Scientists from France and Spain have applied the maths of fluid dynamics to human crowds, creating better predictions for crowd behaviour and a protocol for improved safety.
Dense crowds create some of the most dangerous environments in modern society with dangers to individuals including suffocation, stampedes, and getting pressed against walls.
Published in the prestigious journal, Nature, the researchers ignore previous approaches that focus on individual behaviour, and then scales up. Instead, they take a top-down approach and treat the crowds as a continuous medium with properties like density and velocity.
Opening of the 2023 edition of the San Fermìn festival, Pamplona, Spain. Credit: Bartolo Lab, ENS de Lyon.
“Stir your morning tea or coffee and watch,” write the authors led by François Gu of ENS Lyon in France. “To explain the formation of a vortex in your hot beverage, physicists, engineers and mathematicians treat fluids as continua and ignore the complex dynamics at the molecular scales.”
To study crowd behaviour, Gu and colleagues videoed the opening ceremony of the San Fermín festival in Pamplona, Spain (infamous for its running of the bulls event held in the following days). Every year, more than 5,000 people crowd into a plaza measuring 50 metres by 20 metres (164 feet by 65 feet).
The authors found that once the crowd reached a density of nine people per square metre, it behaved like a fluid with wave-like movements occurring in large pockets of the crowd. These waves or oscillations coordinated the motions of hundreds of individuals without any external prompts, such as instructions given by presenters or pushing from someone in the crowd.
Instead, the size of the space afforded to the crowd appeared to drive the timing of the oscillations, with smaller spaces having shorter oscillations. This insight, and the related physics equations the authors define based on the data they collected, could help event organisers predict crowd motion.
To show that their findings are broadly applicable, the authors applied their model to video of the 2010 Love Parade incident in Germany in which a panicked crowd behaviour resulted in 21 deaths and more than 500 injuries. The authors’ model correctly predicted the crowd movements at the onset of the disaster.
“Our findings provide a practical strategy to anticipate dangerous crowd behaviour in confined environments,” conclude the authors.
