If pedestrian flows move in opposite directions, traces form under certain conditions that enable efficient way through. In other cases, however, there is a chaotic crowd. A study has now dealt with the transition between these conditions. Accordingly, the flow of people flow efficiently as long as everyone goes more or less straight. However, as soon as several individuals move at an angle of more than 13 degrees to the direction of the river, chaos occur. The results could have an impact on urban planning and, for example, make it possible to make pedestrian crossings more efficient.
Be it in an overcrowded shopping arcade, a station hall or on a wide pedestrian crossing in the city center: If many people want in different directions, a confusing crowd quickly arises that slows down everyone involved. It looks a little better when people strive for two directly opposite directions. In such cases, alleys often form spontaneously in the pedestrian stream, through which the individuals who want to go in the same direction can go together together.
Flows of people on the pedestrian crossing
“The dynamic processes within the crowd affect security, but the prediction of the kind of pedestrian current is not easy,” explains a team around Karol Bacik from the Massachusetts Institute of Technology (with) in Cambridge. In order to find out what marks the transition between orderly and chaotic pedestrian flows, the researchers combined mathematical simulations and controlled experiments.
As a scenario, the research team chose a strongly frequented pedestrian crossing. In what path do the individuals meander through the crowd, how do they differ and how does that affect the path of the other individuals and the collective movement? In order to answer these questions mathematically, Bacik and his team use equations that are usually used to describe fluid currents. “If you don’t think of individual molecules, but the entire amount that flows, you can use liquid -like descriptions,” explains Bacik. “So you can make predictions without having detailed knowledge of all people in the crowd.”
Apparent abbreviation leads to chaos
The result: As long as most people cross the pedestrian path on a straight path, streets spontaneously form, which ensure an efficient flow of the human current. But if people differ too much from this direction of river – for example because they want to cut their way by crossing the street at an angle – a disordered crowd is created. The excretion of individuals forced the alternative maneuver of others, so that ultimately everyone involved progresses more slowly. Based on their calculations, the researchers found that the critical angle of the deviation was 13 degrees. Compared to minor deviations, the alley is stable, but it collapses in larger ones.
In order to check whether these results fit reality, the team carried out a number of experiments in which large groups of volunteers asked to cross a stylized pedestrian crossing in a sports hall. The researchers presented the start and target points of the test subjects, so that they either cross the road directly or at an angle. And indeed: the experimental results matched the mathematical predictions. The transition from an orderly to an disordered current was, for example, with the theoretically predicted deviation angle of 13 degrees. In addition, the experiments confirmed that the crowd is becoming less and less efficient with increasing disorder.
Applications in urban planning
“Our work could give anyone to a public space to anyone who has a public space when it comes to ensuring a safe and efficient pedestrian flow,” says Bacik. For example, the study indicates that narrower pedestrian crossings can be more efficient than width because they enable fewer deviations from the straight-out route.
For future projects, the researchers are also interested in using and checking their results in complex real environments. “So far we have focused on the simplest scenarios in which people cross the street, but if we take into account the special features of a specific city, our model can make tailor -made predictions about how people will behave,” said the team.
Source: Karol Bacik (Massachusetts Institute of Technology, Cambridge, USA) et al., Proceedings of the National Academy of Sciences, DOI: 10.1073/PNAS.2420697122