TN295 
 
 
 No. 9261; 
 
 

 
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IC 9261 
 
 BUREAU OF MINES 
 INFORMATION CIRCULAR/1990 
 
 Fire Location Model 
 
 By John C. Edwards 
 
 „ YEARS ,<>, 
 ^^AU OF ^' 
 
 U.S. BUREAU OF MINES 
 1910-1990 
 
 THE MINERALS SOURCE 
 
Mission: Asthe Nation's principal conservation 
 agency, the Department of the Interior has respon- 
 sibility for most of our nationally-owned public 
 lands and natural and cultural resources. This 
 includes fostering wise useof our land and water 
 resources, protecting our fish and wildlife, pre- 
 serving the environmental and cultural values of 
 our national parks and historical places, and pro- 
 viding for the enjoyment of life through outdoor 
 recreation. The Department assesses our energy 
 and mineral resources and works to assure that 
 their development is in the best interests of all 
 our people. The Department also promotes the 
 goals of the Take Pride in America campaign by 
 encouraging stewardship and citizen responsibil- 
 ity for the public lands and promoting citizen par- 
 ticipation in their care. The Department also has 
 a major responsibility for American Indian reser- 
 vation communities and for people who live in 
 Island Territories under U.S. Administration. 
 
Information Circular 9261 
 
 Fire Location IVIodei 
 
 By John C. Edwards 
 
 UNITED STATES DEPARTMENT OF THE INTERIOR 
 Manuel Lujan, Jr., Secretary 
 
 BUREAU OF MINES 
 T S Ary, Director 
 

 ^0' 
 
 
 Library of Congress Cataloging in Publication Data: 
 
 Edwards, John C. 
 
 Fire location model / by John C. Edwards. 
 
 p. cm. - (Information circular / Bureau of Mines; 9261) 
 
 Includes bibliographical references (p. ). 
 
 Supt. of Docs, no.: I 28.27:9261. 
 
 1. Mine fires-Prevention and control-Data processing. 2. Smoke-Diffusion 
 rate-Data processing. 3. FORTRAN (Computer program language) I. Title. II. 
 Series. III. Series: Information circular (United States. Bureau of Mines); 9261. 
 
 TN295.U4 [TN315] 622 s-dc20 [622'.82] 90-2096 
 
 CIP 
 
CONTENTS 
 
 Page 
 
 Abstract 1 
 
 Introduction 2 
 
 Model description 2 
 
 Application 3 
 
 Conclusions 9 
 
 Appendix-FORTRAN computer program 10 
 
 ILLUSTRATIONS 
 
 1. Mine ventilation plan 4 
 
 2. Mesh structure for computer model 5 
 
 3. Travel times for each jiirway 5 
 
 4. Time lag for smoke detectors 7 
 
 5. Partition of network into zones by lag time 8 
 
 TABLES 
 
 1. Input data file 3 
 
 2. Airway dimensions 3 
 
 3. Computer-generated minimum travel time paths 6 
 

 UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT 
 
 cfm 
 
 cubic foot per minute 
 
 min 
 
 minute 
 
 ft 
 
 foot 
 
 pet 
 
 percent 
 
 e 
 
 square foot 
 
 
 
FIRE LOCATION MODEL 
 
 By John C. Edwards^ 
 
 ABSTRACT 
 
 A fire location computational model was developed by the U.S. Bureau of Mines. The model can 
 determine all the possible paths in a mine that smoke can travel from a fixed fire source to a smoke 
 detector. The associated FORTRAN computer program can be utilized to determine the minimum 
 travel time from a source fire to a smoke detector. The difference in travel time from an isolated fire 
 source to two or more detectors can be used to isolate those airways in which the source fire is located. 
 
 ^Research physicist, Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA. 
 
INTRODUCTION 
 
 The early detection of a fire in a mine is necessary for 
 the informed implementation of miner evacuation. The 
 placement of smoke detectors throughout the mine net- 
 work is the obvious strategy to follow. In general, several 
 detectors will be installed. The inherent complexity of 
 the mine network, in the case of a metal or nonmetal 
 mine, can pose a formidable problem for the interpretation 
 of the signals received by several smoke detectors located 
 throughout the mine network. The smoke from a source 
 fire will travel with the mine ventilation, and be diluted at 
 airway jimctions. The prediction of Jiirway ventilation in a 
 mine network with the edrflow controlled by fans and natu- 
 ral ventilation is amenable to computer generated solutions 
 both for the 2drflow quantity and the concentration of the 
 products of combustion that emanate from a fire source.^ 
 If the mine ventilation is known, either measured or pre- 
 dicted with the mine ventilation computer program,^ dif- 
 ferences in arrivid times of smoke from a source fire to 
 several detectors can be used to isolate the location of the 
 fire. As part of its research program to develop a mine 
 fire detection strategy, the U.S. Bureau of Mines devel- 
 oped a FORTRAN computer program that can be used to 
 determine the minimum travel time from a fire source to 
 a smoke detector. This requires an enumeration by the 
 program of all the possible paths available to the smoke. 
 This approach, while a significant factor in the isolation of 
 
 a mine fire location, is not without limitations. The total 
 number of possible paths increases rapidly with an increase 
 in the number of airways. The computations presented in 
 this report are limited to paths that individuaUy consist of 
 at most nine airways. However, the structure of the pro- 
 gram permits an extension of the model to paths that are 
 defined by any finite number of eiirways provided adequate 
 computer memory is available. 
 
