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IC 8919 
 
 Bureau of Mines Information Circular/1983 
 
 Guidelines for Siting 
 Product-of-Combustion Fire 
 Sensors in Underground Mines 
 
 By C. D. Litton 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 
Information Circular 8919 
 1 
 
 Guidelines for Siting 
 Product-of-Combustion Fire 
 Sensors in Underground Mines 
 
 By C. D. Litton 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 James G. Watt, Secretary 
 
 BUREAU OF MINES 
 Robert C. Horton, Director 
 
This publication has been cataloged as follows: 
 
 Litton, C. D. (Charles D.) 
 
 Guidelines for siting product-of-combustion fire sensors in under- 
 ground mines. 
 
 (Information circular/ United States Department of the Interior, Bu- 
 reau of Mines ; 8919). 
 
 Includes bibliographical references. 
 Supt. of Docs, no.: I 28.27:8919. 
 
 1. Mine fires— Prevention and control. 2. Fire detectors— Location. 
 3. Combustion gases. I. Title. II. Series: Information circular (United 
 States. Bureau of Mines) ; 8919. 
 
 [TN315] 
 
 622s [622'. 8] 82-600343 
 
 
■Ok 
 
 CONTENTS 
 
 I 
 
 4 
 J- 
 
 Page 
 
 Abstract 1 
 
 Introduction 2 
 
 Spacing and siting guidelines 2 
 
 Spacing 2 
 
 Vertical placement 4 
 
 Lateral placement 5 
 
 Fire detection criterion 5 
 
 Products of combustion 6 
 
 Sensor spacing categories 7 
 
 Category 1 mine entries 7 
 
 Category 2 mine entries 7 
 
 Category 3 mine entries 8 
 
 Category 4 mine entries 8 
 
 Sampling-type fire detectors 8 
 
 Appendix A. — Derivation of low-flow sensor spacings 10 
 
 Appendix B. — Derivation of tube traveltimes 12 
 
 ILLUSTRATIONS 
 
 1. Entry parameter (Ye) as a function of the entry height-to-width ratio (H/W) 3 
 
 2. POC parameter (Y x ) as a function of the ratio of alarm threshold to produc- 
 
 tion constant [(X a -X )/K x ] 3 
 
 3. Spacing categories and appropriate spacing equations for mine entries 4 
 
 TABLE 
 
 1. Production constants for coal and wood 3 
 
GUIDELINES FOR SITING PRODUCT-OF-COMBUSTION FIRE 
 SENSORS IN UNDERGROUND MINES 
 
 By C. D. Litton 1 
 
 ABSTRACT 
 
 This Bureau of Mines report presents a set of guidelines for determin- 
 ing the distribution of product-of-combustion fire sensors in under- 
 ground mines. Sensor spacing is defined in terms of sensor alarm 
 threshold, ventilation flow rate, and mine entry dimensions. Sensor 
 spacing guidelines are presented for detection of fires from two primary 
 combustibles, coal and wood, which are common to the majority of under- 
 ground mines. The guidelines are based on data from full-scale and 
 intermediate-scale fire tests conducted by the Bureau of Mines. 
 
 — . 
 
 Supervisory physical scientist, Pittsburgh Research Center, Bureau of Mines, 
 Pittsburgh, Pa. 
 
INTRODUCTION 
 
 A major goal of the Bureau of Mines 
 safety research program is to improve the 
 degree of safety afforded underground 
 miners. Rapid and reliable detection of 
 mine fires can contribute to this goal by 
 improving miners' chances for escape dur- 
 ing actual fire emergencies. 
 
 It is apparent that the use of sensi- 
 tive and reliable product-of-combustion 
 (POC) fire sensors in underground mines 
 is increasing, owing primarily to the 
 greater availability of such sensors, as 
 well as an added awareness of the need 
 for rapid and reliable underground fire 
 detection systems. As the use of such 
 sensors grows, the required distribution 
 of these sensors within mine entries will 
 need to be determined in order to provide 
 realistic and adequate fire detection. 
 Previous Bureau reports 2 have discussed 
 
 this problem and outlined the various 
 parameters involved. 
 
 This report summarizes the previous 
 data and presents subsequent guidelines 
 for determining POC fire sensor distribu- 
 tions within mine entries. These guide- 
 lines may be easily used by those respon- 
 sible for either designing or approving 
 the design of POC fire detection systems 
 in underground mines. 
 
 It is not the intent of this report to 
 suggest or recommend specific fire sen- 
 sors or sensing systems. Rather, the 
 report proposes a strategy for determin- 
 ing the most effective distribution of 
 whatever sensors are selected. It is 
 important that one using these guidelines 
 know in advance the type of sensor to be 
 used and its characteristics. 
 
