Exit capacity and the faster-is-slower effect
Social force model, real units, 1 grid dot = 1 metre
Guided experiments
Normal walking is about 1.3 m/s. Helbing's panic runs used up to 5 m/s.
Room is 12 m by 10 m.
Layout
Funnel walls run back 2 m at 45 degrees from the door frame.
0.85 m is a typical single leaf; 1.8 m a pair of doors.
Small column 0.9 m inside the door, slightly off-centre. Move it under Edit layout.
Compliance check for 100 people
The hand calculation assumes a steady 80 people per metre per minute. Compare it with the simulated time at high speed: a code-compliant width does not guarantee that flow if the crowd pushes.
What this shows
Faster is slower. When people push toward a narrow exit, body contact and friction at the door frame make them jam into arches that briefly stop the flow. In our runs, 100 people through a 1 m door cleared fastest at a brisk 2 to 3 m/s (about 57 s for 90% out) and slower at a panicked 5 m/s (about 71 s), with pressures well over the injury threshold. Helbing, Farkas and Vicsek first showed this effect in 2000.
Pillars and funnels. A small column just inside the exit is often said to speed evacuation. In this model it mainly lowers peak pressure at the door (about 14% in our runs) and slightly slows the flow. A funnel does the same. Treat both as pressure-relief measures, not a substitute for exit width.
Why codes discount an exit. Two exits roughly halve the clearance time, until one is lost to fire. Then everyone uses the other door and the time goes back to the single-door figure. That is why Approved Document B sizes exits with the largest one assumed unavailable.
Sources
- Helbing, Farkas & Vicsek (2000). Simulating dynamical features of escape panic. Nature 407, 487-490.
- Helbing, Farkas & Vicsek (2000). Freezing by heating in a driven mesoscopic system. Physical Review Letters 84, 1240.
- Helbing & Molnár (1995). Social force model for pedestrian dynamics. Physical Review E 51, 4282.
- Johansson, Helbing & Shukla (2007). Specification of the social force pedestrian model by evolutionary adjustment to video tracking data. Advances in Complex Systems 10, 271-288.
- Approved Document B, Volume 2 (2019 edition, as amended), Tables 2.2 and 2.3.
- NFPA 101 Life Safety Code, section 7.3.3.
Each person is a body with mass that wants to walk at a chosen speed toward a goal. They keep their distance from others and walls, and when bodies touch they compress and rub against each other. The exit and surge scenarios use the parameters from Helbing, Farkas and Vicsek (Nature, 2000); the corridor uses a velocity-anticipating version of the model that reproduces lane formation.
Most crowd deaths happen where people are forced together: exits, corridors and barriers. Hand calculations assume a steady flow, but a pushing crowd can move slower than a calm one and build pressure that injures people. Seeing that happen is the fastest way to understand why exit width, layout and density limits matter.
- Size exits with the largest one assumed blocked, as Approved Document B requires, and remember a compliant width assumes an orderly crowd.
- Keep people calm and moving steadily at exits. Rushing raises pressure and can slow the flow.
- Separate two-way flows in busy corridors and entrances with a physical barrier or one-way routing.
- Watch front-of-stage density. Above about 5 people per square metre, a push from the back reaches the barrier as a pressure wave.