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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
TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. TheM Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate
their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a
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The Bureau's technical work is performed by the National Measurement Laboratory, the National
Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials
Science and Engineering
.
The National Measurement Laboratory
Provides the national system of physical and chemical measurement;
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• Basic Standards2
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mechanisms to transfer results of its research to the ultimate user. TheLaboratory consists of the following centers:
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Engineering2
Manufacturing Engineering
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Chemical Engineering 2
The Institute for Computer Sciences and Technology
Conducts research and provides scientific and technical services to aid
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stitute consists of the following centers:
• Programming Science andTechnology
• Computer SystemsEngineering
The Institute for Materials Science and Engineering
Conducts research and provides measurements, data, standards, reference
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addresses the scientific basis for new advanced materials technologies; plans
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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address
Gaithersburg, MD 20899.2Some divisions within the center are located at Boulder, CO 80303.
'Located at Boulder, CO, with some elements at Gaithersburg, MD.
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
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
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
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
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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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