Methods to calculate the response time of heat and smoke detectors installed below large unobstructed ceilings


Recently developed methods to calculate the time required for ceiling mounted heat and smoke detectors to respond to growing fires are reviewed. A computer program that calculates activation times for both fixed temperature and rate of rise heat detectors in response to fires that increase in heat release rate proportionally with the square of time from ignition is given. This program produces nearly equivalent results to the tables published in Appendix C, Guide for Automatic Fire Detector Spacing (NFPA 72E, 1984). A separate method and corresponding program are provided to calculate response time for fires having arbitrary heat release rate histories. This method is based on quasi-steady ceiling layer gas flow assumptions. Assuming a constant proportionality between smoke and heat released from burning materials, a method is described to calculate smoke detector response time, modeling the smoke detector as a low temperature heat detector in either of the two response time models.

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g/(c p T ϱ )

c p :

specific heat capacity of ambient air

C s :

smoke mass concentration


effective binary diffusion coefficient


acceleration of gravity


vertical distance from fuel to ceiling


light intensity

Io :

initial light intensity


light beam length

\(\dot m\) s :

smoke gas mass production rate per unit volume


optical density per unit length (see Equation 8)

\(\dot Q\) :

fire energy release rate

\(\dot Q\) :

energy release rate per unit volume


radial distance from fire axis to the detector


response time index, the product of the detector thermal time constant and the square root of the gas speed used in the test to measure the time constant.9



t *2 :

dimensionless time t/[A−1/5 α −1/5 H4/5)

(t *2 ) f :

dimensionless time for time delay for gas front travel

T :

ambient temperature


gas temperature at detector location

T s :

temperature of detector sensing elements


T — T

ΔT *2 :

dimensionless temperature differences ΔT/[A2/5(T f /g)α 2/5 H−3/5]


gas speed at the detector location

U *2 :

dimensionless gas speed U/[Aα H]1/5

Y s :

local ratio of smoke mass to total mass in flow

α :

proportionality constant for t2-fire growth = Q/t2

ϱ :

ambient air density


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Reference: David D. Evans and David W. Stroup, “Methods to Calculate the Response Time of Heat and Smoke Detectors Installed Below Large Unobstructed Ceilings,”Fire Technology, Vol. 22, No. 1, February 1985, p. 54.

Note: This paper is a contribution of the National Bureau of Standards and is not subject to copyright.

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Evans, D.D., Stroup, D.W. Methods to calculate the response time of heat and smoke detectors installed below large unobstructed ceilings. Fire Technol 22, 54–65 (1986).

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Key words

  • Heat detectors
  • smoke detectors
  • response time
  • t2-fires
  • gas flow
  • computer routines