Evaluating thermal fire detection systems (English units)

NBS

PUBLICATIONSA111D2 Mb70flfl

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 02467088Stroup, David W/Evaluatlng thermal fire

QC100 .U57 N0.712 1986 5.3 C.1 NBS-PUB-C

o

CO

QNBS SPECIAL PUBLICATION 71 2

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Evaluating Thermal Fire

Detection Systems(English Units)

///////////// //////

QC

100

U57

No. 712

1986

////////

David Stroup • David Evans • Phyllis Martin

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Evaluating Thermal Fire

Detection Systems[English Units]

David W. Stroup

David D. EvansPhyllis Martin

National Bureau of Standards

National Engineering Laboratory

Center for Fire ResearchGaithersburg, Maryland 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1986

Library of Congress Catalog Card Number: 86-600519

National Bureau of Standards Special Publication 712

Natl. Bur. Stand. (U.S.), Spec. Publ. 712, 557 pages (Apr. 1986)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICEWASHINGTON: 1986

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402

CEf^

TABLE OF CONTENTScL

Page1

LIST OF TABLES v

LIST OF FIGURES v

NOMENCLATURE vi

Abstract 1

1. INTRODUCTION 2

2. DESCRIPTION OF THE MODEL 3

2.1 Characteristic Fire 4

2.2 Temperature and Velocity Correlations 5

2.3 Detector Response Model 7

2.4 Velocity Correlation for r/H < 0.3 9

3. IMPLEMENTATION OF THE MODEL: COMPUTER PROGRAMS 10

3.1 General Program Structure 10

3.2 Main Program 12

3.2.1 Data Input Section 12

3.2.2 Calculation Initialization 12

3.2.3 Conversion and Output Section 13

3.3 Activation Time Equation Solution:Fixed Temperature 13

3.4 Activation Time Equation Solution:Rate of Temperature Rise 14

4. IMPLEMENTATION OF THE MODEL: TABLES OF RESULTS 14

5. EXAMPLES 16

5.1 Using the Tables 16

5.1.1 Example 1: Comparison with NFPA 72ETable Results 16

5.1.2 Example 2: Fixed Temperature vs.

Rate of Rise 17

5.2 Example 3: Using the Computer Program 19

6. SUMMARY 21

7. REFERENCES 21

APPENDIX A - DETACT-T2 (FORTRAN VERSION) 33

iii

TABLE OF CONTENTS (continued)

Page

APPENDIX B - DETACT-T2 (PC BASIC VERSION) 43

APPENDIX C - DETECTOR ACTIVATION TIME TABLES:FIXED TEMPERATURE 51

APPENDIX D - DETECTOR ACTIVATION TIME TABLES:RATE OF TEMPERATURE RISE 301

NOTE: Appendixes C and D are available in metric units in anotherversion of this report.

iv

LIST OF TABLES

Page

Table 1. Heat Release Rates of Warehouse Materials 23

Table 2. Maximum Heat Release Rates fromFire Detection Institute Analysis 27

Table 3. RTI Values for any Listed Detector(Fixed Temperature Type) 28

Table 4. RTI Values for any Listed Detector(Rate of Rise Type) 29

LIST OF FIGURES

Page

Figure 1. Plot of t 2 Fire Growth Curves 30

Figure 2. Plot of Dimensionless Velocity Correlation 31

v

NOMENCLATURE

A g/(C T p )P oo oo

Cp specific heat capacity of ambient air

C,j constant used in equations 9 and 11

constant used in equations 10 and 11

g acceleration of gravity

H vertical distance from fuel to ceiling

•

Q fire energy release rate

.*Q dimensionless fire energy release rate

r radial distance from fire axis to the detector

RTI response time index, the product of the detector thermal time constantand the square root of the gas velocity used in the test to measure thetime constant [8].

t time

t^ dimensionless time, t/ LA a H J

(t^)^ dimensionless time for time delay for gas front travel

ambient temperature

T gas temperature

Tg

temperature of detector sensing elements

AT T - T

VI

NOMENCLATURE ( continued

)

* 2/5 2/5 -3/5AT^ dimensionless temperature difference, AT/ [A (T^/g) a H ]

U gas velocity at the detector location

Um

maximum gas velocity

* 1/5dimensionless gas velocity, U/[A a H]

2 • 2a proportionality constant for t - fire growth = Q/t

ambient air density

x detector thermal time constant

vii

Evaluating Thermal Fire Detection Systems [English Units]

David W. StroupDavid D. EvansPhyllis Martin

ABSTRACT

This report presents a methodology for evaluating heat detection systemsinstalled in buildings. Previous work for use primarily in designing newthermal fire detection systems was used as a starting point. The previous workwas enhanced and supplemented to make it more useful for evaluating existingsystems. The resulting equations were programmed into a user interactivecomputer program. This program is available in both BASIC and FORTRAN and willrun on mainframes as well as personal computers. In addition, a modifiedversion of the FORTRAN program was used to develop an extensive set of tableslisting detector activation times for given building geometries, detectorcharacteristics, and fire growth rates. These tables are useful for quickevaluation of alternative heat detector installations. Finally, practicalexamples are included to illustrate the use of the tables and computerprograms

.

Keywords: fire alarm systems; fire detection; fire detection systems; firehazard assessment; fire protection; fire suppression; heat detectors; sprinklersystems

.

1

1. INTRODUCTION

Studies of the response of heat detectors to fire driven flows under

confined ceilings have been conducted since the early 1970's [1,2,3,4,5]!.

Results of these largely experimental studies have been used to develop

correlations of data that are useful under a broad range of fire conditions and

building geometries. These correlations have been used to construct

engineering methods to determine heat detector spacing, sprinkler response

time, and smoke detector alarm times for industrial buildings where large

undivided ceilings over storage and manufacturing facilities are common. The

National Fire Protection Association (NFPA) has adopted an alternate design

method for determining heat detector spacing which is based on some of these

correlations.

This alternate design method is contained in Appendix C of the NFPA 72E

standard [6], "Guide for Automatic Fire Detector Spacing," which consists of

tables listing maximum allowable detector spacings for given room sizes and

fire growth rates calculated from correlations of experimental measurements.

The tabular form of presentation is useful for specifying design requirements

in new installations. However, the tables are inconvenient to use in

evaluating changes to existing detector systems where the spacing is fixed.

There appears to be a need for a method which determines detector activation

times for specified building geometries, detector characteristics, detector

spacings, and fire growth rates. This method would be useful in evaluating the

1 Numbers in brackets refer to literature references at the end of this repor

2

expected fire detection time for existing and proposed systems for use in

determining available safe egress time, and the relative effectiveness of

different detectors used at the same spacing.

This paper presents the results of work to develop an alternative method

appropriate to existing installations. As part of this study, the basis for

the calculation method published in Appendix C of the NFPA 72E standard was

determined. Alternate correlations of the experimental data, used to develop

the results presented in Appendix C of NFPA 72E, have been used to construct a

FORTRAN program (DETACT-T2). This computer program evaluates the response time

of heat detector systems [7]. In this work, a modified version of the

DETACT-T2 program was used to generate tables of detector response times for a

wide range of building geometries, detector characteristics, and fire growth

rates. These calculated values for response time agree to within 5 percent of

those published in the tables contained in Appendix C of the NFPA 72E standard.

2. DESCRIPTION OF THE MODEL

The problem of heat detector response is solved by predicting the time

dependent temperature of the detector sensing element up to the point when it

is heated to the specified alarm conditions. In order to predict the

temperature of a heat detector element, it is necessary to describe the fire

and the fire generated environment to which the detector is exposed. The

primary fire related parameters which influence the response of heat detectors

are the gas temperature and velocity. Once the fire-generated environmental

3

characteristics are known, a model of the response of the thermal sensing

element in the detector is employed to calculate the detector element

temperature as a function of time.

2.1 Characteristic Fire

Extensive full-scale tests have been conducted to determine the response

of heat detectors [1-4] . These tests have studied two classes of fires. The

first of these are steady fires. These fires have energy release rate

histories which do not change with time. Results from work using this type of

fire may be used to calculate heat detector response if the quasi-steady state

assumption is invoked. In this case, a varying energy release rate history is

approximated as a series of steady fires. In this type of analysis, the

transport time of the gases to the detector is ignored. This usually results

in a predicted actuation time which is earlier than that encountered in actual

practice. This may or may not be acceptable depending on the case.

Another class of fires for which research results are available are called

"t-squared" (t 2) fires. These fires have energy release rate histories which

increase proportionally with the second power of time from ignition. This

class of fires was used to develop the tables in the NFPA 72E document and will

be used in this paper.

Appendix C of the NFPA 72E standard lists three fires which have t 2 type

fire growth behavior. A slow developing fire is defined as one which would

A

take 600 seconds (10 minutes) from the time of flaming ignition until it

reaches a heat release rate of 1000 BTU/s (1055 kW). A medium growth rate fire

reaches a heat release rate of 1000 BTU/s (1055 kW) approximately 300 seconds

(5 minutes) after flaming ignition occurs. The fast developing fire requires

150 seconds (2.5 minutes) to reach a heat release rate of 1000 BTU/s (1055

kW). In addition, a fourth t 2 fire has been developed in this report. This

fire has been defined as one which takes 75 seconds (1.25 minutes) to reach a

heat release rate of 1000 BTU/s (1055 kW). These four fire growth curves are

plotted in Figure 1.

Table 1 is a reproduction of a table in NFPA 72E. It lists various

warehouse commodities and their maximum fire heat release rates per unit floor

area covered by the commodity. The time required for a fire, occurring in a

particular commodity, to reach a heat release rate of 1000 BTU/s is also

listed. If possible, each commodity is identified with a specific fire growth

behavior - slow, medium, fast, or ultrafast fire. Table 2 is a reproduction of

another table found in Appendix C of NFPA 72E. It lists the maximum heat

release rates for various furnishing type fuel items. Both of these tables are

useful for estimating fire growth rates that may be expected from various fuel

packages.

