Mar 24, 2025 10:49 PM
(This post was last modified: Mar 24, 2025 10:49 PM by C C.)
https://www.eurekalert.org/news-releases/1077638
INTRO: Next time you cross a crowded plaza, crosswalk, or airport concourse, take note of the pedestrian flow. Are people walking in orderly lanes, single-file, to their respective destinations? Or is it a haphazard tangle of personal trajectories, as people dodge and weave through the crowd?
MIT instructor Karol Bacik and his colleagues studied the flow of human crowds and developed a first-of-its-kind way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.
In a paper appearing in the Proceedings of the National Academy of Sciences, the researchers consider a common scenario in which pedestrians navigate a busy crosswalk. The team analyzed the scenario through mathematical analysis and simulations, considering the many angles at which individuals may cross and the dodging maneuvers they may make as they attempt to reach their destinations while avoiding bumping into other pedestrians along the way.
The researchers also carried out controlled crowd experiments and studied how real participants walked through a crowd to reach certain locations. Through their mathematical and experimental work, the team identified a key measure that determines whether pedestrian traffic is ordered, such that clear lanes form in the flow, or disordered, in which there are no discernible paths through the crowd. Called “angular spread,” this parameter describes the number of people walking in different directions.
If a crowd has a relatively small angular spread, this means that most pedestrians walk in opposite directions and meet the oncoming traffic head-on, such as in a crosswalk. In this case, more orderly, lane-like traffic is likely. If, however, a crowd has a larger angular spread, such as in a concourse, it means there are many more directions that pedestrians can take to cross, with more chance for disorder.
In fact, the researchers calculated the point at which a moving crowd can transition from order to disorder. That point, they found, was an angular spread of around 13 degrees, meaning that if pedestrians don’t walk straight across, but instead an average pedestrian veers off at an angle larger than 13 degrees, this can tip a crowd into disordered flow.
“This all is very commonsense,” says Bacik, who is a instructor of applied mathematics at MIT. “The question is whether we can tackle it precisely and mathematically, and where the transition is. Now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow.”
The study’s co-authors include Grzegorz Sobota and Bogdan Bacik of the Academy of Physical Education in Katowice, Poland, and Tim Rogers at the University of Bath in the United Kingdom.
Right, left, center. Bacik, who is trained in fluid dynamics and granular flow, came to study pedestrian flow during 2021, when he and his collaborators looked into the impacts of social distancing, and ways in which people might walk among each other while maintaining safe distances. That work inspired them to look more generally into the dynamics of crowd flow.
In 2023, he and his collaborators explored “lane formation,” a phenomenon by which particles, grains, and, yes, people have been observed to spontaneously form lanes, moving in single-file when forced to cross a region from two opposite directions. In that work, the team identified the mechanism by which such lanes form, which Bacik sums up as “an imbalance of turning left versus right.” Essentially, they found that as soon as something in a crowd starts to look like a lane, individuals around that fledgling lane either join up, or are forced to either side of it, walking parallel to the original lane, which others can follow. In this way, a crowd can spontaneously organize into regular, structured lanes.
“Now we’re asking, how robust is this mechanism?” Bacik says. “Does it only work in this very idealized situation, or can lane formation tolerate some imperfections, such as some people not going perfectly straight, as they might do in a crowd?” (MORE - details, no ads)
INTRO: Next time you cross a crowded plaza, crosswalk, or airport concourse, take note of the pedestrian flow. Are people walking in orderly lanes, single-file, to their respective destinations? Or is it a haphazard tangle of personal trajectories, as people dodge and weave through the crowd?
MIT instructor Karol Bacik and his colleagues studied the flow of human crowds and developed a first-of-its-kind way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.
In a paper appearing in the Proceedings of the National Academy of Sciences, the researchers consider a common scenario in which pedestrians navigate a busy crosswalk. The team analyzed the scenario through mathematical analysis and simulations, considering the many angles at which individuals may cross and the dodging maneuvers they may make as they attempt to reach their destinations while avoiding bumping into other pedestrians along the way.
The researchers also carried out controlled crowd experiments and studied how real participants walked through a crowd to reach certain locations. Through their mathematical and experimental work, the team identified a key measure that determines whether pedestrian traffic is ordered, such that clear lanes form in the flow, or disordered, in which there are no discernible paths through the crowd. Called “angular spread,” this parameter describes the number of people walking in different directions.
If a crowd has a relatively small angular spread, this means that most pedestrians walk in opposite directions and meet the oncoming traffic head-on, such as in a crosswalk. In this case, more orderly, lane-like traffic is likely. If, however, a crowd has a larger angular spread, such as in a concourse, it means there are many more directions that pedestrians can take to cross, with more chance for disorder.
In fact, the researchers calculated the point at which a moving crowd can transition from order to disorder. That point, they found, was an angular spread of around 13 degrees, meaning that if pedestrians don’t walk straight across, but instead an average pedestrian veers off at an angle larger than 13 degrees, this can tip a crowd into disordered flow.
“This all is very commonsense,” says Bacik, who is a instructor of applied mathematics at MIT. “The question is whether we can tackle it precisely and mathematically, and where the transition is. Now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow.”
The study’s co-authors include Grzegorz Sobota and Bogdan Bacik of the Academy of Physical Education in Katowice, Poland, and Tim Rogers at the University of Bath in the United Kingdom.
Right, left, center. Bacik, who is trained in fluid dynamics and granular flow, came to study pedestrian flow during 2021, when he and his collaborators looked into the impacts of social distancing, and ways in which people might walk among each other while maintaining safe distances. That work inspired them to look more generally into the dynamics of crowd flow.
In 2023, he and his collaborators explored “lane formation,” a phenomenon by which particles, grains, and, yes, people have been observed to spontaneously form lanes, moving in single-file when forced to cross a region from two opposite directions. In that work, the team identified the mechanism by which such lanes form, which Bacik sums up as “an imbalance of turning left versus right.” Essentially, they found that as soon as something in a crowd starts to look like a lane, individuals around that fledgling lane either join up, or are forced to either side of it, walking parallel to the original lane, which others can follow. In this way, a crowd can spontaneously organize into regular, structured lanes.
“Now we’re asking, how robust is this mechanism?” Bacik says. “Does it only work in this very idealized situation, or can lane formation tolerate some imperfections, such as some people not going perfectly straight, as they might do in a crowd?” (MORE - details, no ads)