The physics that keeps a crowd from becoming a stampede

Every July, at the opening ceremony of the San Fermín festival signaling the imminent start of the running of the bulls in Pamplona, Spain, more than 5,000 people cram into the city’s central plaza.

Participants have described the raucous crush of people to Denis Bartolo, a physicist at the École Normale Supérieure in Lyon, France, who hasn’t dared step foot in the plaza himself. “It’s not just that you’re feeling uncomfortable,” he said he’d been told. “It becomes painful like you can feel pressure on your chest.”

Over several years, he studied the event hoping to one day help prevent stampedes that can turn lethal in large events. In a paper published in the journal Nature, Bartolo, and his colleagues say it may be possible to predict the spontaneous motion of a large crowd once the density of people crosses a critical threshold.

Bartolo’s team mounted cameras on the balconies of two buildings and found that the crowds turned out to be less chaotic than they might have otherwise appeared. Within the sea of people, circular oscillations were detected. “We are talking about hundreds, if not thousands, of people, all following the same circular trajectory in sync,” Bartolo said.

In addition, the orbital motions, in which each person traces out a rough circle from their starting point in the crowd, took 18 seconds to complete in this particular plaza.

The team then examined surveillance footage of the 2010 Love Parade in Duisburg, Germany, where 21 died in a stampede, and detected the same oscillations emerging just before the stampede. The researchers found that above a certain density, these movements emerge spontaneously. They don’t depend on some internal or external force, such as people actively pushing one another.

Bartolo suggests monitoring crowds for these motions. Detecting them can offer wa arning of danger ahead. By catching oscillations when they’re small, event organizers could ask the crowd to disperse or stand still, before the orbits grow in size and lead to people being crushed or trampled.

This article originally appeared in The New York Times.