2.2 Temperature and Velocity Correlations

Values of the time dependent gas velocity and temperature for t 2 fires may

be obtained from work by Heskestad and Delichatsios [4], From experiments and

5

use of dimensional arguments, they developed correlations of maximum

temperature rise and velocity for unconfined ceiling layer flows as a function

of radial distance from the axis of fire plume impingement. These correlations

of dimensionless maximum temperature rise and dimensionless maximum velocity

are:

AT2

=

0,

t2

- 0.954 (1 + r/H)

0.188 + 0.313 r/H

-0.63

H A/3

t2

* (t )

, t2

> (t2

)f

U2 / VAT

2= 0.59 (r/H)

(1)

(2)

where

AT,

= t / [A"1/5

a"1/5

HA/5

]

= U / [A1/5

a1/5

H1/5

]

= AT / [A2/5

(T /g) a2/5

H_3/5

]

a

= g / [C T pJ*n 00 oo

= Q / t2

(t2

)f

= 0.954 (1 + r/H)

These equations may be used to predict the fire-generated environment (gas

temperature and velocity) near a detector.

6

2.3 Detector Response Model

Characterization of the thermal response of heat detector and sprinkler

thermal sensing elements is discussed by Heskestad and Smith [8], and Evans

[9] . The model for the detector sensing element temperature is based on a

convective heat transfer process. The first order differential equation that

describes the rate of temperature increase of the sensing element is:

dT U1/2

s[T - T ] (3)

dt RTI s

This equation predicts the temperature change of a detector with known thermal

characteristics to a given time dependent gas flow temperature and velocity.

In particular, the rate of change of the detector element temperature at any

time is equal to the gas velocity to the one-half power multiplied by the

difference between the temperature of the hot fire generated gas flow near the

detector and the temperature of the detector element. All divided by the

detector RTI or response time index.

The RTI is a measure of the detector 1 s thermal lag and can be determined

for sprinkler or heat detector sensing elements using the plunge test [8].

NFPA 72E reports detector sensitivity in terms of time constants, t. At any

given time, the time constant for a given type of detector may be calculated

from the RTI using:

t = RTI / U ' (4)

7

Tables 3 and 4 relate heat detector listed spacings to RTI values for fixed

temperature detectors and rate of rise detectors respectively. These Tables

were derived from results published in references 3 and 5.

Beyler [10] used the correlations of Heskestad and Delichatsios [4] to

derive a new form of equation (3). He was able to solve this new form of the

heat detector response equation analytically. Using the condition that the

initial detector element temperature is equal to ambient temperature (Tg= T^,),

the equations for calculating the response of fixed temperature and rate of

temperature rise detectors are, from Beyler:

dT (4/3) (AT/AT*) (AT*)lM

v(1 - e"

Y) (5)

dt (t/t*) (0.188 + 0.313 r/H)

T - T (0) = (AT/ATs s

where

* *||

(i

2> *T2 I

1 "LL e"

Y)

(6)

y f

ft)

i/2

{&t s (t^)(o - i88+ °- 3i3r/H)

4

Using equations (1) and (2), equations (5) and (6) may be solved to predict the

response of sprinkler and heat detector sensing elements to fire-driven ceiling

jet flows.

8

2.4 Velocity Correlation for r/H < 0.3

While this exact solution to equation (3) is applicable to any r/H value,

the dimensionless velocity correlation, previously discussed, is only valid for

r/H values greater than 0.3. In an effort to extend the usefulness of the

detector response calculations, an analysis was made of the available data for

ceiling jets at r/H values less than 0.3. Results of this analysis indicated a

lack of much quantitative information for this region. Therefore, an analysis

to develop a rational estimation of velocities in the ceiling-jet close to the

plume axis was undertaken by studying a simple extension of the velocities in

the plume.

The dimensionless velocity and temperature change relations proposed by

Heskestad and Delichatsios [4] together with equations proposed by Zukoski

et. al. [11] to describe fire plume maximum temperature and velocity

distributions were taken as a starting point.

U* = U / [A1/5

a1/5

H1/S

] (7)

AT* = AT / [A2/5 (T/g) o

2/5H"

3/5] (8)

ATm / T, = C

T(Q*)

2/3(9)

Um

= Cw g

1/2H1/2

(Q*)1/3

(10)

These equations were used to obtain an expression of dimensionless maximum gas

velocity in the same form as equation (2).

9

/ 7atJ = cw / Vc

T (11)

Using values suggested by Zukoski et. al. [11], the dimensionless gas velocity

is found to be a constant at r/H values less than 0.3. The complete

dimensionless gas velocity equation for all values of r/H is:

( 3.87 / V97lT5, r/H S 0.3U2

1 VAT2

=\ -0 63

(12)1 1

I 0.59 (r/H)U ' bJ

, r/H > 0.3

This equation is plotted in Figure 2. The two curves merge nicely. This

equation together with the previously discussed correlations and analytic

solution may be used to calculate any aspect of the response of thermal

detectors to t 2 fires.

3. IMPLEMENTATION OF THE MODEL: COMPUTER PROGRAMS

3.1 General Program Structure

The equations discussed in Section 2 were programmed into a user

interactive computer code called DETACT-T2. To evaluate the response of a

detector, the user enters values for ambient air temperature, detector

activation temperature and rate of temperature rise, detector RTI, fuel to

ceiling distance, detector spacing, and a fire growth rate constant, a (for t 2

fires). The program solves the appropriate equation to obtain the response

time for a fixed temperature detector and a rate of rise detector with the

10

given characteristics. The fire energy release rate at each time step is also

calculated.

The computer program is available in two versions. One version, contained

in Appendix A, is written in FORTRAN 77. The program contains approximately

400 lines of source code and requires about 64k of computer memory in compiled

form for execution. The source code may be compiled on any computer supporting

an ANSI standard FORTRAN 77 compiler. The program has been compiled and run

successfully on IBM^ and compatible personal computers operating under

MS-DOS-^. A specially modified version of this program was used to generate the

tables discussed in section 4.

The other version of the program, listed in Appendix B, is written in

BASIC. It consists of approximately 350 lines of source code. This program

has also been successfully tested on IBM and compatible micro-computers. Both

programs have essentially the same structure and use the same variable names.

To insure convergence, all variables are in double precision.

The program consists of three major sections. The main program reads and

lists the required input data, performs the calculations necessary to set up

the equations, calls the solution subroutines, and writes out the results. The

second section is a subroutine which uses a Newton-Raphson technique to solve

the equation describing the activation time of a fixed temperature detector.

* IBM is a trademark of International Business Machines Corporation anddoes not represent an endorsement by the National Bureau of Standards.

J MS and Microsoft are trademarks of Microsoft Corporation and do notrepresent an endorsement by the National Bureau of Standards.

The last section is a subroutine which uses a bisection method to solve the

rate of temperature rise detector activation time equation. Each of these

sections is described in more detail below.

3.2 Main Program

3.2.1 Data Input Section

This section of the main program requests information from the user

concerning the building geometry, the detector characteristics, and the fire

growth rate. The user may also elect to enter data in either English or

S.I. units.

3.2.2 Calculation Initialization

Several preliminary calculations must be made before the activation time

equations may be solved. These calculations are done in the second section of

the main program. In this section, the dimensionless time, velocity, and

temperature are calculated. Based on the user-specified detector spacing, the

maximum radial distance of the detector from the fire is calculated. After

these calculations have been completed, the two activation time calculation

subroutines are called. The results from these subroutines are converted into

activation times, and the heat release rates are calculated.

12

3.2.3 Conversion and Output Section

The last section of the main program writes out the solutions to the

equations. The results are printed in both English and S.I. units.

3.3 Activation Time Equation Solution: Fixed Temperature

The equation describing the activation time of a fixed temperature

detector cannot be solved explicitly for activation time. Therefore, a

numerical technique must be used. A Newton-Raphson technique was selected for

use in solving the fixed temperature detector equation. This technique is

discussed in most numerical methods textbooks [12].

The Newton-Raphson (or simply Newton's) method is one of the most powerful

and well-known numerical methods for finding a root (solution) of f(x) =0. To

use this routine, the activation time equation is first adjusted to fit the

appropriate form. This method converges very rapidly for the cases considered

here.

13

3.4 Activation Time Equation Solution: Rate of Temperature Rise

A bisection technique was selected for use in solving the rate of rise

activation time equation. This technique is also discussed in most numerical

methods textbooks [12]. It was chosen for use in this instance because the

Newton method would have introduced stability problems into the calculation.

This method also converges very rapidly for the cases considered here.

4. IMPLEMENTATION OF THE MODEL: TABLES OF RESULTS

The computer programs calculate detector activation times one case at a

time. In many instances, it is necessary to evaluate a number of

alternatives. It would be tedious and inconvenient to run a computer program

to examine each case of interest. In light of this fact, the FORTRAN version

of the computer program was used to generate an extensive set of tables. These

tables list detector activation time as a function of building geometry,

detector characteristics, and fire growth rate constants.

Each entry in the tables was checked by first calculating the response

time of the given detector numerically. Then the calculated time is

substituted into the exact form of the equation, and it is solved for the

temperature of the detector sensing element at that time. In each case, the

calculated temperature agreed with the originally assumed one to within an

accuracy of 0.005 percent.

14

The tables cover a wide range of parameter variations. Tables have been

developed for each of the four fire growth rates that were described earlier.

Tables are available in both English and S.I. units. The English units tables

are contained in Appendixes C and D of this report. The S. I. units tables are

available in the metric version [13].

