MINE TRACKS THEIR LOCATION AND CONSTRUCTION Jfa Qrcaa-J/ ill Book (n 1m PUDUSHERS OF B O O K. S FOR-/ Coal Age v Electric Railway Journal Electrical \\forld ^ Engineering News-Record American Machinist * The Contractor Engineering 8 Mining Journal ^ Power Metallurgical 6 Chemical Engineering Electrical Merchandising MINE TRACKS THEIR LOCATION AND CONSTRUCTION TREATING BRIEFLY ON THE MATERIALS USED AND THE PRINCIPLES INVOLVED IN THE DESIGN AND IN- STALLATION, WITH A SET OF RULES FOR A STANDARD PRACTICE BY J. McCRYSTLE, E. M. FIRST EDITION SECOND" McGRAW-HILL BOOK COMPANY, INC. 239 WEST 39TH STREET. NEW YORK LONDON: HILL PUBLISHING CO., LTD. 6 & 8 BOUVERIE ST., E. C. 1918 A/3 *f COPYRIGHT, 1918, BY THE MCGRAW-HILL BOOK COMPANY, INC. THE MAPLE PRESS YORK PA INTRODUCTION The gradual displacement of animals by mechanical haulage as the motive power in mine transportation, the successive increases in the weight of the locomotives em- ployed and the improvements in car journals and rolling stock, admitting of longer, heavier trains at relatively high velocities, are making imperative a closer attention to the track material used in mines. Short-radius curves are falling into disuse wherever traffic is at all heavy. These curves are frequently the limiting factor in the length of the trip. The long wheel- base of the motors is not adapted to them, they are the site of continual derailments, the haulage speed must be reduced at their approach, the cars cannot be pushed around them without danger of the bumpers "locking," their maintenance is excessive, and for many other reasons the use of sharp curves is questionable economy. The introduction of the steel car for mine transportation also demands a higher grade of trackwork than was re- quired for the wooden car; the deficiencies of the roadbed, to which the semi-pliant material of the latter adapted itself, tends to loosen the construction of the more rigid steel car. With the more progressive mining companies, the old practice of building frogs, switches, etc., at the mine- to suit the conditions as they arose with the crude facilities of the average smithshop, is being supplanted by the use 436311 vi INTRODUCTION of better-constructed commercial equipment, to which the curves are standardized. For it is obvious that the highest perfection in the design and quality of the material will accomplish little if this material is improperly installed. With many mining companies, I have found, that after they are satisfied as to the merit of the equipment, the subject of trackwork is neglected, and the manner of in- stallation and the specific application, the selection of the frogs, switches, etc., goes by default to the foreman or trackman. Generally speaking, no efficient trackwork can be accomplished without some prescribed rules to govern this work. Moreover, it will be found in endeavoring to compile a standard practice for the guidance of the trackmen, that while most textbooks and handbooks on this subject are replete with data on the standard-gage track, they are curiously lacking when applied to the narrow gages. It is necessary to delve through many topics to find any in- formation at all on the subject, and then often its treat- ment is intelligible to no one but an engineer. With the foregoing in mind, the following treatise has been prepared in order to furnish those in charge of the trackwork and the laying out of trackwork with the neces- sary data in a convenient form, compiled from the usages of several companies where trackwork has been taken up systematically. The introduction of the rules in the latter part of this book is in line with the policy of the standard-gage roads to standardize practices and material, and fix definitely the responsibility for the various operations. The first part of the book deals briefly with the reasons governing the rules and the mathematical computations involved. The opinion that a mine car will run on any kind of track and that any- INTRODUCTION vii thing is good enough for mine work cannot be too strongly discouraged. Wellington and other authorities have been quoted. I wish to thank Mr. H. G. Houtz for the preparation of the sketches and Mr. M. B. Gerhard for much valuable assistance. It is hoped that a consistent application of the practices suggested will result in lengthened trips and lower haulage costs; easier, more economic track maintenance with a minimum of equipment in stock, and, finally, help to reduce delays in transportation ascribable to trackwork. J. McCRYSTLE. October, 1917. CONTENTS PAGE INTRODUCTION v CHAPTER I RAIL 1 Stiffness Strength Durability Advantages of Heavy Rail Acid Water Method of Laying Defects in Laying Rail Benders Allowance for Temperature Track Creep Wooden Rail, Advantages and Disadvantages. CHAPTER II TIES 12 Preferred Material Determination of the Spacing Im- properly Supported Ties Effect on Rail Stiffness Coor- dination of Rail Weight and Tie Frequency Tables Calcu- lation of Rail Deflection Tamping Length Angle Bars and Fish Plates Steel Ties Corduroying Length for Switches Notched Ties Size of Spikes Use of the Plates and Rail Braces Effect on Rail Flange Roadbed and Bal- last Material for Ballast Drainage. CHAPTER III PROJECTION OF HAULAGE ROADS 31 Determining Factors Curves, Methods of Laying Out Economic Radius of Curves Effect on Traffic Alignment on Surface, Preliminary Work Maximum Degree of Curve Curve Calculations and Formula Calculation and Loca- tion of Short Radius Curves Standard Practice. CHAPTER IV GRADES 45 Definition Determining Factors Traffic, Drainage Local Features Underground Projections Theoretic Grades Equalization of Drawbar Pull Computation Effect on ix x CONTENTS Locomotive Capacity Expedients for Facilitating the Handling of Cars Effect on Mining Grade Requirements with Plain and Patent Bearings Constructing Grades Grade Boards Effect of Rail Curvature. CHAPTER V GRAVITY GRADES. . '. 59 Effect on Rolling Stock Shafts and Slope Landings Empty and Loaded Car Requirements Compensation for Curva- ture Reversing of Compensation Formulas and Computa- tions Rail Superelevation on Curves Increasing the Track Gauge on Curves, Underlying Principles Wheel Basis of Cars Guard Rail, Location and Method of Placing. CHAPTER VI FROGS AND SWITCHES G8 Standardization Frog Numbers Plates Frogs Cast Frogs Width of Flangeways Long Throats Frogs for Different Types of Work and Haulage Shrouds for Frogs Cast, Rigid and Spring Shrouds Movable Point Frogs Tracks Crossings Split Switches and Latches Switches for Mine Work Switch Attachments Formulas Stub Switches Tables Turnouts, Calculation of Lead, Rail Length, Radius, etc. Mine Practice Turnout Tables Construction of Turnouts Turnouts off Curves. CHAPTER VII LOCATING THE TURNOUT ' 91 Method of Installing Frog and Switch Bent Switch Points Clearance at Heel Ladder Tracks Angle of Ladder Distance between Frogs. CHAPTER VIII BOOK OF RULES 93 Responsibility Education of Trackmen Conservation of Material Coordinating Field and Office Work Stand- ard Practices General Rules Roadbed Ties Rail and Spikes Curves Angle Bars, Tie Plates and Rail Braces Frogs and Switches, INDEX. . 103 MINE TRACKS THEIR LOCATION AND CONSTRUCTION CHAPTER I RAILS With the exception of gravity roads on the heavier grades where wood rail is still preferred on account of its higher coefficient of friction, standard tee rail is now in general use for mine tracks. In determining the proper weight or section of steel rail for any work, the type of haulage, the weight of the cars and locomotive, the spacing of the ties, and in some cases the reaction of the acid or sulphur water must be thoroughly considered. The approximate rules heretofore used in the determination of the rail section have usually erred in making the rail section too light. The severity of future as well as present traffic must be consid- ered, since rail once laid is almost invariably utilized as long as the cars will travel over it, regardless of the increase in tonnage both of the trip and locomotive. In computing the safe load for steel rail laid with 16 ties to the 30-ft. rail, 10 Ib. per yard for each 2240 Ib. of weight on each wheel is usually taken; this, with an 8-ton four- wheel motor, would mean 2 tons on each wheel, or 20-lb. rail. This weight, while safe, is evidently not enough for any but chamber work light-weight rail is a costly economy. The flat wheels common to mine cars, the swaying side motion due to the play of the axles in the boxes and the side slant of the roadbed, the inferior ballast allowing some 1 '''MINE TRACKS of the ties to sink and causing the rail to span a number of ties, thus creating greater bending moments, the acid action of the water on the steel, the scrap value of any reclaimed track, the cutting effect on the treads of the locomotive wheels, etc., are too often forgotten in the purchase of rail. Again, gangways or headings starting out with short mule hauls are converted to motor hauls, and later employed as main haulageways without any improvement in the original track. As a consequence, the rail becomes a series of humps and hollows, the maintenance of the rolling stock and roadbed is excessive, the roadbed is rendered dirty by the car offal, the trips have few cars, frequent derailments occur, and the initial economy in the light weight of the rail is soon overcome. As Wellington aptly expresses it, in buying rail " we must, unfortunately, use an intelligence somewhat higher than a hay scale." In rail we require: (1) Stiffness, (2) strength and (3) durability, rather than tons of steel. If the strength of various sections is compared, it will be found that these requisites can be purchased at a lower unit rate in the larger sections. In "stiffness" we have that property which al- lows the rail to span the ties and support the load without deflecting, affording thereby a smooth running surface for the cars; in "strength" we have that quality which bears the load without breaking, while in "durability" we have the ability to resist wear over extended periods of time. The stiffness varies as the square of the weight, and the strength as the % power, while the price per ton is nearly constant. If the unit weight is assumed as being 30 Ib. per yard, then the stiffness will increase as follows: THIRTY POUNDS PER YARD STIFFNESS = 1 16% per cent, increase in weight (35 Ib. per yard) stiffness = 1.36 or a 36 per cent, increase. RAILS 3 33% per cent, increase in weight (40 Ib. per yard) stiffness = 1.78 or a 78 per cent, increase. 50 per cent, increase in weight (45 Ib. per yard) stiffness = 2.25 or a 125 per cent, increase. 66% per cent, increase in weight (50 Ib. per yard) stiffness = 2.79 or a 179 per cent, increase. 100 per cent, increase in weight (60 Ib. per yard) stiffness = 4.00 or a 300 per cent, increase. The ultimate strength will increase as follows: THIRTY POUNDS PER YARD ULTIMATE STRENGTH = 1 16% per cent, increase in weight (35 Ib. per yard) ultimate strength = 1.26 or a 26 per cent, increase. 33% per cent, increase in weight (40 Ib. per yard) ultimate strength = 1.54 or a 54 per cent, increase. 50 per cent increase in weight (45 Ib. per yard) ultimate strength = 1.84 or a 84 per cent, increase. 66% per cent, increase in weight (50 Ib. per yard) ultimate strength = 2.15 or a 115 per cent, increase. 100 per cent, increase in weight (60 Ib. per yard) ultimate strength = 2.83 or a 183 per cent, increase. The advantages of the heavy section over the light, as regards stiffness and strength, would show a higher com- parison as the rail wears or wastes away from any cause whatsoever. In determining the durability of rail, it is obvious that a great amount of wear cannot be expected if the weight selected conforms closely to the immediate duty it has to perform. We can assume for practical purposes that half the total weight is in the head, and that about half of this weight, or one-quarter the weight of the rail, can be worn away before the rail is discarded, if a sufficient margin of metal has been allowed; otherwise, the rail will fail before it has attained much more than a high polish. In mining work, particularly underground, with the trackmen in absolute charge, trackwork, derailments, rail MINE TRACKS breakage, etc., are taken as part of the day's routine and pass unnoticed, except that part which appears indirectly in the high maintenance charges. If we assume that a wear of J^ the weight of the head is allowed as a safety factor in the lighter rail, then the dura- bility of light and heavy sections will compare as follows : 1 "3 o Available" for wear 1 42 X o> ** *-c >, o I "S o> TJ i a "gS C rt o 3 fi a c - s"* ^ 1*1 G c .