Can we predict crowd behavior patterns using simple laws of physics?

The clash of predicting behavioral patterns and physics concepts is something we see very rarely. However, with the ideal gas law, it is possible to predict the behavior of a crowd in almost any given environment. All the variables involved in the equation represent a specific part of group behavior and allow such predictions to be possible.

There are few instances where the concepts of physics can be applied to predicting crowd behavior. Though there are sciences, such as neuroscience and biology, that use the concepts of physics to explain the reasons for certain phenomena in human behavior, the prediction of crowd behavior remains a field dominated by the social sciences such as psychology. However, it is possible to predict behavior with thermodynamic concepts including the ideal gas law. The ideal gas law describes the behavior of ideal gas particles in a closed system with the equation: PV = nRT or P = nRT/V for our purposes where R is the ideal gas constant. 

Since pressure, P, describes the net force exerted on the sides of a container per square unit, we can use pressure to model the force exerted by people in a closed room. The number of moles of gas is represented by n which would be directly proportional to pressure, P. This means that increasing the number of people in a room would increase the internal pressure they exert on the walls. Logically, this makes sense. In a crowded room, we can imagine that people are pushing are colliding and pushing each other until cascades to those against the four walls. On the other hand, if it were only one person in the same room, there would be a noticeable difference in the force exerted on the walls. Furthermore, T represents the temperature of the ideal gas and is proportional to the kinetic energy of the molecules. Thus, by increasing the energy of those in the room, the internal pressure will also increase according to the ideal gas law. Imagine two identical rooms with the same number of children. If in one room, all the children are on a sugar rush, theoretically, they would collide with the wall more often and perhaps with more force, due to their energy, than a room filled with children just waking. Finally, volume is represented by V and is inversely proportional to pressure. Considering two rooms with different dimensions but the same number of people with the same energy, the smaller of the rooms would experience greater force on the walls. This is because the density of people is so much greater in the smaller room that they collide with each other and the walls more often, resulting in greater pressure.

Despite this equation’s intended use to predict the behavior of ideal gases, it proves to be a relatively accurate model when considering the above analogies. Though the analogies are only applied to rooms, they can be extended to predict the dangers of a crowd exiting a stadium or even protests.


Shlok Bhattacharya

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