For use with English units, tables cover detector spacings of 0 to 60 feet

and fuel to ceiling heights of 4 to 80 feet. RTI values range from 0 to 800

(ft-s) 1/2 for fixed temperature detectors and from 100 to 2000 (ft-s) 1 ' 2 for

rate of temperature rise detectors. Temperature differences for fixed

temperature detectors range from 10 to 140 degrees F, and available rate of

temperature rise values are 15, 20, and 25 degrees F/minute.

The tables of detector activation times are organized according to: type

of detector (fixed temperature or rate of temperature rise), detector spacing,

and type of fire (ultrafast, fast, medium, or slow). Appendix C contains the

tables listing activation times for fixed temperature heat detectors, and

Appendix D contains the tables listing activation times for rate of temperature

rise detectors. In each appendix, the tables are arranged in order of

increasing detector spacing (i.e. 0 ft, 2 ft, 4 ft, etc.). For each spacing,

the tables are arranged according to fire type. Ultrafast is first, followed

by fast, medium, and slow.

The asterisks next to some of the table entries indicate that the detector

location places it within the r/H < 0.3 region. This region is where the

theoretical dimensionless velocity correlation, discussed in section 2.4, is

15

applicable. These values are flagged because the calculation of gas velocity

in this region is based primarily on a theoretical analysis and not on a

combination of theory and experiment. In addition, this region is not

considered in the NFPA 72E Appendix C.

Finally, just as in Appendix C of NFPA 72E, for the tables in this report,

the fire plume is assumed to impinge on the ceiling at the center of the square

array of detectors spaced as indicated. So for detectors spaced at 10

ft (3.048 m), the distance of each detector from the gas impingement point

would be 7.07 ft (10 <Jl/2). Each table indicates this distance in parenthesis

after the table spacing value.

5. EXAMPLES

5.1 Using the Tables

5.1.1 Example 1: Comparison with NFPA 72E Table Results

The first example will show that these new tables agree quite well with

the results from the tables in Appendix C of NFPA 72E even though each set of

tables were generated using different correlations of experimental data.

Assume a system of detectors is installed using a 14 foot spacing in a room

with a 12 foot ceiling height. A medium fire growth rate is expected. The

detectors have an RTI rating of 50 (ft-s) 1/2 which corresponds to a 22.4 second

time constant. The ambient temperature is 70 degrees F and the rated

16

activation temperature of the detector is 190 degrees F. This gives a

temperature difference of 120 degrees.

AT = Tact - Tamb = 190 - 70 = 120 degrees F

Looking in Appendix C, a detection system installed using a 1A foot

spacing would detect a medium growth rate fire A. 91 minutes after ignition. If

we next look for similar conditions in the 72E tables [NFPA, p. 72E-36], we

find that a detector installed under these conditions with a time constant of

25s will activate when a medium growth rate fire reaches a heat release rate of

1000 BTU/s. A medium growth rate fire will reach this heat release rate 300

seconds or five minutes after ignition.

The detector listed in the NFPA table has a time constant of 25s. This is

slightly higher than the 22. As for the detector listed in the NBS table.

Therefore, it is expected that the detector listed in the NBS table would have

an activation time slightly lower than the one in the NFPA table. After

extensive cross checks between the new NBS tables and the 72E tables, the

results were found to agree to within 5 percent.

5.1.2 Example 2: Fixed Temperature vs. Rate of Rise

This example will show how alternative heat detector installations may be

compared using the tabular results. In particular, the differences between

fixed temperature and rate of rise detectors will be compared. Suppose a

detection system is installed in a room with a ceiling height of AO feet and

17

detection of a medium fire is desired. The detectors are spaced 20 feet

apart. Currently, fixed temperature detectors with an RTI of 200 (ft-s) 1 ' 2 and

an activation temperature rating of 170 degrees F are installed in the room.

Ambient temperature is 70 degrees F. (Temperature differential of 100

degrees.) Will the use of rate of rise detectors with the same RTI as the

fixed temperature detectors and an activation rate of rise rating of 15 degrees

F/min yield a lesser time to activate a detector in response to a medium growth

rate fire?

From Appendix C, the activation time of the fixed temperature detectors,

installed using a 20.0 foot spacing and exposed to a medium growth rate fire,

is 12.27 minutes. The time required to activate the rate of rise detectors is

obtained from Appendix D. The activation time for these detectors is 15.29

minutes. From Figure 1, the heat release rate at activation of the rate of

rise detectors would be 9342 BTU/s compared to 6016 BTU/s for the fixed

temperature detectors.

It would take about three minutes longer to activate the rate of rise

detectors, and the fire heat release rate would have increased by about 3326

BTU/s. This is interesting in light of the generally held belief that rate of

rise detectors activate before fixed temperature detectors. This is not true

when the detectors are located in areas with high ceilings and the fire does

not grow rapidly. This example illustrates how quick and sometimes surprising

comparisons may be made using the tabular form of the detector activation time

results.

18

5.2 Example 3: Using the Computer Program

The last example will be used to show how the computer programs work.

Both the BASIC version and the FORTRAN version ask similar questions and

operate in a similar manner so this discussion is applicable to both programs.

The problem will be to calculate the activation time for fixed temperature and

rate of rise detectors installed, using a 10 foot spacing, in an area with a

ceiling height of 12 feet. The detectors have an RTI of 670.8 (ft-s) 1/2. The

detector activation temperature is 130 degrees F, and the activation rate of

rise is 15 degrees F/min. Ambient temperature is 70 degrees F. (User input is

preceded by a > and, where possible, typed in lower case.)

ENTER 1 FOR ENGLISH UNIT INPUT2 FOR METRIC UNIT INPUT

>1

ENTER THE AMBIENT TEMPERATURE IN DEGREES F.

>70

ENTER THE DETECTOR RESPONSE TIME INDEX (RTI) IN (FT-SEC)**l/2.>670.8

ENTER THE DETECTOR ACTIVATION TEMPERATURE IN DEGREES F.

>130

ENTER THE DETECTOR RATE OF RISE IN DEGREES F/MIN.>15

ENTER THE CEILING HEIGHT IN FEET.>,12

ENTER THE DETECTOR SPACING IN FEET.>10

ENTER: S FOR SLOW FIRE GROWTH RATE,M FOR MEDIUM FIRE GROWTH RATE,F FOR FAST FIRE GROWTH RATE,U FOR ULTRAFAST FIRE GROWTH RATE, OR0 FOR OTHER.

>m

19

RESULTS

:

CEILING HEIGHT =12.0 FEET (3.66 METERS)DETECTOR SPACING =10.0 FEET ( 3.05 METERS)

DETECTOR RTI = 670.8 (FT-SEC)**l/2 ( 370.3 (M-SEC)**l/2)

FIRE GROWTH RATE CONSTANT = .1111E-001 BTU/(SEC**3)(.1171E+002 JOULES /SEC**3)

FOR TEMPERATURE ACTUATED DETECTOR:

ACTIVATION TEMPERATURE = 130.0 DEGREES F (54.4 DEGREES C)

TIME OF ACTIVATION =4.96 MINUTES

HEAT RELEASE RATE = .9859E+003 BTU/SEC(.1040E+004 KILOJOULES/SEC)

FOR RATE OF RISE ACTUATED DETECTOR:

ACTIVATION RATE OF RISE = 15.00 DEGREES F/MIN( 8.33 DEGREES C/MIN)

TIME OF ACTIVATION =3.04 MINUTES

HEAT RELEASE RATE = .3707E+003 BTU/SEC(.3911E+003 KILOJOULES/SEC)

The results show that the fixed temperature heat detector would activate

approximately 5 minutes after the fire reaches a flaming state. The heat

release rate at this time would be 986 BTU/s. A rate of rise detector would

activate at about 3 minutes with a corresponding heat release rate of 371

BTU/s. (If metric units had been selected, the input requests would have

called for data in metric units instead of English units.)

20

6. SUMMARY

This report presented a methodology for evaluating heat detection systems

installed in existing buildings. Previous work for use primarily in designing

new systems was enhanced and supplemented to broaden its application. The

resulting equations were programmed into a user interactive computer program.

This program is available in both BASIC and FORTRAN and will run on mainframes

as well as personal computers. In addition, a modified version of the FORTRAN

program was used to develop an extensive set of tables listing detector

activation times for given building geometries, detector characteristics, and

fire growth rates. These tables are useful for quick evaluation of alternative

heat detector installations among other uses. Practical examples were utilized

to illustrate the use of the tables and computer programs.

7. REFERENCES

[1] Alpert, R.L. "Calculation of Response Time of Ceiling - Mounted FireDetectors", Fire Technology , 8, 1972, p. 181.

[2] Alpert, R.L. "Turbulent Ceiling - Jet Induced by Large - Scale Fires",Combustion Science and Technology , 11, 1975, p. 197.

[3] Heskestad, G. and Delichatsios , M.A. "Environments of Fire DetectorsPhase I; Effects of Fire Size, Ceiling Height and Material, Volume II -

Analysis", Technical Report Serial No. 22427, RC 77-T-ll, FactoryMutual Research Corporation, Norwood, Massachusetts 02062, 1977.

[4] Heskestad, G. and Delichatsios, M.A. "The Initial Convective Flow in

Fire", Seventeenth Symposium (International) on Combustion , TheCombustion Institute, Pittsburgh, Pennsylvania, 1978, pp. 1113 - 1123.

[5] Schifiliti, Robert "Use of Fire Plume Theory in the Design andAnalysis of Fire Detector and Sprinkler Response", MS thesis, WorcesterPolytechnic Institute, 1985.

21

[6] Standard on Automatic Fire Detectors, NFPA 72E - 1984, Appendix C,

National Fire Protection Association, Batterymarch Park, Quincy,Massachusetts 02269.

[7] Evans, D.D. and Stroup, D.W. "Methods of Calculating the Response Timeof Heat and Smoke Detectors Installed Below Large UnobstructedCeilings", NBSIR 85-3167, U.S. Department of Commerce, National Bureauof Standards, Gaithersburg, Maryland 20899, 1985.

