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The Dynamics of Crowd Disasters: An Empirical Study
Dirk Helbing, Anders Johansson, Habib Zein Al-Abideen
TL;DR
Human-crowd data on panic and critical conditions are scarce, so the paper analyzes video recordings from the Mina/Makkah crowd disaster. It identifies successive transitions to stop-and-go and turbulent flows, linking extreme-density dynamics to trampling hazards and safer-event planning.
Problem
Experimental data on critical conditions in human crowds are scarce, limiting understanding of turbulent dynamics that cause serious trampling accidents at extreme densities.
Method
The paper analyzes unique video recordings using a computer algorithm to extract pedestrian positions, speeds, local densities, and flows.
Results
The analysis reveals two sudden transitions, from laminar to stop-and-go flows and then to irregular turbulent motion, while movement persists at densities up to 10 persons per square meter.
Takeaways & Limitations
The findings identify local density, flow, and pressure-related crowd dynamics as relevant to locating and anticipating critical conditions during mass events.
Takeaways & Limitations
Current crowd-panic simulation models fail to reproduce the turbulent dynamics because they neglect increased propulsion force at extreme densities.
Abstract
from arXiv · showhide
Many observations in the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on January 12, 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and ``turbulent'' flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particularly, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.
INTRODUCTION
Pedestrian-dynamics models have described several self-organization phenomena, but panic stampedes remain a major unresolved problem with limited human-crowd data. This paper analyzes unique video recordings of a crowd disaster in Mina/Makkah to investigate critical high-density flows.
- Many-particle models have described lane formation and bottleneck-direction oscillations in pedestrian counterstreams.
- Research on pedestrian dynamics expanded to clogging, intermittent flows, force models, cellular automata, and empirical video analysis.
- Panic stampedes remain a serious mass-event concern, with hundreds of lives lost in crowd disasters each year.
- The study uses high-performance video analysis of unique Muslim pilgrimage recordings from Mina/Makkah, Saudi Arabia.
DATA ANALYSIS AND FUNDAMENTAL DIAGRAM
The study combines local video-based measurements of pedestrian density, speed, and flow with a fundamental-diagram analysis of extreme crowd conditions. It finds that compression and nonzero motion persist at very high densities, producing flow behavior that challenges standard traffic-like assumptions.
- The video analysis covers a 27.7m×22.5m area in front of a 44m-wide entrance during the January 12, 2006 Hajj crowd disaster.The evaluated central dataset contains more than 30 million position-velocity pairs from a 20m×14m area between 11:45am and 12:30.
- Pedestrian positions and speeds were extracted over time with a computer algorithm based on digital transformation, contrast enhancement, motion prediction, and pattern recognition.The algorithm was calibrated manually and tested in field experiments, with an accuracy of about 95%.
- The local density, speed, and flow measurements are combined through the fluid-dynamic relationship Q(ρ) = ρV(ρ).The fundamental diagram displays the absolute value of flow as a function of density.
- The analysis evaluates local crowd conditions because criticality depends on spatially local measurements rather than only large-area averages.The measurement radius is controlled by R, with larger R producing a greater effective measurement area and lower variance in local-density measurements.
- When local density exceeds 6 persons per square meter, local flow decreases by a factor of 3 or more, causing outflow to fall below inflow and crowd compression to increase.Maximum local densities can be about twice the average densities, and local values greater than 10 persons per square meter were observed for R = 1m.
- Average local speeds and flows remain finite at extreme densities, with a second flow maximum at 9 persons/m2 rather than complete stoppage.The result differs from vehicle traffic, where drivers maintain safety distances and stop to avoid collisions.
TRANSITION FROM LAMINAR TO STOP-AND-GO AND “TURBULENT” FLOWS
The recordings show two successive transitions: laminar flow became stop-and-go when outflow fell below a bottleneck threshold, then irregular “crowd turbulence” emerged at higher density. The turbulent regime involved multidirectional motion, pressure release, and falling and trampling, while existing models failed to reproduce it.
- Laminar to stop-and-go: Around 11:53am, laminar flow suddenly changed into upstream-moving stop-and-go waves that persisted for more than 20 minutes.The waves were not caused by the Hajj rituals.
