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. The crowd starts the morning dressed in white. By noon, much of their clothing has been dyed pink by the free-flowing sangria.
Participants in the event 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. “The density of people is so high that 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 filmed and studied the event with the goal of perhaps one day helping prevent stampedes that can turn lethal in large public events. In a paper published Wednesday in the journal Nature, Dr. Bartolo and his colleagues say it may be possible to predict the spontaneous motion of a large crowd in a confined space once the density of people crosses a critical threshold.
Studying large, densely packed crowds is notoriously difficult. “You cannot just invite a thousand people to participate in an experiment,” Dr. Bartolo said. Even if he could, “I wouldn’t know how to guarantee their safety,” he added.
That’s why the San Fermín festival was so appealing. It involves thousands of people who gather predictably, and relatively calmly, each year.
Dr. Bartolo and his colleagues mounted cameras on the upper balconies of two buildings on opposite sides of the plaza to film the attendees amassed below. “If you take a look at the video, indeed the dynamics seem to be erratic, chaotic, turbulent,” he said. But he wondered whether he could tease out an organizing principle that governed the movements of the crowd.
Analyzing the footage presented a challenge akin to studying the flow of water. “Of course you cannot detect the position of every single molecule of water. It’s impossible,” Dr. Bartolo said. And yet there are mathematical techniques from the field of fluid dynamics that allow researchers to measure the flow of a material by inspecting its direction and velocity. Dr. Bartolo applied these same methods to the San Fermín festival.
The crowds turned out to be less chaotic than they appeared. Instead, the researchers detected circular oscillations within the sea of people. “We are talking about hundreds, if not thousands, of people, all following the same circular trajectory in sync,” Dr. Bartolo said.
In addition, the orbital motions, in which each person traces out a rough circle from their individual starting point in the crowd, took 18 seconds to complete in this particular plaza. The timing was so reliable that Dr. Bartolo said “you can set your clock” to the dynamics of this crowd, even if the movements might initially seem random.
The research team then applied what they’d learned to a deadly stampede. They examined surveillance footage of the 2010 Love Parade in Duisburg, Germany, where 21 died and hundreds more were injured in a stampede. “And we detected the very same oscillations,” which emerged just before the deadly stampede, Dr. Bartolo said.
When the researchers built a mathematical model of crowd mechanics, they found that above a critical density of people, these circular movements emerge spontaneously. They don’t depend on some internal or external force, such as people actively pushing one another.
As a safety precaution, Dr. Bartolo suggests monitoring densely packed crowds for these orbital motions. Detecting them can offer advance warning of the emergence of dangerous and uncontrolled movements. By catching oscillations when they’re small, he says 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.
“We’re not quite there yet,” Annalisa Quaini, a computational mathematician at the University of Houston who wasn’t involved in the study, said of such real-world applications. It’s one thing to have a well-lit venue filmed with high-quality cameras. But grainy nighttime security footage, for instance, may not reveal the telltale circular movements.
Still, Dr. Quaini called the research an important contribution to understanding the collective behavior of large dense crowds.
“This is a huge effort,” she said. “And one day, we will be able to use it in a practical setting.”
