In June 2000, the London Millennium Footbridge linking Bankside with the City of London was officially opened with a charity walk. However, participants caused the bridge to sway as they fell into step with each other, and after just two days the bridge was closed for two years while modifications to eliminate the wobble were carried out. Turns out staying with the sway would have had its benefits, as researchers have found that it reduces the amount of energy expended when walking across the bridge.

The physics behind the swaying of the bridge is easily explained, with the natural side-to-side motion of people's footsteps as they fell into sync causing the suspension bridge to sway back and forth. However, researchers at Ohio State University (OSU) set out to discover why, even as people felt the bridge swaying beneath them, they continued walking the same way. The answer is what Manoj Srinivasan, assistant professor of mechanical engineering and director of the Movement Lab at OSU, and his colleagues have dubbed "the principle of maximum laziness."

Srinivasan and his team are attempting to develop a complete theory explaining why people walk like they do, which could help in the design of prosthetics and other assistive walking devices, as well as robots. What fascinated him was how people crossing the Millennium Bridge spontaneously fell into cadence to start the bridge swaying, which prompted more people – be it consciously or unconsciously – to fall into the same cadence and cause the bridge to sway even more.

Although stability is understandably the primary concern when walking, the researchers say that the next highest priority appears to be conserving energy, and this is just what those crossing the bridge were doing. According to Srinivasan, walking on a swaying surface requires around 5 percent less energy than walking on a stationary surface.

"Of course people have to be stable, but once they are stable, they want to move in a manner that makes them the least tired," says Varun Joshi, doctoral student and lead author of the study. "Five percent doesn’t sound like a lot of energy savings, but it’s about equivalent to walking with or without a school backpack. It’s not a huge burden, but something people notice."

So even if it will result in saving only a small amount of energy, the researchers say that people are likely to alter the cadence and length and width or their strides. To test their theory, they created a computer model of a simplified human body walking on both a flat treadmill surface and a treadmill surface with the springiness and swaying capability of the original Millennium Bridge design.

While the model bobbed up and down as we normally do when walking on a flat surface, on the swaying surface the model bobbed up and down less while achieving the same forward motion. In other words, the model didn't need to push off from the ground as much to achieve the same result, meaning less effort was required by the legs. However, the researchers say the frequency of the swaying and the properties of the bridge have to be just right for such energy reductions to occur – properties which the Millennium Bridge lost with the addition of dampers before its reopening in 2002.

A video showing the computer model can be viewed below, while the team's study can be found in the journal Proceedings of the Royal Society A.

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