^H 3 '- c 2 C 05 Qi 3d 43 5 43 J^ .2 S ill '*J 09 ** C '3 '3 a-* s* 3 a ^-^ H- * cos^ 30 15.0 7.5 3.0 12 5.5 1.830 H 35 17.5 8.75 3.5 14 6.0 1.710 Yi 40 20.0 10.00 4.0 16 6.5 1.625 % 45 22.5 11.25 4.5 18 7.0 1.550 % 50 25.0 12.50 5.0 20 7.5 1.500 Ho 55 27.5 13.25 5.5 22 8.0 1.454 Hi 60 30.0 15.00 6.0 24 8.5 1.420 H 2 Or, using 30-lb. rail as a unit, the metal available for wear would compare as follows: Available for wear before head would become as light Increase in Weight in Ib. per Weight in weight per yard head only yard, per Maximum Minimum cent. Ib. per cent. Ib. per cent. 30 15 7.5-100 3.0-100 35 17** 10.0-133^ 5.5-183% 16% 40 20 12.5-166% 8.0-266% 33% 45 22^ 15.0-200 10.5-350 50 50 25 17.5-233H 13.0-433% 66% 55 27H 20.0-266% 15.5-516% 83% 60 30 22.5-300 18.0-600 100 RAILS Briefly, if we were about to build a permanent (so-called) narrow-gage road for mine traffic, for which 30-lb. steel would ordinarily be used, we would gain, by using a 60-lb. section, the economy in maintenance, a more easily oper- ated road with its attendant benefits, fewer ties, fewer derailments and a larger scrap value when the rail was reclaimed. Furthermore, we would have a stiffness 4 times, an ultimate strength 2.83 times and a durability 3 to 6 times as great, for a rail expenditure but double that for 30-lb. steel. Some concerns, by purchasing " second hand" rail from the railroad companies, obtain the heavier rail for the same price per lineal foot as for new sections J^ to % their weight. This quality of rail for most mining purposes will serve as well as new sections. In localities where acid water abounds the corroding of the steel is frequently the limiting factor in the life of the rail. It would be futile to lay heavy section rail in locations where the water would soon destroy it. As the web and edges of the flange are the portions destroyed first, an in- spection of the standard dimensions will evidence that, by increasing the weight, we do not secure a proportionate in- crease in the acid-resisting properties of the rail. Rail weighing 25 Ib. per yard has been taken as the basis or unit. Weight of rail Increase in weight, per cent. Web Ends of flange Thickness Increase in thickness, per cent. Thickness Increase in thickness, per cent. 25 ... 1% 4 .. 11 4 .. 30 20 21^ 4 11 11 4 35 40 2 %4 21 *%4 9 40 60 2 %4 32 1% 4 27 45 80 2 %4 42 1% 4 35 50 100 2 %4 47 1 %4 36 60 140 3 >64 63 J %4 64 6 MINE TRACKS In the standard tee rail, adopted by the American Society of Civil Engineers, 42 per cent, of the metal is in the head, 21 per cent, in the web and 37 per cent, in the flange. The top corners are curved to a jKe-in. radius, and the car wheels are designed to give on this as little friction as possi- ble; as the rail due to the wear approaches more closely to the shape of the flange the friction is augmented. The height of the rail is identical with the width of the flange, so if this dimension is measured the weight can be determined. The table shows the weight of rail per yard corresponding to the height or flange width. Weight Width of flange or height, in inches Weight Width of flange or height, in inches 25 m 45 3*^6 30 3 50 3% 35 3^ 60 4K LAYING RAIL In laying rails, the joints should be staggered; that is, the joints of one rail should as nearly as possible come opposite the center of the rail lengths of the opposite rail. Lengths less than 10 ft. should not be used. In Fig. 1 are shown a number of defective joints exceed- ingly common in mine-track construction. No. 1 shows what is known as a "dish." This is usually caused by the rolling stock pounding down the joint. In No. 2, two objec- tions will be noticed ; first, the ends of the rail are not butted closely together, and second, the rails are on different levels. No. 3 shows two rails which are not in alignment, probably caused by not using joint fastenings. No. 4 is an example RAILS 7 of improper curvature, or lack of curvature in bending and laying the rail. The joint should be just as symmetrical and easy running as the remainder of the curve. When the cars travel over a joint such as No. 1, or a "high joint" (the contrary condition to No. 1, caused by the rail creeping or being improperly laid or ballasted), it FIG. 1. Some common faults in rail joints. necessarily forces one of the wheels to rise above the rail; the consequence is that quite often the flange mounts the rail and the car is thrown off the track. When the track- man seeks to remedy the condition, what often seems the natural thing to do is to elevate the rail which the car has mounted, when really the difficulty is frequently on the opposite rail. The objection to a joint such as illustrated in No. 2 (Fig. 1) is apparent. While it may not cause a derailment, it 8 MINE TRACKS sets the entire trip bumping and jogging, racks the rolling stock and loosens all the "topping" on the cars. The objections to a joint such as is shown in No. 3 are not always as striking as on this figure. The track is apparently not true to gage at the end of one of the rails, and the end of the adjoining rail is probably loose. When no joint fastenings are employed, the rail may spring later- ally during the passage of a car and immediately thereafter revert to its natural position. This may derail the car, which, if going at some speed, will travel considerably be- yond the defective point and tend to mislead thereby in its detection. No. 4 (Fig. 1) is the most usual form of bad track. The rail is not curved uniformly, and a swaying motion is im- parted to the cars; if the velocity is sufficient, the flange may run directly over the rail. To be sure, all derailments cannot be ascribed to the track, and in some instances they can be traced directly to the car. However, if the track is in perfect condition the car must be unusually bad before it will leave the track. All rails should be laid true to the correct gage of the track except where allowance is made for curvature. The practice of slightly reducing the gage of the track to allow for the deficiencies of the gage of the car wheel is question- able, since this expedient impairs the wheel gage of any new cars. Fig. 2 shows an ordinary rail bender, or "Jim Crow," adapted for bending heavy rails or "dishing" them. The contrivance consists of two eye-bolts, two old sticks of tim- ber, two mine ties and a rail bender. The greater the spac- ing of the ties, the greater will be the power of the bender. Rail which has previously been used for locomotive haul- age will frequently be found to be brittle and break during RAILS 9 bending. This condition is due to the crystallization of the steel from the constant impact of the wheels and docs not, as is often erroneously believed, arise from the return passage of electric currents. The effect, if any, of the elec- tricity would be to soften the metal. However, where the bonding of the rails is deficient, the electric current some- times leaves the rail and runs through the soil, again return- FIG. 2. Rail bender, adapted for "dishing" rails. ing to the rail. This leaving and reentering the rail causes an electrolytic action, and the rail sometimes disintegrates at the points of exit and entry. Where the rails have crystallized, or become brittle, they should be either annealed before bending or be bent while hot. Where rails are laid underground, the small variation in the temperature will not require any allowance at the joints for expansion; when they are laid on the surface, however, 10 MINE TRACKS the space left for the expansion of 30-ft. rails should be as follows: Temperature when Space to be allowed rail is laid for expansion 24 deg. and less % in. 25 deg. to 49 deg. % 6 in. 50 deg. to 74 deg. % in. 75 deg. to 94 deg. y[ G in. 95 deg. and over Nothing On tracks on a heavy grade the rails have a tendency to " creep" or move down the grade. This may be caused either by the braking of the train, or the tractive force of the locomotive, or a combination of both; the effect of the braking being the more appreciable due to the unevenness of its application, and will be more evident in the down track or roads having one way traffic. The " creep" is caused by a longitudinal thrust, com- municated by the wheels to the rail, and is equivalent to 20 per cent, of the weight of the locomotive where the cars are not equipped with brakes, and 20 per cent, of the com- bined weight of the cars and locomotives on a down grade where the brakes on the cars and locomotive are applied. This "creep" destroys the alignment of the track and curves, and at sites where it is found impossible to re-align the track without cutting the rail, the excess length should be bent outward and permitted to slide without distorting the track. This is accomplished by inserting a switch point at the bent rail to make a sliding contact instead of the usual unyielding butt connection. Their use at the upper end of the curves will be found advantageous. WOODEN RAIL In flat pitch mining, where the car is taken by gravity from the working face, with the wheels spragged to retard RAILS 11 the velocity, wood rail is frequently used on account of its higher coefficient of friction, or resistance to sliding. This coefficient for cast iron on steel is 0.20, and for cast iron on oak 0.49, or about 2J times as great for the wooden rail. It is problematical whether the use of wood rail is war- ranted under any conditions. Many mines have discon- tinued its use without any noticeable inconvenience on their heavier pitching " slants," or chambers. The required fric- tion is obtained by running a plank along the outside of a light tee rail. The tread of the wheel being wider than the head of the rail allows the wheels to slide upon both the plank and the tee rail. Among the objections to wood rail are: The lack of durability; the rounding of the corners and the splintering of the wearing surface, due to the action of the wheels; the lack of uniformity of the cross-section and the inclina- tion to warp, common to all wood. Owing to these draw- backs and the ease with which the car wheels mount wooden rail, the cars are much more subject to derailments than when steel rail is employed. Wood rails are usually laid in ties which have been notched to the proper gage and are held in place by the notches and steel spikes. They can be laid almost as rapidly as the light weight steel rail. The rail is usually ordered about 3X5 in. in section and in 12 to 16-ft. lengths of beech, birch, maple, oak or ash. Care should be taken to have such rails sound with square edges, and to have them stored in a man- ner to prevent warping. CHAPTER II TIES The dimensions of mine ties should be consistent with the rail and spikes used, and the mode of haulage. In order to insure stability, the ties should in no case extend less than 8 in. beyond the web of the rail; nor should they be less than 4J^ ft. in length. In addition, the ties should have two parallel faces at least 3% in. wide. The pre- ferred woods are locust, oak, chestnut, hemlock, ash, iron- wood, hickory and hard pine. With usual conditions, the number of cross-ties cannot be too great for service until their closeness to each other impedes tamping, which limit is reached when about 40 per cent, of the rail rests upon the ties. The determination of the tie spacing is dependent on (1) the weight of the rail, (2) the packing and ballast of the ties, and (3) the weight and volume of the traffic With a tie having a 6-in. face the minimum spacing to allow adequate tamping would, therefore, be 15 in. This, however, is a tie frequency that practically it is almost impossible to obtain under the more usual mining conditions in which the workmen driving the headings or chambers, are also required to extend their own track. With these men, the track work being but a secondary consideration, the natural tendency is to give it only enough attention to fulfill their immediate needs and satisfy the none too strict exactions of the mine foremen. In ascertaining the proper tie spacing or the weight of rail suitable, the following consideration must not be lost sight of. 12 TIES 13 (1) Allowance should be made for unusual impact stresses caused by the "flat spots" on car wheels. These "flat spots" are quite common on wheels in mines having long grades requiring sprags. The load transferred to a rail by a flat wheel on a car in motion is in the nature of a blow or suddenly applied load, and will therefore be more severe than a smoothly applied moving load. (2) Consideration should be given to the frequent occur- rence of ties that are not adequately supported by the ballast, which may be due not only to improper tamping, but also to the washing out, or disintegration of the ballast. This occurrence will at least double the stipulated span of the rail. (3) Due thought should be given to the great loss in rail stiffness caused by but a small increase in space between the ties. A failure to observe this will soon be evident in "dishes" in the rail, and the effects on the traffic. It will be recognized readily that if the ties are welL packed, any increase in the number of ties used for a given distance will increase the strength and stiffness of the rail. Accord- ingly, if the rail furnished is too light for the traffic, this deficiency may to a large extent be overcome by the use of more ties. Ties must be well tamped before they can be expected to perform their proper function of supporting the rail and load. A few concrete examples will perhaps make clear the foregoing considerations in the computation of the weight of rail and tie spacing with various rolling stocks. Example. It is desired to establish a safe weight of rail for use with a 4-wheel, 8-ton locomotive, having a 4-ft. wheel base, drawing cars with a maximum gross weight of 7 tons, and having a 2>^-ft. wheel base over ties having 6-in. faces and spaced on 24-in. centers. 