[8] Heskestad, G. and Smith, H. "Investigation of a New SprinklerSensitivity Approval Test: The Plunge Test", FMRC Technical Report22485, Factory Mutual Research Corporation, Norwood, Massachusetts02062, 1976.

[9] Evans, D.D. , Madrzykowski, D. "Characterizing the Thermal Response ofFusible-Link Sprinklers", NBSIR 81-2329, U.S. Department of Commerce,National Bureau of Standards, Gaithersburg, Maryland 20899, 1981.

[10] Beyler, C.L. "A Design Method for Flaming Fire Detection", FireTechnology , 20, 4, 1984, p. 5.

[11] Zukoski, E.E., Kubota, T., and Cetegen, B. "Entrainment in FirePlumes", Fire Safety Journal , 3, 1980, pp. 107 - 121.

[12] Burden, R.L., Faires, J.D., Reynolds, A.C. Numerical Analysis ; Boston,Massachusetts; Prindle, Weber & Schmidt; 1981, pp. 600.

[13] Stroup, D.W., Evans, D.D. , and Martin, P. "Evaluating Thermal FireDetection Systems [S.I. Units]", NBS Special Publication 713, U.S.

Department of Commerce, National Bureau of Standards, Gaithersburg,Maryland 20899, 1986.

22

TABLE 1. WAREHOUSE MATERIALS"

MaximumHeat

Time to ReleaseReach per Unit

1000 BTU/s Floor Area(sec) (BTU/s/ft 2

)

Classification(s - slow)

(m - medium)(f - fast)

(u - ultrafast)

1. Wood pallets, stack1.5 ft high (6-12%moisture) 150-310 110 m-f

2. Wood pallets, stack5 ft high (6-12%moisture) 90-190 330

3. Wood pallets, stack10 ft high (6-12%moisture) 80-110 600

A. Wood pallets, stack16 ft high (6-12%moisture) 75-105 900

5. Mail bags, filled,stored 5 ft high 190 35

6. Cartons, compart-mented, stacked 15

ft high 60

7. Paper, vertical rolls,stacked 20 ft high 15-28

8. Cotton (also PE,

PE/Cot, Acrylic/Nylon/PE), gar-ments in 12 ft highrack 20-42

200 u

9. Cartons on palletsrack storage, 15-30

ft high 40-280 m-f

Adapted from Table C-2-2.2.1(a) of Ref. 5

23

TABLE 1. WAREHOUSE MATERIALS (continued)

Time toReach

1000 BTU/s(sec)

MaximumHeatReleaseper UnitFloor Area(BTU/s/ft 2

)

Classification(s

(m(f

(u -

- slow)medium)

- fast)ultrafast)

10. Paper products,densely packed in

cartons, rackstorage, 20 ft high 470 - m-s

11. PE letter trays,filled, stacked 5 ft

high on cart 190 750 f

12. PE trash barrels in

cartons stacked 15 ft

high 55 250 u

13. FRP shower stalls in

cartons, stacked 15

ft high 85 110 u

14. PE bottles packed in

Item 6 85 550 u

15. PE bottles in car-tons, stacked 15 ft

high 75 170 u

16. PE pallets, stack 3 ft

high 130 - f

17. PE pallets, stack 6-8

ft high 30-55

18. PU mattress, single,horizontal 110 - f

19. PF insulation board,rigid foam, stacked15 ft high 8 170

20. PS jars packed in

Item 6 55 1200

24

TABLE 1. WAREHOUSE MATERIALS (continued)

MaximumHeat Classification

Time to Release (s - slow)Reach per Unit (m - medium)

1000 BTU/s Floor Area (f - fast)(sec) (BTU/s/ft 2

) (u - ultrafast)

21. PS tubs nested in

cartons, stacked 14

ft high 105 450 f

22. PS toy parts in car-tons, stacked 15 fthigh 110 180 f

23. PS insulation board,rigid, stacked 14 fthigh 7 290

24. PVC bottles packedin Item 6 9 300 -

25. PP 1"iih<» naplcpd in

Item 6 10 390

26. PP and PE film inrolls, stacked 14 fthigh 40 350

27. Distilled spirits inbarrels, stacked 20 fthigh 23-40

28. Methyl alcohol 65

29. Gasoline 200

30. Kerosine 200

31. Diesel Oil 180

Abbreviations

:

FRP - Fire Retardant PlasticPE - PolyethylenePF - Phenolic ResinsPP - Polypropylene

25

PolysytrenePolyurethanePolyvinyl Chloride

TABLE 2. MAXIMUM HEAT RELEASE RATES FROMFIRE DETECTION INSTITUTE ANALYSIS

ApproximateValuesBTU/s

1 . Medium wastebasket with milk cartons 100

2. Large barrel with milk cartons 140

3. Upholstered chair with polyurethane foam 350

4. Latex foam mattress (heat at room door) 1200

5. Furnished living room (heat at open door) 4000 - 8000

* Adapted from Table C-2-2.2.1(b) of Ref. 3

27

TABLE 3. RTI VALUES FOR ANY LISTED DETECTOR*(FIXED TEMPERATURE TYPE) [(ft-s) 1/2 ]

AllListed UL Listed Activation Temperature FMSpacing Listed

1 9R°1J ijj r 1 AS 0 TT 1 fifl°T7iuu r 1 7n°ir 15U J! iGmp

10 894 738 586 436 358 217 436

15 559 425 349 246 199 101 246

20 369 302 235 157 116 38 157

25 277 224 174 107 72 107

30 212 179 136 81 49 81

AO 159 128 92 40

50 132 98 67

70 81 54 20

NOTE: These RTIs are based on an analysis of the UnderwritersLaboratories and Factory Mutual listing test procedures. Plunge test (seeRef . 7) results performed on the detector to be used will give a moreaccurate response time index.

Abbreviations

:

FM - Factory MutualUL - Underwriters Laboratories Inc.

* Adapted from Table C-3-2.1.1 of Ref. 5

28

TABLE 4. RTI VALUES FOR ANY LISTED DETECTOR*(RATE OF RISE TYPE) [(ft-s) 1/2 ]

ListedSpacing\tt)

UL Listed

13 r/min

Activation Rate

ZU r/min

of Temp

Z_>

. Rise

J? /min

10 1834 1308 984

12.5 1453 1073 805

15 1185 872 637

20 872 581 425

30 559 380 280

40 447 291 206

50 425 246 161

Abbreviation:

UL - Underwriters Laboratories Inc.

* Adapted from Ref . 3

29

o

o o o o o o o o o oo o o o o o o o o oo o o o o o o o o oo 0) 00 1^ CO in CO C\J

(s/njg) aiva 3SV313U JLV3H

30

This page intentionally left blank.

32

APPENDIX A. DETACT-T2FORTRAN VERSION

33

c

PROGRAM DETACTC

C THIS IS PROGRAM DETACT-T2

.

C IT CALCULATES THE RESPONSE OF THERMAL DETECTORS, BOTH FIXED TEMPERATUREC AND RATE OF TEMPERATURE RISE, TO FIRES WHOSE HEAT RELEASE RATE GROWSC PROPORTIONALLY WITH THE SQUARE OF TIME FROM IGNITION.C

C WRITTEN BY DAVID W. STROUP, CENTER FOR FIRE RESEARCH, NBSC

C THIS PROGRAM IS A CONTRIBUTION OF THE NATIONAL BUREAU OF STANDARDS ANDC IS NOT SUBJECT TO COPYRIGHT.C

C VERSION 1.1

C

C ****************************** NOTATION ********************************

C

C INPUT:

C J - UNITS CODE (1 OR 2)

C 1 - INPUT DATA IN ENGLISH UNITSC 2 - INPUT DATA IN METRIC UNITSC TAMB - AMBIENT TEMPERATUREC RTI - DETECTOR RESPONSE TIME INDEXC TACT - DETECTOR ACTIVATION TEMPERATUREC ROR - DETECTOR ACTIVATION RATE OF RISEC HF - CEILING HEIGHTC ZF - DETECTOR SPACINGCM - GROWTH FACTOR CODE, CHARACTER VARIABLE (S, M, F, U, OR 0)

C ALPHA - FIRE GROWTH RATE CONSTANTC

C OUTPUT:C T - TIME OF ACTIVATION FOR FIXED TEMPERATURE DETECTORC QD - HEAT RELEASE RATE AT TIME OF ACTIVATION, T

C TR - TIME OF ACTIVATION FOR RATE OF RISE DETECTORC QDR - HEAT RELEASE RATE AT TIME OF ACTIVATION, TRC IERR - ERROR CODE (0 OR 1)

C 0 - SUCCESSFULC 1 - UNSUCCESSFULC

c ************************************************************************

c

IMPLICIT DOUBLE PRECISION (A-H,0-Z)CHARACTER MDATA IRTTY,IWTTY/5,6/DATA GE , CPE , RHOE/ 32 . 2D0 , 0 . 2AD0 , 0 . 07 35D0/

DATA GM , CPM , RHOM/ 9 . 8D0 , 1 . 0035D0 , 1 . 1 768D0

/

IERR = 0

WRITE (IWTTY,1)1 FORMAT (' DETACT-T2 VERSION 1.0'/

& ' WRITTEN BY D.W. STROUP (1985)'//

& 1 CONTRIBUTION OF THE 7

34

& 1 NATIONAL BUREAU OF STANDARDS (U.S.).'/

& 1 NOT SUBJECT TO COPYRIGHT. 1

//

& 1 CALCULATES DETECTOR ACTUATION TIME'/& 1 BELOW UNCONFINED CEILINGS WITH '/

& 1 TIME SQUARED FIRE GROWTH RATES.'//)C

C ENTER INPUT DATAC5 CONTINUE

WRITE (IWTTY,10)10 FORMAT (• ENTER: 1 FOR ENGLISH UNIT INPUT' /8X,' 2 FOR METRIC UNIT I

&NPUT ' /

)

READ (IRTTY,*) J

IF (J.EQ.l) THENWRITE (IWTTY,20)

20 FORMAT (' ENTER THE AMBIENT TEMPERATURE IN DEGREES F.7)READ (IRTTY,*) TAMBWRITE (IWTTY,30)

30 FORMAT (' ENTER THE DETECTOR RESPONSE TIME INDEX (RTI) IN (FT-SEC)&**l/2. 7)READ (IRTTY,*) RTIIF (RTI.LE.0.000001D0) RTI = 0.000001D0RTIR = RTIWRITE (IWTTY,A0)

AO FORMAT (' ENTER THE DETECTOR ACTIVATION TEMPERATURE IN DEGREES F.'

