Crowd Evacuation Simulator

Every dot on the canvas is a particle obeying Newton's second law. The forces acting on it are not real forces in the mechanical sense — most of them stand in for a decision a person makes — but treating them as forces reproduces measured crowd behaviour remarkably well. The formulation here is the one Dirk Helbing, Illés Farkas and Tamás Vicsek published in Nature in 2000:

The first term is the will to move. Each person has a desired speed v₀ and a desired direction e, and accelerates toward that target velocity over a relaxation time τ. Crucially the force scales with v₀: someone who wants to run pushes on the person in front of them roughly four times as hard as someone strolling. That single fact is the seed of everything strange on this page.

The remaining terms are the crowd pushing back. They split into a psychological part that acts at a distance and two physical parts that only switch on when bodies are actually in contact.

Run the auto-sweep and the plot comes out U-shaped. Total evacuation time falls as desired speed rises from a stroll to a brisk walk — that part is obvious — and then it turns around and climbs again. Past roughly 2 to 3 m/s in this room, every additional unit of urgency costs the crowd time. This is the faster-is-slower effect, and it is one of the most robust results in pedestrian dynamics: it has been reproduced in simulation, in laboratory experiments with human volunteers, and in granular flows of sand and grain through hoppers.

The mechanism has three linked stages, all of which you can watch on the canvas:

• Arching. People converging on a narrow opening from many directions jam into a stable arch across the doorway, exactly like grain bridging in a silo. Each person in the arch is held in place by the compression of their neighbours. The arch bears load, and nobody in it can move.
• Clogging. Once an arch forms, flow through the door stops entirely. Because the driving force scales with v₀, a more urgent crowd presses harder into the arch, which makes the arch stronger and more stable rather than breaking it apart. Effort is converted into compression instead of motion.
• Intermittent bursts. The arch eventually collapses by chance, a handful of people shoot through, and a new arch forms. Watch the flow-rate readout: at low desired speed it sits at a steady value, and at high desired speed it stutters between zero and short spikes. The average of that stop-start pattern is lower than the smooth flow it replaced.

The friction term κ is what makes stage two irreversible. In a frictionless crowd, pressure from behind would simply squeeze people out of the gap. With tangential friction between touching bodies, the crowd locks up: the harder it is squeezed, the more resistant it becomes to shearing, which is precisely the behaviour of a jammed granular material.

A practical way to see it: set desired speed to 1.5 m/s, let a run finish and note the time. Now set it to 5.0 m/s and run the same crowd again. The second crowd is trying to move more than three times as fast and typically takes longer to clear, while the peak contact force readout climbs by an order of magnitude.

Load the Pillar preset. A column is placed a short distance upstream of the door and slightly off its centreline — deliberately in the way. Common sense says blocking part of the approach to an exit must make evacuation slower. Under panic conditions it often does the opposite.

The column works by preventing the arch from forming. It splits the converging stream into two lanes before it reaches the doorway, and it absorbs the pressure of the people behind — load that would otherwise be transmitted into the arch is instead carried by the building. The people immediately in front of the door are shielded, so the crowd there stays below the density at which it locks up, and flow stays continuous instead of intermittent.

The off-centre placement matters. A column exactly on the axis of the door tends to split the crowd symmetrically and can create two competing arches; offsetting it breaks the symmetry and biases the flow, which empirically works better. Position is a genuinely sensitive parameter — too close and the column narrows the effective aperture, too far and it stops shielding the door at all. Use Place obstacles to move a column around and you will find configurations that make things distinctly worse as easily as ones that help.

The word "stampede" is almost always the wrong description of a crowd disaster, and the popular image of a panicking mob trampling people underfoot is not what investigators find. Fatal crowd incidents are overwhelmingly crowd crushes: people die standing up, from compressive asphyxia, when density becomes high enough that the chest cannot expand to breathe. The cause is density and pressure, produced by how a space and its flows were managed, not by a moral failing of the people inside it.

Crowd density is the number that matters, and its consequences are well characterised:

Agent-based crowd simulation is a standard tool in fire safety engineering and venue design. Where prescriptive building codes give exit widths from occupant-count tables, performance-based design uses simulation to demonstrate that a specific building empties in an acceptable time. The usual criterion compares RSET (required safe egress time — detection, alarm, pre-movement, and travel) against ASET (available safe egress time, from a fire model, until conditions become untenable). RSET must be comfortably shorter, with margin.

• Specific flow. The design constant for a doorway is about 1.2 to 1.4 people per metre of effective width per second. Effective width discounts boundary layers along the door frame, which is why a wider door does not scale linearly.
• Pre-movement time. Often the dominant term in RSET and nothing to do with walking speed. People finish conversations, gather belongings, look for staff instructions, and wait to see what others do. Real evacuations are frequently lost in the first ninety seconds, not at the doors.
• Bottleneck identification. Simulation is most valuable for finding the place where flow actually chokes — usually a stair discharge, a turnstile line, or a corridor merge, not the final exit door.
• Density mapping over time. Modern practice checks that no region of the plan exceeds a density threshold for a sustained period, rather than only checking a total clearance time. Two designs can clear in the same time with completely different peak densities.
• Ingress and steady state, not just egress. Many real crowd disasters have happened at entrances and during normal circulation rather than during an emergency evacuation, so crowd modelling for major events covers arrival and dwell as well as exit.

The practical lesson from the faster-is-slower effect is a design lesson rather than a behavioural one. You cannot ask a frightened crowd to be less urgent, so the fix is never "tell people not to panic". It is to build and manage spaces where high urgency does not produce high density: more and wider exits, staged release, routes that do not converge on a single point, clear early information so pre-movement time is short, and monitoring that catches dangerous density before it becomes irreversible.

Treat the numbers on this page as a demonstration of a mechanism, not as engineering output. Real egress analysis uses validated software, calibrated population profiles with a distribution of walking speeds and body sizes, mobility-impaired occupants, staff intervention, and comparison against measured data. What a simple social force model does well is show why a bottleneck behaves the way it does.