lateral vibration. Observations on

J. Phys. Chem. B

  • J. Phys. Chem. B
  • 2001

C. R. Science

  • C. R. Science
  • 1997