Anyone who has crossed a very busy street has lived it: sometimes pedestrian traffic is organized spontaneously in invisible lanes where each person finds their space. On other occasions, the same place becomes a tangle of erratic trajectories, where everyone dodges all without a clear pattern. What determines that a situation derives in order or in chaos? An international team of researchers has found the key: There is a critical angle from which the pedestrian flow is completely disorganized.
The finding, led by the mathematician Tim Rogersof the Bath Universityand the physicist Karol Bacikof the Mithas been published in the magazine Proceedings of the National Academy of Sciences. Through a theoretical model, computer simulations and experiments with volunteers, the study shows that When pedestrian trajectories differ more than 13 degrees from each other, the natural lanes disappear and disorder is imposed.
A physics of human movement
The team has used physics tools to analyze what they call “Active matter”a concept that encompasses systems composed of entities that move for themselves, such as bacteria, animals or people. Although pedestrians make conscious decisions, their collective behavior It can be modeled as a flow of particles with preferential trajectories They adjust to avoid collisions.
In bidirectional scenarios, such as a narrow zebra crossing where people walk in opposite senses, parallel lanes are formed spontaneously. But when the space design allows oblique trajectories – for example, in wider or diagonal steps -, The variety of addresses increases and, with this, the risk of collapse in the organization of the group.
The angle that changes everything
The key is what the authors define as Angular dispersionthat is, the variation in the individual directions of the pedestrians. If this dispersion exceeds 13 degreesthe balance is broken and The lanes disappearwhich slows traffic and can generate dangerous situations. “The more tidy a flow is, the more efficient it becomes. When the order is lost, the entire group advances more slowly”Bacik explains.
This threshold was confirmed in experiments carried out in a gym, where participants had to cross a rectangular space from assigned input and output points. When the destination points were aligned, lanes were formed; When they were distributed randomly, chaos arose.
From the theory to the street
Beyond the theory, the study raises concrete applications in urban design. “Our model allows to predict how a crowd will behave depending on how the public space is configured”Rogers points out. This can be applied not only to zebra crossings, but also to train stations, stadium tickets, festivals or airports, where The poorly managed pedestrian flow can lead to accidents.
One of the recommendations is that It is not always necessary to expand the crossessince a greater width can favor oblique angles and with it disorganization. Similarly, place a diagonal step towards a point of attraction – a subway mouth, for example – can alter the flow of flow.
Simulate crowds, anticipate problems
The study also opens new ways to simulate urban behaviors without resorting to complex psychological models. Instead, researchers use equations similar to those used to describe fluids, which allows anticipate friction or congestion points from space geometry and circulation habits.
One of the study innovations has been to apply a parameter of order – a mathematical measure of the degree of alignment in the flow – that allows quantify the exact moment in which the transition between order and disorder occurs. In the tests, when this indicator fell to zero, the chaos was total.
A public security problem
Although research is in the field of physics and mathematics, its implications directly reach urbanism and public space management. In high density contexts – such as concerts, manifestations or evacuations -, Understand the conditions that favor order can save lives.
“Our intention is to provide simple tools so that those who design urban spaces can promote safe and efficient flows”, Says Bacik. In fact, the authors already work to apply their models to real crosses in cities in Europe and the United States, adjusting the variables to the local reality.
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