 The model developed in this report has apphcations 
 both in the planning for the location of detectors in a 
 mine, and in the mine emergency stage. To determine 
 the optimum location of fire detectors, the mine network 
 can be divided into zones, each of which is associated with 
 a difference in calculated smoke arrival time between a 
 pair of detectors. For established mine ventilation, this 
 promotes the efficient selection of detector sites. In the 
 event of a fire, the information is then available to deter- 
 mine in which zone the fire is located. This can assist in 
 miner escape route planning. A fire can alter the ventila- 
 tion, and possibly induce flow reversal. If the new ventila- 
 tion produced by the fire can be quzmtified, then the pro- 
 gram can be applied for the given distribution of detectors 
 and new ventilation to isolate the zone in which the fire 
 occurs. In practice, observations made within the mine in 
 the event of a mine emergency can be used to further iso- 
 late the zone in which the fire is located. 
 
 MODEL DESCRIPTION 
 
 The strategy of the model is to determine the differ- 
 ence between signal (smoke) arrival times at several 
 detectors. This should isolate the region of the mine in 
 which the source fire is located. The mine network is rep- 
 resented by a grid of airways that intersect at junctions. 
 For the current model, it is assumed that each junction 
 forms the intersection of exactly two airways. The network 
 of intersecting airways is arranged as an intersection of M 
 rows zmd N columns. This is possible since it is assimied 
 that exactly four airways join at a junction. If less thzm 
 four airways join at a jimction for a particular mine repre- 
 sentation, then additional airways with zero airflow are 
 
 Edwards, J. C, and R, E. Greuer. Real-Time Calculation of 
 Product-of-Combustion Spread in a Multilevel Mine. BuMines IC 8901, 
 1982, 117 pp. 
 
 Edwards, J. C, and J. S. Li. Computer Simulation of Ventilation in 
 Multilevel Mines. Paper in Proceedings, Third International Mine 
 Ventilation Congress, Harrogate, England. Inst, of Min. and Metall., 
 London, 1984, pp. 47-51. 
 
 Orederkirk, S. J., W. H. Pomroy, J. C. Edwards, and J. Marks. 
 Mine Stench Fire Warning Computer Model Development and In-Mine 
 Validation Testing. Paper in Proceedings, Second U.S. Mine 
 Ventilation Symposium (Univ. NV-Reno, Sept. 23-25, 1985), ed. by 
 P. Mousset-Jones. Balkema, 1985, pp. 29-35. 
 
 ^First work cited in footnote 2. 
 
 added to complete the matrix representation of the 
 network. 
 
 The approach is a systematic determination of all possi- 
 ble paths from an assumed fire source location to the air- 
 way designated as the detection airway. For a path con- 
 taining a specified number of airways (I), there is a 
 maximum of 4' distinct possible paths that emanate from 
 a selected jimction. This might be visualized as a tree 
 structure in which the termination of each limb is the 
 source of four airways. Of these paths, a smaller nxmiber 
 will contain the detection airway. Of the latter quantity, a 
 further subset will be consistent with the established air- 
 flow throughout the mine network. A specific application 
 is for a fixed ventilation in the mine. If a flow reversal 
 should occur as a resxilt of a fire, the program is applied 
 for the new ventilation plan. From this last selected group, 
 there will be a single path representative of the minimum 
 travel time. The difference between the minimum travel 
 times to two detectors from a fixed fire source at a speci- 
 fied jimction is characteristic of a region of the network 
 that may contain other such jimctions. To establish these 
 regions, this procedure is repeated for each and every 
 junction in the network. The evaluation of the minimum 
 time travel paths is accomplished with the FORTRAN 
 computer program in the appendix. 
 

 
 Table 1. -Input data file 
 
 ■ BRANCH.DAT 
 
 Card 
 
 1 Column 
 
 Format 
 
 Symbol 
 
 Definition 
 
 1 
 
 6-10 
 
 15 
 
 MSP 
 
 Total number source junctions. 
 
 
 16-20 
 
 '5 
 
 MST 
 
 Total number detection airways. 
 
 2 
 
 1-80 
 
 4(5x,l5)^ 
 
 ISP 
 
 Source junction numbers. 
 
 3 
 
 1-80 
 
 4(5x,l5)^ 
 
 1ST 
 
 Detection ainway numbers. 
 
 4 
 
 6-10 
 
 15 
 
 NJ 
 
 Number of junctions. 
 
 
 16-20 
 
 15 
 
 NBT 
 
 Number of airways. 
 
 
 26-30 
 
 15 
 
 N 
 
 Number of columns for 2d template. 
 
 
 36-40 
 
 15 
 
 M 
 
 Number of rows for 2d template. 
 
 5^ . . . 
 
 6-10 
 
 15 
 
 NO 
 
 Airway number. 
 
 
 16-20 
 
 15 
 
 NA 
 
 Start junction for ainvay NC. 
 
 
 26-30 
 
 15 
 
 NB 
 
 Rnish junction for airway NC. 
 
 
 33-43 
 
 F10.5 
 
 Q 
 
 Volumetric airflow in ainway NC (cfm). 
 
 
 46-56 
 
 F10.5 
 
 DS 
 
 Length of airway NC (ft). 
 