14 MINE TRACKS Weight on one locomotive wheel = ~ = 4000 Ib. Weight on one car wheel = 4 = 3500 Ib. Since the rail is continuous over the ties, the rail between adjacent ties can be regarded as a beam with fixed ends. The effect of a suddenly applied load is twice that of a stationary load. The usual allowable stress per square inch in steel shapes used as beams is 16,000 Ib., compression or tension, when stationary loads are considered. Hence, the allowable stress in this example will be 8000 Ib. per square inch. Now the maximum bending moment produced on a beam by a single concentrated load = -^Pl where P = load in pounds and I = space between supports in inches. But the bending moment (M) in any beam also equals S-, where S equals allowable stress per square inch and - = section c modulus of the beam. Hence, Or 8000 X - - JfX 4000 X 18 C which reduces to I 1 X 4000 X 18 g/ c = 8 X 8000 % = By consulting tables of "T" rail sections in Cambria Steel Company's Handbook, it is seen that: The section modulus of 16 Ib. rail = .75 The section modulus of 20-lb. rail = 1.30. From the above it is evident that a 16-lb. rail is too light, TIES 15 and therefore the 20-lb. rail, although the section modulus is somewhat higher than required, is used. In the above illustration, it will be noted that the weight on one locomotive wheel, which is greater than that due to one car wheel, is used, and further that each tie is accepted as doing its full duty. In the event, however, of a tie failing to contribute its proper support, which is very often the case, the span of the rail would be increased from 18 to 42 in. On this in- creased span there ordinarily will be space for two car wheels, but only one locomotive wheel, in which case: Maximum bending moment due to locomotive = %Pl as before. In any condition where the wheel base is more than 0.586 of the span, the bending moment due to two loads, as with the two wheels on the mine car, would not be as great as the bending moment due to the weight on a single wheel in the center of the span. This relation is true regardless of the position of the two wheels. In the case cited then, in which one tie is not contributing support and the span instead of 18 in. is now 42 in., the greatest weight on one wheel, whether from the loco- motive or car wheel, would be used in the preceding formula, S = y%Pl. Substituting the known quantities in the formula and using the weight on one locomotive wheel as an illustration, with the 42-in. span, the following value of 2.625 is obtained for This, by referring to tables of C "T" rail sections, is found to indicate 35-lb. rail. The preceding formulae show that the bending moment "M," and consequently the section modulus -> vary C directly as the span and the load. 16 MINE TRACKS The following tables, based on allowable stress of 8000 Ib. per square inch, show the section modulus, with the corresponding weight of rail, and the allowable weight per wheel for the usual tie spacings encountered. The designated weights per wheel, starting at 1000 Ib., and varying by successive increments of 1000 Ib. up to 10,000 Ib., will cover any wheel loads liable to be encountered in mine practice. TABLES OF RAIL SECTIONS AND TIE SPACING (Ties with 6-in. faces) Weight on one wheel Specified tie centers 24 in. Resulting span (42 in.) on alter- nate ties Section modulus Weight of rail, pounds per yard Section modulus Weight of rail, pounds per yard 1,000 0.281 8 0.656 16 2,000 0.562 12 1.312 20 3 ? 000 0.843 16 1.969 30 4,000 1.125 20 2.625 35 5,000 1.406 25 3.281 40 6,000 1.688 25 3.937 45 7,000 1.969 30 4.594 50 8,000 2.250 30 5.250 55 9,000 2.531 35 5.906 55 10,000 2.813 35 6.562 60 Specified tie centers 21 in. Resulting span (36 in.) on alter- nate ties 1,000 0.234 8 0.562 12 2,000 0.468 12 1.124 20 3,000 0.702 16 1.686 25 4,000 0.936 16 2.250 30 5,000 1.170 20 2.812 35 6,000 1.404 25 3.376 40 7,000 1 . 638 25 3.938 45 8,000 1.872- 30 4 . 500 50 0,000 2.106 30 5.062 55 10,000 2.340 35 5.626 55 TIES 17 TABLES OF RAIL SECTIONS AND TIE SPACING. (Continued) (Ties with 6-in. faces.) Specified tie centers 18-in. Resulting span (42 in.) on alter- nate ties Weight on one wheel Section Weight of rail, Section Weight of rail, modulus pounds pei- modulus pounds per yard yard 1,000 0.187 8 0.463 12 2,000 0.374 12 0.936 16 3,000 0.561 12 1.404 25 4,000 0.748 16 1.872 30 5,000 0.936 16 2.340 35 6,000 1.123 20 2.808 35 7,000 1.310 20 3.276 40 8,000 1.497 25 3.744 45 9,000 1.684 25 4.212 45 10,000 1.871 30 4.630 50 Specified tie centers Resulting span (24 in.) on 15 in. alternate ties 1,000 0.141 8 0.374 12 2,000 0.281 8 0.748 16 3,000 0.422 12 1.122 20 4,000 0.563 12 1.496 25 5,000 0.703 16 1.872 30 6,000 0.844 16 2.246 30 7,000 0.985 20 2.620 35 8,000 1.125 20 2.994 40 9,000 1.266 20 3.368 40 10,000 1.407 25 3.742 45 NOTE: Rail sections are American Society of Civil Engineers' standards. From the preceding table, the weight of rail required for a given tie spacing arid weight per wheel, can be taken direct, or if a certain weight of rail has been determined 18 MINE TRACKS upon, the tie spacing can be fixed to give the required support. It will be evident to anyone familiar with the ballast, tamping, and drainage around mines, that a different standard of tie spacing and rail will be required for under- ground as distinct from surface track. Track on the surface will usually be found much superior to track of similar equipment underground. This is due to a variety of causes, such as inferior align- ment, poorer ballast, smaller ties not spaced uniformly, and more exacting drainage conditions. Track frequently considered satisfactory in the mines would not be tolerated on the surface. Where the ballast and tamping are in good shape and readily open to inspection, as on the surface, the rail sections shown for the specified centers will, I believe, be found satisfactory. For the usual condition underground, the heavier sections shown are recommended as none too heavy. It is not practical to vary the rail weight to satisfy every condition. The large companies usually adopt a standard for their entire system, as it would entail too much incon- venience and confusion to order rail suitable to specific conditions. The tie spacing, however, is not subject to arbitrary restrictions, and can usually be adapted by the local colliery officials to suit the considerations peculiar to any section. The greatest attention should be given to selecting the proper weight rail or tie spacing to conform with the other material used, their installation, and the severity of the traffic. In favor of using heavy rail, the greater durability, stiffness and strength,, the fewer ties required with the consequently smaller expense of renewals, the higher TIES 19 scrap value, the easy maintenance of the alignment, the saving in the upkeep on the rolling stock due to the better riding qualities, and the potential ability to meet unforeseen increases in the traffic, must not be forgotten. You will note that the rail section calculated for 24 in.- tie centers corresponds to the weight as determined by the empirical rule given for well ballasted track in Chapter I, on "Rail." It might be interesting to note in connection with the tables of rail and tie spacings, what degree of stiffness, as indicated by the deflection, will be obtained. The maximum allowable deflection or sag under load will evidently be realized when the stresses caused by the wheel load reach the elastic limit of the steel, which for medium steel, referring to "Merriman's Civil Engineer's Pocket Book," is 36,000 Ib. Accepting this value and assuming the case of the 8-lb. rail recommended for 24- in. tie centers (18-in. clear span) with a 1000-lrir wheel load, to find the maximum allowable and actual deflec- tion, and the allowable load within this elastic limit, we have the following formulae: (1) M (Bending Moment) = S (36,000 Ib.) X * (Sec- tion Modulus). (2) M (Bending Moment) = JP (Superimposed load) X I (the span). In formula (1) the section modulus of 8-lb. rail is ascertained, by referring to tables of "T" rail sections, to be 0.31. Substituting, M = 36,000 X 0.31 = 10,850 in.-lb. The allowable value of "P" with the given span, and the 8-lb. rail, is determined by substituting in formula ol\f (2); where M = %Pl', transposing, P = ; substitu- 20 MINE TRACKS 10 850 ting the known values, P = 8 X - - or 4820 lb., which o as the stipulated moving load is but 1000 lb. or equivalent to 2000 Ibs. static, gives a safety factor of almost 2% based on the elastic, limit. The maximum allowable deflection or sag is expressed by Pit the formula D = inoi m which P and I are the same as in the preceding formulae; E is modulus of elasticity 29,000,000; and I, the moment of inertia, obtained from the table of "T" rail sections, being 0.23 for an 8-lb. rail. Substituting these values to find the maximum allowable , . 4820 X fl8) 3 deflection, and solving: D = ^ x ^^-^-^ = 0.02188 in. Calculating the deflection for a wheel load of 1000 lb. (mov- 2000 X (18) 3 ing load 2000 lb. static load) ; D -- . = 0.0091 inches, which shows that the rail specified is well within the limit of maximum stress. If it can be accepted that each tie will contribute its full quota of support to the rail, the 8-lb. section will be suitable for the stipulated tie centers of 24 in., but, however, actual experience has proved that this is not to be depended upon, so that some allowance must be made for imperfections in the tie support. In the tables previously advanced, the rail for the given tie centers, and the rail required for alternate tie centers has been given. The use of the rail for the alternate centers is considered, in the light of actual experience, none too heavy for the specified centers, allowing as it does for the failure of every other- tie. Many mining companies con- sider it economical in the end to go even further than this. TIES 21 It is difficult to say just where to draw the line, but the assumed condition of alternate ties failing, makes a fair allowance for ordinary roadbed without going to extremes. With the 8-lb. rail on the 42-in. span, the maximum allowable bending moment is found by the preceding for- mula to be 2065 in.-lb., and the allowable deflection 0.1195 in. As the moving load of 1000 Ib. is equivalent to a static load of 2000 Ib., it will be seen that practically no FIG. 3. Light tic poorly tamped. factor of safety is allowed, and the 8-lb. rail is to~o light for the increased span. The resulting deflection will approach very closely the maximum allowable deflection of O.li95in. As stated before, no fixed rules can be given for determ- ining absolutely the proper rail section to be adopted. The preceding formulae and illustrations are given in order that the tie spacing and rail can be coordinated for any given conditions at hand or anticipated. Even the tables presented are but a guide to the selection of the most suita- ble rail and tie spacing. Each tie should be tamped uniformly and particular attention given to tamping under that portion upon which the rail rests. Fig. 3 illustrates a case of light ties and improper tamping. Fig. 4 shows the effect on the rail of poor tamping or ballast. 22 MINE TRACKS Again, referring to Fig. 3, it may be stated that with improper ballast or tamping a tie of excessive length will be distorted more readily than one of proper length. While the long tie justly meets with much favor on account of its greater bearing qualities, there is a limit to which this length can be advantageously utilized. The tie may be considered as inverted, with the rails for the supports, and the pressure on the roadbed due to the weight of traffic acting as a uniformly distributed load on the tie. FIG. 4. Effect of poor tamping on rail. The portions of the tie outside of the rails are then canti- lever beams, and the portion between the rails, a beam with fixed ends. In order to obtain a tie length in which the overhanging ends will be of the same strength as the center portion, it will be found mathematically that the length of the tie should be 1.8 times the distance between the rail centers. Of course, if the tie is heavier than required, this length can be exceeded within limits. There are so many indeter- minate factors entering into the computation of the tie thickness that it is futile to attempt to formulate any definite rules. Experience is the only reliable guide in this matter. However, it may be said that if the rail com- TIES 23 ports with the traffic and the spike in turn is adapted to the rail, then a tie with a cross-section great enough to carry the spike without splitting and allowing it to protrude below, will be of sufficient strength if its length is not greatly in excess of 1.8 times the gage. When placing ties at rail joints where angle bars are employed, selected ties of uniform size should be used. These should be so spaced as to give the angle bar suffi- FIG. 5. A. Proper angle bar support incorrect fish plate support. B. Proper fish plate support. Incorrect angle bar support: cient bearing and permit efficient spiking the rail joint itself to be suspended midway between the ties. The joint should not be directly supported. Where strap plates or fishplates are used, a selected tie should be placed directly under the joint. This also applies where the rails are butted together and not bolted. The ties should be spaced as close as practicable at the rail joint. The closer tie spacing would seem to be peculiarly adapted to headings where the acid water quickly destroys the rail, the use of the lighter sections with a greater tie frequency recommending itself on account of the low initial cost and the ability to withstand the acid proportionally better 24 MINE TRACKS than the more heavy rail. There is, of course, also the lesser loss in the event that the rail cannot be reclaimed or is destroyed prematurely. The use of the steel tie for mine work is generally con- fined to low veins where height is at a premium. As the usual method is to lay such ties on the floor of the haulage- way or chamber without any ballast, the acidity of the water must be given due consideration. If properly placed and taken care of, they will outlast wood ties, especially in chambers where the frequent removal and relaying of track is the limiting factor in the life of the tie. Some mines use the steel tie interspersed at intervals with wood ties, in the capacity of a tie-rod to hold the rails to gage. The practice known as " corduroying " that is, placing additional ties, or laggings, between other ties should not be employed where it is necessary to reinforce decayed ties or to help bear the stresses of heavier traffic, except possibly where mule haulage is the means of transportation. This practice prevents efficient tamping