The Physics Of A Crowd

14:21 minutes

a massive crowd of people celebrating and raising their arms up at midnight with confetti in the air. in new york city
New Year’s Eve in Times Square, 2014. Credit: Shutterstock

Earlier this week, hundreds of thousands of revelers huddled together under the pouring rain in Times Square for an annual tradition: to watch the New Year’s ball drop. But once the clock struck midnight, the song was sung, and the loved ones were kissed, all anyone wanted to do was get out of there. The problem? How does a mass of 100,000 people move out of a few square blocks in midtown Manhattan? Luckily, scientists are studying this type of problem.

In a paper published this week in the journal Science, a group of researchers discovered that a crowd of runners at the starting line of a marathon moves sort of like a wave, adhering to a few basic principles of physics. In an accompanying review article in Science, Stanford University professor Nicholas Ouellette writes that this hydrodynamic model is the best one for studying crowd movement, whether it’s a group of humans, a flock of birds, or a swarm of insects. He joins Ira to discuss the recent research.

Further Reading

  • Read the original crowd flow study published this week in Science.
  • Phys.org explores Ouellette’s research on studying swarm behaviors in starlings to help design drones.
  • Ouellette writes about the thermodynamics of collective behavior.
  • Find out about more of the research coming out of Ouellette’s Environmental Complexity Lab at Stanford University.

Segment Guests

Nicholas Ouellette

Nicholas Ouellette is an associate professor of Civil and Environmental Engineering at Stanford University in Palo Alto, California.

Segment Transcript

[MUSIC PLAYING] IRA FLATOW: Earlier this week, hundreds of thousands of revelers huddled together in the pouring rain in Times Square for an annual tradition to watch New Year’s Ball Drop. Yeah. But once the clock struck midnight, the song was sung, loved ones were kissed, and all anybody wanted to do was a get out of there.

Problem is, how do you get thousands of people to safely move out of a crowded few square blocks of midtown Manhattan? Well, this is actually something that scientists study. Researchers reported in the journal Science that a crowd of people at the starting line of a marathon move sort of like a wave, adhering to a basic principle of physics.

So can understanding the fluid dynamics of crowd movement help us to get to the exit door a little bit faster than the next guy? Here to explain it all is Dr. Nicholas Ouellette, Associate Professor of Civil and Environmental Engineering at Stanford. He’s the author of a perspectives article in the journal Science, discussing the recent research. Welcome to Science Friday.

NICHOLAS OUELLETTE: Thanks for having me on the program.

IRA FLATOW: Let me start with the most obvious question, why do scientists want to study the way crowds move?

NICHOLAS OUELLETTE: That’s a great question. And one of the things I really like about working in this area is that there’s not just one answer to that, and there’s lots of different communities of scientists who are all interested in this question.

From the standpoint of human crowds in particular, there are fundamental questions we want to understand about how, say, to design spaces so that people can use them effectively. You mentioned clearing out Times Square. You might want to think about how you might design stadiums or big venues like that, so that people can easily get in and out.

And then we’d also like to prevent possible crowd disasters. We all hear stories about crowd panic, when people get trampled. That’s clearly a bad thing. There’s a hope that by understanding, at a more fundamental level, how human crowds behave, we may be able to prevent that kind of situation.

IRA FLATOW: So how did the authors on this study do different? What did they do differently from other studies of crowd movement?

NICHOLAS OUELLETTE: Well, they took advantage in a really clever way of what you might call a natural experiment about how crowds behave. So as you said, they went to the start of a marathon to do this work.

So I’m not a marathon runner myself, but reading the paper, what they did was– so marathons clearly have a lot of people running in them. This was the Chicago Marathon, so it’s a major event. There’s lots and lots and lots of people involved in it. And you can’t just let everyone start running at once, that would cause complete chaos.

So what happens is that you organize the participants based, to some degree, on how fast you expect them to run, and you let them go in segments. So a group at the front gets to go first. Then you move up the people behind them, they get to run, and so on and so on.

And what the authors of this piece found was that that event, where the race organizers said, OK, the next cluster of people gets to move to the front, they told the people at the front of that cluster, now it’s time to move forward.

But the information, that it was time to move, they observed that it propagated back through the crowd as a wave, in much the way you might expect a surface wave on a lake to move when you drop a rock in it.

IRA FLATOW: That’s interesting. So people can be treated, when you look at a large mass of them, as large particles that we study as waves would move? Drops of water, lots of drops of water.

