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are altruistic in their behavior.

This article will address fire-evacuation analysis related to smoke-control applications.

The most common types of smoke-control systems are pressurized stairwells, pressurized

elevators, zoned smoke control, and atrium smoke control. Evacuation analysis often is

needed for smoke-control systems, but is essential for atrium smoke-control systems that

rely on smoke filling. With smoke-filling systems, occupants should have sufficient time to

leave an atrium before smoke descends upon them.

During building fires, elevators almost always are taken out of service, and vertical

evacuation takes place via stairways. In a few situations, elevators are used for

evacuation, but this article will address only vertical evacuation via stairways. (For

information about calculating evacuation time via elevators, see “Design of Smoke Control

Systems for Elevator Fire Evacuation Including Wind Effects”4 and “Protected Elevators

for Egress and Access During Fires in Tall Buildings.”5)

The primary approach to estimating evacuation time consists of a hydraulic analogy that

simulates people as fluid particles. This analogy can be generated with and without the

consideration of human behavior. (For more detailed information about estimating

evacuation time, see “SFPE Handbook of Fire Protection Engineering”1 and “Principles of

Smoke Management.”6) However, many computer models can be used to estimate

evacuation time with and without the consideration of human behavior. A National

Institute of Standards and Technology study examined 28 of these computer models. 7

TOTAL EVACUATION TIME

Evacuation time consists of pre-movement time and movement time. For example:

tt = tpm + ռtm

where:

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tt = total evacuation time (in minutes)

tpm = pre-movement time (in minutes)

tm = modeled evacuation time for an egress route (in minutes)

ռ = evacuation efficiency

The approach described in this article assumes that people follow a directed route to their

destination, typically the outdoors or an area of refuge. Such a directed route does not

account for the possibilities of proceeding in the “wrong” direction (e.g., traveling in

circles or being blocked by smoke or fire). For this reason, an efficiency factor commonly

is added to the modeled evacuation time.

There is no consensus about what value should be used for evacuation efficiency, but 1.5

is the minimum. For many applications, an efficiency value of 2 would be more

reasonable. For example, a value of 2 might be considered for a building with two egress

paths, one of which might be blocked by smoke or fire.

PRE-MOVEMENT TIME

Pre-movement time is the time from the ignition of a fire to a person's becoming aware of

it and deciding to move. There are many ways a person can become aware of a fire. Some

common cues of a fire include seeing flame, smoke, or the fire department; feeling heat;

smelling smoke; hearing noise or a fire alarm; being told; and loss of electrical power. For

a detailed discussion of the ways that occupants become aware of a fire, see “SFPE

Handbook of Fire Protection Engineering.”1

People often wait for some time after hearing a fire alarm to respond. Part of the reason

for such waiting is experience with false alarms. It is reasonable to expect much less

waiting time when people become aware of a fire by seeing fire or smoke.

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TABLE 1. Types of fire-alarm signals used in drills in a London subway station.

A study of human responses to various types of fire-alarm signals in drills was conducted

at mid-afternoon in a London subway station.8 Video cameras recorded individuals'

responses, and interviews supplemented the video recording. Five types of alarms were

used in the study (Table 1). Alarms were initiated 5 sec after a train arrived at the station.It can be seen from Table 2 that pre-movement time amounted to as much as 9 min for

an alarm bell only, but was much less with verbal announcements. However, caution

needs to be exercised with the use of verbal announcements, as they involve complex

human-behavior issues.

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TABLE 2. Responses to various fire-alarm signals in a London subway station.

MODELED EVACUATION TIME

Approaches that can be used to calculate evacuation time include component-by-

component ana lysis and constrained-flow analysis. Component-by-component analysis

involves a determination of the time it takes for a population to traverse each egress

component. The density of flow along each egress component must be determined to

measure velocity and flow rate. Component-by-component analysis can be used to

analyze complex flow situations involving merging, diverging, and converging flows.

Component-by-component analysis is more complicated and time-consuming than

constrained-flow analysis. If a component-by-component analysis is required, acomputer-generated evacuation model should be considered.

