Why a dense crowd sometimes starts to sway

Crowd measurements in Pamplona reveal that a critical density can give rise to coordinated orbital movements. A model explains the role of confinement and a particular kind of friction.

In a tightly packed crowd, people can no longer choose their path freely. Measurements taken during several editions of the San Fermín festival in Pamplona show that, above a critical density, groups of hundreds of people can start turning together, without any external signal directing their movement. This phenomenon, studied by physicists, resembles neither a simple surge nor a back-and-forth sway.

A transition identified in Pamplona

The research team observed the crowd gathered in Plaza Consistorial before the launch of the Chupinazo, the ceremony that opens the festival. Observations were repeated in 2019, 2022, 2023 and 2024, from elevated vantage points; some measurements, however, rely solely on data from 2022, 2023 and 2024. The square, measuring around 50 metres by 20, accommodates several thousand participants each year.

The researchers tracked two quantities: density, meaning the number of people per unit of area, and the speed of movement in different places. Average density rose as the square filled up, but it did not tell the whole story: some local areas were far more tightly packed than others.

In their measurements, fluctuations in movement changed markedly when density reached around 4 people per square metre, with an uncertainty of 0.5 people per square metre. Beyond this observed threshold, collective movements became more pronounced and more organised. This is a finding specific to the conditions studied, not a universal boundary for classifying all crowds or a safety benchmark to apply in the field.

One detail is important in understanding what is happening: the crowd does not simply start moving faster. The researchers found that the direction of movement became coordinated on a large scale, while local speed did not follow the same regular pattern. In other words, the crowd can change direction collectively without everyone speeding up and slowing down together.

Orbital paths, not a back-and-forth sway

In the dense regime, the oscillations have a period of around 18 seconds. The word “oscillation” might bring to mind a mass swaying first one way, then the other. That is not what the measured trajectories show: people follow orbital movements, turning around areas of the crowd. The direction of the collective flow changes periodically, but its intensity does not show the same regular oscillation.

This distinction sets the phenomenon apart from the waves of slowing down and starting up again observed in crowds moving mainly in the same direction. It also distinguishes it from the vortices generated by participants at some concerts. In Pamplona, the researchers describe circulation patterns emerging in a confined crowd, without a common direction imposed from outside.

This organisation is described as “chiral”: the movement has a direction of rotation. The term does not imply that every person consciously decides to turn, or that everyone follows an identical path. It refers to a collective property of the movement observed on a large scale.

Why friction can produce sideways movement

To explain this dynamic, the physicists built a mechanical model. It does not attempt to predict each pedestrian’s choices individually. Instead, it seeks to describe how local interactions and constraints can produce collective movement, just as fluid models explain certain flows without tracking every molecule.

In a very tightly packed crowd, people support and push against one another. Walls limit movement, while contact between feet and the ground creates friction. In the proposed model, this friction does not always act simply as a force opposing movement. Combined with confinement and the constraints between people, it can help deflect movement sideways. The authors call this particular response “odd friction”, which does not behave like ordinary friction in the simplest models.

A comparison helps put the idea in context, without equating the two systems: an electron subject to a magnetic field can be deflected sideways by the Lorentz force. The crowd model produces a sideways deflection in a collective mechanical context. People are not electrons, and this analogy describes neither their experience nor their intentions. It serves to identify a form of non-reciprocal physical response, in which the direction of the force is not simply the same as the direction of movement.

The theoretical result links this sideways response to confinement: beyond a certain density, the model produces a transition to turning, coordinated movements. This explanation is tested against the measurements from Pamplona. It does not claim that a crowd behaves like inert matter: it shows that certain large-scale properties can be accounted for without knowing the motivations of every participant.

A comparison with Duisburg, not a controlled experiment

The team also analysed publicly available footage from the beginning of the Love Parade disaster in Duisburg in 2010. The researchers report oscillations with characteristics similar to those observed in Pamplona, in a context where estimated density was very high. This video analysis provides a point of comparison with a tragic event; it is not an experiment that could be safely reproduced.

The difference between the two situations is essential. In Pamplona, repeated observations concern a dense ceremony monitored in conditions the study describes as safe. The footage from Duisburg makes it possible to examine whether comparable collective movements occur in a dangerous context. It does not show that all crowd disasters follow the same mechanism, or that density alone is enough to explain their causes.

The authors suggest that tracking oscillations in footage could help identify the emergence of uncontrolled collective movements. This is a monitoring approach to be evaluated, not a prevention system already validated in all configurations. The observations mainly concern a simple, confined space; streets with complex layouts, multiple routes and the different reasons people have for moving all make the analysis more difficult.

The fundamental significance of the work is therefore specific: it links a field measurement, a collective transition and a mechanical model that explains why friction and spatial constraints can together produce spontaneous rotation. Understanding this transition does not make a dense crowd a perfectly predictable system. It does, however, give researchers a way to distinguish movements that might seem confused from a distance, but which here follow a measurable pattern.