and impairs the drainage of the roadbed. At switches, many companies are in favor of having the ties in graded lengths, so as to furnish support and hold in alignment both tracks up to and including the frog. The ties used in conjunction with wood rail are usually made with notches. These are cut to the gage of the track, so as to hold the rails and prevent them from tipping or spreading. While it is not always done, it is better to have the bottom side of the tie faced to prevent the tie from turn- ing and the track from creeping. It is the general opinion that ties will last longer if the bark is removed, and that the hewed tie is more serviceable than the sawed tie. TIES HOOK SPIKES 25 The dimensions of the proper hook spike to be employed should be in accord with the weight of the rail and the cross-section of the tie. The weight of the rolling stock does not require, nor will the general run of mine ties permit the use of as large a spike as is employed on standard- gage track. Where the ties will stand it, the following sizes of spikes are recommended: Weight of rail per yard Size of spike in inches measured under head Average number per keg of 200 Ih. 45 to 70 5 l / 2 by % 6 375 40 to 60 5 by% 6 400 35 to 40 5 by^ 450 30 to 35 4Mby^ 530 25 to 35 4 by^ 600 20 to 30 4K by KG 680 16 to 25 4 by% 1,000 16 to 25 3K by KG 900 With such ties as are ordinarily used, however, the X M-i n - spike will probably be the largest permissible size. In driving the spike, the last blows should be light, to avoid breaking the spike under the head and to make a tighter bind; also, the two inside spikes should be near one side of the tie and the two outside spikes near the opposite side, to prevent tie splitting. If, when a spike is withdrawn, a wooden plug is driven into the spike hole, the life of the tie will be prolonged considerably. Unless the spikes are known to be in good condition, it is doubtful whether it pays to remove them when track is reclaimed; it is comparatively costly to straighten 26 MINE TRACKS them, and if they are not in good shape the trackman will probably throw away the poorer ones. Moreover, old spikes are difficult to drive. Many trackmen, when the ties are to be reused, allow the outer spikes to remain and deliver the ties with these spikes in them to the new location; or when the ties are of no further value, they are burned and the spikes then collected. There is no doubt that with the majority of mining companies there is a vast waste in the consumption of spikes, and if a check is kept on the amount of track laid this can be readily verified. Usually it will be found more economical to distribute the spikes in a systematic manner than to spend too much time on their reclamation. A good practice is to have someone who is conversant with the needs of the different workmen oversee the distribution of the spikes. ANGLE BARS AND FISHPLATES When a locomotive or a trip of cars runs on rails, a wave of elasticity precedes it. The object of the joint fastening should be to make this wave continuous across the joint. The ideal rail joint should have the same strength, stiffness and elasticity, both vertically and laterally, as the rails which it joins. That the angle bar is much superior to the fishplate in achieving this object will be apparent from a study of the two. The strap plate and the simplest forms of angle bar are the only types employed for mine tracks. In Fig. 5-A is shown an angle bar properly placed with the rail gap suspended between the ties. By this arrange- ment the stress at the joint, where there is always more or less pounding from the traffic, is distributed upon two TIES 27 ties instead of one through the bridging action obtained from the shape of the angle bar. The stress at the joint is transmitted to this angle bar in such manner as to produce tension in the lower, or angle, portion of the bar. If a tie is placed directly under the joint, as in Fig. 5-B, and it becomes depressed or battered, which it will in a short time, the rail is compelled to bridge between the adjoining ties, thereby doubling the span and in- viting a long dish in the rail that the angle bar can but poorly prevent, having no support and virtually carrying the tie that should uphold it. The fishplate lends very little vertical support, so that the tie should be placed as in Fig. 5-B, which you will note is the contrary to the position used for angle bars. However, the lateral support, or resistance to the side motion or spreading of the rails, which is contributed by both the angle bar and fishplate must not be_ ignored. The four spikes required for one joint where the rails are butted together, are not only very independable in main- taining the alignment but soon destroy the tie. While the foregoing may appear to be a needless explana- tion of self-evident facts, it is none the less true that this matter is often suffered to go by default. At some mines where angle bars are used great pains are taken to insert a tie directly under the joint spanned by the angle bar, and any good effects expected to accrue from the use of this type of rail connection are thereby lost. TIE-PLATES AND RAIL BRACES Tie-plates and rail braces have had a restricted use on mine tracks, although there are many locations where they might be employed profitably. Frequently the flange of the rail wears to a paper- 28 MINE TRACKS edge and the rail must be removed, although the head may be but little worn. This is due to particles of grit which intrude between the rail and the tie. By observing a train of mine cars being drawn by a locomotive, a con- siderable side motion will be perceived. This side motion tends to force the rails outward as each car passes, the elasticity of the rails returning them to their original position. In time, a groove is worn in the spike, allowing a still greater motion to the rail, and when grit accumulates under the flange the rubbing of the rail on the grit grinds away the flange. The use of tie-plates, which, in their simplest form, are merely plates provided with spike holes and an offset that resists the lateral thrust of the rail, prevents this motion and consequently the wearing away of the flange. The tie-plate holds the spikes, so that to obtain any side motion it would be necessary to force both spikes, while the offset in the plate prevents cutting the groove in the spike. The tie-plates purchased from a manufacturer are further strengthened by having the bottom cut or serrated so as to resist any sliding motion. The tie-plate can also be used to advantage on track where the heavy traffic forces the rail into the tie which at intervals compels adzing the tie to give the rail a true bearing. The cutting of the rail into the wood soon destroys the tie. The amount of labor, taken in conjunction with the cost of the tie, the preservation of the rail achieved and the inconvenience entailed in doing this work, and opera- ting upon a defective support, will afford a figure from which may be judged when and where tie-plates are an economy. It must also be remembered that the plate, properly handled, should last indefinitely. TIES 29 The application of rail braces should be limited to those curves that are difficult to maintain in gage. The braces prevent the tipping and the spreading of the rails and protect the tie. It should not be necessary to use both tie-plate and rail braces on the one location. ROADBED AND BALLAST The best ballast that can be procured will be of little avail if not properly tamped. If a tie is unsupported, it is but an added weight on the rail. The materials in general use for mine-track ballast are cinders, slate or vein refuse, slate from the breakers and broken rock. The broken rock affords the best drainage and service, but on account of its high cost is little used for ballast around surface mine tracks. In tunnels and rock head- ings or gangways the smaller rock made when excavat- ing is sometimes thrown to one side to be used as ballast. Any lump should be broken to a size that would pass through a 3-in. ring. Where there is much passage of men and mules, the track should be given a light surfacing of ashes. The material usually employed for ballast is cinders. It is generally procured readily from the colliery boiler plant and affords fair drainage and a fair degree of service. The ashes, if kept in close contact with the rail, will hasten its corrosion. The refuse from the beds, or veins, is almost with- out exception of a friable nature and disintegrates rapidly, forming dust or mud. It affords poor drainage and is easily washed from the roadbed. If dry, the passage of the cars swirls the refuse into the journals of the car and dries up the lubrication. It becomes mixed with the coal, and in bituminous mines would be a factor in a dust explosion. 30 MINE TRACKS Altogether, it is short-sighted economy to use this material for ballast. Breaker slate is sometimes used for ballast. It affords a fair roadbed until it disintegrates and becomes dust or mud. Coal is a very expensive and inefficient ballast. Where practicable, there should be at least 3 in. of ballast beneath the ties; it should be well tamped, particu- larly under the portion of the tie supporting the rail. The ditch should be sufficiently deep to drain the road- bed and thereby assist in preventing the decay of the ties. The drainage ditch should be driven with the heading, where necessary, and maintained clear of obstruc- tions or accumulations. As it is quite difficult to secure a good roadbed, or track, where this is a part of the work of the miner driving the opening, and since it is inconvenient to furnish proper ballast to supply his immediate needs as he advances, it will usually be found advisable for the trackman to go over the completed work at intervals. CHAPTER III PROJECTION OF HAULAGE ROADS Where the pitch of coal measures is heavy, the haulage- ways are driven to follow along either the top or bottom slate of the bed at a grade sufficient to afford good drainage or balance the drawbar pull on the empty and loaded cars. When the pitch is flat, the entire mine is projected and developed along definite lines. In light, rolling pitches, the problem is more complex, compelling a use of both the grade and projection methods, and frequently where there is more than one bed, a close adherence to the lines of any past workings. As the track must conform to the headings or gang- ways as they have been driven, some system must be employed in order to have them driven symmetrically. In the heavy pitching beds, if the top or bottom rock is followed too closely, many irregularities and sharp turns will ensue. To preclude this, a definite minimum radius curve must be adopted and a simple method to attain this established, which the miner can understand and use conveniently. Where there is " double timber" or props at regular intervals, what is known as the " chord-offset" method will be found useful. The offset or distance in the dark for any set is ascertained by squaring the established 31 32 MINE TRACKS distance between the centers of sets of props and dividing by the radius. Let D = Offset, or distance in the dark in feet; C = Distance in feet, center to center of props ; R = Radius of the curve; then FIG. 6. Method of driving curves by offsetting. D = (see Fig. 6) In the case of a 40-ft. radius curve, a rib radius of 35 ft. and timber placed 5 ft. between centers, substituting we have OK C D-g -!?/., or 8^ 'n. PROJECTION OF HAULAGE ROADS 33 Any two timbers in line on the gangway are then taken, and at a point 5 ft. from the proposed point of curve a prop is placed 4J in. (one-half of 8J^ m -) out of line of the aforesaid two sets. Then the prop just erected is used to line with the prop at the point of curve, and the Top Split Gangway D fvN ftiJw\ . 5o'fad.--fl-c j' 1 27 ! /x 4'iM// ?\ B Y--50'&d ' il ,v.^, t. 1 v v \ il ^ ^ i ^ _|f/^i!=i U r;'-r Haulageway 26-27 25?I5 for 116-0 FIG. 7. Lines of sight and offsets for driving curves. next is offset S^i in.; and so on, 8>^ in. on all subsequent props until the desired curve is completed. In the event that no timber is being used, the same results can be attained by driving points on line at definite intervals in the ties or roof, C is then made the distance 34 MINE TRACKS between the points, R is the radius intended, and D is the offset distance, the first offset being but half the regular offset. Where the headings or tunnels are driven on transit lines, offsets are taken at from 5 to 10 ft. from the line for any curves. Fig. 7 shows a typical plan for driving by this method, which is preferred for long or large radius curves. It will be noticed that the lines overlap. This permits setting up the transit a convenient distance from the working face, so as not to interfere with the work. The heading is at no time without line. A few days are allowed for any delay arising in the establishment of new lines, and the points are at a safe distance from the blasting at the face. TO DETERMINE THE MOST ECONOMIC RADIUS CURVE TO USE UNDERGROUND To assist in attaining the best possible track layout underground consistent with the expenditure entailed, the conditions governing the radius of the curve should be analyzed before any standard radius is adopted. On account of the high cost of turning curves, the ad- ditional time it would take to drive those of large radii and the amount of the product necessarily tied up by large curves, the radii must be much shorter than those permissible on the surface. However, there is no reason in installing the smallest curve that cars will travel around without the bumpers interlocking, merely because the initial cost is low. An ideal curve would be one with which the sum of (1) the initial cost, (2) the maintenance during the life of the curve and (3) the expense of traffic haulage will be a PROJECTION OF HAULAGE ROADS 35 minimum. The consummation of this ideal can be ap- proached only by assuming curves of various radii and estimating the costs of the several items. Unless occurring at a site where the roof is poor or the bottom heaves, the shorter the curve the lower will be the initial expenditure. In estimating the cost of curves, certainly, on the shorter ones the cost of the gangway or tunnel required to reach the point attained by the larger curves should be considered, particularly as it is customary to leave considerable pillar each side of a tunnel or main heading. When turning curves of large radii, the wide part of the opening just beyond the frog can sometimes in the heavy pitches be located in solid rock, thereby dispens- ing with the use of timber and obviating any allowance for maintenance. As the life of curves is frequently over 30 years, and wood timber has a serviceableness as low as 18 months, the items of labor and material for timber removals, in addition to the risk of a derailed car knocking down the roof supports, with the delays in traffic incident to retimber- ing, must be thoroughly considered. The use of steel timber will be found advantageous for the long spans encountered at locations where a semipermanent job is required and no "heaving" or "squeezing" is to be expected. In turning off tunnels where several beds to be worked lie close together, a lower upkeep will be realized by a " wing" tunnel to the outer bed and continuing on the same line to the inner ones, than by having a number of wide areas to maintain from a number of curves off the main haulageway. This also forestalls the cramping of the switchwork and radii, which closely situated veins ordinarily demand. 