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On its opening day, the London Millennium Bridge began to wobble unexpectedly. You might observe something strange here: along with the sway of the bridge, the pedestrians are walking in a synchronized pattern. What’s happening here? Why are normal people walking with perfect synchronization? This experiment answers that question. At first, these metronomes are oscillating randomly. However, after waiting for a few seconds, they all oscillate in perfect harmony. What happens is that the metronomes transfer some energy to the platform, and this energy is then transferred back to the metronomes until they all synchronize perfectly. This phenomenon, spontaneous synchronization, also happened on the Millennium Bridge. All suspension bridges have a slight sway. Consider these two pedestrians walking out of sync. Their walking will cause the bridge to sway a little. Similar to the experiment, the energy of these oscillations is given back to the pedestrians, and after some time, these two pedestrians will unknowingly start walking in synchronization. Walking along with the sway is more comfortable for humans. When more pedestrians join in, the sway becomes noticeable. It's a well-known fact that if people walk on a bridge in synchronized motion, the results can be catastrophic for the bridge. If the frequency of people’s walking matches the natural frequency of the bridge, the amplitude of the oscillations will keep increasing, just like when I apply an external force to this pendulum at the same frequency as its natural oscillation. Eventually… What you’ve just witnessed is an important phenomenon in physics: resonance. If you combine these two crucial concepts with the unique geometry of this suspension bridge, you can understand what happened on June 10, 2000. You might even be able to suggest a solution to the problem. The Millennium Bridge is a lateral suspension bridge. Generally, the main cables of a suspension bridge are very tall. The engineers behind this bridge didn’t want to obstruct the pedestrians' view, so they placed the suspension cables off to the sides at a much lower height—a shallow cable profile. This results in a slender and beautiful geometry - the blade of light. Even the pier body is beautiful, with a tapering elliptical cross-section. Transverse arms connect these shallow cables, and the 4-meter-wide road deck is built on these arms, complete with handrails. One small issue with all bridges is asymmetrical loading. If you look closely, you'll see this bridge is quite wide, which gives it good torsional resistance. The engineers even made sure that the natural frequency of the bridge would never match the frequency of pedestrians' footsteps. More specifically, they studied the vertical motion of the bridge. When we walk, the lateral force is typically too small to be considered. The typical lateral frequency of the human gait is 1.3 Hertz. Take a look at the natural lateral frequencies of this bridge in three different sections. They are nowhere close to 1.3 Hertz. Engineers thought the bridge was safe from lateral motion as well. But they were wrong. Let’s observe the forces developed during a typical walk.
The red arrows show the forces you apply to the bridge. The lateral force we apply while walking is extremely small. Especially when people are walking in random directions, all these forces should cancel each other out, and there should be no issue. The question is, do they get canceled? Forces may cancel out for normal objects, but not for objects that can undergo oscillatory motion. Let’s apply random motion on a system which can oscillate. We cas see the oscillation never get cancelled. The same thing happens on suspension bridges. Although unnoticeable at first, the bridge started to sway a little laterally. Now, the phenomenon we saw in the experiment comes into effect: spontaneous synchronization. The people on the bridge behave like the metronomes, and the bridge behaves like the platform. In this case, the phenomenon is more precisely called synchronous lateral excitation. The bridge begins to oscillate further. Essentially, people found it more comfortable to walk in sync with the oscillating bridge. As the bridge moved, pedestrians instinctively adjusted their stance and gait to keep their balance. People began to match the bridge's natural lateral frequencies, walking at 0.5 and 0.7 Hertz instead of their usual 1.3 Hertz. This, of course, led to resonance and a dramatic increase in the bridge's oscillation amplitude. Arup—the company behind the bridge's design—was in utter disbelief. While they had a theory about "synchronous lateral excitation," they needed to gather data to confirm it and to determine how much damping would be required to counteract the effect. The first step was to experiment on the bridge with different numbers of pedestrians. With a small number of people, the bridge had no issues. The center and south spans of the bridge were more flexible. They observed that when the number of pedestrians crossed 166 in these areas, the wobble became noticeable. Engineers were confident that they would be able to save the bridge by retrofitting it. Their solution was dampers. They used two kinds of dampers for this purpose: viscous and tuned mass dampers. In total, 37 viscous fluid dampers were fitted. These devices, which are similar to large shock absorbers, work by forcing a thick fluid through a small opening. When the bridge sways, the dampers resist the motion and dissipate the energy as heat, effectively reducing the magnitude of the oscillations. Additionally, 52 tuned mass dampers were installed between the transverse arms and the deck. When the bridge begins to move, the dampers move in opposition, counteracting the forces and stabilizing the structure. In January 2002, just before the bridge was reopened, Arup conducted a secret test. Seven hundred staff members were brought in to walk across the bridge. This test ensured that the dampers would perform as expected under a significant pedestrian load. The bridge remained stable, and the sway was reduced to just a few millimeters. After these modifications, which cost around £5 million, the bridge was reopened to the public in 2002 and has remained stable ever since.