&/)READ (IRTTY,*) TACTWRITE (IWTTY,50)

50 FORMAT (' ENTER A DETECTOR RATE OF RISE IN DEGREES F/MINUTE. 7)READ (IRTTY,*) RORWRITE (IWTTY,60)

60 FORMAT (' ENTER THE CEILING HEIGHT IN FEET.'/)READ (IRTTY,*) HFWRITE (IWTTY.70)

70 FORMAT (' ENTER THE DETECTOR SPACING IN FEET. 1

/)READ (IRTTY,*) ZF

WRITE (IWTTY,80)80 FORMAT (' ENTER: S FOR SLOW FIRE GROWTH RATE 7

& ' M FOR MEDIUM FIRE GROWTH RATE 1

/

& ' F FOR FAST FIRE GROWTH RATE'/& 1 U FOR ULTRAFAST FIRE GROWTH RATE OR'/& ' 0 FOR OTHER'/)READ (IRTTY, A10) MIF ( (M.EQ. ' s' ) .OR. (M.EQ. ' S' ) ) ALPHA = 0.00277778D0IF ((M.EQ. 'm' ). OR. (M.EQ. 'M' )) ALPHA = 0.01111111D0IF ((M.EQ.'f').OR.(M.EQ.'F')) ALPHA = 0.0AAAAA5D0IF ((M.EQ. 'u' ). OR. (M.EQ. 'U' )) ALPHA = 0.1777778D0IF ((M.EQ. 'o' ). OR. (M.EQ. '0' )) WRITE (IWTTY,90)IF ((M.EQ. 'o' ). OR. (M.EQ. '0' )) READ (IRTTY,*) ALPHA

90 FORMAT (' ENTER THE FIRE GROWTH RATE CONSTANT (ALPHA) IN BTU/SEC/S&EC/SEC. '/)

100 CONTINUE

35

ELSEC

C METRIC UNIT INPUTC

WRITE (IWTTY,110)110 FORMAT (* ENTER THE AMBIENT TEMPERATURE IN DEGREES C. 1

/)

READ (IRTTY,*) TAMBWRITE (IWTTY,120)

120 FORMAT (' ENTER THE DETECTOR RESPONSE TIME INDEX (RTI) IN (M-SEC)*&*l/2.7)READ (IRTTY,*) RTIIF (RTI.LE.0.000001D0) RTI = 0.000001D0RTIR = RTIWRITE (IWTTY,130)

130 FORMAT (' ENTER THE DETECTOR ACTIVATION TEMPERATURE IN DEGREES C. 1

&/)READ (IRTTY,*) TACTWRITE (IWTTY.140)

140 FORMAT (' ENTER A DETECTOR RATE OF RISE IN DEGREES C/MINUTE. 1

/)

READ (IRTTY,*) RORWRITE (IWTTY.150)

150 FORMAT (' ENTER THE CEILING HEIGHT IN METERS. 1

/)

READ (IRTTY,*) HFWRITE (IWTTY,160)

160 FORMAT (' ENTER THE DETECTOR SPACING IN METERS.'/)READ (IRTTY,*) ZFWRITE (IWTTY.80)READ (IRTTY, 410) MIF ( (M.EQ.

1 s' ) .OR. (M.EQ. 1 S ' ) ) ALPHA = 2.930555556D0IF ((M.EQ. 'm' ). OR. (M.EQ. 'M* )) ALPHA = 11 . 72222222D0IF ((M.EQ. 'f ' ). OR. (M.EQ. 'F' )) ALPHA = 46.88888889D0IF ((M.EQ. 'u' ). OR. (M.EQ. 'U 1

)) ALPHA = 187 . 5555556D0IF ((M.EQ. 'o' ). OR. (M.EQ. '0' )) WRITE (IWTTY,170)IF ((M.EQ. 'o* ). OR. (M.EQ. '0' )) READ (IRTTY,*) ALPHA

170 FORMAT (1 ENTER THE FIRE GROWTH RATE CONSTANT (ALPHA) IN WATTS/SEC/

&SEC.7)180 CONTINUE

ENDIFC

C ******************* CALCULATIONS *************************************

C

R = 0.5D0*DSQRT(2.0D0)*ZFROH = R/HFROR = ROR/ 60. DOIF (J.EQ.l) THENTAMB = TAMB + 460. DOTACT = TACT + 460. DOA = GE/(CPE*TAMB*RHOE)G = GEELSETAMB = TAMB + 273. DOTACT = TACT + 27 3. DO

36

A = GM/(CPM*TAMB*RHOM*1000.D0)G = GMENDIFTOTS 2 = A*-* ( - 1 . DO / 5 . DO ) *ALPHA** ( - 1 . DO / 5 . DO ) *HF** (4. DO/ 5 .DO)

DLTODL = A**(2. DO/5. D0)*(TAMB/G)*ALPHA**(2. DO/5. DO)& *HF**(-3.D0/5.D0)UOUS2 = A** ( 1 . DO / 5 . DO ) *ALPHA** ( 1 . DO / 5 . DO ) *HF** ( 1 . DO / 5 . DO

)

DELTD = TACT - TAMBIF (ROH.GT.0.3D0) THENUODLTH = 0.59D0*ROH**(-0.63D0)ELSEUODLTH = 3.87D0/(9.115D0**0.5D0)ENDIFTS2F = 0.954D0*(l.D0+ROH)A2 = (4. DO/3. DO) *DLTODL*UOUS2** ( - 0 . 5D0 ) *UODLTH** ( - 0 . 5D0 ) *RTI

/

& (TOTS2*(0 . 188D0+0 . 313D0*ROH)

)

C = 1.D0+DELTD/A2CALL NWTN (C,Y,IERR,IWTTY)IF (IERR.EQ.1) GO TO 380DELTS2 = ( 4 . DO / 3 . DO )*UOUS2** ( - 0 . 5D0 ) *UODLTH** ( - 0 . 5D0 ) *RTI*Y/& (TOTS2*(0 . 188D0+0 . 313D0*ROH)

)

TS2 = 0 . 954D0*( 1 .D0+ROH)+(0 . 188D0+0 . 313D0*ROH)*DELTS2**( 3 .DO/4 . DO)TS2 = TS2 + TS2FT = TS2*A** ( - 1 . DO / 5 . DO ) *ALPHA** ( - 1 . DO / 5 . DO ) *HF** ( 4 . DO / 5 . DO

)

QD = ALPHA*T**2IF (RTIR.LE.2.0D0) RTIR = 2.0D0Dl = (4.D0/3.D0)*DLTODL/(TOTS2*(0.188D0+0.313D0*ROH))D2 = (3 .DO/4 .D0)*UOUS2**0 . 5D0*UODLTH**0 . 5D0*( 1 .D0/RTIR)*TOTS2& *(0.188D0+0.313D0*ROH)CALL BISECT (Dl ,D2,ROR,DELTS2,IERR,IWTTY)IF (IERR.EQ.1) GO TO 380TS2R = 0.954D0*(l.D0+ROH)+(0.188D0+0.313D0*ROH)*DELTS2

& **(3.D0/4.D0)TS2R = TS2R + TS2FTR = TS2R*A** ( - 1 . DO / 5 . DO ) *ALPHA** ( - 1 . DO / 5 . DO ) *HF** ( 4 . DO / 5 . DO

)

QDR = ALPHA*TR**2C

C Mckidcick-k-k-k PRINT OUT RESULTS ^^^^^^A^^^jVVtVc^^^yc^Vc********************

c

ROR = ROR*60.D0WRITE (IWTTY,190)

190 FORMAT ('1 RESULTS:')IF (J.EQ.l) THEN

C

C ENGLISH (METRIC) OUTPUTC

HF2 = HF * 0.3048D0ZF2 = ZF * 0.3048D0WRITE (IWTTY,200) HF,HF2,ZF,ZF2

200 FORMAT ('0 CEILING HEIGHT = \F6.2,' FEET (',F6.2,' METERS) 1

/

& 5X,' DETECTOR SPACING = ',F6.2,' FEET (',F6.2,' METERS) 1

)

RTI2 = RTI * (0.3048D0**0.5D0)

37

WRITE (IWTTY.210) RTI,RTI2210 FORMAT ('0 DETECTOR RTI = ',F6.1,' (FT-SEC)**l/2 (',F6.1,' (M-S

&EC)**l/2)'

)

ALPHA2 = ALPHA * 1055. DOWRITE (IWTTY,220) ALPHA,ALPHA2

220 FORMAT ('0 FIRE GROWTH CONSTANT = ',E12.4,' BTU/(SEC**3) 1

/

& ' ('.E12.4,' JOULES/SEC** 3 )'

)

WRITE (IWTTY.400)READ (IRTTY.410) MWRITE (IWTTY.230)

230 FORMAT (/'O FOR TEMPERATURE ACTUATED DETECTOR:')TACT = TACT - 460. DOTACT2 = (5.D0/9.D0)*(TACT-32.D0)WRITE (IWTTY.240) TACT,TACT2