36 MINE TRACKS Viewed solely from the haulage standpoint, the determin- ing factors of the curve radius can be covered under two heads: (1) The cost of resistance due to curvature on the total estimated number of cars to be hauled; (2) the probable number of cars to be hauled in each trip and the rate of travel. The amount of resistance due to curvature varies with each type of car, and to a lesser degree with each car of a given type. The resistance expressed in terms of grade with curves of from 30- to 100-ft. radius, 42-in. gage, 42-in. wheelbase, will run 0.015 ft. to 0.025 ft. per 100 ft. of track for each degree of curvature. That is, with a 50-ft. radius or a 115-deg. curve, moderately clean track, fair running cars with both wheels keyed to the axle, approxi- mately a 1.8 per cent, grade would be necessary to equal the same drawbar pull as on a tangent. A smaller com- pensation would be sufficient where the wheels turn loose on the axles and the wheelbase is less. The value of the radius expressed in degrees can be obtained by dividing 5730 by the radius in feet. This formula will have to be employed especially in small radius curves. The actual arc is used to find the degree, rather than the 100-ft. chord, the practice on standard- gage roads. By using the actual arc, a 50-ft. radius = , n = 115-deg. curve. By the use of the 100-ft. chord, ou a 50-ft. radius = ^7 = 180-deg. curve, showing a disparity of 65 deg. Assuming a curve with a central angle of 90 deg. on a grade of 0.5 per cent, and allowing the same rate of resistance per degree on a 25-ft. and 50-ft. radius curve, the motor traveling over them would have to PROJECTION OF HAULAGE ROADS 37 mount the sum of the grade and the curve resistance, the equivalent of a 4.5 per cent, grade for 39 ft. and a 2.5 per cent, grade for 78 ft. respectively. From the be- ginning of the 50-ft. radius to the point of tangency, there would be with the curve resistance the equivalent of 1.96 ft. vertical, while to travel between the same points by way of the 25-ft. radius curve, including the 25 ft. of tangent on each end of the curve to reach the same geographical point, would be a total of 2.02 ft. vertical, or essentially the same vertical rise in both cases. While actually with the smaller radius curve there would be a lower rate of resistance per degree, this would be more than balanced by the increased resistance due to the slower speed compelled by the sharper curve. If the resistance due to grade and curvature between the similarly located points is accepted as equal, then there remains in favor of the 50-ft. radius the greater speed at which the trip can travel, the reduced danger of cars jumping the track, the greater ease with which the trolley will follow the wire, a haul 11 ft. shorter, and in some cases 11 ft. less of tunnel. With a heading producing six trips per day of twelve 5-ton cars each, this 11 ft. twice per trip would consume enough power to draw one ton 7920 ft. each day, or 375 miles per year. In estimating the number of cars per trip, the future output, as well as the length of haul, must be considered. The number of cars traveling over a certain haulage road daily may sometimes be trebled by a tunnel to other beds. This increased output may mean the installation of a larger, or possibly the use of an additional, locomotive. If the curves are too sharp, the larger machine cannot traverse them, and this leaves no choice but the additional motor with its expense for attendance and upkeep. 38 MINE TRACKS For obvious reasons no compensation is allowed for curvature underground, and if a locomotive is required to work at its capacity, the additional resistance to be overcome due to curvature may be the factor limiting the length of the trip. With the large curve a locomotive may pull through on its momentum, but on a curve of small radius the velocity must be reduced when the curve is approached. ALIGNMENT ON THE SURFACE The general practice in the location of narrow-gage railroads on the surface is to first run a topography survey and then plot this to a suitable scale. If the relative posi- tion and elevation of both the beginning and destination of the proposed road are known, it may be found practicable to run a rough grade line between them. Using this as a base, enough of the surface features on each side may be located to permit any desired deviation from the original base line. Sufficient accuracy is usually attained by using circle levels taken with a transit to the objects and ground to be located, and only in special cases need the topography be located with a wye level or Locke level. When the location has been plotted and any outcroppings of veins and other influencing features shown, the proposed line is laid out on paper and submitted for approval. This approval, however, in the case of narrow-gage mine roads, is usually permission to use a certain maximum and ruling grade, and the adoption in general of the layout. It is not intended that the layout be adhered to rigidly, and the engineer is permitted to use his judgment in making any minor changes in the grade or route. It is ail infrequent occurrence that the mine track leaves the company's lands, and no right-of-way is required. PROJECTION OF HAULAGE ROADS 39 These facts and the comparative flexibility of the narrow- gage road, with its almost unlimited allowance in curvature, render the field work for a narrow-gage road a comparatively simple matter. As this work is usually assigned to the regular mine engineer corps, which frequently is not particularly familiar with it, the customary methods pursued are given. FIG. 8. Method employed in locating a curve on the surface. One practice in some use is to scale the location from the plan and then duplicate it in the field. Because of possible inaccuracies in the preliminary survey, the pos- sible divergence of the approved location from the base line, and the errors in scaling it, this method is not to be recommended. 40 MINE TRACKS A preferable way is to place stakes on grade at 50- to 100-ft. intervals, depending on the nature of the ground, and then use these stakes as a guide in selecting the straight track or tangents. The radius of a curve is partly deter- mined by establishing the point of intersection and measur- ing the distance from this point to where it is desired to locate the line of curve (see Fig. 8). The radius required is found by the formula, Distance measured Radius = - . f-/ r* exl.-sec >-2 central angle If the country is heavily wooded and the tangents cannot be selected readily in the field, the grade stakes should be located and plotted and the line chosen. The tangents are then established in the field by measure- ments from the stakes and the intersection and curves run in. The prime consideration in most mine roads is to have the grading and excavating a minimum; this, of course, can best be accomplished by the use of grade stakes. In standard-gage practice, a 1-deg. curve is one on which a 100-ft. chord will subtend a central angle of 1 deg. ; a 2-deg. curve, a central angle of 2 deg. with a 100-ft. chord; a 3-deg. curve, a central angle of 3 deg. with a 100-ft. chord, and so on, the radius being calculated by trigonometry from the degree and chord. The curve is easily laid out by deflection angles and 100-ft. chords. In computing the various parjbs of a curve, the following formula will cover most cases (see Fig. 8). R = Radius of curve, D = Degree of curve, T Tangent distance, E = External distance, A Angle subtending chord or sub-chord, A = Central angle. PROJECTION OF HAULAGE ROADS 41 (1) External angle = central angle; the external angle is that one measured by the transit upon the intersection of the tangents. pi (2) Radius = ^ ^ , l/ , E is found as described above. (3) Sin Y^D = ~n, the angle corresponding to sin ^D can then be found in a table of natural sines and cosines, and doubling this angle will give the degree of the curve. (See pages 43 and 88 for short radii formula.) (4) Tangent = R X tan %A; when the radius is known, before the curve can be staked out, it is necessary to know the p.c. or point where the curve commences. When this is found, the tangent distance is measured from the point of intersection, and will locate the p.c.; measuring the same distance on the line of the other tangent will establish the p.t., the end of curve, or point of tangent. t (5) Radius = to i/^' H frequently happens that the point of curve must be located at a certain definite point, as at the end of a bridge or switch. The tangent distance is then measured and the proper radius of the curve calculated from this formula. (6) The deflection angle for a 100-ft. chord is one- half the degree of curvature. (7) If there is no table of external secants convenient, use a table of natural sines and cosines, and divide the cosine of one-half the central angle into 1, and then sub- tract 1 from the result; this will be the external secant. For example, if one-half the central angle is 18 deg., the cosine is 0.9511; dividing this into 1 gives 1.05146, and subtracting 1, we have 0.05146, the external secant. 42 MINE TRACKS (8) When the curve is to be staked out at less than 100 -ft. intervals, as is the case in narrow-gage work, sub-chords must be used. The angle for the sub-chord deflection is . , , , , f , , . . sub-chord determined by the formula sin J%4 = - ^ --- The 2/t/ angle corresponding to sin %A will be found in a table of natural sines. If the angle is known, as is the case with the last deflec- tion for a curve, the formula becomes, % sub-chord = R sin J^A. The deflection angle for any chord is always equal to one-half the central angle subtending it. For 100-ft. chords, the deflection angle would be one-half the degree of curve. In formula 8 the angle equivalent to sin ^A would be the correct one to turn for the proposed sub-chord. When the radius of the curve has been determined and the p.c. (point of curve) exactly located, the distance is measured from the last numbered stake to the p.c. The stake here located is numbered, and the transit set up over it. If the p.c. is not at the end of an even chord length, it will be necessary to work out the deflection for the sub- chord, as shown under formula 7. The p.c. is the point of curve in the direction the survey is being run, and the p.t. (point of tangent) the end of the curve. The first deflection from the p.c. will be the angle J^Z) from the tangent line for the distance of the chord. If the second stake on the curve can be put in from the p.c., the angle required is added to the first angle and turned from the p.c. The distance, however, is measured from the last stake. This process continues as far ais can be staked out from the p.c., or until the p.t. is reached. The deflection angles should be added until they equal one-half the central PROJECTION OF HAULAGE ROADS 43 angle, which should intersect the p.t., if the work has been done correctly. The measurements are taken each time from the last stake. If it is impossible to see from the p.c. to the p.t. and all the intermediate points, the transit can be set on any in- termediate stake and the curve continued therefrom. When the transit is set up on the curve, the vernier is set at zero, backsighted on the last place over which the transit was set up and the telescope reversed. By turning the vernier to the last angle turned, the line will be tangent to the curve at the set-up, and deflection angles can again be added until the p.t. is reached. The transit should then be set up on the p.t. and can be again turned tangent by reversing the telescope and turning the last angle. The sum of the de- flection angles must equal one-half the central angle, and with the angles turned upon backsighting, equal the total central angle. The chords are always measured from stake to stake, as shown in Fig. 8, from p.c. to a, from a to b, b to c, etc. In all American handbooks for standard-gage track, and in formula 3 of