Quotes of the Day

No one has ever been sure of exactly how many people attended the Love Parade music festival in Duisburg, Germany on July 24, 2010. The original estimate was 800,000; police later revised that down to 400,000. Either way, it was far too many: the site could safely accommodate only 250,000.

Officials are completely certain about how many people were injured in the crowd stampede that occurred a few hours into the festival — exactly 510. They're certain too of how many died: 21. As with all such crowd mismanagement disasters, investigators were quick to try to assign blame — to the police, the event planners, the design of the venue and, of course, the victims themselves. They surely panicked, went collectively mad. That's the nature of a stampede, isn't it?

Now, however, a two-year investigation conducted by complexity researchers Dirk Helbing and Pratik Mukerji of the Swiss Federal Institute of Technology, has identified an additional, critical culprit in the Duisburg stampede: physics — particularly the complex science of fluid dynamics. Their paper, just published online in EPJ Data Science, relies on police reports, planning records, personal accounts and other documentary evidence, as well as a few additional tools that weren't available to crowd-control investigators in the past: YouTube videos, Google Earth maps and 360-degree photography. The disaster, Helbing and Mukerji conclude, was less a result of human error — though that was surely at work too — than of "amplifying feedbacks and cascading effects, which are typical for systemic instabilities." In other words, they wrote: "Things can go terribly wrong, in spite of no bad intentions from anyone."

For two researchers who take pains to absolve rather than indict the usual suspects in an event like this, Helbing and Mukerji begin with a scathing description of the Love Parade site — which was wholly unsuited to the job it was being asked to do. The venue was an old railyard once used for receiving and storing freight. It was bounded by railroad tracks on the east and a freeway on the west — which were nearly as good as walls for penning people in. There was only one principal way to enter exit or enter the event site: a deep, high-walled ramp that fed into a long tunnel. A 360-degree photo of the site is included in the paper, and while the German captions make the exact details opaque to an English-speaking audience, the cattle-chute quality of the set-up is unmistakable.

Making things worse, while the ramp and tunnel were 85 ft. (26 m) and 66 ft. (20 m) wide respectively, that was nowhere near enough to accommodate up to half a million people. Crowd-control fences at one point in the tunnel exacerbated things, cutting its width almost in half and creating a dangerous bottleneck. And since the way out of the railyard was the same as the way in, the relatively small stream of people who for various reasons were trying to exit even as the event was beginning became a reverse flow against the much larger river of people trying to enter. That reduced tunnel capacity by up to 14%. By 3:00 PM — or three hours after the site opened — about 750 people were streaming into the grounds per minute and 250 were leaving. In order for a safe flow rate to have been maintained, there should have been no more than 1.75 people occupying any given square meter of space. Instead, there were up to five.

Once a crowd gets jammed that tightly, a number of behavioral factors come into play. First, a need to flee. "The density, noise and chaos in a ... crowd cause a natural desire to leave," the authors write. This is made worse by the fact that while it's easy to see the general direction a mass of people are moving if you're even a few feet above them, when you're part of the scrum, you're essentially blind. That leads to anxiety — which is a short step from fear, which is a very short step from panic.

At 4:02 PM, according to police records, there was a sudden, violent surge in the crowd — some of it moving toward a narrow stairway that was one of the few things visible above the sea of heads; at 4:24, people who could not reach the stairs began climbing light poles to escape; at 4:38, the first signs of victims losing consciousness began; at 4:53, the first emergency vehicles arrived, as did helicopters dangling evacuation ropes. Police tried to control the crowd by forming a cordon, but it was quickly breached. The video record of that moment is nothing short of chilling — but what you can see on the screen is only part of the story.

Human bodies moving en masse have been compared to fish in a school or molecules in water, but the better analogy is to fine grains in a stream of sand. One body pressing up against another exerts a force, which is added to that second body as it presses up against a third. This leads to a rapid accumulation of weight and energy, which propagates quickly and violently in all directions. "At occupancies of about seven persons per square meter, the crowd becomes almost a fluid mass," the paper explains. "Force chains may form [leading to] an uncontrollable kind of dynamics, which is called crowd turbulence or a crowd quake."

The power of such a human temblor is hard to overstate. Victims can be lifted out of their shoes and their clothing is often torn away. Compression makes breathing difficult — a problem exacerbated by the accelerated respiration that comes with panic — and while people killed in a stampede are often said to have been crushed to death, what typically kills them is asphyxiation. As more people succumb, they go limp and fall, which leads to a cascade of stumbles and pile-ups. People at the bottom of the resulting heaps may asphyxiate too from the sheer weight of those on top of them.

For all the awful physics behind the Love Parade disaster, Helbing and Mukerji stress that the same fluid dynamics can be used to prevent similar tragedies in the future. Ample check valves — in the form of multiple exits — need to be built into crowd control corridors to relieve pressure in the same way it's relieved in a steam pipe. Density must be limited to a predetermined number of people per square meter, which reduces the propagation of forces from one body to the next. Crowds moving in different directions should never be permitted to collide or intersect. Just as traffic circles can make merging with or exiting a stream of cars easier, so too can circularizing foot traffic prevent collisions and gridlock.

And in case civic planners and event coordinators consider all this too difficult, Helbing and Mukerji include a helpful example of a venue they believe was perfectly designed to handle the modern physics of crowd control: the Roman Coliseum, constructed a cool 2,000 years ago. With its seating capacity of 73,000 and its 76 exits built completely around its base, it could be evacuated in as little as five minutes. No modern stadium — even ones with just half the seating capacity — has yet matched that feat. Until all such mass venues can, we will always be at risk of another Love Parade.

• Jeffrey Kluger