240 FORMAT ('0 ACTIVATION TEMPERATURE = \F6.1,' DEGREES F (1 ,F6.1,

& 1 DEGREES C)')T = T / 60. DOWRITE (IWTTY,250) T

250 FORMAT ('0 TIME TO ACTIVATION = \F8.2,' MINUTES 1

)

QD2 = QD * 1.055D0WRITE (IWTTY.260) QD.QD2

260 FORMAT ('0 HEAT RELEASE RATE = 1 ,E12.4,' BTU/SEC'/& 1 C.E12.4,' KILOJOULES/SEC) 1

)

WRITE (IWTTY.400)READ (IRTTY.410) MWRITE (IWTTY,270)

270 FORMAT (//'O FOR RATE OF RISE ACTUATED DETECTOR:')ROR2 = ROR * (5. DO/9. DO)WRITE (IWTTY.290) ROR.ROR2

290 FORMAT ('0 ACTIVATION RATE OF RISE = ',F6.2,' DEGREES F/MIN (',

& F6.2,' DEGREES C/MIN)')TR = TR / 60. DOWRITE (IWTTY,250) TRQDR2 = QDR * 1.055D0WRITE (IWTTY.260) QDR.QDR2WRITE (IWTTY,400)READ (IRTTY.410) MELSE

C

C METRIC (ENGLISH) OUTPUTC

HF2 = HF * (1.D0/0.3048D0)ZF2 = ZF * (1.D0/0.3048D0)WRITE (IWTTY,300) HF,HF2,ZF,ZF2

300 FORMAT ('0 CEILING HEIGHT = '.F6.2,' METERS (',F6.2,' FEET)'/& 5X, 'DETECTOR SPACING = ',F6.2,' METERS (',F6.2,' FEET)')RTI2 = RTI * ((l.D0/0.3048D0)**0.5D0)WRITE (IWTTY.320) RTI,RTI2

320 FORMAT ('0 DETECTOR RTI = 1 ,F6.1, ' (M-SEC)**l/2 C,F6.1,' (FT-S

&EC)**l/2)'

)

ALPHA2 = ALPHA * (1 .DO/ 1055. DO)

WRITE (IWTTY.330) ALPHA,ALPHA2

38

330 FORMAT ('0 FIRE GROWTH CONSTANT = ',E12.4,' JOULES/ (SEC**3)

7

& 1 (' ,E12.4, 1 BTU/SEC**3)'

)

WRITE (IWTTY,400)READ (IRTTY,410) MWRITE (IWTTY,230)TACT = TACT - 27 3. DOTACT2 = (9. DO/5. DO) * TACT + 32. DOWRITE (IWTTY,340) TACT , TACT2

340 FORMAT ('0 ACTIVATION TEMPERATURE = ',F6.1,' DEGREES C (',F6.1,& 1 DEGREES F) 1

)

T = T / 60. DOWRITE (IWTTY,350) T

350 FORMAT ('0 TIME TO ACTIVATION = ' ,F8.2, ' MINUTES')QD = QD / 1000. DOQD2 = QD * (1.D0/1.055D0)WRITE (IWTTY,360) QD , QD2

360 FORMAT ('0 HEAT RELEASE RATE = \E12.4,' KILOJOULES/SEC

7

& 1

(' ,E12.4,' BTU/SEC) 1

)

WRITE (IWTTY.400)READ (IRTTY.410) MWRITE (IWTTY.270)ROR2 = ROR * (9. DO/5. DO)WRITE (IWTTY,370) ROR,ROR2

370 FORMAT ('0 ACTIVATION RATE OF RISE = ',F6.2,' DEGREES C/MIN (',

& F6.2,' DEGREES F/MIN) 1

)

TR = TR / 60. DOWRITE (IWTTY.350) TRQDR = QDR / 1000. DOQDR2 = QDR * (1.D0/1 .055D0)WRITE (IWTTY,360) QDR , QDR2WRITE (IWTTY,400)READ (IRTTY.410) MENDIFWRITE (IWTTY.420)READ (IRTTY,410) MIF ((M.EQ. 'Y' ) .OR. (M.EQ. 'y' )) GO TO 5

STOP 'PROGRAM COMPLETED'380 CONTINUE

WRITE (IWTTY,390)390 FORMAT (' *******> ERROR IN DETACT ROUTINE <*******«)

400 FORMAT (//' <RETURN> TO CONTINUE')410 FORMAT (Al)

WRITE (IWTTY,420)420 FORMAT (' TRY ANOTHER CASE (Y/N) ?'/)

READ (IRTTY.410) MIF ((M.EQ. 'Y' ). OR. (M.EQ. 'y' )) GO TO 5

STOP 'PROGRAM ABORTED'END

C

SUBROUTINE NWTN (C , P , IERR, IWTTY)C

C THIS IS ROUTINE NWTN. IT SOLVES THE FIXED TEMPERATURE DETECTOR

39

C ACTIVATION TIME EQUATION USING A NEWTON-RAPHSON METHOD.C

IMPLICIT DOUBLE PRECISION (A-H.O-Z)PO = 0.1D0TOL = 0.00001D0NO = 1000I = 1

IERR = 0

10 CONTINUEIF (I.LE.NO) THENIF (P0.GT.50.D0) THENX = 0.0D0ELSEX = DEXP(-PO)ENDIFFX = PO + X - C

FPMX = 1.0D0 - XIF (FPMX.LT.0.00000001D0) GO TO 30

P = PO - (FX/FPMX)IF (ABS(P-PO).LT.TOL) THENIERR = 0

RETURNELSE1 = 1+1PO = P

ENDIFGO TO 10

ENDIFIERR = 1

WRITE (IWTTY,20) I

20 FORMAT (' NEWTON-RAPHSON FAILED AFTER NO ITERATIONS, NO = ',14)

RETURN30 WRITE (IWTTY,A0)AO FORMAT (' SLOPE OF EQUATION TOO CLOSE TO ZERO FOR 7

& 1 NEWTON-RAPHSON METHOD.

7

& 1 ERROR RETURN'

)

IERR = 1

RETURNEND

C

SUBROUTINE BISECT (Dl ,D2,ROR,P,IERR,IWTTY)C

C THIS IS ROUTINE BISECT. IT SOLVES THE RATE OF RISE DETECTOR ACTIVATIONC TIME EQUATION USING A BISECTION METHOD.C

IMPLICIT DOUBLE PRECISION (A-H.O-Z)IERR = 0

TOL = 0.00001D0NO = 1000

A = 0.0D0B = 1000. 0D0RLMT = TOL / 20.0

AO

10 CONTINUEIF ((D2*B).GT.50.D0) THENX - 0.0D0ELSEX - DEXP (-D2*B)ENDIFFXB * D1*B**0.25DO-D1*B**0.25*X-RORIF (FXB.LT.0.0D0) THENA - B

B = B + 500. DO

GO TO 10

ENDIFI = 1

20 CONTINUEIF (I.LE.NO) THENP = A+(B-A)/2.0D0IF ((D2*P).GT.50.D0) THENX = 0.0D0ELSEX = DEXP (-D2*P)ENDIFFX = Dl*P**0.25D0-Dl*P**0.25D0*X-RORIF (((FX.GT. -RLMT) .AND. (FX.LT.RLMT) ) .OR.

& (((B-A)/2.D0).LT.TOL)) THENIERR = 0

RETURNELSE1 = 1+1IF ((D2*A).GT.50.D0) THENX = 0.0D0ELSEX = DEXP (-D2*A)ENDIFFXA = Dl*A**0.25D0-Dl*A**0.25D0*X-RORIF ((FXA*FX).GT.0.0D0) THENA = P

ELSEB = P

ENDIFENDIFGO TO 20

ENDIFIERR = 1

WRITE (IWTTY.30) I

30 FORMAT (' BISECTION ROUTINE FAILED AFTER NO ITERATIONS, NO = ',14)

RETURNEND

41


42

APPENDIX B. DETACT-T2BASIC VERSION

A3

10 PRINT "DETACT-T2 VERSION 2.0"

20 PRINT "WRITTEN BY D.W. STROUP (1985)"30 PRINT 11 "

AO PRINT "CONTRIBUTION OF THE"50 PRINT "NATIONAL BUREAU OF STANDARDS (U.S.)."60 PRINT "NOT SUBJECT TO COPYRIGHT. 11

70 PRINT " "

80 PRINT "CALCULATES DETECTOR ACTUATION TIME"90 PRINT "BELOW UNCONFINED CEILINGS WITH 11

100 PRINT "TIME SQUARED FIRE GROWTH RATES 11

110 PRINT " 11

120 REM130 REM INPUT:1A0 REM J

150 REM160 REM170 REM TAMB180 REM RTI190 REM TACT200 REM ROR210 REM HF220 REM ZF230 REM M2A0 REM ALPHA250 REM260 REM OUTPUT:270 REM T

UNITS CODE (1 OR 2)

1 - INPUT DATA IN ENGLISH UNITS2 - INPUT DATA IN METRIC UNITSAMBIENT TEMPERATUREDETECTOR RESPONSE TIME INDEXDETECTOR ACTIVATION TEMPERATUREDETECTOR ACTIVATION RATE OF RISECEILING HEIGHTDETECTOR SPACINGGROWTH RATE FACTOR CODE, CHARACTER (S, M, F, U, ORO)FIRE GROWTH RATE CONSTANT (FOR M = 0)

TIME OF ACTIVATION FOR FIXED TEMPERATURE DETECTORHEAT RELEASE RATE AT TIME OF ACTIVATION, TTIME OF ACTIVATION FOR RATE OF RISE DETECTORHEAT RELEASE RATE AT TIME OF ACTIVATION, TRERROR CODE (0 OR 1)

0 - SUCCESSFUL1 - UNSUCCESSFUL

280 REM QD290 REM TR300 REM QDR310 REM IERR320 REM330 REM3A0 REM350 CLEAR360 REM370 REM ENTER INPUT DATA380 REM390 READ GE//,CPE//,RHOE//