 
 59-64 
 
 F5.1 
 
 AR 
 
 Cross-sectional area of airway NC (ft^). 
 
 'Total required equals number of airways (NBT). 
 
 ^Defines four values, each with format 15 and separated by five blank spaces. 
 
 It is already apparent that the Umiting characteristic of 
 this model is the number of paths, 4', each of which 
 contains I airways, that must be constructed by the com- 
 puter program. This total coimt includes retracement 
 along airways. The memory restrictions of the computer 
 system for the application in this report have limited the 
 definition of a path to at most nine airways. Each node in 
 the network is the soiuce of 4' = 262,144 distinct paths. 
 This restriction involves superfluous counting, and must 
 be unproved upon in a subsequent effort. However, the 
 method is accurate, and serves to demonstrate a strategy 
 for smoke detection in a mine network. 
 
 Utilization of the model requires the preparation of 
 several templates (diagremis). The first template is a 
 representation of the physical mine network by branches 
 that intersect at nodes. The steady-state airflow for the 
 mine network is either measured, or calculated with the 
 mine ventilation computer program.* 
 
 The second template is a relabelling of the mesh air- 
 ways and junctions to make it compatible with the model 
 format requirements for the computer program. As stated 
 earUer, the jimctions aie. arremged in M rows and N 
 columns. The junctions, MN in number, are ordered se- 
 quentiadly with junctions 1, 2,..., N in the first row, 
 junctions N+ l,N-i-2,...,2N in the second row, and junctions 
 MN-N-i-l,MN-N-i-2,...,MN in the top row, row M. The 
 junction numbers in the first column are 1,N+1,...,MN- 
 N+1, in the second column aie junctions 2,N-I-2,...,MN- 
 N+2, and the last coliunn, column N, is formed by jimc- 
 tions N,2N,...,MN. Although the structiu-e of the mesh is 
 critical from a program apphcation viewpoint, it is not 
 necessary to maintain a proportionahty among airway 
 lengths that scales with the junction separation distances. 
 Table 1 shows the required format for the input data file, 
 BRANCH.DAT. In the next section, an application is pre- 
 sented that demonstrates the program utUity. 
 
 APPLICATION 
 
 Consider the mine ventilation plan for a section of a 
 triple entry with crosscuts as shown in figure 1. The ven- 
 tilation is established by a fan in airway No. 21. The 
 dimensions of the jiirways are shown in table 2. For this 
 study, because of the limitation upon the munber of air- 
 ways that can constitute a path, only a section of the triple 
 entry is considered. The ventilation plan was estabUshed 
 with an application of the Bureau's ventilation computer 
 
 program.' It was possible to eliminate junction 14 and 
 combine airways 20 and 21 into a single cdrway in the ven- 
 tilation plan prior to construction of the second template 
 without any loss of information. 
 
 First work cited in footnote 2. 
 ^First work cited in footnote 2. 
 
 Table 2.-Alrway dimensions 
 
 Airway 
 
 1 . 
 
 2 . 
 
 3 . 
 
 4 . 
 
 5 . 
 
 6 . 
 
 7 . 
 
 8 . 
 
 9 . 
 10 
 11 
 12 
 
 DS, ft AR, ft^ 
 
 5,000 
 
 2,000 
 
 2,000 
 
 2,000 
 
 200 
 
 200 
 
 2,000 
 
 2,000 
 
 200 
 
 200 
 
 2,000 
 
 2,000 
 
 54 
 54 
 54 
 54 
 36 
 36 
 54 
 54 
 36 
 36 
 54 
 54 
 
 Airway 
 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 20 
 21 
 22 
 23 
 
 AR Cross-sectional area of airway. 
 DS Length of airway. 
 
 DS, ft AR, ft^ 
 
 200 
 
 200 
 
 2,000 
 
 2,000 
 
 200 
 
 200 
 
 5,000 
 
 4,990 
 
 10 
 
 200 
 
 200 
 
 36 
 36 
 54 
 54 
 36 
 36 
 54 
 54 
 54 
 36 
 36 
 
Qy 
 
 (4) 
 
 3,812 
 
 3,812 
 
 ■^ 
 
 (5) 
 
 867 
 
 2,355 
 
 6h- 
 
 1 1 
 
 (6) 
 
 (7) 
 
 (9) 
 
 1,456 
 
 4> 
 
 KEY 
 
 V^ Junction 
 (7) Airway 
 ^Airflow direction 
 
 13,783 Airflow, cfm 
 
 (3) 
 
 2,944 
 
 €> 
 
 (2) 
 
 6,420 
 
 (II) 
 
 9,365 
 
 ay 
 
 ;i) 
 
 (13) 
 
 11,937 
 
 3,259 
 
 (b- 
 
 (8) 
 
 2,670 
 
 t. 
 
 (15) 
 
 21,302 
 
 
 
 (17) 
 
 21,302 
 
 (10) 
 
 8,168 
 
 2,355 
 
 4) 
 
 (12) 
 
 4,418 
 
 <t- 
 
 (19) 
 
 (22) 
 
 (14) 
 
 29,706 
 
 22,186 
 
 (18) 
 
 21,302 
 
 (21) 
 
 (23) 
 
 5,615 
 
 A (16) A (20) ^^ (7 A 
 
 ; 43,488 
 
 43.488 
 
 Figure 1 .-Mine ventilation plan. 
 
