Doors, stairs and merging flows

Introduction

Picture a stair in a tall office building during a full evacuation. People from the floors above are already filing down it. On your floor, a hundred people have reached the door to the landing and want to join. The stair is a fixed width and is nearly full. Who goes first: the people already on the stair, or the people waiting at the door?

The answer turns out to depend on something as mundane as which wall the door is in. This lesson works from the simple question, how wide should a door be, to that subtler one, because evacuation capacity is decided at the places where flows meet and narrow, not in the open corridors between them.

Sizing an exit: two rulebooks

Building regulations do not ask the designer to simulate a crowd. They give a rule that turns a number of occupants into a minimum width. England’s Approved Document B (volume 2, the 2019 edition with its 2020 and 2022 amendments) does it with a short table:

Two further rules matter as much as the table. Widths below 1,050 mm are not to be interpolated, and when a space has more than one exit, the largest is discounted: you assume a fire may make it unusable and check that the others can still take everyone.

The American equivalent, NFPA 101, uses a single factor per person: 0.2 inches for level components and ramps, 0.3 inches for stairs, about 5.1 mm and 7.6 mm. These values come from a secondary summary of the code, and the code also sets minimum widths for each component that the factors alone do not show. Figure 1 plots both rules.

Worked example

A function room on the first floor of a hotel holds 400 people. Under Approved Document B it is above 220, so each person needs 5 mm: 400 × 5 = 2,000 mm of exit width. Under the NFPA level factor the answer is 400 × 0.2 in. = 80 in., about 2,030 mm. The two codes agree to within 2%.

Now give the room three exits and apply the discounting rule. If each is 1,000 mm, discounting one leaves 2,000 mm: just enough. If they are 1,200, 1,000 and 800 mm, discounting the 1,200 leaves 1,800 mm: not enough, even though the total is 3,000 mm. The largest exit is the one most worth losing in the calculation, because it is the one whose loss hurts most.

Stadium exits: rates of passage

Sports grounds use a different rule, built from flow rather than from a width per person. The Green Guide credits each metre of exit width with a rate of passage: 82 people per metre per minute on level surfaces and 66 on stepped ones, and it asks that a stand can empty within a normal maximum egress time of 8 minutes. The exit capacity of a route is then a product you already know from module 1, flow per metre times width, multiplied by time.

The SGSA’s own worked example takes a stand served by four stairways of 1.5 m: (4 × 1.5 m) × 8 min × 66 p/m/min = 3,168 people. However many the terrace could hold, 3,168 is as many as it can empty in eight minutes, and the capacity lesson in module 7 shows how that limit enters the ground’s final capacity.

The rates themselves have a history. The 4th edition (1997) used 109 p/m/min on the level and 73 on stairs; the 5th edition (2008) lowered them to 82 and 66 following BS EN 13200-1. The lower stepped rate is consistent with Fruin’s Levels of Service, whose stairway bands carry lower flows than his walkway bands.

Where flows merge

In a multi-storey building the stairs are shared. Each floor’s occupants have to merge, joining a stream already moving on the stair, at the landing where their floor’s door opens. A stair can only carry so many people per minute, so every person who joins from a floor is a person from above who has to wait, and the question of who gets priority decides who is delayed.

Galea, Sharp and Lawrence, of the University of Greenwich’s fire safety engineering group (FSEG), examined this in 2008 while working out how evacuation models should represent merging in multi-floor buildings. Their findings:

• As the density on the stair rises, the flow of people entering it from the floor falls.
• When the floor door opens onto the landing beside the flight arriving from above, merging is biased towards the floor: its occupants get in first and the stair stream is held back.
• When the door is on the opposite side, merging is roughly balanced at high density.
• For high-rise buildings they recommend the opposite-side connection.

They also cite two earlier studies: Hokugo, who found about 60% of the merged flow came from the floor when both streams started together and about 50% when one was already established, and Takeichi, who found the adjacent layout gave the floor an advantage of up to 28%.

Experiments in a real stair tell a similar story. Boyce, Purser and Shields observed merging that was “approximately 50:50 across the duration of the merge period”, but with the floor door adjacent to the incoming stair, “floor occupants took priority during periods of slower movement”.

Why should a designer care about fairness on a landing? One way to see it (our reading, not a claim from the papers) is that priority is a choice about whose delay to accept. In a tall building, a door that favours each floor in turn keeps clearing the lower floors and leaves the people highest up, who have the furthest to go, queuing at every landing on the way down. A balanced merge spreads the delay. Either way, the stair’s capacity, not the speed anyone walks, sets how fast the building empties. Lesson 4 shows how much of the World Trade Center evacuation was spent standing still on stairs.