A00 DATA 32.2//,0.2A//,0.0735//

A10 READ GM//,CPM//,RHOM//

A20 DATA 9. 8//, 1.0035//, 1.1768//

A30 IERR% = 0

AAO PRINT " ENTER: 1 FOR ENGLISH UNIT INPUT"A50 PRINT " 2 FOR METRIC UNIT INPUT"A60 INPUT "SELECTION = ",J%A70 IF J%<>1 GOTO 7A0

A80 REMA90 REM ENTER DATA IN ENGLISH UNITS500 REM

AA

510 INPUT "AMBIENT TEMPERATURE <DEGREES F> = ",TAMB#

520 INPUT "DETECTOR RESPONSE TIME INDEX, RTI <(FT-SEC)~(l/2)> = ",RTI#

530 IF RTI//<. 0000001// THEN LET RTI// = . 000000 1//

540 RTIR// = RTI//

550 INPUT "DETECTOR ACTIVATION TEMPERATURE <DEGREES F> = ",TACT//

560 INPUT "DETECTOR RATE OF TEMPERATURE RISE <DEGREES F/MIN> = ",ROR#

570 INPUT "ROOM CEILING HEIGHT <FEET> = ",HF//

580 INPUT "DETECTOR SPACING <FEET> = ",ZF//

S FOR SLOW FIRE GROWTH RATE,"M FOR MEDIUM FIRE GROWTH RATE,"F FOR FAST FIRE GROWTH RATE,"U FOR ULTRAFAST FIRE GROWTH RATE, OR"

590 PRINT "ENTER:

600 PRINT "

610 PRINT "

620 PRINT 11

630 PRINT 11

780

790

0 FOR OTHER FIRE GROWTH RATE"640 INPUT "SELECTION = ",M$650 IF (M$="s" OR M$="S") THEN LET ALPHA# = .00277778//

660 IF (M$="m" OR M$="M") THEN LET ALPHA// = .01111111//

670 IF (M$="f" OR M$="F") THEN LET ALPHA// = .04444445//

680 IF (M$="u" OR M$="U") THEN LET ALPHA// = .17777778//

690 IF (M$="o" OR M$="0") THEN INPUT "FIRE GROWTH RATE <BTU/SEC~3> = ", ALPHA//

700 GOTO 940710 REM720 REM ENTER DATA IN METRIC UNITS730 REM740 INPUT "AMBIENT TEMPERATURE <DEGREES C> = " ,TAMB#750 INPUT "DETECTOR RESPONSE TIME INDEX, RTI <(M-SEC)^(l/2)> = ",RTI//

760 IF RTI//<. 0000001// THEN LET RTI// = .0000001//

770 RTIR// = RTI//

INPUT "DETECTOR ACTIVATION TEMPERATURE <DEGREES C> = ",TACT//

INPUT "DETECTOR RATE OF TEMPERATURE RISE <DEGREES C/MIN> = ",ROR//

800 INPUT "ROOM CEILING HEIGHT <METERS> = ",HF//

810 INPUT "DETECTOR SPACING <METERS> = ",ZF//

820 PRINT "ENTER: S FOR SLOW FIRE GROWTH RATE,"M FOR MEDIUM FIRE GROWTH RATE,"F FOR FAST FIRE GROWTH RATE,"U FOR ULTRAFAST FIRE GROWTH RATE, OR"

830 PRINT "

840 PRINT "

850 PRINT "

860 PRINT " 0 FOR OTHER FIRE GROWTH RATE"870 INPUT "SELECTION = ",M$

OR M$="S") THEN LET ALPHA// = 2.9305556//

m" OR M$="M") THEN LET ALPHA// = 11.722222//

f" OR M$="F") THEN LET ALPHA// = 46.888889//u" OR M$="U") THEN LET ALPHA// = 187.55556//

o" OR M$="0") THEN INPUT "FIRE GROWTH RATE <J/SEC~3> = ", ALPHA//

r *\ 5\ x /C *c

880 IF (M$="890 IF (M$="900 IF (M$="910 IF (M$="920 IF (M$="930 REM940 REM ****

950 REM960 R// = .5// * SQR(2//) * ZF//

970 ROH// = R// /HF//

980 ROR// = ROR// / 60//

990 IF J%<>1 GOTO 10501000 TAMB// = TAMB// + 460//

1010 TACT// = TACT// + 460//

1020 A// = GE///(CPE//*TAMB//*RHOE//)

CALCULATIONS * "* >,{************** >» « >'< < « * « >'<*>** «******

45

1030 G// = GE#10AO GOTO 10901050 TAMB# = TAMB# + 273//

1060 TACT// = TACT// + 273#1070 A# = GM///(CPM//*TAMB//*RHOM//*1000//)

1080 G# = GM//

1090 T0TS2//=A/f ( - l///5//)*ALPHA/f ( - l///5//)*HF/r (4///5/Z)

1100 DLTODL//=A// '( 2# / 5# ) * ( TAMB///G// ) *ALPHA// " ( 2/// 5// )*HF# ~

( - 3// / 5//

)

1110 UOUS2#=A#"(l#/5#)*ALPHA#^(l#/5#)*HF#'(l#/5/01120 DELTD# = TACT// - TAMB#1130 IF (ROH#>.3) THEN U0DLTH//=.59*R0H/f (- .63//) ELSE U0DLTH//=3.87///(SQR(9. 115//))

1140 TS2F// = .954// * (1// + ROH//)

1150 P// = T0TS2//*(.188//+.313//*R0H//)

1160 A2//=(4///3//)*DLT0DL//*UQUS2/f (- .5//)*U0DLTH/f (- . 5//)*RTI///P#

1170 C// = 1// + DELTD// / A2//

1180 GOSUB 26501190 IF IERR%=1 GOTO 25501200 DELTS2//=(4///3//)*U0US2/f (- .5//)*U0DLTH/f (- .5//)*RTI//*Y///P//

1210 TS2//=.954//*(l//+ROH//)+( . 188//+. 313//*R0H//)*DELTS2/f (3///4/Z)

1220 TS2// = TS2// + TS2F//

1230 T//=TS2//*A//"(-l///5//)*ALPHA//^(-l///5//)*HF//^(4///5//)

1240 QD// = ALPHA// * T//~2!

1250 IF RTIR//<=2// THEN LET RTIR// = 2//

1260 D 1 //= ( 4// / 3// ) *DLTODL// / P//

1270 D2//=(3///4//)*U0US2/f . 5//*UODLTH/f . 5//*( 1///RTIR//)*P//

1280 GOSUB 29501290 IF IERR%=1 GOTO 25501300 TS2R//=.954//*(l//+R0H//)+( • 188//+.313//*R0H//)*DELTS2/f (3///4/Z)

1310 TS2R// = TS2R// + TS2F//

1320 TR//=TS2R//*A//^ ( -l///5//)*ALPHA//^ ( -l///5//)*HF//^ (4///5/Z)

1330 QDR// = ALPHA// * TR/f 2!

1340 ROR// = ROR// * 60//

1350 REM1360 REM PRINT OUT RESULTS1370 REM1380 PRINT "RESULTS:"1390 IF J%<>1 GOTO 19601400 REM1410 REM ENGLISH (METRIC) OUTPUT1420 REM1430 HF2// = HF// * .3048

1440 ZF2// = ZF// * .30481450 PRINT " "

1460 PRINT " CEILING HEIGHT = ";CSNG(HF//);" FEET"1470 PRINT *'

(M ;CSNG(HF2//);" METERS)"

1480 PRINT " "

1490 PRINT " DETECTOR SPACING = " ;CSNG(ZF//) ;" FEET"

1500 PRINT " (";CSNG(ZF2//);" METERS)"1510 PRINT " "

1520 RTI2// = RTI// * ( . 3048//" . 5//)

1530 PRINT " RTI = " ;CSNG(RTI//) ;" (FT-SEC)"0.5";" (" ;CSNG(RTI2//) ;" (M-SEC)"0.5)

1540 PRINT " "

46i

1550 ALPHA2// = ALPHA// * 1055//

1560 PRINT " FIRE GROWTH RATE = " ;CSNG(ALPHA//) ;" BTU/(SEC~3)"1570 PRINT "

(M ;CSNG(ALPHA2//); ,, J/(SEC~3))"

1580 PRINT " 11

1590 INPUT "<RETURN> TO CONTINUE ";0$

1600 PRINT 11 11

1610 PRINT " 11

1620 PRINT 11 FOR TEMPERATURE ACTUATED DETECTOR:"1630 TACT// = TACT// - 460//

1640 TACT2// = (5///9/Z) * (TACT// - 32//)

1650 PRINT " "

1660 PRINT " ACTIVATION TEMPERATURE = " ;CSNG(TACT//) ;" DEGREES F"

1670 PRINT " (";CSNG(TACT2//);" DEGREES C)"1680 PRINT 11 "

1690 T// = T// / 60//

1700 PRINT " TIME TO ACTIVATION = ";CSNG(T//) ;" MINUTES"1710 PRINT " "

1720 QD2// = QD// * 1.055//

1730 PRINT 11 HEAT RELEASE RATE = 11 ;CSNG(QD#) ;" BTU/SEC"

1740 PRINT " (";CSNG(QD2//);" kJ/SEC )"

1750 PRINT 11 11

1760 INPUT "<RETURN> TO CONTINUE ";0$1770 PRINT " "

1780 PRINT 11 11

1790 PRINT " FOR RATE OF RISE ACTUATED DETECTOR:"1800 ROR2// = ROR// * (5///9/Z)

1810 PRINT " "

1820 PRINT " ACTIVATION RATE OF RISE = " ;CSNG(ROR//) ;" DEGREES F/MIN"

1830 PRINT " (";CSNG(ROR2//); M DEGREES C/MIN)1840 PRINT " "

1850 TR// = TR// /60//

1860 PRINT 11 TIME TO ACTIVATION = ";CSNG(TR//);" MINUTES"1870 QDR2// = QDR// * 1.055//

1880 PRINT 11 "

1890 PRINT " HEAT RELEASE RATE = " ;CSNG(QDR//) ;" BTU/SEC"

1900 PRINT 11 (";CSNG(QDR2//); n kJ/SEC )"

1910 PRINT " "

1920 PRINT " "

1930 INPUT 11 TRY ANOTHER RUN (YES/NO) ";0$1940 IF (0$="Y" OR 0$="y") GOTO 1201950 GOTO 25301960 HF2// = HF// * (1I/.3048)1970 ZF2// = ZF// * (11/.3048)1980 REM1990 REM METRIC (ENGLISH) OUTPUT2000 REM2010 PRINT " 11