 SPACING AND SITING GUIDELINES 
 
 For convenience, the spacing and siting 
 guidelines for POC fire sensors in under- 
 ground mines are presented first, along 
 with instructions for their general use. 
 Explanatory material, on which the guide- 
 lines are based, can be found in the sec- 
 tions that follow. 
 
 2 Litton, C. D. Product-of -Combust ion 
 Fire Detection in Mines. Paper in Under- 
 ground Metal and Nonmetal Mine Fire Pro- 
 tection. Proceedings: Bureau of Mines 
 Technology Transfer Seminars, Denver, 
 Colo., Nov. 3, 1981, and St. Louis, Mo., 
 Nov. 6, 1981. BuMines IC 8865, 1981, 
 pp. 28-48. 
 
 Litton, C. D., M. Hertzberg, and A. L. 
 Furno. Fire Detection Systems in Con- 
 veyor Belt Haulageways. BuMines RI 8632, 
 1982, 26 pp. 
 
 . The Growth, Structure, and De- 
 tec tability of Fires in Mines and Tun- 
 nels. Proc. 18th Internat. Symp. on Com- 
 bustion, Waterloo, Ontario, Canada, Aug. 
 17-25, 1980. The Combustion Institute, 
 Pittsburgh, Pa., 1981, pp. 633-639. 
 
 SPACING 
 
 To determine the appropriate spacing 
 between POC fire sensors within a 
 mine entry, these steps should be 
 followed: 
 
 1. Determine the average 
 (H) and width (W) . 
 
 entry height 
 
 2. Take the ratio of height to width 
 (H/W) and, from figure 1, determine the 
 appropriate value for the entry parameter 
 (Ye). 
 
 3. Determine the type of sensor to be 
 used (CO, CO2 , or smoke) and its alarm 
 threshold (X a ); that is, the POC concen- 
 tration that will activate the sensor 
 alarm. 
 
 4. Determine the primary combustible 
 within the entry (either coal or wood) 
 and, from table 1, select the production 
 constant (K x ) for the product to be 
 detected. 
 
45 
 
 40 
 
 LU 
 
 k 35 
 
 UJ 
 
 I- 
 LJ 
 2 
 < 
 
 < 
 Q. 
 
 E 30 
 
 UJ 
 
 25 
 
 20 
 
 1 1 1 1 1 i r 
 
 - f Sr- 
 
 y E =22.7(3.05) a875H/ w 
 
 0.1 0.2 0.3 0.4 0.5 0.6 0.7 °o 
 
 ENTRY HEIGHT-TO-WIDTH RATIO ( H / w ) 
 
 FIGURE 1. - Entry parameter (y E ) as a func- 
 tion of the entry height-to-width ratio (H/W). 
 
 TABLE 1. - Production constants for coal 
 and wood 
 
 K, 
 
 1 
 
 K C0 
 
 K co 2 
 
 K SMP 
 
 K 
 
 SMP 
 
 POC concen- 
 tration units 
 
 PPm 
 
 PPm 
 
 particles per 
 
 cm 3 . 
 mg/m 3 
 
 Coal 
 
 7.2 x 
 
 1.10 
 
 6.70 
 
 10 4 
 
 0.45 
 
 Wood 
 
 2.5 x 
 
 0.95 
 
 6.90 
 
 10 5 
 
 0.30 
 
 SMP Smoke particles. 
 Subscript indicates sensor type. 
 
 5. Determine (or estimate) the aver- 
 age background level (X ) of the product 
 to be detected. 
 
 6. Subtract X from X a and divide the 
 result by the appropriate K x -value. 
 
 7. From figure 2, determine the value 
 of the POC parameter (Y x ) at the value of 
 
 x a -x 
 
 K> 
 
 - defined in step 6. 
 
 _L 
 
 _L 
 
 10 
 
 20 30 40 50 
 
 60 70 
 
 80 
 
 FIGURE 2. - POC parameter (y x ) as a func- 
 tion of the ratio of alarm threshold to produc- 
 tion constant [(X^-XJ/KJ. 
 
 8. Determine the average ventilation 
 velocity (Vf), in feet per minute, within 
 the entry and, in figure 3, draw a ver- 
 tical line at this velocity parallel to 
 the y-axis. 
 
 9. Multiply H by W to determine the 
 average entry cross-sectional area (A) 
 and, in figure 3, draw a horizontal line 
 at this A-value parallel to the x-axis. 
 
 10. The point of intersection of the 
 vertical and horizontal lines in figure 3 
 defines the appropriate spacing category 
 to be used for this entry, and the ap- 
 propriate spacing equation. 
 
 For illustrative purposes, consider the 
 following example. 
 
