Have you ever wondered why walking from point A to B can be easy in some places, and incredibly frustrating in others? Well, scientists were curious about it too, and have now worked out the mathematical equation that underpins how we navigate sidewalks, and why, collectively, it descends into chaos so quickly.
Researchers have uncovered the scientific logic at the root of pedestrian traffic flow, and it’s more fascinating than you might think. And it’s not the number of people, but their individual behavior, that drives it.
In 2021, an instructor of applied mathematics published research on crowd flow and social distancing, giving him and his team the idea to study pedestrian behavior more acutely. Two years later, they looked at “lane formation” – which is observed in particles, grains, and ultimately people. Essentially, they found that if it looked like a lane was forming in a crowd, people would either join it or walk parallel to it.
Back then, they used the model of a crosswalk to develop a theory as to how much “angular spread” – pedestrians veering off these invisible lanes – it would take for order to descend into chaos. And they found that all it took was someone to veer off this lane by around 13 degrees to sow the seeds of collective disorder.
“Now we’re asking, how robust is this mechanism?” said the researcher. “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?”
In the new study, the team switched focus from what degree it takes to cause disorder, to instead looking at the moment this disorder is triggered.
“If you think about the whole crowd flowing, rather than individuals, you can use fluid-like descriptions,” explained the researcher. “It’s this art of averaging, where, even if some people may cross more assertively than others, these effects are likely to average out in a sufficiently large crowd. If you only care about the global characteristics like, are there lanes or not, then you can make predictions without detailed knowledge of everyone in the crowd.”
Using fluid flow, the researchers altered the parameters to apply to the crosswalk and pedestrians, and simulated the foot traffic with a group of people crossing the floor of a gymnasium as they would a road.
Out of this, they found that pedestrians in a crosswalk are more likely to form lanes, when they walk relatively straight across, from opposite directions. This order largely holds until people start veering across at more extreme angles. Then, the equation predicts that the pedestrian flow is likely to be disordered, with few to no lanes forming.
Karol Bacik, et al
“This all is very commonsense,” says the researcher. “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.”
In their experiment, participants crossing from each other side wore hats with unique barcodes on the top, with an overhead camera capturing the movement and tracking individuals. This was repeated many times to better assess patterns. And much like the team’s earlier 13-degree prediction, it was around this point where the invisible lanes that had formed would break up. And, not surprisingly, the more people veering off the path by 13 degrees or more, the amount of disorder also increased.
How long does it take for this to occur? That depends on many other factors – for example, we’ve all tried to cross a road in a straight line from A to B, when someone has decided they need to walk in a more direct line to, say, the bus stop, or a cyclist has veered into the foot-traffic zone. Which is why the team wants to now test this in a variety of real-world situations.
“We would like to analyze footage and compare that with our theory,” said the researcher. “And we can imagine that, for anyone designing a public space, if they want to have a safe and efficient pedestrian flow, our work could provide a simpler guideline, or some rules of thumb.”
So, the next time you’re in a crowd that seems more difficult than it should be, have a look around to see just who isn’t sticking to the “13-degree rule” …
The study was published in the Proceedings of the National Academy of Sciences.
Source: MIT via EurekAlert!