 The 22 branches and 15 junctions are renumbered to 
 conform to the prescription for the second template 
 (fig. 2). There are M = 3 rows and N=5 columns. The 
 time of travel along each airway is calculated from the 
 airway volumetric flow rate (O), airway length (DS), and 
 airway cross-sectional area (AR). The airway travel times 
 £U"e shown in figure 3. 
 
 For the demonstration of the program's capability, 
 airways 13, 22, and 14, were designated to contain de- 
 tectors. The progrcun's evaluation of the minimum travel 
 time paths, consisting of less thjm nine airways, which 
 originate from each of the 15 junctions are enumerated in 
 table 3. It was not possible to reach airway 14 from junc- 
 tion 13 with a path composed of nine or less airways. 
 
 These results must be treated with caution. Although 
 the computer program as used in this apphcation will 
 sccuch out minimum travel time paths composed of at 
 most nine curways, there might be a path containing more 
 than nine 2iirways that represents a smcdler travel time. 
 Such is the case for the evaluation of the smoke travel 
 time from junctions 1 and 6 to airway 13. Table 3 shows 
 the minimum travel time path of 118.65 min from junction 
 1 to ciirway 13 containing 7 airways, namely airways 5, 14, 
 
 19, 15, 11, 12, and 13. However, the ll-airway path con- 
 tainmg anways 5, 14, 19, 20, 21, 22, 18, 9, 4, 8, and 13, 
 which represents a travel time of 113.29 min, is excluded. 
 A similar problem occurs with junction 6. For junction 6, 
 table 3 Usts the minimum travel time path containing 6 
 airways: airways 14, 19, 15, 11, 12, and 13, and a travel 
 time of 115.59 min. In actuality, the minimum travel time 
 path consists of the 10 airways, airways 14, 19, 20, 21, 22, 
 18, 9, 4, 8, and 13, and is associated with a travel time of 
 110.23 min. In each of these exceptions, the relative error 
 in the travel times is less than 5 pet. 
 
 This exaunple poses the question as to the maximimi 
 extent of the mesh formed from mine airways that can be 
 considered without exceeding the constraint that the min- 
 imum travel time path will not contain more than nine 
 airways. This would remain a problem even if the con- 
 straint of nine airways is increased. There is not a direct 
 answer to this quandary. In this particular application, the 
 total number of airways is 22, slightly greater than twice 
 the maximum nine Jiirways that can be used to construct 
 a path. The error involved affects less than 10 pet of the 
 junctions, with an error in travel time of less than 5 pet for 
 the affected junctions. This leads to the qualitative result 
 
(14) 
 
 
 (5) 
 
 (Z> 
 
 19) 
 
 ;io) 
 
 (1) 
 
 KEY 
 
 Q£) Junction 
 (7) Airway 
 ^Airflow direction 
 
 at 
 
 (20) 
 
 (15) 
 
 <Z> 
 
 (II) 
 
 (6) 
 
 2y^ 
 
 (2) 
 
 @- 
 
 (21) 
 
 (16) 
 
 
 (12) 
 
 (7) 
 
 ^ 
 
 (3) 
 
 ^ 
 
 (221 
 
 (17) 
 
 Qy 
 
 (13) 
 
 (8) 
 
 <f> 
 
 (4) 
 
 Figure 2.-Mesh structure for computer model. 
 
 ■® 
 
 (18) 
 
 ■m 
 
 (9) 
 
 4) 
 
 45.86 
 
 KEY 
 
 6.21 Airway travel time, min 
 
 28.33 
 
 36.68 
 
 11.53 
 
 12.67 
 
 1.89 
 
 8.30 
 
 1.12 
 
 0.60 
 
 74.18 
 
 40.45 
 
 24.44 
 
 12.17 
 
 3.06 
 
 2.21 
 
 0.88 
 
 0.24 
 
 19.23 7.84 6.21 
 
 Figure 3.-Travel times for each airway. 
 
 0.34 
 
 0.17 
 
Table S.-Computer-generated minimum travel time paths 
 
 Source junction Airway path (see fig. 2) Minimum travel 
 and detection branch time, min 
 
 Junction 1: 
 
 13 5,14,19,15,11,12,13... 118.65 
 
 22 5,14.19,20,21,22 94.17 
 
 14 5, 14 4.95 
 
 Junction 2: 
 
 13 6, 11, 12, 13 79.27 
 
 22 6,11,16,21,22 67.99 
 
 14 1,5, 14 50.81 
 
 Junction 3: 
 
 13 7, 12, 13 37.50 
 
 22 7,16,21,22 26.21 
 
 14 2, 1,5, 14 70.04 
 
 Junction 4: 
 
 13 8, 13 12.41 
 
 22 8, 17, 22 13.52 
 
 14 3,2,1,5,14 77.88 
 
 Junction 5: 
 
 13 4, 8, 13 18.62 
 
 22 4, 8, 17, 22 19.73 
 
 14 4, 3, 2, 1, 5, 14 84.08 
 
 Junction 6: 
 
 13 14,19,15,11,12,13 115.59 
 
 22 14,19,20,21,22 91,11 
 
 14 14 1.89 
 
 Junction 7: 
 
 13 11, 12, 13 77.06 
 
 22 11,16,21,22 65.78 
 
 14 10, 14 76.06 
 
 Junction 8: 
 