the foregoing, all calculations, degrees of curve, etc., are based on the underlying principle that a 100-ft. chord determines the degree of curve. It is obvious that it is not very convenient to use this 100-ft. chord method with short-radii curves, and it is mathematically impossible to use it with curves of less than 50-ft. radius, as will be seen by formula 3. Many engineers have resorted to computing short tables for their own use for this class of work, but the majority of such tables are decidedly incomplete. If we assume, however, for the shorter-radius curve that a 1-deg. curve is one in which a 10-ft. chord subtends a 1-degree central angle, all the numerous labor-saving tables 44 MINE TRACKS developed in the standard fieldbooks can be adopted and applied to this work by merely moving the decimal point mentally one place. For example. A 1-deg. curve would then have a 573-ft. radius instead of a 5730-ft. radius; the long chords, externals, tangent distances, etc., would be one-tenth as great. The angle, of course, would not change. If a 10-ft. chord was thought too short for use, the long chord for two stations (or three stations, as desired) would be taken from the tables. Or if no standard fieldbook is at hand, the foregoing for- mulae may be used without any change with the exception of formula 3, which would, on the 10-ft. chord basis, be sin The table entitled " Radii, Degrees of Curve and Ordi- nates," appearing later, gives degrees of curve on this method for radii from 15 to 200 feet. It will be found convenient in most cases, when the radius on either the 100-ft. or 10-ft. chord plan corre- sponds to a fractional degree of curvature, to take the nearest degree and change the radius to agree therewith. For example, if the radius corresponded to 9 deg. 43 min., it will simplify the field work usually to make it a 10-deg. curve, and alter the radius, etc., correspondingly. CHAPTER IV GRADES In railroad work the number of feet of rise or fall per unit of distance is called the grade; the number of feet of rise or fall per 100 ft. horizontal, the per cent, of grade. On the surface the grade for locomotive traffic is de- termined, first, by the size of the locomotive and the number of cars it is required to haul; second, by the elevation it is desired to attain in a certain distance; and third, by the topography of the route. Underground, where the headings are driven on line, the grade follows the pitch of the heading, rope haulage and planes being introduced when the grade becomes too heavy for locomotive traffic. On the heavier pitching measures the gangways are usually driven on a regular grade, which follows the strike of the bed. In determining this grade, the drainage, haulage, and to a certain extent the loading of the cars, should be considered. In lightly pitching or rolling measures, before any lines for headings or chambers are adopted, the probable contours of the bed should be shown in advance of the workings, so that an idea of the grade that is likely to be encountered may be formed. A study of the contours and close attention to the grade as the heading advances will serve to forestall using the heavier grades requiring rope 45 46 MINE TRACKS haulage or the employment of other forms of haulage than locomotives or mules. A specific grade cannot be adhered to rigidly in the light pitching or so-called flat measures, but nevertheless more attention should be given to approximating this grade. Too often the workings are projected with very little consideration toward anything other than releasing a certain area of coal, the lines being followed regardless of the grade. This enta'ils high transportation costs. A combination of the line and contour method, while affording a less symmetrical layout, secures a more economic haulage. A good rule, applicable in many cases where headings are driven by alignment, is to first determine the lines as far as practicable to conform with both the area to be worked and the best possible grade, then to establish a maximum grade and give each line with the under- standing that this line shall be followed only so long as the inclination of the strata does not compel exceeding this grade. Should this inclination be encountered, fur- ther advices can be then given, based on the latest de- velopments, before the heading is continued. In the determination of a standard gangway grade for the gangways in the heavier pitching beds, the first requisite should be that the grade be sufficient to take care of the drainage and allow the water to maintain its channel free from any accumulations of silt or sediment. Good drainage is a requirement in any type of haulage, and in the maintenance of the ballast and trackwork it is a necessity. A ditch with a semicircular cross-section will have the greatest carrying capacity, while one with a half- hexagon cross-section is the nearest practical approach thereto for mine work. GRADES 47 The following is an approximation of Cutters' formula for ditches, / 100,000 r*s ~~^ 1 8r+15 in which V = Mean velocity per second; r Hydraulic radius; that is, the cross-section of the water in the ditch in feet, divided by the perimeter of the ditch in contact with the water; s = The slope; that is, the fall divided by the length. FIG. 9. Practical drainage ditch. The following table shows the carrying capacity and mean velocity for a ditch with a half-hexagon cross-sec- tion per foot of bottom width. (See Fig. 9.) Grade per 100 feet Mean velocity in feet per second Cubic feet per second Cubic feet per minute Gallons per minute 4 in 1.84 2.39 143 5 1,075 6 in 2.25 2 92 175 5 1,315 8 in 10 in 2.60 2.90 3.38 3.78 202.5 226 8 1,520 1,700 12 in 3.19 4 14 248 4 1,863 A wide, shallow ditch with the same cross-sectional area and grade will have less current velocity, will carry less water, and will choke up much more easily than one of a narrower and deeper form. The velocity should not 48 MINE TRACKS be less than 1J^ ft. per second, or the suspended particles will be precipitated along the bottom of the ditch. Where drainage is not the prime consideration, a theo- retic grade can be computed, whereby the slope of the road in favor of the loaded cars will compensate for the extra resistance due to the additional weight. In other words, a proper utilization of the grade will allow the drawbar pull on a trip of loaded cars to equal that of an equal number of empty cars. The motor or mules will thus be able to pull as many cars from the face loaded as were brought in empty. The prevailing grade in mines where it is possible to establish a grade with no consideration but that of haul- age runs from 4 in. to 6 in. per 100 ft.; that is, a 0.33 per cent, and 0.5 per cent, grade respectively. Within the last few years it has been realized that this grade is rather too light unless some type of anti-friction bearing is used. Accordingly, many companies have fixed their standard gangway grade at from 6 in. to 10 in. per 100 ft. It is obvious that the greater the difference in weight between an empty and loaded car, the steeper should be the grade in favor of the load to overcome the greater resistance due to the load. The amount of track resistance is almost proportional to the weight on the rails, and as the modern practice has been to enlarge the capacities of cars, the grade should likewise be augmented following any increase in car loading; or the additional resistance from the increased load should be overcome by reducing the journal friction by an improve- ment in the bearings. The following example will illustrate the usual method of computing the theoretic grade which will equalize the drawbar pull on empty and loaded cars. GRADES 49 Example. A certain colliery has in use all-steel cars weighing empty 5080 Ib. each and loaded with coal an aver- age of 12,230 Ib. As the track is dirty and not very well laid, the total frictional resistance will be assumed as 30 Ib. per ton for an empty car and 25 Ib. per ton on a loaded car; in other words, the coefficient of friction (or ratio of the resistance to the weight) will be 0.015 and 0.0125 respectively. It is desired to find the grade that will equalize the draw-bar pull on an empty car with a loaded car. Let = The sine of the angle of the desired grade; W = Weight of empty car; W = Weight of loaded car; C = Coefficient of friction for empty car; C" = Coefficient of friction for loaded car; then (W C) + W sin = (W C') - W sin Substituting values in the above case, (5080 X 0.015) + 5080 sin = (12,230 X 0.0125) - 12,230 sin 0. 76.2 + 5080 sin = 152.875 - 12,230 sin 0. 17,310 sin = 76.675, sin = .00443, . which multiplied by 100 will give the rise in 100 ft., which is 0.443 ft., or 5^ in. On straight track, with 5J4-in. grade per 100 ft. in favor of the load, a mule would be able to pull as many loaded cars out as it could pull empty cars in the opposite direction. The preceding formula does not consider the weight of the motor or locomotive, the effective weight of which will also depend on the grade. If in the foregoing example we wished to use an 8-ton 50 MINE TRACKS motor having a tractive effort of 3000 Ib. on the level, and secure an equal draw-bar pull and maximum loading, the formula will be somewhat different. Let M = Weight of motor; F = Tractive effort of motor. Then F + M sin < F - M sin < (TF'0) - W sin (WC) + W sin Solving, = 5 in. per 100 ft. With the same motor compelled to handle cars loaded with rock, the formula in order to make the grade balance the extra resistance of a full trip of rock, the weight of each car being 17,000 Ib., would be, letting W" = weight of a loaded rock car, F + Msin F - M sin (W'C')~- W"sin~(WC) + Wsin or = 7 in. (almost) per 100 ft. The grade on straight track should then be between 5 and 7 in. per 100 ft., and the above motor would be able to pull in about 28 empty cars and the same number out, loaded. When it is considered that curved track makes up a large portion of every gangway and that the tracks are dirtiest immediately after the cars have been loaded from chutes (all of which has a greater effect on the loaded car), it will be apparent that this theoretic grade should be increased to assist in overcoming these contingencies. Other considerations that would still further increase GRADES 51 the grade in favor of the load are the usual methods pursued in panel mining and the loading of the cars. It is customary in panel mining to drive the coal gang- ways first, and when they have advanced far enough to begin robbing, to tunnel to a haulage gangway, cutting off the outer section. This frequently increases the length of the tunnels and necessitates a proportionate decrease in the grade of the haulage. As a consequence, where the tunnels are long, the inclination of the haulage road, which by all means should have the best grade, is much reduced, and wet roadbed, choked ditch and small trips naturally result. Since the installation of mechanical haulage in mines loading from chutes, the loaders are compelled to move the cars at the loading places by their own efforts. Four cars per trip are not infrequently loaded from one chute. On the lighter grades, to move the cars sufficiently to accomplish this loading would require an additional man, and to forestall .this expense the foreman resorts to increas- ing the grades immediately beneath the chutes and inserting an equalizing diminution between them. This expedient facilitates the loading of the cars, but renders the roadbed a succession of flat places and inclines, with pools of water in the "dead spots." It raises the haulage cost, destroys the rolling stock and imparts a bumping and jerking to the cars in motion. It is needless to state that a proper grade would remove the necessity for this distortion. In the gangways where the grades have been produced by trusting to the judgment of the workmen, the inclination usually is from 8 to 12 in. per 100 ft., and I am inclined to believe that these grades have more to recommend them than the lesser ones. One objection to the heavier grade is that its first in- 52 MINE TRACKS jog MDJQ spunoj GRADES 53 54 MINE TRACKS stallation reduces the available lift as the gangway ad- vances; this, however, will remedy itself in all subsequent levels. In the case of light pitching beds, increasing the grade of new headings may mean a too serious shortening of the available lift, and in those headings already driven the flat grades will limit the length of the trip. These objections, as well as that arising from the necessity of moving the cars while loading, can be overcome to a great extent by the use of bearings that reduce the journal friction. An improved type, such as the Hyatt roller bearing (as has been demonstrated by dynamometer tests), will require on the level but about 40 per cent, of the draw- bar pull necessary with the common type of bearing, or conversely, on the level a motor will pull 2^4 times as many cars if they are equipped with antifriction bearings as it will if plain bearings are used. The accompanying charts, Figs. 10 and 11, are from actual tests and show the draw-bar pull of roller bearing and plain bearing cars. Both tests were over the same run. The low starting effort required for the improved bearing should be noted. The grade formula will have to be applied to determine the results for level track. Substituting in the formula, and using the same weights : (WC) + (W sin ) = (W C") - (TF sin 0) (5080 X 0.006) + 5080 sin = (12,230 X 0.005) - 12,230 sin 30.48 + 5080 sin = 61.15 - 12,230 sin 17,310 sin = 30.67 Sin = 0.00177. This multiplied by 100, will give the per cent, of grade, which is 0.177 ft., or 2% inches. Thus with suitable antifriction bearings it would require GRADES 55 on a grade of 2^ in. per 100 ft. the same effort to