Researchers led by Denis Bartolo, a physicist at the École Normale Supérieure (ENS) of Lyon, France, have constructed a theoretical model that forecasts the movements of confined, densely-packed crowds. The study could help predict potentially life-threatening crowd behaviour in confined environments.
To investigate what makes some confined crowds safe and others dangerous, Bartolo and colleagues – also from the Université Claude Bernard Lyon 1 in France and the Universidad de Navarra in Pamplona, Spain – studied the Chupinazo opening ceremony of the San Fermín Festival in Pamplona in four different years (2019, 2022, 2023 and 2024).
The team analysed high-resolution video captured from two locations above the gathering of around 5000 people as the crowd grew in the 50 x 20 m city plaza: swelling from two to six people per square metre, and ultimately peaking at local densities of nine per square metre. A machine-learning algorithm enabled automated detection of the position of each person’s head; from which localized crowd density was then calculated.
“The Chupinazo is an ideal experimental platform to study the spontaneous motion of crowds, as it repeats from one year to the next with approximately the same amount of people, and the geometry of the plaza remains the same,” says theoretical physicist Benjamin Guiselin, a study co-author formerly from ENS Lyon and now at the Université de Montpellier.
In a first for crowd studies, the researchers treated the densely packed crowd as a continuum like water, and “constructed a mechanics theory for the crowd movement without making any behavioural assumptions on the motion of individuals,” Guiselin tells Physics World.
Their studies, recently described in Nature, revealed a change in behaviour akin to a phase change when the crowd density passed a critical threshold of four individuals per square metre. Below this density the crowd remained relatively inactive. But above that threshold it started moving, exhibiting localized oscillations that were periodic over about 18 s, and occurred without any external guiding such as corralling.
Unlike a back-and-forth oscillation, this motion – which involves hundreds of people moving over several metres – has an almost circular trajectory that shows chirality (or handedness) and a 50:50 chance of turning to either the right or left. “Our model captures the fact that the chirality is not fixed. Instead it emerges in the dynamics: the crowd spontaneously decides between clockwise or counter-clockwise circular motion,” explains Guiselin, who worked on the mathematical modelling.
“The dynamics is complicated because if the crowd is pushed, then it will react by creating a propulsion force in the direction in which it is pushed: we’ve called this the windsock effect. But the crowd also has a resistance mechanism, a counter-reactive effect, which is a propulsive force opposite to the direction of motion: what we have called the weathercock effect,” continues Guiselin, adding that it is these two competing mechanisms in conjunction with the confined situation that gives rise to the circular oscillations.
The team observed similar oscillations in footage of the 2010 tragedy at the Love Parade music festival in Duisburg, Germany, in which 21 people died and several hundred were injured during a crush.
Early results suggest that the oscillation period for such crowds is proportional to the size of the space they are confined in. But the team want to test their theory at other events, and learn more about both the circular oscillations and the compression waves they observed when people started pushing their way into the already crowded square at the Chupinazo.
If their model is proven to work for all densely packed, confined crowds, it could in principle form the basis for a crowd management protocol. “You could monitor crowd motion with a camera, and as soon as you detect these oscillations emerging try to evacuate the space, because we see these oscillations well before larger amplitude motions set in,” Guiselin explains.
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