 13 12, 13 36.61 
 
 22 16,21,22 25.33 
 
 14 12,13,9,4,3,2,1,5,14.. 120.87 
 
 Junction 9: 
 
 13 13 12.17 
 
 22 17, 22 13.28 
 
 14 13,9,4,3,2,1,5.14 96.42 
 
 Junction 10: 
 
 13 9, 4, 8, 13 18.79 
 
 22 9, 4, 8, 17. 22 19.89 
 
 14 9, 4, 3, 2, 1, 5, 14 84.25 
 
 Junction 11: 
 
 13 19,20,21,22,18,9,4,8.. 108.35 
 
 22 19.20,21,22 89.22 
 
 14 19,15,10,14 112.70 
 
 Junction 12: 
 
 13 20,21,22,18,9.4,8,13.. 80.02 
 
 22 20,21,22 60.89 
 
 14 15, 10, 14 84.37 
 
 Junction 13: 
 
 13 21,22,18,9,4.8,13 43.33 
 
 22 21. 22 24.21 
 
 14 (1) (1) 
 
 Junction 14: 
 
 13 22.18,9,4,8.13 31.80 
 
 22 22 12.67 
 
 14 22.18.9,4,3,2.1,5,14.. 97.26 
 
 Junction 15: 
 
 13 18, 9. 4. 8. 13 19.12 
 
 22 18, 9, 4. 8, 17, 22 20.23 
 
 14 18,9.4.3.2,1,5,14 84.59 
 
 ^Excessive ainways (greater than 9) in path. 
 
 that the mesh under consideration should be composed of In order to increase the range of applicability of the 
 no more airways them twice the nimiber of allowed airways computer program, several options are aveulable. The 
 that can define a path. This hypothesis reqtiires additional most direct route is an increase in computer memory and 
 
 testing. speed. An alternative is to develop a method that can be 
 
used to subdivide a mine network into smaller networks; 
 apply the program to individual smaller networks; and 
 properly synthesize the information developed from the 
 smaller networks in order to develop minimum travel time 
 paths for smoke in the mine. This is a subject of future 
 research. 
 
 The minimum travel time data in table 3 can be used to 
 estimate the difference in smoke arrival time at the end 
 of designated airways from each junction considered to be 
 the location of the source fire. Figure 4 shows the relative 
 differences in the smoke minimum arrival time at the end 
 of airways 13, 14, and 22 for each hypothetical source 
 junction. The negative sign indicates a reversal in the 
 order of arrivid of smoke at the end of each of the desig- 
 nated airways. 
 
 As an example, consider a fire located at junction 11. 
 According to table 3, the minimum travel time from 
 
 junction 11 to airway 13 is 108.35 min. The m inim um 
 travel time from jimction 11 to airway 22 is 89.22 min. 
 The time lag between the time of first arrival of the smoke 
 at the end of airways 13 and 22 is 19.13 min, and is so 
 indicated in figure 4. 
 
 It is apparent from the application presented in figure 
 4 that a single pair of detectors does not uniquely deter- 
 mine the fire source. A consideration of detectors only in 
 airways 13 and 22 leads to a partition of the mesh into 
 four zones. Each zone is defined by those airways that, if 
 they contained the source fire, would produce the desig- 
 nated arrival time difference at the detectors in airways 13 
 and 22. The airways are determined by inspection of 
 figure 4. The junctions identified with a fixed time differ- 
 ence and the airflow direction in the airways associated 
 with each of the junctions determines the airways that 
 form a particular zone. Zone 1 contains jimctions 1 and 
 
 NA 
 
 Junction 
 Airway 
 
 KEY 
 
 Time lag, min, for airways 
 
 Airflow direction 
 Not available 
 
 '13-22 
 ! 13-14 
 .22-14 
 
 (19) 
 
 19.13 
 
 -4.35 
 
 •23.48 
 
 19.13 
 
 -4.35 
 
 ■23.48 
 
 -©r 
 
 (14) 
 
 24.48 
 
 I 13.70 
 
 89.22 
 
 (t> 
 
 (10) 
 
 (15) 
 
 I 1.28 
 
 1.00 
 
 - 10.28 
 
 ^ 
 
 (5) 
 
 24.48 
 
 I I 3.70 
 
 89.22 
 
 (I) 
 
 (6) 
 
 <h 
 
 11.28 
 28.46 
 17.18 
 
 (20) 
 
 -^3 
 
 (21) 
 
 9.12 
 NA 
 NA 
 
 (II) 
 
 <g> 
 
 (22) 
 
 19.13 
 •65.46 
 ■84.59 
 
 (16) 
 
 11.28 
 -84.26 
 -95.54 
 
 ■® 
 
 (12) 
 
 ® 
 
 -I.I I 
 
 -65.47 
 -64,36 
 
 (17) 
 
 (2) 
 
 -I.I I 
 -84.25 
 -83.14 
 
 ®r 
 
 (7) 
 
 <D 
 
 (3) 
 
 (8) 
 
 ^ 
 
 11.29 
 -32.54 
 -43.83 
 
 -I. II 
 -65.47 
 -64.36 
 
 (13) 
 
 (18) 
 
 -1. 10 
 -65.46 
 -64.36 
 
 ® 
 
 (4) 
 
 (9) 
 
 <D 
 
 -I.II 
 
 -65.46 
 -64.35 
 
 Figure 4.-Time lag for smoke detectors. 
 
