Skip to main content
Home
plus.maths.org

Secondary menu

  • My list
  • About Plus
  • Sponsors
  • Subscribe
  • Contact Us
  • Log in
  • Main navigation

  • Home
  • Articles
  • Collections
  • Podcasts
  • Maths in a minute
  • Puzzles
  • Videos
  • Topics and tags
  • For

    • cat icon
      Curiosity
    • newspaper icon
      Media
    • graduation icon
      Education
    • briefcase icon
      Policy

      Popular topics and tags

      Shapes

      • Geometry
      • Vectors and matrices
      • Topology
      • Networks and graph theory
      • Fractals

      Numbers

      • Number theory
      • Arithmetic
      • Prime numbers
      • Fermat's last theorem
      • Cryptography

      Computing and information

      • Quantum computing
      • Complexity
      • Information theory
      • Artificial intelligence and machine learning
      • Algorithm

      Data and probability

      • Statistics
      • Probability and uncertainty
      • Randomness

      Abstract structures

      • Symmetry
      • Algebra and group theory
      • Vectors and matrices

      Physics

      • Fluid dynamics
      • Quantum physics
      • General relativity, gravity and black holes
      • Entropy and thermodynamics
      • String theory and quantum gravity

      Arts, humanities and sport

      • History and philosophy of mathematics
      • Art and Music
      • Language
      • Sport

      Logic, proof and strategy

      • Logic
      • Proof
      • Game theory

      Calculus and analysis

      • Differential equations
      • Calculus

      Towards applications

      • Mathematical modelling
      • Dynamical systems and Chaos

      Applications

      • Medicine and health
      • Epidemiology
      • Biology
      • Economics and finance
      • Engineering and architecture
      • Weather forecasting
      • Climate change

      Understanding of mathematics

      • Public understanding of mathematics
      • Education

      Get your maths quickly

      • Maths in a minute

      Main menu

    • Home
    • Articles
    • Collections
    • Podcasts
    • Maths in a minute
    • Puzzles
    • Videos
    • Topics and tags
    • Audiences

      • cat icon
        Curiosity
      • newspaper icon
        Media
      • graduation icon
        Education
      • briefcase icon
        Policy

      Secondary menu

    • My list
    • About Plus
    • Sponsors
    • Subscribe
    • Contact Us
    • Log in
    • Millennial wobbles

      1 September, 2000
      September 2000


      Back to the Constructing our lives package

      The Millennium Bridge across the Thames opened in June 2000 and was subsequently closed two days later because of the now-famous "wobbles". Given that, at any instant, two thousand people were suspended above a very dangerous river, this presented a serious problem.

      Wobbling bridge

      One mode of oscillation
      Courtesy of Cambridge University Dept of Engineering

      It also presented a very interesting problem. The "wobbles" appeared to be caused by an unusual effect of synchronised walking. As the crowd walked at random across the bridge, it moved a little. This was to be expected: like all suspension bridges it is rather flexible. What was not expected was that these small motions would affect the way that the people walked and lead to a positive bio-feedback loop. Feeling the small motions underfoot, people adjusted their steps, possibly subconsciously, in order to walk more comfortably. This meant adjusting their footfall to move in synchronisation with what the bridge was doing. However, this reinforced the motion, leading to larger oscillations, which then caused more people to join in, and so forth.

      This is not the old chestnut about soldiers needing to break step when crossing a suspension bridge. In the marching-soldiers problem, there is no change of gait. They merely feed energy directly into a vertical mode. On the Millennium Bridge, it is all about the way people CHANGED the way they were walking.

      This phenomenon of phase synchronisation may be a new effect to engineers designing footbridges, but it is well known throughout the wider physical and biological sciences. One classic example is the behaviour of groups of fireflies. At dusk, the males of certain species land on the bushes on the riverbanks of Southeast Asia, all flashing at random, and then as the evening progresses, each male sees what the nearby males are doing and gradually adjusts its rate of flashing until, eventually, the whole bush is flashing on-off-on-off in perfect synchrony. If one flashes a torch at a bush of fireflies, one can entrain them to follow the flashing of the torch, and many interesting effects can be created. If the torch is flashed gradually faster, the fireflies can no longer keep up with it, and perform instead an interesting quasiperiodic behaviour - here it comes, faster, faster, faster - oh, we missed it, let's slow down and wait for it to come round again, here it comes, faster, faster... and so on.

      There are many other examples: the menstrual synchrony of groups of females living in close proximity, the fact that we only ever see the same face of the moon, the synchronisation of two pendulum clocks on a shelf, the behaviour of coupled electronic oscillators and so forth.

      The similarity between the firefly bush and the crowded bridge is not just a poetic resonance but a useful mathematical analogue. In order to understand what is happening on the bridge, the engineers would do well to read what the mathematicians have written about the fireflies.


      About the author

      Allan McRobie is Reader in Structural Engineering at the University of Cambridge with a particular interest in bridge dynamics.

      Read more about...
      oscillation
      biofeedback loop
      phase synchronisation
      • Log in or register to post comments

      Read more about...

      oscillation
      biofeedback loop
      phase synchronisation
      University of Cambridge logo

      Plus is part of the family of activities in the Millennium Mathematics Project.
      Copyright © 1997 - 2025. University of Cambridge. All rights reserved.

      Terms