Concerts and events with big crowds can sometimes become dangerous, especially when the concentration of the crowd becomes excessive, as happened in the disasters of Mecca (2006), of Loveparade (2010) or the concert by the US rapper Travis Scott in Houston (2021). This is because when the number of people is very high in a restricted space, the crowd begins to behave like a fluid And this means that the movements of a portion of crowd strongly influence those of the rest of the people, leading to dangerous situations. Let’s see how this concentration can be described with the density of the crowd, a number that can help us when we are in the middle of a many people and how science studies dangerous assemblies through mathematics in hope, in the future, to help us prevent certain disasters from being repeated.
The dynamics of the crazy crowd: a number that indicates the risk
On the occasion of large events, or other very crowded situations, serious accidents can happen, even fatal, especially when the density of the crowd It is too high, that is, if there are too many people too close to each other. There density It is a number that indicates how many people There are in a limited space. As a reference to describe the density, you usually take the number Of people in a square meter.
If in an assembly we can count on average they are up to 4 people For each square meter, then people succeed in move Enough freely And quickly in the crowd. But if the density It reaches 5 people per square meter we begin to warn the contact of people from all sides and the assembly can become dangerous. There crowd In these cases he begins to behave as if it were a fluid, And check the movements of individual people.
In this situation, if a person falls, he will not be able to get up and other people will fall on her, therefore we talk about Crowd Collapse. If the density of the crowd is greater, you also risk the Crowd Crash: People are too tightly close to the other, so much so that they cannot breathe and risk asphyxiation and/or crushing the chest case.
Too many people: the disaster Loveparade and La Mecca
In a high density situation, to trigger certain movements of the crowd that can then lead to Crowd Crash or Crowd Collapseare enough of the random (or uncontrolled) movements of some people (perhaps frightened), or the massing at a way out.
A tragic example of Crowd Crash that’s the one July 24, 2010 to Duisburg (Germany) on the occasion of the Loveparadea Dance Music Festival. The access route to the event took place through a ramp that at some point was closed by the organizers due to the overcrowding. Unfortunately, however, the ramp was at the end of a long tunnel (240m) that the crowd continued to take, ignoring the notices, in the direction of access: in a short time a overcrowding At the exit of the tunnel and a crowd that caused 510 injured and 21 deaths mainly for Crush the thoracic case.
One of the most studied cases is that of the disaster of Mecca January 2006in which over 300 pilgrims died at the Jamarat bridge. The video images of the tragedy were analyzed with a algorithm which made it possible to identify three phases:
- Initially, while the crowd approached the bridge, there is one to one decrease from the speed and to a thickening from the crowd;
- Later the crowd started a phase of repeated arrests and restarts that they are propagated like awave in the direction of the flow of the crowd that continued to thicken towards the bridge;
- Finally, perhaps because of the panic, some people started a move casually in all directions and this caused a “turbulence“In the crowd during which most of the deaths and serious injuries occurred.
How science studies dangerous assemblies
The study of the dynamics of the crowd, also for the purposes of preventing disasters, is a still open research field that mainly uses:
- study of movies of disasters that actually took place;
- Study of movies of fictitious situations which reproduce crazy in different situations;
- mathematical models with equations (even differentials) that describe the variables involved;
- computer simulations.
In 2023 a study was published, conducted at the University of Bath, who managed to identify some mathematical schemes in the way people move in a assembrail by creating some ordered files, which may vary aspect based on people’s behavior. In the case of crowded pedestrian crossingsfor example, are created spontaneously parallel file In the two verses of crossing, but if all pedestrians keep the right when they cross another pedestrian, the files are inclined.
The research developed at the University of Bath has not stopped and the team, led by T. Rogers, wondered what happens if pedestrians devote slightly from the crossing management: from the very recent study (published in March 2025) it has been found that if thedeviation angle exceeds 13 ° then the ordered files disappear and the movement of the crowd becomes messy.
When the crowd draws parables: the mathematics of movements
In more complex situations, such as that of the video below that simulates a crime of crowds of the King’s Cross station in London, other types of mathematical curves.
https://www.youtube.com/watch?v=hdvute3-qo
In this case there are two group Of people, One who crosses a room in one direction, the other that crosses it in the perpendicular direction but aiming at a smaller way out. You can see how the people belonging to the two different groups are unconsciously arranged according to form -shaped lines parable.
The reason why these studies are conducted is clear: the hope is that, being able to predict the movements of the crowds in certain situations, catastrophic results can be avoided.