 1. H = 6 ft; W = 20 ft. 
 
 2. From figure 1, at H/W = 6/20 
 = 0.3, ye = 30.4. 
 
 3. Sensor type: CO; alarm threshold 
 (X a ) = 20 ppm. 
 
oo 
 
 At 
 
 
 
 Category 2 
 
 A-l4v/'(x E -y x ) 
 
 Category I 
 A-(v f A)^( XE - Xx ) 
 
 00 200 300 400 500 
 ENTRY VENTILATION VELOCITY (v f ),ft/min 
 
 ^V 
 
 oo 
 
 FIGURE 3. - Spacing categories and appropriate spacing equations for mine entries. 
 
 i x < (vfA) 1 / 2 (Te-Yx) 
 < 190 (30.4 - 19.0) 
 
 4. Primary combustible: coal; from 
 table 1, Kqq for coal = 1.10. 
 
 5. Entry background CO level (X ) 
 = 4 ppm. 
 
 6. (X a -X o )/K C0 = 14.5. 
 
 7. From figure 2, at (X a -X o )/Kc 
 = 14.5, Y x = 19.0. 
 
 8. Average entry ventilation velocity 
 (v f ) = 300 ft/min. 
 
 9. Average entry cross section (A) 
 = H x w = 6 x 20 = 120 ft 2 . 
 
 10. The point of intersection of the 
 Vf-vertical line and the A-horizontal 
 line, in figure 3, falls within cate- 
 gory 1. For category 1, the appropriate 
 sensor spacing equation is 
 
 < 2,166 ft. 
 
 This is the maximum recommended spacing 
 between these sensors in this entry. 
 
 VERTICAL PLACEMENT 
 
 Because the hot gases from a fire will 
 rise owing to buoyancy forces, combustion 
 products will initially be stratified 
 near the roof of an entry. As this 
 stratified gas layer moves away from the 
 fire, the resultant cooling and dilution 
 will eventually produce a well-mixed flow 
 of combustion products. Data from full- 
 scale fires indicate that some degree of 
 stratification can exist at distances of 
 
hundreds 
 fire. 
 
 of feet from the source of the 
 
 Because of this eff 
 sors should be located 
 tance from the entry 
 exceed 25% of the ave 
 For example, in an ent 
 6 ft, the maximum dist 
 at which a POC sensor 
 is 1-1/2 ft. This ref 
 of the actual sampli 
 detector used. 
 
 ect, POC fire sen- 
 at a vertical dis- 
 roof that does not 
 rage entry height, 
 ry with a height of 
 ance from the roof 
 should be located 
 ers to the location 
 ng intake of the 
 
 LATERAL PLACEMENT 
 
 In general, the point of origin of a 
 fire is quite unpredictable. It may 
 
 occur along the floor, ribs, or roof of 
 an entry. In order to provide optimum 
 protection, it is recommended that the 
 fire sensors be located within 2 ft of 
 the approximate midpoint of the entry. 
 
 For entries in which the point of ori- 
 gin of the fire can be better estimated 
 (such as a belt entry), the sensors 
 should be located in such a manner that 
 they provide for the estimated best cov- 
 erage of that entry. As an example, in a 
 belt entry where the conveyor is on one 
 side of the entry, it would be more 
 judicious to locate the sensors above the 
 centerline of the belt conveyor than to 
 locate them in the middle of the entry. 
 
 FIRE DETECTION CRITERION 
 
 The basis for development of POC fire 
 sensor spacing guidelines is the perfor- 
 mance of a series of ideal 160° F heat 
 sensors spaced at intervals of 10 ft 
 within an underground mine entry. The 
 estimated alarm times for this ideal 
 thermal system define the detection 
 criterion for POC fire sensors: Any POC 
 fire-sensing system must have an alarm 
 time less than or equal to this thermal 
 alarm time. 
 
 where T a = maximum downstream air tem- 
 perature, °F, at a dis- 
 tance I downstream; 
 
 T = ambient air temperature, °F; 
 
 Qf = fire heat release rate, 
 Btu/min; 
 
 p = density of air = 0.075 lb/ 
 ft 3 ; 
 
 The data obtained from full-scale mine 
 fires 3 are used in the following para- 
 graphs to estimate the fire sizes and 
 alarm actuation times for the ideal 
 160° F heat sensors with spacing inter- 
 vals of 10 ft. 
 
 Temperature data obtained during full- 
 scale mine fires 4 indicate that the maxi- 
 mum downstream air temperature at a dis- 
 tance & is related to the heat release 
 rate of the fire, the entry ventilation 
 velocity, and the entry dimensions by the 
 equation 
 
 Q f = p c p v f A I2JE0 (0.305 I) 
 
 1.75 H/W 
 
 , (1) 
 
 -"Second and third works cited in foot- 
 note 2. 
 