CONSTRAINED-FLOW ANALYSIS

The constrained-flow approach is appropriate for an egress system that has a point at

which a line of waiting p eople forms. Considering that the constraint is the exterior

stairwell door and all occupants start their evacuation simultaneously at time zero, the

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modeled evacuation time is estimated as:

tm = ta + tc

where:

tm = modeled evacuation time for an egress route (in minutes)

ta = time for first person to arrive at the exterior stairwell door (in minutes)

tc = time for population to pass through the exterior stairwell door (in minutes)

If all stairwell doors are the same width, the constraint will be at the exterior stairwell

door. If the width of the exterior door is less than the sum of the widths of the interior

stairwell doors that are used for evacuation, the exterior door still is the constraint.

Considering that the first person to reach the exterior stairwell door is walking down thestairs from the floor above, the time to reach the exterior door is about 0.5 min. The time

for the population to pass through the exterior stairwell is estimated as:

TABLE 3. The time it takes for a person to pass through the exterior

stairwell door depends on the door's width

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tc = ßP

where:

ß = time for a person to pass through the exterior stair door (in minutes)

P = population evacuating through the stairs

The time it takes for a person to pass through the exterior stairwell door, ß, depends on

the door's width (Table 3).

EXAMPLE CALCULATION

Let's determine the evacuation time for a five-story building with two stairways and 200

people on each floor (Figure 1). The doors leading into and out of the stairways are 32-in.

wide. The pre-movement time, tpm, is estimated at 8 min, and the evacuation efficiency,

ռ, is taken to be 2.

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FIGURE 1. Evacuation paths for a five-story building with two stairways

and 200 people on each floor

The people on the first floor would exit directly to the outside without using the stairs.

The population of the remaining floors using the two stairways is calculated as:

4(200) = 800 people

It is considered that half of the people would use one stairway, and half would use the

other. Therefore, the population using a stairway is P = 400. As seen in Table 3, ß = 0.025

for a 32-in.-wide exterior stairwell door. The time for population to pass through the

exterior stair is estimated as:

tc = ßP = 0.025(400) = 10 min

The modeled evacuation time is:

tm = ta + tc = 0.5 + 10 = 10.5 min

The total evacuation time is:

tt = tpm + ռtm = 8 + 2(10.5) = 29 min

SUMMARY

Evacuation time can be estimated by a hydraulic analogy to simulate people as fluid

particles. It is important that estimates of evacuation time include pre-movement timeand evacuation efficiency. The constrained-flow approach is appropriate for a large

number of buildings in which the exterior stairwell door is the flow constraint. For more

complex egress routes, a component-by-component analysis can be done, and

information about this kind of analysis is available from other sources. For such

complicated routes, readers may consider using a computer-evacuation model.

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REFERENCES

A smoke-control consultant, John H. Klote, DSc, PE, developed and conducts a series of

smoke-control seminars for the Society of Fire Protection Engineers. For 19 years, he

conducted fire research for the National Institute of Standards and Technology. He is

1. Society of Fire Protection Engineers. (2002). SFPE handbook of fire protection

engineering. Quincy, MA: National Fire Protection Association.

2. Quarentelli, E.L. (1979, October). Five papers from the panel session on panic.

Paper presented at the Second International Seminar on Human Behavior in Fire

Emergencies, Washington, DC.

3. Keating, J. (1982). The myth of panic. Fire Journal, 3, 57-61, 147 .

4. Klote, J.H. (1995, April). Design of smoke control systems for elevator fire

evacuation including wind effects. Paper presented at Elevators, Fire, and

Accessibility, Second Symposium, N ew York, NY.

5. Bukowski, R.W. (2003, October). Protected elevators for egress and access during

fires in tall buildings. Paper presented at the CIB-CTBUH Conference on Tall

Buildings, Kuala Lumpur, Malaysia.

6. Klote, J.H., & Milke, J.A. (2002). Principles of smoke management . Atlanta:

American Society of Heating, Refrigerating and Air-Conditioning Engineers.

7. Kuligowski, E.D. (2004, June). Review of 28 egress models. Paper presented at the

Workshop on Bu ilding Occupant Movement During Fire Emergencies,

Gaithersburg, MD.

8. Proulx, G., & Sime, J.D. (1991, July). To prevent ‘panic’ in an underground emergency: Why not tell people the truth. Paper presented at the Third

International Symposium on Fire Safety Science, Edinburgh, Scotland.

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