How Fluid Dynamics Can Help You Navigate Crowds

From high above, a crowd of people looks much like a colony of ants swarming around. From even farther away, individuals seem to blend into a mass of fluid flowing through an area. And to some extent, the dynamics of a crowd can be studied with the same techniques used to study fluid dynamics or large systems of interacting particles. As a result, physicists and computer scientists can offer us some insight into how to navigate, say, a protest march or a presidential inauguration.

People who study crowds use a combination of observational studies and mathematical modeling to understand how these seething masses typically behave. In the past 20 years or so, researchers have discovered that pedestrians tend to be self-organizing. For instance, crowds naturally form lanes that form when people are walking in opposite directions, as in a hallway. When two groups of people are walking at right angles to each other, they find a way to pass through each other without stopping.

Of course, there are some notable differences between crowds and interacting particles. Namely, “particles don’t have intention,” says Dirk Helbing, a researcher at the Swiss Federal Institute of Technology in Zurich who studies computational social science. But some of the same natural laws apply to both situations, meaning crowd researchers have had success in using similar models to study crowds as physicists use to study particle flow.

Crossing flows

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For each crowd-goer, there are two main forces at work. The first is the driving force that propels each individual toward their goal. The second is the social force that prevents them from colliding with other people. Interestingly, that social force is related to the repulsive force between two electrons, which is inversely proportional to the square of the distance between them—in other words, the force decreases as the distance between the particles increases.

But in the case of humans, time replaces distance, reported researchers Brian Skinner, Ioannis Karamouzas, and Stephen J. Guy in 2014 in the journal Physical Review Letters (the animation above is from their study). Think about it: You don’t have to take evasive actions when you’re walking next to someone going the same direction as you, even if you are very close together. But you will move out of the way if you are walking straight toward another person. People adjust their paths based on subconscious mental calculations of how long it will take for them to collide with each other.

Most of the time, crowds flow along this way, each person using this inverse square law to avoid collisions while getting to their own destination. (That is, they give themselves enough time to react to people around them.) But as the density of the crowd increases, that organizing principle begins to break down. When people are so densely packed that they have to touch each other, they often can’t modulate their walking speed and direction to avoid collisions.

It’s those very dense situations that can lead to the kinds of mass crowd disasters that have headlined the news in recent years. During the 2006 hajj pilgrimage to Mecca, for instance, hundreds were killed and more than 1,000 injured when pilgrims rushing massive stone walls tripped over luggage that had fallen from moving buses. This was not the first time a deadly stampede had occurred during the ritual, which attracts around 2 million people annually: In 1990, more than 1,000 pilgrims died when a stampede broke out in an enclosed tunnel.

Similarly, in 2010, Germany’s Love Parade electronic dance festival turned tragic when thousands of festival-goers tried to funnel through a narrow tunnel onto festival grounds. The tight bottleneck caused panic among the crowds, and the parade swiftly turned into a crushing mass. Ultimately 21 festival-goers died from suffocation, and at least 500 more were injured; the parade was permanently shut down.

For obvious reasons, it is unethical to design a study to see how people behave in dangerously crowded situations. But by viewing videos of crowd disasters such as these, researchers have gained insight into how they happen—and how they can be avoided.

As a crowd gets denser, the smooth flow of pedestrians moving forward and avoiding collisions gives way to what are called stop-and-go waves. These are basically what they sound like: the crowd is too dense for people to move forward continuously, so people move forward into any gaps. Then, they stop and wait for another opportunity to move forward. Stop-and-go waves do not always portend disaster. But, Helbing says, “the stop-and-go wave is an advance warning signal for the situation in the crowd becoming critical.”

Things get really dangerous if the crowd continues to get denser, or people make unexpected movements. At that point the flow can become turbulent and chaotic, with people being pushed randomly in different directions. Disasters can break out when, say, one person stumbles, causing someone else to be pushed into their place and either trampling them or stumbling themselves. Helbing says that is sometimes described as the “black hole effect,” with more and more people sucked in. “It’s really a terrible thing,” Helbing says.

Because the nature and behavior of human crowds is so unpredictable, crowd researchers are reluctant to give general advice on how to navigate them. (The strategy they usually advise is to stay out of the crowd in the first place.) For better or worse, much of the responsibility for crowd safety falls on the organizers of the event rather than the individuals participating in it. As the hajj and Love Parade disasters have shown, organizers should try to avoid bottlenecks and areas where flows in different directions are likely to cross each other.

But if you are going to find yourself in a large crowd anytime soon, they do have a few tips. Depending on the density of the crowd, people tend to look about 1-3 seconds in the future, with people looking at longer time horizons in sparse crowds than in dense ones. “The further you can look into the future the better you can move through a crowd,” says Skinner. “Looking 3 or 4 seconds into the future gives you an advantage over people who are only looking 1 or 2 seconds into the future.” So if you keep your head up and scan a larger area, you may be able to anticipate problems and plan a better route.

Your options are different depending on whether the crowd is in an open or enclosed location, Karamouzas says. If it’s in an open location and you start to notice stop-and-go waves or feel unsafe for other reasons, you can get out of the crowd. If the area is fenced or walled in, on the other hand, “trying to do so could create more panic.” Helbing underscores that point: “You should avoid going against the flow. It makes things much worse,“ he says. He adds that in a large enclosed space, it seems the sides are more dangerous than the middle, though he notes that there are not enough studies to know that for sure or understand why. But most importantly, he says, “always know where the emergency exit is located.”

To review: Keep vigilant, go with the flow, and keep your exit options open. Flow safely!