 4 Second work cited in footnote 2. 
 
 and 
 
 Cp = heat capacity of air = 0.26 
 Btu/(lb'°F); 
 
 Vf = ventilating air velocity, 
 f t/min; 
 
 I = distance from fire to down- 
 stream thermal sensor, ft; 
 
 H = entry height, ft; 
 
 W = entry width, ft; 
 
 A = entry cross-sectional area 
 (H x W), ft 2 . 
 
 Using equation 1, the detection crite- 
 rion is developed as follows. The maxi- 
 mum downstream distance is set equal to 
 10 ft; T a equals 160° F; and T is 
 assumed to have a value of 65° F. From 
 
equation 1, the fire size at which the 
 maximum air temperature reaches 160° F at 
 a distance of 10 ft downstream becomes 
 
 Q T = 0.206 v f A (3.05) 1 ' 75 H/w , (2) 
 
 where the subscript T denotes the fire 
 size at the time of thermal alarm. 
 
 From data previously reported, 5 the 
 rate at which the fire size increases, 
 from the instant of flaming ignition, is 
 given by 
 
 Q f = 4.0 x 10" 4 v f 2 t 2 , (3) 
 
 where t is the time, in minutes. 
 
 By setting Q f = Q T and solving for t in 
 equation 3, the time to thermal alarm 
 (t T ) can be determined: 
 
 t T = 22.7 (3.05) 
 
 0.875 H/W (v f A) 1/2 
 
 r f 
 
 (4) 
 
 Equations 2 and 4 define the approxi- 
 mate fire size at time of alarm and the 
 resultant alarm time for a series of 
 ideal 160° F heat sensors spaced at in- 
 tervals of 10 ft. Further, the 10-ft 
 spacing is constant, independent of the 
 entry dimensions. In essence, then, 
 equations 2 and 4 define the fire size at 
 alarm and the alarm time for ideal 160° F 
 heat sensors within any entry; and for 
 known values of H, W, and Vf , the actual 
 fire sizes and times can be calculated. 
 
 The criterion can be stated as follows: 
 Any fire detection system installed 
 within an entry of height H, width 
 W, and ventilation velocity Vf must 
 respond (alarm) in a time less than or 
 equal to the time required for a series 
 of ideal 160° F heat sensors spaced at 
 10-ft intervals to respond if located 
 in the same entry. This thermal re- 
 sponse time, which serves as the basis 
 for comparison, is defined in equa- 
 tion 4. 
 
 Since t T is a function of H and W, it 
 is convenient to define a parameter, Ye» 
 called the entry parameter, as 
 
 Y E = 22.7 (3.05) - 875 H / w . 
 
 (5) 
 
 This parameter is plotted in figure 1 as 
 a function of H/W. 
 
 With this defined entry parameter, ty 
 can be rewritten as 
 
 t T = Y E 
 
 (v f A) 
 
 1/2 
 
 (6) 
 
 The following sections apply this de- 
 tection criterion to the development of 
 spacing guidelines for POC fire sensors 
 in underground mines. This criterion can 
 also be used to define spacings for heat 
 sensors with alarm thresholds other than 
 the assumed 160° F, through the use of 
 equation 1. 
 
 PRODUCTS OF COMBUSTION 
 
 The quantity of any combustion product 
 will increase as the fire size increases. 
 In a ventilated mine entry, the bulk 
 average increase in concentration for 
 some product (X) is equal to the rate of 
 generation of that product divided by the 
 volumetric ventilation rate (simple dilu- 
 tion). The equation that defines this 
 bulk average concentration increase is 
 
 where Xj = total concentration of prod- 
 uct X; 
 
 X = ambient background concen- 
 tration of product X; 
 
 Y x = quantity of X produced per 
 mass of combustible con- 
 sumed (the yield of X); 
 
 X T -X - 
 
 Of 
 
 VfA 
 
 (7) 
 
 'Second work cited in footnote 2 
 
 and H c = heat of combustion of the 
 material burning. 
 
 When X T equals the alarm threshold 
 concentration (X a ), equation 7 can be 
 
rearranged to obtain the approximate fire 
 size (Q x ) required to produce X a : 
 
 H 
 
 Q x = v f A ==£ (X a -X ). 
 
 (8) 
 
 By setting Qf = Q x in equation 3, the 
 time at which the POC concentration will 
 reach the alarm threshold (t x ) can be 
 determined. 
 
 t x = 50 
 
 •°Gi 
 
 (x a -x ) 
 
 1 /2 ( Vf A) 1 / 2 
 v f 
 
 . (9) 
 
 By setting the ratio Y x /H c equal to 
 100 K x , equation 9 becomes 
 
 tx . 5.0 Q*g*>) (Tf C; • (10) 
 
 The parameter K x is defined as the pro- 
 duction constant for product X and is 
 also a function of the combustible that 
 is burning. K x -values for the products 
 CO, CO2 , and smoke particles (SMP) have 
 been obtained from full-scale and 
 intermediate-scale fire tests for both 
 coal and wood 6 during flaming combustion 
 and are listed in table 1. 
 