move a loaded car with the grade as is required for an empty car moving against it. The antifriction bearing will run several months on one lubrication, thereby eliminating to a great extent the embarrassment of stiff cars and the employment of car oilers. They will be found advantageous in locations where the available elevation for compensating grades is limited and in reducing the elevation required for the car planes in overcoming differences in grade, also on light pitching slopes where the cars are barely able to drag the rope, and in eliminating men required for pushing around dumps, shaft landings, and tipples. CONSTRUCTING GRADES Grades on the surface are secured by running levels over stakes set at regular intervals and then marking upon the stakes the cuts or fills required to reach the grade selected, to which the surface is then cut or filled. In the flat measures underground, the headings are generally driven on line, the grade of the heading being the profile of the bottom rock along the line of heading. In the gangways or headings which are not driven on line, it is apparent that neither of the methods given can be used; by the first method the heading would have to be already driven before the grades could be run and marked; by the second method a line would have to be given, which, of course, would be impossible in the heavy pitching seams. Under this last condition, and also for tunnels, the grade is extended by means of a grade board; that is, a board equipped with a spirit level set in its top, or with a plumb-line which hangs from an upright in the center of the board. The grade is carried by having one end of the board 56 MINE TRACKS higher than the other, this extra height being the amount that the grade in question would rise or fall in the length of the board. This extra height is known as the "toe." Grade boards are usually cut in fractional lengths of 100 ft., such as 6J4 ft., 10 ft., 12^ ft., etc., so that the toe can be readily calculated and the board will be of a length convenient for use. The following table gives the toes to the nearest KG m - f r a 10-ft. grade board on grades from per cent, to 10 per cent. : TOES FOR 10-FT. GRADE-BOARD FROM TO 10 PER CENT. EVERY ^6 IN. Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. 0.00 2.00 2Kfi 4.00 4 1 K 6 6.00 iy. 8.00 95^ 0.05 Me 2.05 / 1 D 2^ 4.05 /ID 4% 6.05 1 /4: 7^6 8.05 47 ' O 9% 0.10 H 2.10 2% 6 4.10 4% 6.10 7% 8.10 m 0.15 Me 2.15 2% 4.15 5 6.15 7Ke 8.15 9% 0.20 H 2.20 2^6 4.20 5He 6.20 7^ , 8.20 9% 0.25 5 /16 2.25 2% 4.25 5^ 6.25 7% 6 8.25 9% 0.30 H 2.30 2^6 4.30 5Ke 6.30 7% 8.30 9^16 0.35 KG 2.35 2% 4.35 sy 6.35 7% 8.35 10 0.40 H 2.40 2% 4.40 5^L6 6.40 7% 8.40 lOHe 0.45 X* 2.45 2% 4.45 5% 6.45 7^6 8.45 IOH 0.50 H 2.50 3 4.50 5Ke 6.50 7% 8.50 IOM^ 0.55 % 2.55 3He 4.55 5K 6.55 7^6 8.55 io>i 0.60 H 2.60 3M 4.60 5% 6 6.60 7^6 8.60 IOK^ 0.65 % 2.65 3%6 4.65 5^ 6.65 8 8.65 10% 0.70 7 /8 2.70 3^ 4.70 5^6 6.70 8He 8.70 lOKe 0.75 15 /16 2.75 3^6 4.75 5^ 6.75 8^ 8.75 10^ 0.80 1 2.80 3% 4.80 5^6 6.80 8^6 8.80 10% 6 0.85 iHe 2.85 3Ke 4.85 5% 6.85 8M 8.85 10% 0.90 IH 2.90 3H 4.90 5^6 6.90 8^6 8.90 10% 0.95 1^6 2.95 3Ke 4.95 5^6 6.95 8% 8.95 10% 1.00 IH 3.00 3 5.00 6 7.00 8Ke 9.00 10^6 GRADES 57 TOES FOR 10-FT. GRADE-BOARD FROM TO 10 PER CENT. EVERY IN. (Continued) Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. Per cent. Toe, in. 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 w 1% 1% 2% 2 3 -{ 6 2^6 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 3% 3We 3% 3% 3 We 4 4% 5.05 5.10 5.15 5.20 5.25 5.30 5 . 35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6% 6^6 i 6% 6% 6W 6 7^6 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8% 8% m 8 Wo 9 9^6 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 9.45 9.50 9.60 9.65 9 70 9.75 9.80 9.85 9.90 9.95 10.00 11 12 Another convenient way is to make the level board 100 in. long. The required grade per cent, expressed in feet is then equal to the toe required in inches; the length of the board is to 100 ft. as 1 is to 12, or as 1 ft. is to an inch. For Example. On a grade board 100 in. long, if the grade required is 0.75 per cent., the toe is 0.75 in., or % in. The toe ends of grade boards are given some dis- 58 MINE TRACKS tinguishing mark to avoid confusion, particularly in the flatter grades. Wherever possible, gangways and headings should be driven on a calculated grade, or approach as closely thereto as is practical. This should be done if only for the sake of haulage, but its importance in the event of future de- velopments warranting a tunnel to connect parallel haulages, or in case of panel mining, is inestimable. A system of headings or gangways graded to conform with one another will save many regrets and afford many economic possibilities. On the surface, especially where the adopted grade is a factor in limiting the length of the trip of cars, the inclina- tion on curves should be reduced; so that the grade allowed on the curves plus the resistance due to curvature will equal the grade on the straight track. The compensation or allowance for curvature is usually spoken of in terms of the grade proportional to the degree of curve as discussed under the most economic radius to use underground, page 34. For Example. If the prevailing grade for the road is 2.5 per cent., then on a 100-ft. radius, or 57-deg. curve, the compensation per 100 ft. would be 57 X 0.010 to 57 X 0.025, or 0.6 to 1.4 ft. respectively, depending on the particular cars used. The grade on the curve should be 1.9 to 1.1 ft. per 100ft. CHAPTER V GRAVITY GRADES In the vicinity of shafts, slopes, planes, etc., where cars are required to move without any mechanical aid, it is customary to depend on gravity for their movement. It is impossible to adopt a gravity grade that will work equally well with all the cars; a grade upon which some cars will run smoothly will permit others to run away and will not be sufficient for still. others. Most of this difficulty arises from the oiling of the cars, the flat wheels developed in many instances, the nonuniform condition of mine cars in general, and the temperature and the weather. The grade in the immediate vicinity of a shaft should be sufficiently steep and long enough to permit the car to gain headway quickly, and bump off the car delivered to the landing. If an empty car is to drive a loaded one off the cage, greater allowance should be given than if the re- verse was the case. While no absolute rule can be given, a loaded car on a grade of 5 per cent, for 12 ft. will be found in most in- stances to work well for removing empties from the cage. When the cage floor is inclined in favor of the car motion, a 2 per cent, to 2.5 per cent, grade with occasional assistance from the cage tender has given satisfactory results. With the empty car driving off the loaded one, a grade of 5 per cent, for 20 ft. should be allowed; or with occa- sional help from the foot- or headman, a 2.5 per cent, to 3 per cent, grade. 59 60 MINE TRACKS The grade of the track leaving the cage should be about 2 per cent, to 2.5 per cent, in order to assist the car in leaving the shaft quickly. It is customary to have about 50 ft. in the vicinity of the shaft, plane or slope landings somewhat steeper than the minimum grade required for the car to start unassisted, so as to expedite handling the cars. The remainder of the turnout grade should run about 1.5 per cent, to 1.7 per cent, for loaded cars and from 1.6 per cent, to 1.9 per cent, for empty cars, on the straight track. A stretch of 50 to 100 ft. should be made level at the end of the turnout to retard motion and prevent the cars from running upon the main track. When a curve occurs on a gravity grade, the compen- sation should be reversed; that is, the compensation should be added to the regular grade used for the tangents in order to 'allow for this curve resistance. The method of computing compensation has been treated previously. To illustrate: If the grade for straight track was 1.6 per cent, on a 100-ft. radius, or 57-deg. curve, the compensation should be 0.6 to 1.4 ft. per 100 ft. The grade on the curve would thus be 2.2 to 3 per cent. Experience will determine the proper allowance to use for the cars employed. Cars with the wheels turning loose on the axles will require a less compensation than those having the wheels keyed to the axle. The curve friction which the compen- sation is intended to equalize is due to the pressure of the flanges and the sliding, both lateral and longitudinal, of the wheels on the rail head. In order to secure an easy running curve, three considera- tions are necessary: First, to elevate the outer rail to GRAVITY GRADES 61 allow for the centrifugal force of the moving cars; second, to widen the gage of the track; third, to ease the approaches to the curve. The elevating of the outer rail is termed the super- elevation, and its amount is dependent on the velocity at which the cars are to travel, the radius of the curve, the gage of the track and the weight of the cars. This superelevation may be computed from the formula: = 32.16# in which = Superelevation required, in inches; V = Velocity at which the cars are to travel, in feet per second; g = Gage of the track, in inches; R = Radius of the curve, in feet. The numeral 32.16 is the force of gravity. By the foregoing formula the superelevation for a velocity of 6 miles per hour (the maximum velocity allowed by law in a number of states for haulages underground) and a 30-in. gage track should be as follows : For a 40 ft, radius curve 1% in. For a 50 ft. radius curve \% in. For a 60 ft. radius curve \y in. For a 80 ft. radius curve l % in. For a 100 ft. radius curve M in. For a 150 ft. radius curve ^ in. For a 200 ft. radius curve % in. This superelevation varies directly as the gage, so that if the gage was 40 in., the superelevation would be 4 %o> or 1^ times as great; or for 20 in. 2 Mo> or % as great as that shown in the table. 62 MINE TRACKS The elevation varies, as will be noted in the formula, as the square of the velocity; that is, if the velocity is 12 miles per hour, instead of the figure for 6 miles per hour, for which the table was computed, the superelevation would be ( x %) 2 or 4 times as great. FIG. 12. Well-laid narrow-gage reverse curve. For Example. If the gage was 40 in. and the velocity 12 miles per hour, the superelevation would be 4 9lo X (i%)2 = 1^ x 4, or 5>i times that shown in the table. The maximum superelevation, however, should not exceed about }/i of the gage. In applying the superelevation the best practice is to start same a distance back along the straight track ap- GRAVITY GRADES 63 preaching the curve and give the outer rail the elevation gradually, and at the same time start to gently curve the track, increasing the curvature more and more until when the curve proper is reached it will have the required maximum curvature and full superelevation. The distance used to reach the full curvature and super- elevation will depend largely on the amount of straight track on either approach to the curve; where possible, it is good practice to elevate 1 in. in the length of a rail and apply the curvature in the same distance. To gain a super- elevation of 2 in., would mean starting two rail lengths in advance of the nominal curve and achieving the elevation in that distance. When the superelevation and curvature are applied skillfully, there should be no jar to the traffic when the curve is reached. The maximum speed should be used in figuring the super- elevation. This increase in height of the outer rail when within safe bounds tends to reduce the curve resistance. When the cars are moved by rope in both directions over a curve the inner rail should be elevated instead of the outer, as the motive force tends to draw the cars toward the inside of the curve. When they are pulled by rope and allowed to return by gravity, pulling the rope with them, the outer rail should be raised but not to the full superelevation. INCREASING GAGE OF TRACK ON CURVES The cars in traveling around a curve do not move con- centric to the axis of the curve, as is commonly supposed, but rather in a series of short tangents. Fig. 13 shows the normal position of the wheels in traveling around a curve. One front wheel hugs the outer rail while the opposite 64 MINE TRACKS back wheel tends to hold to the inner rail. The friction resulting from the action of the front outer wheel of course cannot be avoided; the flange friction of the hind inner wheel, however, can be reduced or eliminated by widening the gage of the track. The position that the rear axle and wheels will assume when free to move is radial to the curve, so that when the gage of the track is increased sufficiently, * ~ Gauge of Track > < Gauge on Curve ^ Radius _J | ^ 1 ^ 1 I 1 ! 1 FIG. 13. Position of car wheels on a curve. no friction will result from the lateral pressure of the rear inner wheel flange against the rail. Another reason why the track gage should be increased on curves is that if any advantage is realized from the coning of the tread on the car wheels in consuming the extra length of the outer rail (which is very doubtful, as the position assumed by the rails bears no relation to that required by the coning), it can be better effected by permit- ting the lateral action necessary. GRAVITY GRADES 65 Also, as the hind lateral pressure is reduced, there is less force tending to narrow the wheel gage and produce an excess play on the axles, which trouble is quite common where the wheels revolve on the axle. The distance which the gage of the rails can be increased is small, depending on the widths of the wheel treads, the condition of the wheel gage and the radius of the curve; one in. is about the maximum with ordinary rolling stock. The distance which the rear outer wheel stands from the outer rail on a curve, is the theoretic distance that the gage should be widened, and is equal to the versed sine of the chord subtended by twice the length of wheelbase. Expressing this relation as a formula: Let / = Theoretic distance in feet that the gage should be increased beyond the gage of the car wheels ; L = Length of wheelbase of the cars, in feet; R = Radius of curve, in feet; A = Angle subtended by the wheelbase. sin A = p K Then I = R vers sin A. For Example. If the car has a 5-ft. wheelbase, the theoretic distance the gage should be increased on a 1-deg. curve is: sin A = ^^- A = degrees 3 minutes. 