6; zone 2 contains junctions 2, 3, 7, and 8; zone 3 contains 
 junctions 4, 5, 9, 10, and 15; and zone 4 contains junctions 
 11, 12, 13, and 14, If the corrected travel times discussed 
 above were used for junctions 1 and 6, then zones 1 and 4 
 would be merged into a single zone. This will not be done 
 in order to examine the capability of the program with the 
 retention of smjdl errors in predicted minimum travel time 
 for the smoke. Figure 5 shows the partition of the mesh 
 into the foiu- zones. 
 
 The previous discussion has shown that zone 1 is in 
 actuality contiguous with zone 4. The difficulty for the 
 user is that a time difference in signal arrival time for 
 zone 1 would lead to the user to search zone 4 for a fire. 
 However, since the calculated time differences associated 
 with zone 4 is closest to that for zone 1, it is reasonable to 
 search for a fire source in zone 4 after completion of the 
 search in zone 1. 
 
 A similar analysis could be appUed to the pair of detec- 
 tors in airways 13 zmd 14, as well as those in airways 14 
 and 22. As is evident from figure 4, the network can be 
 divided into approximately eight zones in each of these 
 cases. However, there is uncertainty about junction 13. 
 As explained earlier, airway 14 could not be reached by a 
 path containing nine or less airways. For a given pair of 
 detectors, the more zones the network can be divided into, 
 the more accurate will be the determination of the fire 
 location. 
 
 This analysis, although subject to small error, does 
 provide a method for partitioning a mesh section of a mine 
 network into zones, each of which would be associated 
 with a time lag between signal (smoke) arrival times at two 
 detectors. 
 
 KEY 
 
 I; ••.•••J Zone I, 24.5 min Y / A Zone 3, -|.l min 
 ESMI Zone 2, I 1.3 nnin ^3 Zone 4, 19.1 min 
 
 Figure 5.-Partition of network into zones by lag time. 
 
CONCLUSIONS 
 
 The model developed to search out all possible paths 
 from a hypothetical fire source to smoke detectors in 
 distinct airways and to determine the minimum smoke 
 travel time to the detectors has been demonstrated to 
 provide, through a compeu-ison of differences in smoke 
 travel time to a pair of detectors, a rough assessment of 
 the most hkely region that contJiins the fire source. A 
 preliminary guideline shows its apphcability to a section of 
 
 a mine consisting of approximately not more than 22 
 airways. Additional computer memory would permit a 
 direct expansion of the FORTRAN computer program in 
 order to locate a fire in a larger section of a mine. An 
 alternative is to develop a method that applies the program 
 to individual sections of a mine and synthesizes the 
 information into the construction of minrmimi travel time 
 paths for the entire mine. 
 
10 
 
 APPENDIX.-FORTRAN COMPUTER PROGRAM 
 
 DISCLAIMER OF LIABILITY CLAUSE consideration by the U. S. Bureau of Mines, the user 
 
 hereof expressly waives any and all claims for damage 
 
 The U.S. Bureau of Mines expressly declares that there and/or suits for or by reason of personal injury, or 
 
 are no warranties express or impUed which apply to the property damage, including special, consequential or other 
 
 software contained herein. By acceptance £md use of similar damages arising out of or in any way connected 
 
 said software, which is conveyed to the user without with the use of the software contained herein. 
 
 INCLUDE 'WAY2.COM' 
 TYM=SEC^fDS (0.0) 
 LP=6 
 
 CALLINPT 
 DO 10 1 = 1, MSP 
 IMP = ISP (I) 
 DO20J=l, MST 
 IBT=IST (J) 
 
 WRITE (LP,30) IMP,IBT 
 30 FORMAT (/4X,'* ********************** *y4x, 'IMP = ', 2X,I5,3X,'IBT = ',2X,I5/) 
 CALL PATH (IMP) 
 CALL OUTPT 
 20 CONTINUE 
 10 CONTINUE 
 
 DELTA = SECNDS (TYM) 
 WRITE (LP,100) DELTA 
 100 FORMAT (/5X,'ELAPSED TIME = ',1X,E12.5, 2X,'SEC'/) 
 STOP 
 END 
 
 SUBROUTINE MOVE (ILP) 
 INCLUDE 'WAY2.COM' 
 JX(1) = 1 
 JX(2) = N 
 JX(3) = -1 
 JX(4) = -N 
 IF(ILP.EQ.l) THEN 
 
 JX(3)=0 
 
 JX(4)=0 
 ENDIF 
 IF(ILP.EQ.1+(M-1)*N) THEN 
 
 JX(2)=0 
 
 JX(3)=0 
 ENDIF 
 IF(ILP.EQ.M*N) THEN 
 
 JX(1)=0 
 
 JX(2)=0 
 ENDIF 
 IF(ILP.EQ.N) THEN 
 
 JX(1)=0 
 
 JX(4)=0 
 ENDIF 
 
 IF(ILP.GE.2AND.ILP.LE.N-1) JX(4)=0 
 IF(ILP.GE.2+(M-1)*NAND.ILP.LE.M*N-1) JX(2) = 0. 
 IF(MOD(ILP,N).EQ.lAND.ILP.NE.lAND.ILP.NE.l + (M-l)*N) JX(3)=0 
 IF(MOD(ILP,N).EQ.0AND.ILP.NE.NAND.ILP.NE.M*N) JX(1) =0 
 RETURN 
 