 A second global parameter, Y x , called 
 the POC parameter, is defined by the 
 expression 
 
 /, - 5.0' Xa x ° 
 
 1/2 
 
 (11) 
 
 Y x is plotted in figure 2 as a function 
 of (X a -X )/K x . When this parameter 
 is inserted into equation 10, t x becomes 
 
 tx = T x 
 
 (v f A) 1 / 2 
 
 (12) 
 
 In order to satisfy the criterion of 
 equation 6, the time available (t D ) for 
 the transport of the alarm threshold con- 
 centration level of product X from the 
 fire origin to a sensor site is 
 
 to - t T~ t x> 
 
 (13) 
 
 which, in terms of the two parameters, 
 Ye and Y x , becomes 
 
 1/2 
 
 (v f AV^ , , 
 tn = ^- L - L (Yf-Tx). 
 
 (14) 
 
 SENSOR SPACING CATEGORIES 
 
 Because the entry cross sections of 
 underground mines and the imposed entry 
 ventilation rates can vary greatly, a 
 single equation cannot be applied equi- 
 tably for the spacing of all underground 
 mine fire sensors. For this reason, the 
 spacing guidelines are subdivided into 
 four distinct categories of entry cross 
 sections and ventilation flows. (These 
 categories are shown in figure 3.) 
 
 CATEGORY 1 MINE ENTRIES 
 
 For any mine entry in which the entry 
 cross section is <200 ft 2 , the entry 
 ventilation flow is >50 ft/min, and the 
 ratio A/vf is <2.0 f t 'min, the maximum 
 sensor spacing is equal to 
 
 H x < v f t D = (v f A) 1 / 2 (Ye-Yx)> (15) 
 
 "First and second works cited in foot- 
 note 2. 
 
 where it is assumed that the combustion 
 products are convected from the fire 
 origin to the sensor site at a velocity 
 equal to the average ventilation velocity 
 in that entry. 
 
 CATEGORY 2 MINE ENTRIES 
 
 For any mine entry in which the entry 
 cross section exceeds 200 ft^ and the 
 ratio A/vf is <2.0 ft'min, to can be no 
 greater than 
 
 t D < (200/v f ) 1 / 2 (Ye-Y x )» (16) 
 
 and the maximum sensor spacing no greater 
 than 
 
 * x < 14 v f 1/2 ( Ye -y x ). 
 
 (17) 
 
8 
 
 CATEGORY 3 MINE ENTRIES 
 
 For any mine in which the ratio A/vf is 
 i.O ft'min, regardless of entrj 
 section, t D can be no greater than 
 
 t D < (2) 1/2 (y E -T x ) = 1.4 (Y E -Y X )> (18) 
 
 CATEGORY 4 MINE ENTRIES 
 
 For any mine entry in which the venti- 
 >2.0 ffmin, regardless of entry cross lation velocity is <50 ft/min, the maxi- 
 mum sensor spacing is defined by 
 
 £ x < 72 H 1/2 (y e -Y x ) 1/2 « 
 
 (20) 
 
 and the maximum sensor spacing no greater This expression is based upon a no-flow 
 
 than 
 
 approximation, and its derivation can be 
 found in appendix A. 
 
 i x < 1.4 v f (Y E -Y X ). (19) 
 
 SAMPLING-TYPE FIRE DETECTORS 
 
 The guidelines developed in the previ- 
 ous sections apply directly to spot-type 
 detectors, which may be located in fixed 
 positions corresponding to the spacing 
 recommended for a given entry. Con- 
 sequently, for an entry of length & E , 
 with a sensor requiring spacing £ x in 
 that entry, the number of sensors (n) 
 would equal £ E /£ X . 
 
 An alternative to this type of system 
 is a sampling-type fire detector. In- 
 stead of having sensors located at fixed 
 positions, a sampling-type detector has 
 sampling ports connected to one single 
 sensor via hollow-core tubing. Pumps are 
 used to continuously pull samples of air 
 from the sampling port locations to the 
 detector where the samples are analyzed 
 for combustion products. 
 
 For this type of detector, the spacing 
 guidelines cannot be applied directly to 
 location of the sampling ports, because 
 of the additional time that is required 
 for the system to respond, owing to tube 
 traveltimes and sequencing times at the 
 detector station. In order to determine 
 the required spacings for sampling ports 
 for this type of sensor, the additional 
 times must be included in the overall 
 response time of the system (t s ). 
 