NICHOLAS OUELLETTE: That’s the idea here. It’s clearly not the same in detail, but the overall picture of how you might want to think about the crowd, that’s the idea in this paper.

And it represents something of a new approach in studying the broad field of collective movements of animals and humans. In that, instead of thinking about how to talk about the crowd as if it’s made up of people, and saying what each individual person does, the new part here is to say, OK, that crowd that itself is a thing. That thing has properties.

And by studying how the whole crowd responds to an external stimulus, we can understand those properties and make a good physics-based model for how it’s going to behave.

IRA FLATOW: Now, you don’t study people, you study insects and birds and animals.


IRA FLATOW: Is it correct that you have a little setup in your laboratory of midges that fly around?


IRA FLATOW: A 5-foot plastic cube, basically, at home. How many midges are in there?

NICHOLAS OUELLETTE: Oh, I’ve never counted them all.

IRA FLATOW: 1,000?

NICHOLAS OUELLETTE: Probably. We’re interested primarily in what happens when they swarm together, and our swarming events have something like 50 to 100 midges in them.

IRA FLATOW: So they swarm, and do they swarm like birds? Do they swarm like schools of fish, or is it the same kind of action?

NICHOLAS OUELLETTE: One answer to that is that nobody really knows if all these kinds of animal groups move in similar ways. The major difference between the swarms we study in the lab and what you might see in, say, a flock of birds or a school of fish, is that the swarm isn’t going anywhere.

So a flock of birds is definitely moving in some direction, but these kinds of swarms, you see these in the late afternoon, if you’re walking around outside. Sort of a ball of bugs floating in the air in front of you. It’s always right at head height when you’re biking through, and smacks into your face.

IRA FLATOW: Right, right. I know what you’re talking about.


IRA FLATOW: Yeah. Can you learn people, then? Is this applicable to how people move in swarms or groups?

NICHOLAS OUELLETTE: We think so. The idea behind all of this is that there’s only so many things that can happen in the world. The laws of physics are very constraining. And so by studying some kinds of collective behavior and understanding how you could model that, that framework that you develop should be applicable to many other kinds of groups, of animal groups, as well.

In much the same way– the analogy I like to make is that, when you think about how, say, materials work, so different kinds of solids, different kinds of liquids. They’re all different in detail. And solids are not liquids, they’re not gases.

But they’re all recognizable and understandable as materials, and you kind of understand how to describe the behavior of all of them in some kind of unified framework.

IRA FLATOW: If a crowd is moving, you have a large crowd of people moving, can you treat that– let’s say it’s 100,000 people in the marathon, or some people in a ballpark, and you see them do the wave or something like that. Can you treat them statistically, as you would particles or ping pong balls, or something else like that?

NICHOLAS OUELLETTE: Absolutely. Any physicist looking at this, that’s the first thing you would think of doing. Because that’s, ultimately, what we’ve been very successful doing for the past 100 years or so in treating things like gases and liquids. We know they’re made of molecules, we know how to do the statistics of the molecules and average over them to say something about the typical properties of a whole lot of them together.

The wrinkle in animal behavior comes in the fact that animals are not like molecules, and that makes the problem much, much, much more difficult. Molecules have the nice feature that, essentially, they move randomly. In a very precise sense, that means we know how to do the averaging.

But animals and people are not quite random enough to do that, in some sense. So what happens then is that the details of how they move become much more important. And there’s various laws of physics that aren’t quite obeyed in the same way, that make that problem much, much more challenging.

IRA FLATOW: Yeah, because the people in that crowd in Times Square, they want to get out of there. They’re motivated to go someplace, but random molecules are just moving randomly.


IRA FLATOW: So you have to find a way of modeling the difference– so I guess you have to split the hairs, right? You have to go with somewhere between a statistical model, and somewhere between knowing how people or animals would act in a certain direction, or motivation, and find the middle someplace.

NICHOLAS OUELLETTE: That’s right. And that’s the approach that people have taken over the years with a fair amount of success, in trying to do this. So the old standard model for collective movement of animal groups is what technically gets called agent-based modeling.

But really, you can think about it as thinking about the crowd or the flock as being made of individuals. And what you then is you take each individual and you give it some rules.

You say, OK, typically for a flock or a crowd the rules or something along the lines of, don’t get too far from everybody else, don’t bang into them, so don’t get too close. And if you’re not too far not too close, then try to go in the same direction as everybody around you, and that will maintain some kind of smooth motion.