2020 PRINT " CEILING HEIGHT = " ;CSNG(HF//) ;" METERS"

2030 PRINT " (";CSNG(HF2//); M FEET)"2040 PRINT " "

2050 PRINT " DETECTOR SPACING = " ;CSNG(ZF//) ;" METERS"2060 PRINT " (";CSNG(ZF2//); !I FEET)"

47

2070 PRINT " "

2080 RTI2// = RTI// * ((l!/.3048)\5//)2090 PRINT " RTI - ";CSNG(RTI//);" (M-SEC)^0.5"; H (";CSNG(RTI2//) (FT-SEC)*0.5)2100 PRINT " "

2110 ALPHA2// = ALPHA* * (11/10551)2120 PRINT " FIRE GROWTH RATE » " } CSNG(ALPHA// )

;" J/(SEC*3)"

2130 PRINT " (";CSNG(ALPHA2//); n BTU/(SEC*3))"2140 PRINT " "

2150 INPUT "<RETURN> TO CONTINUE ";0$

2160 PRINT " "

2170 PRINT " "

2180 PRINT " FOR TEMPERATURE ACTUATED DETECTOR:"2190 PRINT " "

2200 TACT// = TACT// - 273//

2210 TACT2// = (9/// 5//) * TACT// + 32//

2220 PRINT " ACTIVATION TEMPERATURE = " ;CSNG(TACT//) ;" DEGREES C"

2230 PRINT " (";CSNG(TACT2//);" DEGREES F)"2240 PRINT " "

2250 T# = T// / 60//

2260 PRINT " TIME TO ACTIVATION = ";CSNG(T//);" MINUTES"2270 PRINT " "

2280 QD# = QD// / 1000//

2290 QD2// = QD// * (11/1.055)2300 PRINT 11 HEAT RELEASE RATE = ";CSNG(QD//) kJ/SEC"2310 PRINT " (";CSNG(QD2//); M BTU/SEC )"

2320 PRINT " 11

2330 INPUT "<RETURN> TO CONTINUE" ;0$

2340 PRINT 11 "

2350 PRINT " 11

2360 PRINT " FOR RATE OF RISE ACTUATED DETECTOR:"2370 ROR2// = ROR// * (9///5/Z)

2380 PRINT " "

2390 PRINT " ACTIVATION RATE OF RISE = " ;CSNG(ROR//) ;" DEGREES C/MIN"2400 PRINT " (";CSNG(ROR2//);" DEGREES F/MIN)"2410 PRINT " "

2420 TR// = TR// /60//

2430 PRINT " TIME TO ACTIVATION = " ;CSNG(TR//)

;

11 MINUTES"2440 PRINT " "

2450 QDR// = QDR// / 1000//

2460 QDR2// = QDR// * (11/1.055)2470 PRINT " HEAT RELEASE RATE = " ;CSNG(QDR//) ;" kJ/SEC"2480 PRINT " (";CSNG(QDR2//); H BTU/SEC )"

2490 PRINT " "

2500 PRINT 11 "

2510 INPUT " TRY ANOTHER RUN (YES/NO) ";0$

2520 IF (0$="Y" OR 0$="y") GOTO 120

2530 END2540 REM2550 REM *********** ERROR HANDLING ROUTINE ***********

2560 REM2570 PRINT " "

2580 PRINT " !!!!! ERROR IN DETACT-T2 ROUTINE !!!!!"

48

2590 PRINT 11 !!!!! PROGRAM RUN ABORTED ! ! ! !!

"

2600 PRINT " "

2610 INPUT " WOULD YOU LIKE TO TRY AGAIN (YES/NO) ?";0$

2620 IF (0$="Y" OR 0$="y") GOTO 120

2630 END2640 REM2650 REM ** NEWTON RAPHSON ROUTINE TO FIND ACTIVATION **

2660 REM ** TIME OF FIXED TEMPERATURE DETECTOR. **

2670 REM2680 PO// = .1//

2690 TOL// = .00001//

2700 N0% = 10002710 1% = 1

2720 IERR% = 0

2730 REM2740 IF I%>N0% GOTO 28702750 IF (P0//>50//) THEN LET X//=0// ELSE X//=EXP( -PO//)

2760 FX//=P0// + X// - C//

2770 FPMX// = 1// - X//

2780 IF (FPMX//<. 00000001//) GOTO 29002790 P2// = PO// - (FX///FPMX//)

2800 IF (ABS(P0//-P2//)>TOL//) GOTO 28402810 IERR% = 0

2820 Y// = P2#2830 RETURN2840 1% = 1% + 1

2850 PO// = P2//

2860 GOTO 27302870 IERR% = 1

2880 PRINT "NEWTON RAPHSON FAILED AFTER NO ITERATIONS, NO = ",I%2890 RETURN2900 PRINT "SLOPE OF EQUATION TOO CLOSE TO ZERO!!!"2910 PRINT "ERROR IN NEWTON RAPHSON ROUTINE"2920 IERR% = 1

2930 RETURN2940 REM2950 REM ** BISECTION ROUTINE TO FIND ACTIVATION **

2960 REM ** TIME OF RATE OF RISE DETECTOR. **

2970 REM2980 IERR% = 0

2990 TOL// = .00001//

3000 N0% = 10003010 AA# = 0//

3020 B# = 1000//

3030 RLMT// = TOL// / 20//

3040 REM3050 IF (D2//*B//)>50// THEN X// = 0// ELSE X// = EXP(-D2//*B//)

3060 FXB// = Dl// * B//" .25// - Dl// * B//

*.25// * X// - ROR//

3070 IF FXB//>=0// GOTO 31103080 AA// = B#3090 B// = B// + 500//

3100 GOTO 3040

49

3110 1% = 1

3120 REM3130 IF I>N0 GOTO 32603140 P3# = AA# + (B# - AA#) / W3150 IF (D2#*P3#)>50# THEN X# = 0# ELSE X# = EXP (-D2#*P3#)3160 FX// = Dl# * P3# " .25# - Dl# * P3# * .25# * X// - ROR#3170 DELTS2// = P3#3180 IF ((FX//>(-RLMT#)) AND (FX#<RLMT#) ) THEN RETURN3190 IF ((B#-AA#)/2#)<TOL# THEN RETURN3200 REM3210 1% = 1% + 1

3220 IF (D2#*AA#)>50# THEN X# = 0# ELSE X# = EXP(-D2#*AA#)3230 FXA# = Dl# * AA# " .25# - Dl# * AA# " .25# * X// - ROR#3240 IF (FXA#*FX#)>0# THEN AA# = P3# ELSE B# = P3#3250 GOTO 31203260 IERR% = 1

3270 PRINT "BISECTION ALGORITHM FAILED TO CONVERGE AFTER ",I%," ITERATIONS.3280 RETURN

50

APPENDIX C.

DETECTOR ACTIVATION TIME TABLES:FIXED TEMPERATURE

51

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299


300

APPENDIX D.

DETECTOR ACTIVATION TIME TABLES;RATE OF TEMPERATURE RISE

301

X * -X -X -X -X * * * * * -X M * M -X -X -X * -X -X M M M -X * -X -X -X -X

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—i m m n m c<i cm co co Nnn co co st co en st co st st co st m co st m co st m

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302

4C 4C 4C 4C * 4C 4C 4C 4C 4C 4C 4c •a •JC •JC 4C -Jc JC JC JC -JC 4C •JC JC 4C •JC -JC 4c -K

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549

NBS-H4A (rev. 2-ac)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATASHEET (See instructions)

PUBLICATION ORREPORT NO.

NBS/SP-712

2. Performing Organ. Report No. 3. Publ ication Date

April 1986

4. TITLE AND SUBTITLE

Evaluating Thermal Fire Detection Systems [English Units]

5. AUTHOR(S)David W. Stroup, David D. Evans, Phyllis Martin

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

National Bureau of StandardsDepartment of CommerceGaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

Same as item 6

.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 86-600519

I |Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificantbibliography or literature survey, mention it here)

This report presents a methodology for evaluating heat detection systems installedin buildings. Previous work for use primarily in designing new thermal firedetection systems was used as a starting point. The previous work was enhanced and

supplemented to make it more useful for evaluating existing systems. The resultingequations were programmed into a user interactive computer program. This programis available in both BASIC and FORTRAN and will run on mainframes as well as

personal computers. In addition, a modified version of the FORTRAN program was used

to develop an extensive set of tables listing detector activation times for givenbuilding geometries, detector characteristics, and fire growth rates. These tables

are useful for quick evaluation of alternative heat detector installations. Finallypractical examples are included to illustrate the use of the tables and computerprograms

.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

fire alarm systems; fire detection; fire detection systems; fire hazard assessment;

fire protection; fire suppression; heat detectors; sprinkler systems

13. AVAILABILITY

[ST] Unlimited

| |For Official Distribution. Do Not Release to NTIS

[jf] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.20402.

r~j Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OFPRINTED PAGES

557

15. Price

USCOMM-DC 6043-P80

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Evaluating thermal fire detection systems (English units)

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