 For a sampling-type detector, it is 
 usually prudent to determine the number 
 of sample ports (n) required to protect 
 an entry of length £ E . To determine n, 
 the time response of a sampling-type 
 detector can be written as a function of 
 n and other known variables. The time 
 
 response of a sampling-type detector is 
 given by 
 
 t s = t D + t x + t £ + t 
 
 seq > 
 
 (21) 
 
 where t$ = transport time of combus- 
 tion product between sample 
 ports; 
 
 t x = time at which POC concentra- 
 tion will reach the alarm 
 threshold level (previously 
 defined in equation 12); 
 
 t£ = sample traveltime through 
 the longest sampling tube; 7 
 
 and 
 
 •seq 
 
 the time required by the de- 
 tector to sequence through 
 all sampling tubes , which 
 is equal to the number of 
 tubes (n) times the sampl- 
 ing time per tube (t samp ). 
 
 The total response time must be less 
 than or equal to t T (equation 6) in order 
 to satisfy the detection criterion. 
 Since the sample port spacing (£ s ) equals 
 £ E /n, the following equation must be 
 satisfied: 
 
 A E /n + v f (t £ + nt samp ) < l x , 
 
 (22) 
 
 where l x is the recommended spacing for 
 category 1, 2, or 3 mine entries. 
 
 Solving equation 22 for n yields 
 
 See appendix B for derivation of t£ . 
 
a x -v f t £ ) - yu x -v f t £ ) 2 - 4 £ E t samp v f 
 
 n= j- v (23) 
 
 zt samp v f 
 
 and is the defining equation for cate- For a category 4 mine entry (vf < 50 
 gory 1, 2, or 3 mine entries. f t/min) , the resulting equation is 8 
 
 Z 
 
 ^< 60H 1/2 [1.4 (Ye-Yx) " (t£ + nt samp )] 1 / 2 . (24) 
 
 Equations 23 and 24 can be used to de- equal to £ E /n. Expressions for the tube 
 termine the required number of sample traveltimes (t^) to be used in these two 
 ports (n) for an entry of length £ E . The equations can be found in appendix B. 
 
 spacing between sample ports (H s ) is then 
 
 °See appendix A. 
 
10 
 
 APPENDIX A. —DERIVATION OF LOW-FLOW SENSOR SPACINGS 
 
 From data available in the literature, 1 
 empirical expressions were derived for 
 the maximum temperature difference (T max - 
 T ) and maximum gas velocity (v max ) near 
 the roof, as a function of roof height 
 (H), fire heat release rate (Of), and 
 radial distance (r) from the fire origin, 
 for fires developing under static (no- 
 flow) conditions. The respective ex- 
 pressions for T max -T and v max are 
 
 T - T = 
 
 1 max • L o 
 
 . 4.74 (Q f /r) 2/3 
 
 v max is in ft/min; 
 Qf is in Btu/min; 
 
 (A-l) 
 
 and v max = 15.0 Q f 1/3 H 1/2 /r 5/6 , (A-2) 
 
 where T max and T are in ° F; 
 
 Assuming that, under static conditions, 
 the fire will grow at a rate less than or 
 equal to the rate at the minimum velocity 
 of Vf = 50 ft/min, equation 3 2 can be 
 used to define the approximate fire 
 growth rate: 
 
 Qf - t 2 
 
 When Qf = Q T , the approximate 
 thermal alarm can be obtained: 
 
 t T = 21.18 H 3/4 . 
 
 (A-4) 
 
 time to 
 
 (A-5) 
 
 By substituting equation A-4 into equa- 
 tion A-2, the velocity (v max ) at any 
 radial distance (r) becomes a function of 
 time. By taking the integral average of 
 v max , from t = to t = t j , the average 
 velocity (v avg ) at any radial distance 
 (r) can be obtained; that is, 
 
 and 
 
 H and r are in ft. 
 
 These two expressions apply to radially 
 expanding hot product gases, and, for a 
 mine entry, hot gases can spread radially 
 only until they reach the ribs of the 
 entry. Once they reach the ribs, the hot 
 gases will expand along the length of the 
 entry, and at an increased rate. In view 
 of this behavior, the following deriva- 
 tion for POC sensor spacings , using these 
 radially expanding expressions, should be 
 viewed as conservative estimates. 
 
 As before, the basis for comparison 
 will be a series of ideal 160° F heat 
 sensors spaced at intervals of 10 ft. 
 Since the hot gases are free to expand 
 radially under static conditions, the 
 maximum distance they will travel before 
 being detected will be one-half the spac- 
 ing, or 5 ft. Using this value for r in 
 equation A-l and assuming T = 65° F, the 
 fire size at which T max = T a = 160° F can 
 be obtained. It is 
 
 Q T = 448.6 H 3/2 . 
 