- Laminar to stop-and-go: Stop-and-go waves began when outflow dropped below 0.8 persons per meter and second, supporting a bottleneck coordination model.The model predicts intermittent flow when inflow exceeds outflow.
- Stop-and-go to “turbulent” flow: At around 12:19, a second instability produced irregular motion in all directions as densely packed people were moved involuntarily by the crowd.These displacements could make people stumble, after which fallen individuals were trampled by the continuing crowd motion.
- Properties of crowd turbulence: Crowd turbulence exhibited sharply peaked velocity-increment distributions, self-similar displacement scaling, and hierarchical fragmentation into correlated clusters.Unlike fluid turbulence, the recordings showed no large eddies; excessive stress instead produced stick-slip rupture and cluster formation.
- Pressure and consequences: The study defines crowd pressure as local density multiplied by local velocity variance, linking extreme-density dynamics to violent displacements.Under turbulent conditions, additional energy input in compressed areas made the resulting displacements practically impossible to control.
- Model limitation: Existing crowd-panic simulations failed to reproduce turbulent dynamics because they neglected increased propulsion forces at extreme densities.This limitation distinguishes the observed crowd state from models that omit density-dependent propulsion.
SUMMARY AND OUTLOOK
The study identifies two sudden transitions in extremely dense crowds: laminar flow becomes stop-and-go, then “turbulent” motion that can trigger trampling. Simulating both transitions by merely increasing bottleneck inflow remains unresolved.
- SUMMARY AND OUTLOOK: Two sudden transitions lead from laminar to stop-and-go flow and then to “turbulent” crowd motion that can trigger trampling.Stop-and-go begins when density is high and flow drops below a critical value; turbulence sets in with overcritical crowd pressures.
- SUMMARY AND OUTLOOK: Even at local densities up to 10 persons per square meter, crowd motion does not stop completely, producing overcritical densities.
- SUMMARY AND OUTLOOK: The critical values depend on the measurement parameter R used to evaluate local densities, speeds, and variances.
- SUMMARY AND OUTLOOK: Simulating both transitions with a many-particle model by increasing inflow to a bottleneck remains an unresolved challenge.
Practical Implications
The findings are expected to apply to other mass gatherings and provide practical indicators for locating and timing critical crowd conditions. Pressure, rather than density or velocity alone, is identified as the decisive warning quantity.
- Practical Implications: The mechanisms are expected to transfer to other mass gatherings, where turbulent waves occur in dozens of crowd-intensive events each year.
- Practical Implications: The decisive quantity for identifying critical locations and times is pressure, defined as speed variance multiplied by density.
- Practical Implications: A crowd accident began about 10 minutes after turbulent motion started, when pressure exceeded 0.02/s^2.
- Practical Implications: Pressure monitoring can provide advance warning because the accident occurred more than 30 minutes after average flow crossed its critical threshold.
- Practical Implications: The study concludes that improved crowd control could increase safety during future mass events.
Implications for the Hajj in 1427H
The Hajj organization introduced capacity, monitoring, flow-management, routing, and anti-bottleneck changes after the 1426H accident analysis. These changes produced comfortable, continuous flows and a safe Hajj in 1427H.
- Implications for the Hajj in 1427H: The Jamarahs’ stoning capacity and the flow capacity of the Jamarat Bridge were improved through an elongated, elliptical design.
- Implications for the Hajj in 1427H: Crowd accumulation was prevented on the plaza around the Jamarat Bridge.
- Implications for the Hajj in 1427H: Automated counting from surveillance-camera signals provided continuous information on densities and capacity utilization at critical locations.
- Implications for the Hajj in 1427H: A redesigned plaza enabled security personnel to balance flows among bridge levels and ramps, avoiding overload and flow breakdown.
- Implications for the Hajj in 1427H: One-way operation replaced two-way operation in the street system and plaza to avoid obstructions and counterflows.
- Implications for the Hajj in 1427H: Optimized scheduling and routing distributed registered pilgrims more homogeneously across space and time, while squatters were removed to avoid bottlenecks.
- Implications for the Hajj in 1427H: The implemented changes ultimately achieved comfortable, continuous flows and a safe Hajj in 1427H despite increased pilgrim numbers.