11 
 
 ENfD 
 
 SUBROUTINE INPT 
 INCLUDE 'WAY2.COM' 
 
 10 = l 
 
 OPEN(UNIT = IO,FILE = 'BRANCH.DAT'.TYPE - 'OLD') 
 C *** ISP = SOURCE JUNCTION 
 C **♦ 1ST = DETECTION AIRWAY 
 C ♦*♦ KB = AIRWAY NO 
 C *** TM = TIME IN AIRWAY 
 C *** KS = FLOW DIRECTION OF AIRWAY 
 C ♦** NJ = NO OF JUNCTIONS 
 C *** NBT = NO OF AIRWAYS 
 C **♦ DS = AIRWAY LENGTH 
 
 C *♦* AR = CROSS SECTIONAL AREA OF AIRWAY 
 C *♦* V= LINEAR FLOW VELOCITY IN AIRWAY 
 
 READ(IO,50) MSP,MST 
 
 READ(IO,50) (IST(I),I = 1,MSP) 
 
 READ(IO,50) (IST(I),I = 1,MST) 
 50 FORMAT (8(5X,I5)) 
 
 WRITE (LP,50) MSP,MST 
 
 WRITE(LP,50) (ISP(I),I = 1,MSP) 
 
 WRITE(LP,55) 
 55 FORMAT(/) 
 
 WRITE(LP,50) (IST(I),I=1,MST) 
 
 READ(IO,100) NJ,NBT,N,M 
 100 FORMAT(5X,I5,5X,I5,5X,I5,5X,I5) 
 
 WRITE(LP,120) NJ,NBT,N,M 
 120 FORMAT(5X,'NJ = ',1X,I4,2X,'NBT = ',1X,I4,2X,'N = ',IX,I4,2X,'M = ',1X,I4/) 
 
 DO200 J = 1,NBT 
 
 READ(IO,300)NC(J),NA(J),NB(J),Q(J),DS(J)AR(J) 
 
 WRITE(LP,350) J,NC(J),NA(J),NB(J),0(J),DS(J)AR(J) 
 350 FORMAT(4X,'J,NC,NA,NB,O,DSAR:',4(2X,I4),3(2X,F7.0)) 
 
 11 = NA(J) 
 I2=NB(J) 
 KS(I1,I2) = 1 
 KS(I2,I1) = -1 
 V(J) = Q(J)/AR(J) 
 TM(J) = DS(J)/V(J) 
 KB(I1,I2) = NC(J) 
 KB(I2,I1) = KB(I1,I2) 
 
 200 CONTINUE 
 
 300 FORMAT(3(5X,I5),2(2X,F10.5),2X,F5.1) 
 
 DO500J=l,NBT 
 
 WRITE(LP,600) J,V(J),TM(J) 
 500 CONTINUE 
 600 FORMAT(/4X,'J,V(J),TM(J):'2X,I5,2(3X,E12.5)) 
 
 CLOSE(UNIT=I0) 
 
 RETURN 
 
 END 
 
 SUBROUTINE PATH(IPS) 
 
 INCLUDE 'WAY2.COM' 
 C *♦* PATH GENERATION 
 C *** MATRIX KA(LEVEL/ELEMENT IN LEVEL) 
 
 DO 101 = 1,4 
 
 CALL MOVE(IMP) 
 
 L(1,I) = IMP + JX(I) 
 
 LO(I) = L(l,I) 
 
12 
 
 M1 = (M)*(4**8) + 1 
 
 M2=I*(4**8) 
 
 D0 8MQ = M1,M2 
 
 KP(MQ,1) = KS(IMP,L(1,I))*KB(L(1,I),IMP) 
 8 CONTINUE 
 10 CONTINUE 
 
 DO 5 KI=2,9 
 
 IPW=4**KI 
 C *** IPW PATHS IN LEVEL KI 
 C *** MOVE FROM JUNCTION ON LEVEL KI-1 TO 4 JUNCTIONS ON LEVEL KI THROUGH 4 
 
 DIRECTIONAL MOVES 
 
 DO 15I = 1,IPW 
 
 J = (I-l)/4 + l 
 C *** INDEX K GROUPS IPW ELEMENTS INTO GROUPS OF 4 
 
 K=MOD(I,4) 
 
 IF(K.EQ.O) K=4 
 C *** JUNCTION LO(J) ON LEVEL KI-1 WHERE J = 1,2, ,(IPW-l)/4+ 1 
 
 ILK=LO(J) 
 C *** MOVE FROM ILK IN 4 DIRECTIONS DEHNED BY JX 
 
 CALL MOVE (ILK) 
 C *** poR EACH VALUE OF J THERE ARE 4 VALUES OF I 
 C *** JUNCTION LN(I) ON LEVEL KI 
 
 LN(I) = LO(J) + JX(K) 
 C *** PATH KP FROM 'IMF FIAS AT MOST 9 ELEMENTS 
 
 M1 = (I-1)*(4**(9-KI)) + 1 
 
 M2=r(4**(9-KI)) 
 