 (A-3) 
 
 r c T 
 
 v max (t) dt 
 
 J o 
 
 avg 
 
 68.9 H 
 r 5/6 ' 
 
 (A-6) 
 
 dt 
 
 Equation A-6 defines the average veloc- 
 ity at any radial distance (r) during the 
 thermal alarm time interval (t T ). The 
 average gas velocity (v ) that the hot 
 gases will have in traversing a fixed 
 distance (r ) is the integral average of 
 
 avg 
 
 from 
 
 rr r 
 
 r = o 
 
 to 
 
 r = r 
 
 o > 
 
 that is 
 
 v aV q(r) d r 
 
 ro 
 
 413.4 H 
 -7-5715—' 
 
 (A-7) 
 
 dr 
 
 For ventilation velocities of 50 ft/min 
 or less, the quantity A/vf will be limit- 
 ed to a maximum value of 2, and from 
 equation 18, the maximum transport time 
 
 1 
 
 'Alpert, R. L. Calculation of Response 
 Time of Ceiling-Mounted Fire Detectors. 
 Fire Technol . , v. 8, No. 3, August 1979, 
 pp. 181-195. 
 
 ^Equation numbers without the A-prefix 
 refer to equations occurring in the main 
 text. 
 
11 
 
 (to) is defined in terms of the param- 
 eters y E and Y x by 
 
 t D = 1.4 (Y E -Y X ). (A-8) 
 
 For a POC fire sensor located at a dis- 
 tance r from the fire, the average 
 velocity (v ) required to traverse that 
 distance in a time tp is 
 
 equation A- 12 should be viewed as a con- 
 servative approximation to the derived 
 spacing. For example, with Y x = 15.1 (a 
 CO sensor for 10 ppm above ambient) 
 in an entry of H = 6 ft and W = 20 ft 
 (Ye = 30.4), equation A-12 would require 
 a spacing of 690 ft or less, while equa- 
 tion A-ll would require a spacing of 756 
 ft or less, a spacing about 10% larger. 
 
 Vr, = 
 
 _ L o _ 
 
 tD 
 
 1.4 (Yf-Yx)" 
 
 (A-9) 
 
 Since v from equation A-7 must equal v 
 defined by equation A-9, the following 
 expression can be obtained for r : 
 
 r = 32.12 [H(y E -Y x )] 6 / 11 . (A-10) 
 
 Equation A-10 defines the maximum radial 
 expansion distance for a sensor (defined 
 by Y x ) installed within an entry defined 
 by H and Ye* Since the product gases 
 expand both upstream and downstream, two 
 sensors spaced at an interval of 2 r 
 would be expected to respond at the same 
 time to a fire located midway between 
 them. Consequently, the maximum sensor 
 spacing is defined by 
 
 l x < 2r = 64.24 [H (Y E "Y X ) ] 6/1 1 • (A-ll) 
 
 Assuming a minimum entry height of 
 ~3 ft and reasonable values of Ye - Y x 
 lying between 5 and 30, the quantity H 
 (Ye~Y x ) can be expected to lie between 15 
 and 90, and equation A-ll can be approxi- 
 mated by a more convenient expression 
 given by 
 
 i x < 72 [H(y E -Y x )] 1/2 . (A-12) 
 
 If the ratio of equation A-ll to equation 
 A-12 is taken, it can be shown that, for 
 values of H(ye~Y x ) <12.3, equation A-ll 
 will require a somewhat smaller spacing 
 than that required by equation A-12. For 
 values of H(ye - Y x ) >12.3, the spacing re- 
 quired by A-12 will always be less than 
 the spacing required by A-ll; thus, 
 
 Consequently, for any entry in which 
 the ventilation velocity is <50 ft/min, 
 equation A-12 should be used to determine 
 the appropriate spacing for a POC fire 
 sensor. 
 
 For a sampling-type fire detector, the 
 maximum available transport time (tp) is 
 given by 
 
 t D = 1.4 (Y E "Y X ) - (t£ + nt samp ), (A-13) 
 
 and the average velocity in traversing 
 some distance r Q by 
 
 . (A-14) 
 
 1.4 (Ye-Y x ) " (t£ + nt samp ) 
 
 Setting equation A-14 equal to equation 
 A-7 and solving for r yields 
 
 r = 27 H 6 /' 1 [1.4 (Ye"Y x ) 
 
 - (t A + nt samp )] 6/n . (A-15) 
 
 As before, the sample port spacing (£ s ) 
 should be equal to 2 r , and, applying 
 the same approximation as before (equa- 
 tion A-12), the expression for the sample 
 port spacing becomes 
 
 £ s < 60 H 1/2 [1.4 (ye"Y x ) 
 
 - (t £ + nt samp )] 1 / 2 . (A-16) 
 
 For an entry of length, £ E , the sample 
 port spacing equals H^/n, where n is the 
 number of sample ports spaced at equal 
 intervals. 
 
