Bridges are our way of bandaging holes in the earth that are too vast for our frail bodies to cross. They’re band-aids between mountain crags, stitches across major rivers, temporary fixes cast in steel and stone, enduring only as long as we continue to administer treatment.
Though some can be massive monuments to the endurance of engineering, others are designed to be as delicate as a surgeon’s thread—made for human footsteps, not our motorized, wheeled conveyances. These pedestrian bridges encourage human movement, but are rarely designed to move dramatically themselves.
There are exceptions. I remember the pit in my stomach as some enthusiastic kid decided to jump up and down on the Mile-High Swinging Bridge, leaving my height-petrified 5th-grade self gaping at the chasm 80 feet below. The steel suspension bridge was true to its name, and I felt it move as I clung to the railing. Years later, I walked across the Millennium Bridge in London, which seemed stable enough, with street performers setting up on the solid man-made platform above the Thames.
But the Millennium Bridge was notorious for moving when it wasn’t supposed to. When it opened in 2000, thousands of people were eager to walk across the bridge, but as they poured onto the structure, it started wobbling from side to side. There are videos of the opening day.
“You‘ll see all the people, they start falling in step, they move in sync—then you see the bridge develops significant wobbling,” says Igor Belykh, a professor of applied mathematics at Georgia State University.
Engineers don’t generally want to see a bridge wobble, and the Millennium bridge was quickly closed for repairs.
Belykh is an author of a paper published in Science Advances that explores the Millennium bridge, and other bridges like the Squibb Bridge in Brooklyn, which recently re-opened after its own bout of bounciness.
When a person walks across a bridge, especially a lightweight one like a pedestrian footbridge, they push against it, and they might change their gait to match the subtle movement of the bridge, too. “Suppose you are on a boat. When the boat is steady you walk with your normal gait,” Belykh says. “If there are stormy seas you will adjust your gait to keep your balance.”
A similar thing happens on a bridge at a smaller scale, as people unconsciously adjust their movement to accommodate even a subtle swaying in the bridge. When they step on their right foot, they push the bridge to the right. When they step on their left, they push the bridge to the left. Right, left, right, left.
That’s where this new study comes in. Normally, a person walking on a well-built bridge won’t exert enough force to do anything. But when we join forces, so much is possible. Belykh found that when people change their gait en masse, and there are enough people on the bridge to really put some force behind their new movements, they can cause a wobble. That’s different from old assumptions, which presumed that the wobble just gradually built up as you added more walking people onto the bridge. According to the new study, it’s not a gradual build-up at all; there aren’t enough feet in play to wobble the bridge until suddenly there are.
In the case of the Millennium Bridge, that magic number was about 165.
“At 164 pedestrians, potentially nothing, then boom, the bridge starts wobbling when you have one or two additional pedestrians,” Belykh says. “It’s a very complex relationship.”
But Belykh and his colleagues have come up with a mathematical model that should allow bridge designers and engineers to calculate how many people can safely go over a bridge; models that he hopes might replace the current linear models that are currently used to assess pedestrian bridge design in the United States.
That’s because wobbling bridges aren’t just uncomfortable for pedestrians. If the frequency of the crowd’s movement matches up with the natural frequency of the bridge—the frequency that the bridge tends to move at—unexpected things could happen, including, potentially, a collapse.
That could be solved by putting in a lot of precautionary measures, like mechanical dampers to absorb the forces exerted on the bridge by pedestrians. But designers and engineers don’t want to over-engineer.
“The problem with pedestrian bridges is they are meant to be lightweight,” Belykh says. “Why would you build a huge concrete bridge? It would be overkill, and it would be too expensive.”
In addition to working with engineers to incorporate a model into their methods, Belykh is collaborating with researchers at the University of Bristol to figure out another bridge mystery. While people moving in sync have been blamed for bridge wobbles in the past, the idea that perfectly synchronized marching (like by a platoon of soldiers) could instigate a bridge’s movement isn’t backed up by the evidence. Wobbling seems to be more dependent on the number of people in movement than by their moving in unison, but more research is needed to figure out what the precise cause actually is.
In some ways, bridges and other constructions are large (often expensive) experiments that merge physics, materials sciences and human behavior. And catching flaws in those designs before they become a problem is a huge part of the process. We now know to makes sure that curved glass buildings won’t melt cars below, and to check and make sure that a skyscraper in New York won’t blow over in the wind and to ensure that the air is polluted enough to give your building a nice patina, and not just rust it.
As for bridges, the hope is that if we learn what makes them wobble, we can make sure they don’t fall down.