In his first and arguably most famous novel, The Sun Also Rises, Ernest Hemingway wrote tersely but lovingly about the annual running of the bulls in Pamplona, Spain, during the seven-day Festival of San Fermín. "One man fell, rolled to the gutter and lay quiet," the protagonist, Jake, observes while watching from a balcony. "But the bulls went right on and did not notice him. They were all running together." A new analysis of the physics behind the dynamics of the crowds running from the bulls takes the probability of falling into account, according to a recent paper published in the Proceedings of the National Academy of Sciences.
Local legend holds that the running of the bulls dates back to northeastern Spain in the early 14th century. Cattle herders at the time found that hurrying the beasts through the streets was an efficient way to move livestock from fields or barges to the market—or the bullfighting ring. Young men started racing in front of the charging bulls, competing to see who could make it safely to the bull pens without being overtaken (or worse, trampled and gored). The race eventually became part of the San Fermín festival and is now the festival's most popular event.
Per official records, 15 people have died during the running of the bulls in Pamplona since 1910, usually from being gored. Sometimes bystanders can be injured or killed, too, especially if they're trying to capture live footage of the event with their smartphones. That happened during a different bull run, this time in Villaseca de la Sagra, Spain. In 2015, a 32-year-old man was gored from behind while attempting to share his experience by way of a smartphone recording. The victim died of neck and thigh wounds. Hot tip: maybe running away from charging bulls isn't the best time to try to snap a selfie.
As I've written previously, pedestrian traffic is a fascinating case study in dynamic collective behavior, and hence it holds much interest for physicists. (Back in September, a pair of then-recent papers on pedestrian traffic dynamics were honored with Ig Nobel Prizes in physics and kinetics, respectively.) Physicists typically model such systems as interacting matter particles, with social forces acting on people in similar ways to physical forces. But modeling such a complex system is difficult, in part because of a dearth of high-quality experimental data. This is especially true in the case of pedestrians fleeing from real danger—say, six bulls charging through the streets.
Although the running of the bulls is often offered as an example of so-called "competitive pedestrian dynamics," Daniel Parisi—a co-author of the recent PNAS paper and a physicist at the Instituto Tecnologico de Buenos Aires in Argentina—noticed that the scenario had not yet been studied in detail. So he and his colleagues set about to rectify that deficiency. "Runners, first waiting for and then escaping from bulls, constitute a fascinating annual scenario of real fleeing pedestrians, becoming an invaluable opportunity for studying and understanding extreme pedestrian dynamics," the authors wrote.
The researchers recorded two runs on two consecutive days on July 8 and 9, 2019, in two different spots on Estafeta Street. (The Pamplona running of the bulls was canceled in 2020 and 2021 because of the pandemic.) They were able to extract the trajectories of individual bulls and runners from those recordings for analysis. Runners (and spectators) began the morning milling about the route to the bull ring. Once the ring doors were opened, most of the spectators moved inside. That reduced street congestion since mostly just the runners remained, waiting for the bulls to be released.
The team observed a shockwave of running pedestrians moving at high speed a few seconds before the first bulls arrived, triggering the start of the race. Once the runners in front and the bulls behind them passed, a wake of runners with decreasing speed formed behind. Within 40 or 50 seconds, the system returned to a more normal situation of pedestrians walking at a leisurely pace along the street.
Parisi et al. knew that many prior studies of pedestrian systems relied on a fundamental speed-density diagram to model such systems. The speed of a given group of pedestrians usually decreases as the density of the crowd increases. "Under ordinary circumstances, this behavior can be explained because people try to avoid physical contact and slow down when the available space reduces," they wrote in their paper.
But the researchers were surprised to find that this basic assumption of the model doesn't hold in the case of the running of the bulls: pedestrian speed actually increases with density when people are fleeing from a moving threat. There is a time-dependent aspect since pedestrian speed depends upon the distance between the runners and the bulls. (A charging bull does have a way of instilling a sense of urgency.) Parisi et al. found they had to modify the model to account for not just speed, density, and time dependency, but also the probability that one or more of the pedestrians would fall, which correlates to crowd pressure.
Their analysis of the footage showed that falls frequently coincided with the passage of the bulls, sometimes triggering dangerous pileups (a montón), particularly at the narrowest part of the route at the entrance to the bull ring. This is a classic bottleneck scenario, a dominant factor in the formation of deadly crowd surges—such as the stampede that occurred during the January 2006 Hajj to Mecca, killing 36 people. Pamplona's last pileup occurred in 2013.
"Less available space can cause accidental physical contact of runners, which may affect their motion and trigger their falling," the authors wrote. "Therefore the probability of falling in the bull run will vary drastically over time, being significant only in the transition between [states] coinciding with the bulls' passage." The probability of falling also depends on whether there was already a fallen runner on the ground. Of the 20 falls recorded, 14 were part of a small group of runners who fell. Only six were uncorrelated with other runners.
DOI: PNAS, 2021. 10.1073/pnas.2107827118 (About DOIs).