12 
 
 APPENDIX B.— DERIVATION OF TUBE TRAVELIMES 
 
 In general, the flow through each tube 
 of a sampling-type detector should be 
 laminar. In order to satisfy this con- 
 straint, the Reynolds number should be 
 less than or equal to 1,800. Then, 
 
 Re= T^ l >™°> 
 
 (B-l) 
 
 where p = density of air = 0.075 lb/ 
 ft 3 ; 
 
 n = kinematic viscosity = 7.26 
 x 10 _t+ lb/(ffmin); 
 
 if = sample tube length, ft; 
 
 d s = tube inside diameter, in; 
 
 and tji = tube traveltime, min. 
 
 Solving equation B-l for t£ yields 
 
 t£ > 4.78 x 10 -3 if d s . (B-2) 
 
 For sampling-type gas detectors (CO, 
 CO2) there is an additional constraint on 
 the size of tubing (d s ) that can be used 
 for a given length (if). This constraint 
 is related to the pumping requirements 
 for the system, ' and is given by 
 
 d s > 0.02 if 1/3 . 
 
 (B-3) 
 
 Substituting this expression into equa- 
 tion B-2 yields 
 
 ti > 9.56 x 10" 5 &,- 4/3 , (B-4) 
 
 which defines the tube traveltime solely 
 in terms of the tube length. Clearly, 
 when if = £ max , the maximum tube length 
 in the system, (t^) will have its great- 
 est value. Then the maximum value of t£ 
 is given by 
 
 tg, > 9.56 x 10-5 £ max 4/3. (B _ 5) 
 
 1 Litton, C. D. Design Criteria for 
 Rapid Response of Pneumatic Monitoring 
 Systems. BuMines IC 8912, in press; for 
 information, contact C. D. Litton, Bureau 
 of Mines, Pittsburgh, Pa. 
 
 This is the expression to be used in 
 equation 22 and 23 2 for a sampling-type 
 gas detector. 
 
 For a sampling-type smoke detector 
 (SMP) there is a different constraint on 
 the size of tubing (d s ) that can be used 
 for a given length (if). This constraint 
 is related to the losses of particles 
 that can occur within a tube as the smoke 
 is transported from the sample port to 
 the detector. 3 The constraint is 
 
 d s > 1.95 x 10" 4 if. 
 
 -k 
 
 (B-6) 
 
 When if = £ max , the maximum tube travel- 
 time is 
 
 t £ > 9.32 x 10" 
 
 i 2 
 
 (B-7) 
 
 This is the expression to be used for t^ 
 in equations 22 and 23 for a sampling- 
 type smoke detector. 
 
 Both equations B-5 and B-7 indicate 
 that the larger the value for £ max , the 
 longer the tube traveltime (tjj,). Fur- 
 ther, equations B-3 and B-6 indicate that 
 as if increases , larger tube diameters 
 (d s ) will be required. The values of 
 i max and other sample tube lengths (if) 
 depend upon the location of the detector 
 station relative to the sample ports. 
 The best location of the detector station 
 is central to the location of the sample 
 ports. For sample ports spaced at equal 
 intervals (i s ) along an entry of length 
 i^, and with the detector station located 
 centrally with respect to the sample 
 ports, the maximum tube length (H max ) is 
 given by 
 
 _ ^E~^s 
 
 'max 
 
 (B-8) 
 
 Since i s = A E /n, i max can be rewritten as 
 
 'max 
 
 <m^- 
 
 (B-9) 
 
 ^Equation numbers without the B-prefix 
 refer to equations occurring in the main 
 text. 
 
 3 Work cited in footnote 1 . 
 
In general, it is sufficient to approx- 
 imate the above equation by 
 
 'max 
 
 = 1/2 £ E 
 
 (B-10) 
 
 As a result, for applications in which 
 the detector station can be located 
 centrally with respect to the sample 
 ports , the maximum tube traveltimes can 
 be rewritten as 
 
 t£ > 3.79 x 10" 5 U E ) 4/3 (B-ll) 
 
 for sampling-type CO or CO2 detectors, 
 and as 
 
 13 
 
 for sampling-type SMP detectors. 
 
 For applications in which the detector 
 station cannot be centrally located, the 
 anticipated location of the detector 
 relative to the farthest sample port 
 will define £ max > an d t£ can De deter- 
 mined from 
 B-7. 
 
 'max » 
 either 
 
 equation B-5 or 
 
 It is important to note that all 
 tubes must satisfy the size con- 
 straints defined by either equation B-3 
 or B-6. 
 
 t£ > 2.33 x l(T 7 I- 2 
 
 E > 
 
 (B-12) 
 
 i?rU.S. GOVERNMENT PRINTING OFFICE: 1983-605-015/10 
 
 INT.-BU.OF MINES, PGH., PA. 26626 
 

 
 

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