And if you put that– sorry.

IRA FLATOW: I’m sorry, go ahead.

NICHOLAS OUELLETTE: If you put that all together on the computer and you simulate that kind of model, you get a result that looks qualitatively really, really nice. And so nice that this kind of model has been used in the computer graphics industry, in CGI and movies and in video games for 20 or 30 years, now.

IRA FLATOW: This is Science Friday from WNYC Studios. I’m Ira Flatow, talking about modeling crowds with Nicholas Ouellette, Associate Professor of Civil and Environmental Engineering at Stanford University. You are a civil engineer, I imagine you [? and Jeanie, ?] or civil engineers, they model buildings and highways and things. Do you use the kind of information you learned about crowds in constructing things?

NICHOLAS OUELLETTE: Not in construction, per se, but I think there are a lot of really exciting ideas or ways that engineers are thinking about using this kind of paradigm, these kinds of models in the future for engineering projects.

I’m in Stanford, so I live in Silicon Valley, home of self-driving cars, these days. So it’s very likely that in the fairly near future, we’re going to have a lot of autonomous cars running around on the highways and on the roads. And the most basic thing that you’d want to have happen in that situation is the cars don’t run into each other.

IRA FLATOW: Yeah, I hate it when that happens.

NICHOLAS OUELLETTE: Yeah, that’s typically not a good thing. That’s sort of, at a fundamental level, exactly what the animal groups are good at doing. The difference though, in how engineers have traditionally made that kind of system work and how animals do it, is a question of who’s in charge. Where the control, if you will, comes from.

So if you think about a normal engineered system, we’d like to know where everything is going, we’d like to have someone in charge who knows all the information and can give specific instructions to all the individuals.

That’s, in some sense, how the air traffic control network works. You have people sitting there, they know where all the airplanes are, and they make sure that everything works smoothly.

Now, birds, say, or even human crowds, that’s not the way it works. No one’s in charge. No one’s telling each individual bird in a flock what to do. And yet, the whole system functions really, really well. Birds look at what’s nearby, their local neighborhood of other birds near them. They do something, they behave in some way, and the whole system works really, really smoothly.

There’s then interest in taking that kind of idea and applying it to something like self-driving cars or swarms of drones, to achieve the same kind of robust, well-controlled fault-tolerance system, without any kind of pinch points that may lead to failure.

IRA FLATOW: But those animals must have a way of one animal, the lead animal, or whatever animal is leading them, to communicate with the rest of the other animals which way to go.

NICHOLAS OUELLETTE: Well, typically, we actually think that there is no lead animal. So the properties of the group, the fact that the group is there and functions is what we call an emergent phenomenon, from all of the little local interactions.

Think of a really big flock, thousands of birds, say. A single bird cannot see across the entire flock. It has no idea what’s happening on the other side, yet the whole thing functions as a unit.

IRA FLATOW: Yeah, it’s like watching those school of fish just turn on a dime all together.


IRA FLATOW: So there’s something called an emergent. So emergent knowledge in the flock or the school.

NICHOLAS OUELLETTE: Yeah, people talk about swarm intelligence, and things like that. That the group has some kind of emergent intelligence, reaction to its environment, and some kind of coherent way that is not top-down controlled, but rather just comes out from all of the little local interactions happening together.

IRA FLATOW: And we don’t know what that is.

NICHOLAS OUELLETTE: We don’t exactly know how to do that, no.

IRA FLATOW: But we’d like to, because we’re talking about swarms of bots or cars moving around.

NICHOLAS OUELLETTE: Exactly, exactly. And one of the things that this field has discovered over the years, that I think it is very robust at this point, that we all agree on, is that one of the cool things is that it doesn’t take much individual intelligence or complexity of the individual into the units in that flock or swarm in order for the whole group to do something complicated.

IRA FLATOW: Fascinating.

NICHOLAS OUELLETTE: Yeah. That’s really nice from the standpoint of robotics, say. So you could design a whole lot of simple, relatively stupid robots, where their ability to accomplish a complicated task comes from getting them together, rather than having to build each one with a whole lot of processing power.

IRA FLATOW: I read the Michael Crichton novel about that.


IRA FLATOW: Thank you, Dr. Nicholas Ouellete, Associate Professor of Civil and Environmental Engineering at Stanford University. Have a happy New Year.

NICHOLAS OUELLETTE: Happy New Year to you, as well.

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