 DO20MQ = Ml,M2 
 
 KP(MO,KI) = KS(LO(J), LN(I))*KB(LN(I),LO(J)) 
 20 CONTINUE 
 15 CONTINUE 
 
 DO 12IM = 1,IPW 
 
 LO(IM) = LN(IM) 
 12 CONTINUE 
 5 CONTINUE 
 
 DO 70 1 = 1,262144 
 C *** CHECK FOR PATHS IN AIRFLOW DIRECTION AND LABEL KSP= 1 
 
 KSP(I) = 1 
 
 D0 75JL=1,9 
 
 IF(KP(I,JL).LT.O) KSP(I) = -1 
 75 CONTINUE 
 70 CONTINUE 
 
 NSUM = 
 
 RETURN 
 C *** NSUM = # OF PATHS WITHOUT BACK TRACKING 
 C *** IDENTIFY PATHS WITH AIRWAYS THAT DO NOT REPEAT 
 
 DO 80 1 = 1,262144 
 
 NN(I) = 1 
 
 DO 100J1 = 1,8 
 
 J1U=J1 + 1 
 
 DO 200 J2=J1U,9 
 
 IF(J1.NE J2ANDABS(KP(I,J1)).EQ ABS(KP(I,J2))) NN(I) =0 
 200 CONTINUE 
 100 CONTINUE 
 
 IF(NN(I).E0.1) NSUM = NSUM + 1 
 80 CONTINUE 
 
 RETURN 
 
 END 
 
13 
 
 SUBROUTINE OUTPT 
 INCLUDE 'WAY2.COM' 
 WRITE(LP,5) IMP,IBT 
 5 FORMAT(/4X,'IMP = ',2X,I5,3X,'IBT = ',2X,I5/) 
 
 WRITE(LP,7) NSUM 
 7 FORMAT(/4X,'NSUM = ',2X,I4/) 
 C *** WRITE PATH 
 C DO 10 1 = 1,16384 
 
 C IF(NN(I).EQ.l) THEN 
 
 C WRITE(LP,100) I,(KP(I,J),J = 1,7) 
 
 C ENDIF 
 
 C 10 CONTINUE 
 100 FORMAT(/2X,'I = ',lX,I5,3X,'KP(y ) = ',8(2X,I5)) 
 DO 20 1=1,262144 
 MM(I)=0 
 C *** IDENTIFY PATHS THAT CONTAIN IBT AS A AIRWAY 
 
 DO 30 J = 1,9 
 C IF(KP(I,J).EO.IBTAND.NN(I).EQ.l) THEN 
 
 IF(KP(y).EQ.IBT) THEN 
 C WRITE(LP,100) I,(KP(I,JJ),JJ = 1,9) 
 
 MM(I) = 1 
 ENDIF 
 30 CONTINUE 
 20 CONTINUE 
 TST= 99999. 
 IY=-1 
 JPPY=-1 
 JY=-1 
 
 DO 200 1 = 1,262144 
 
 IF(MM(I).EQ.1AND.KSP(I).GT.0) THEN 
 TS(I) = 0. 
 DO300JP=l,9 
 JPP=JP 
 JPX=KP(IJP) 
 TS(I) = TS(I) + TM(JPX) 
 IF(KP(yP).EQ.IBT) GO TO 400 
 300 CONTINUE 
 400 CONTINUE 
 C IF(MM(I).EQ.l) WRITE(LP,900) I,MM(I)JPP,(KP(yj), 
 
 C UJ = UPP) 
 
 C 900 FORMAT(2X,'I,MM(I),JPP,KP(UJ):',3(2X,I6)/ 
 C 18(2X,I5)) 
 
 C WRITE(LP,500) I,TS(I),(KP(y ) J = 1 JPP) 
 
 IF(MM(I).EQ.1AND.TS(I).LT.TST) THEN 
 TST=TS(I) 
 IY=I 
 JY=JP 
 JPPY=JPP 
 ENDIF 
 ENDIF 
 500 FORMAT(/4X,'I = ',2X,I7,3X,'TS(I) = ',2X,E12.5/4X,'KP(I,J = 1 TO JPX):',8(2X,I7)) 
 200 CONTINUE 
 
 WRITE(LP,600) lY JY JPPY,TST,(KP(IY JJ),JJ = 1,JPPY) 
 600 FORMAT(/4X,'I Y = ',1X,I7,3X,'J Y = ',1X,I7,3X,'JPPY = ',2X,I7,3X,'TST = ',2X,E12.5/4X,'KP(I Y JJ = 1 TO 
 1 JPPY):',8(2X,I7)) 
 RETURN 
 END 
 
14 
 
 IMPLICIT DOUBLE PRECISION (A-H,0-Z) 
 
 COMMON/BLKl/JX(25),NA(25),NB(25),NC(25),MM(262144), 
 
 1 NN(262144),KB(20,20),L(1,4), 
 
 2 KP(262144,9) 
 
 3 ,LO(262144),LN(262144) 
 
 4 ,V(25)AR(25),DS(25),Q(25),TM(25), 
 
 5 TS(262144),KS(25,25),KSP(262144) 
 
 6 ,ISP(15),IST(15) 
 COMMON/BLK2/N,M,NJ,NfBT,IMP,IBT,NSUM,MSP,MST,LP 
 
 1 ,TYM,DELTA 
 
 INT.BU.OF MINES,PGH.,PA 29196 
 
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