Dynamics of crowd disasters: An empirical study

Helbing, Dirk; Johansson, Anders; Al-Abideen, Habib Zein · 2007 · OpenAlex-citations

DOI: 10.1103/physreve.75.046109

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Summary

This study addresses the critical lack of empirical data regarding crowd panic and stampedes, a gap caused by ethical constraints on experimental research. While previous pedestrian dynamics models often relied on fluid-dynamic analogies or simulations, they failed to accurately predict the mechanisms behind crowd disasters. The authors analyze video recordings from the 2006 Hajj pilgrimage in Mina, Saudi Arabia, specifically focusing on the area in front of the Jamarat Bridge where a major accident occurred. The research aims to characterize the transition from stable pedestrian flows to chaotic, dangerous states and to identify variables that can serve as early warning indicators for critical crowd conditions. The researchers employed a high-performance video analysis algorithm to extract position and velocity data for over 30 million pedestrian instances within a 20m×14m central area. This algorithm, calibrated with manual evaluations, achieved approximately 95% accuracy. The study defines local density, speed, and flow using Gaussian weight functions to account for spatial variations. By analyzing the temporal evolution of these metrics between 11:45 am and 12:30 pm on January 12, 2006, the authors constructed fundamental diagrams relating flow to density and identified distinct phases of crowd behavior. The analysis reveals two sudden transitions in crowd dynamics. First, as density increased, the flow shifted from laminar to stop-and-go waves around 11:53 am. This transition occurred when the outflow dropped below 0.8 persons per meter per second, supporting theoretical models of bottleneck coordination failures. Second, at approximately 12:19 pm, the crowd entered a "turbulent" state characterized by random, involuntary displacements in all directions. Unlike vehicle traffic, pedestrians did not stop completely at extreme densities; instead, they exhibited a second flow maximum at 9 persons/m². This turbulence involved stick-slip instabilities and pressure releases analogous to earthquakes, leading to stumbling and trampling. The study defines a "pressure" metric, combining density and velocity variance, which peaked immediately before the accident began. The findings challenge existing simulation models that assume smooth flow cessation at high densities. The identification of "crowd turbulence" and the associated pressure metric provides a quantitative basis for understanding how critical conditions emerge. These insights have practical implications for safety management, allowing organizers to predict where and when accidents are likely to occur. The authors note that these findings directly informed organizational changes that ensured a safe Hajj in the following year, demonstrating the utility of empirical data in preventing crowd disasters.

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