7 = 5730 vers sin A = 0.0022 ft.; in which 5730' = radius of a 1-deg. curve, and 1 cos A = vers sin A . 66 MINE TRACKS This increase in gage should be applied gradually, as explained under superelevation. The theoretic distance required in excess of the wheel gage is as follows: Radius, ft. Wheelbase 1Yt ft. Wheelbase 3 ft. Wheelbase Wheelbase 4 ft. 40 H in. 1% in. 1% in. 2 3 6 in. 50 % in. \M in. !}- in. 2 in. 60 % in. % in. 1M in. 1% in. 75 1 A in. % in. 1 in. 1M in. 100 % in. %6 in. Y in. 1 in. 150 /i in. % in. /^ in. % in. 200 2i6 in. y\ 6 in. % in. ^ in. The foregoing distances apply to the wheel gage, not the track gage, and as mentioned before the increase above the track gage will hardly be permitted to exceed 1 in., unless the treads are unusually wide. Taking the case of a 50-ft. radius curve with a 3j^-ft. wheelbase, the track gage being J^ in. greater than the gage of the wheels,, the theoretic increase is \Y^ in., which, as there is J in. allowance between the track gage and the wheel gage, and the treads of the wheels permit another inch, the full increase can be given. . With a 4-ft. wheelbase and J^-in. play between the gages on a 40-ft. radius curve, if 1 in. above track gage is allowed, there will be %-in. deficiency. This deficiency will have a resisting effect equal to the force required to move the weight on the hind wheels % m - over the length of the curve. GUARD RAILS When guard rails are necessary on curves they should be placed parallel to and at such a distance from the inner GRAVITY GRADES 67 rail that they will restrain the flange of the front wheel from running over the head of the outer rail. Where the wheels are not true to gage, as is often the case with loose wheels, the guards in this position are not very effective. Placing the guard at a distance equal to the tread of the wheels on the outer side of the outer rail and about 1 in. higher is often resorted to. With rope haulage, the guard should be placed at a distance equal to the width of the tread outside the inner rail. At the bottoms of slopes and similar places, since the force is contrary in hoisting and lowering, the guard should be placed outside of both rails. On planes and slopes it is good practice to have guards even though the track is straight. Such guards are usually made of wood and covered with flat or angle iron, and are made as high as the axle and journal box will allow. The type of journal and oil-box used on the cars, together with local conditions, will determine whether the guards should be placed inside or outside of the rails. If the guards, when placed outside the inner rail of the curve, are made of "T" rail, and are spiked to ties distinct from those supporting the main rails, they can be more readily brought back to the tread distance as they wear or are forced out of alignment. If the same or a lesser weight rail is used for the guard rail, than for the main rails, the requisite elevation above the main rails is usually obtained by notching the guard rail ties directly under the one main rail. CHAPTER VI FROGS AND SWITCHES The standardization of turnout equipment furnishes a fertile field for improvement; both time and equipment can be economized and at the same time better results obtained. FIG. 14. Typical plate frog of uniform length for varying weights of rail. In the preparation of standards, every effort should be made to achieve simplicity the adoption of three or four different numbered frogs with possibly two switches of different lengths that can be installed to suit most conditions, if a little forethought is used in laying out the work, will be found ample. The use of a frog of a certain number for chamber work, another for general cases other than the chambers, and a 68 FROGS AND SWITCHES 69 third for locations subject to heavy traffic and high velocity will be sufficient except for special cases. Plate frogs should be designed so they can be made, should the necessity arise, at the colliery blacksmith shop, although ordinarily it will be found advisable to purchase such frogs from a manufacturer who specializes in this kind of equipment. The reasons for this latter choice are, of course, obvious. If the mine employs various weights of rail, by designing a certain number of frogs the same length for the different weights, the one turnout standard will apply. This will also permit in an emergency the replacing or temporary installation of any frog of a certain number with rail of different weights. With this idea in view, a No. 4 frog would be the same length, whether made of 30-, 40- or 60-lb. rail. Fig. 14 shows a typical frog design for a No. 3, 4 or 6 frog to be used with any weight rail up to and including 60 Ib. per yard. The length of the frog must be suffi- cient to permit the easy application of the angle bars. FIG. 15. While frogs are sometimes lettered or numbered ar- bitrarily, the generally accepted practice is to designate the frog by the number found by dividing the length by the spread; that is, the frog number is the ratio of the length to the spread. Thus, referring to Fig. 15: 70 MINE TRACKS Let L = Double or entire length of the frog; A = Spread between gage side of rails at one end of the frog; B = Spread between gage side of rails at the other end of the frog. Then the frog number equals -i '^, or the frog number A. ~f~ JD L' equals -r' If L is measured in inches, then A and B should be in inches; and similarly, if L is in feet, A and B should be in feet. The use of the cast frog is not to be recommended with locomotive haulage, and even with mule haulage and light rail it should be restricted to chamber or room work. While the initial cost of the cast frog is less than for the built-up frog, it will not wear as well; the point breaks off or wears down in a short time; it does not permit an efficient con- nection with the rails; it wears down quickly and con- tributes to many derailments. Many companies require the face of such frogs to be chilled in order to increase the wearing qualities. Fig. 16 shows a shrouded cast frog; the shrouded type being found much superior to the ordinary casting in the pre- vention of derailments. The shroud precludes the possi- bility of the flange hitting the frog point or taking the wrong flange channel when passing from the throat of the frog. It will be noted that the shroud is cast about 1 in. higher than the frog, and at such a distance from the gage lines that the shroud engages the outside of the wheel tread a short distance before the point is reached. The use of the usual guard rail on the inner side of FROGS AND SWITCHES 71 * SECTION ff-A FIG. 16. Plan of shrouded cast frog. FIG. 17. Tee rail shroud with spring. 72 MINE TRACKS the opposite rail is not so positive in its action as the shroud even for wheels tight on the axles, and with the play common to wheels loose on the axles, the guard rail is extremely unreliable. Moreover, the shroud is cheaper and easier to install than the guards. A similar shroud has been found satisfactory with the plate or built-up frog, particularly with the long throats of those of a larger number. If the tread of the locomotive is the same as that of the cars, the shroud is riveted to the plate; otherwise, the SECTION A~A FIG. 17A. Plan of spring-rail shroud frog. shroud is held in the position required for the cars by a spring, which the locomotive pushes back when passing. It will be noted that one spring will serve for either a single or double shroud (see Fig. 17). Fig. 17 A is a plan of a shroud built of ordinary tee rail, the elasticity of the rail constituting the shroud maintaining it in position. In designing either plate or cast frogs, the flange channels should be made as narrow as the flanges of the wheels FROGS AND SWITCHES 73 will permit. There are two objections to a wide flangeway: First, the diameter of the wheels of mine cars is compara- tively small, so that instead of spanning the gap between the point and the wing they drop partly into it, jarring the cars and wearing out the frog; second, the wider the flange- way the longer will be the ''throat" of the frog that is, the distance between the point and the "wing" and the wheels in traveling over the throat, especially of the frogs of Eccenfrlc Lever ^Eccentric FIG. 18. large number, are more liable to depart from their proper course and derail the car by striking the frog point or by taking the wrong flangeway. As stated before, the guard rail placed near the opposite rail cannot be depended upon when the cars have loose wheels. The short length of mine frogs does not adapt them for having one wing on a spring, as may be the case on standard-gage tracks; and further- more, wheels loose on the axle would not operate a spring frog. 74 MINE TRACKS Fig. 18 shows a form of frog built to avoid the gap in the usual type. It is generally connected with the switch lever, so that whichever way the switch is set the frog will be in proper relation. The tongue is held by a pin which allows it to swing to fit either of the rails. About 3 in. are left between the ends of the rails the tongue is made sufficiently long to reach from the frog point and make a close joint with the ends of the rails. This arrangement has been found to work well in pre- venting derailments where cars are pushed. On switches where the cars run always in one direction (E to F in the figure), the cars themselves set the frog point. This movable frog point will usually outlast the ordinary type. In frogs for crossings over other tracks, the flange- ways should be made as narrow as the mine cars will permit. If the mine cars are equipped with wheels which run loose on the axle, the angle of the crossing, if possible, should not be less than 10 deg.; otherwise, derailments may occur when passing through the frogs toward the point. SPLIT SWITCHES AND LATCHES The length of the switch point should be in conformity with the radius of the turnout curve and the speed and character of the traffic. The tapered end of the switch is known as the point; the blunt end, the heel. The switch made of tee rail is termed a split switch; that made of a bar of iron which turns on a pin near its heel is known as a latch. Switch points are designated right and left hand and are not inter- changeable, the right and left hand being determined by standing at the switch point and facing toward the frog. When ordering a single switch point, its position, right or FROGS AND SWITCHES 75 left, must be given. No distinction is necessary with latches as they can be reversed and used for either side. Split switches for mine work should be straight, not curved, so that any pair of mated switch points can be used on a right- or left-hand turnout. When light rail switch points are curved, they frequently break a short distance from the point. The split switch is usually longer than the latch and is operated by a lever. It thereby makes a more efficient bearing against the rail and affords a smoother haulage than does the latch. It is known as a rigid split switch when used without a spring, and as a spring switch when a spring is employed. The spring makes the switch auto- matic and is profitably used at turnouts when the traffic is in one direction. . For ordinary use underground, the spring, if not properly cared for, clogs with mud and is no better than the rigid switch. The bolts attaching the rods connecting the switch points should be sufficiently low so that when the treads of the motor wheels are well worn the flanges will not cut the bolts. It is often advisable to attach the connecting-rods to the flange of the switch points rather than to the web. The latches in general use on mine tracks run from 2 to 5 ft. in length and the split switches from 5 to 10 ft. Due to its easy and cheap installation, the latch is much used for mule haulage and chamber work. The use of the stub switch has been limited around mines. It is assumed that it is a simple curve from the point of the stub to the point of frog; the lead being found by multiplying twice the gage by the number of the frog and the radius by multiplying twice the gage by the frog number squared. For example: If the frog is a No. 3 and the gage 3^ ft., the lead is 21 ft. and the radius 63 ft. 76 MINE TRACKS The following table gives the angles corresponding to the various length switches and frogs: Frog no. Frog angle Split switch lengths, ft. Switch angle for 5-in. throw; switch, J^ in. at point Deg. Min. Deg. Min. M 33 12 5 4 32 2 28 56 5% 4 08 2% 23 04 6 3 | 47 3 19 12 6;Hj 3 27 3H 4 16 14 25 22 7 3 3 15 01 Y 2 12 46 8 X 2 50 5 11 30 9 2 31 5/^ 10 26 10 2 16 6 9 34 7 8 10 . . 8 7 09 FIG. 19. Dimensions of plate frog of 25- to 60-lb. rail. FROGS AND SWITCHES 77 The accompanying tables give dimensions for frogs from No. 3 to 5H for rail from 25- to 60-lb. weight per yard : STANDARD RIVETED PLATE FROGS FOR 25-LB. RAIL 6 c 2 Frog angle jl |j "8 1. 2. General Dimensions IS "s! s A B c D E F G H J Deg. Min. In. In. Ft. In. In. In. In. In. In, In. In. Ft In. In. 3 4 5 19 16 14 12 11 10 12 25 22 46 30 26 IK IK IK || 2 2 2 2 21 24 3 3 6 9 15 15 18 18 18 21 5 4% 2 4> 4 3X 3^6 7 6% 6 6 6 K i 5 5^ 6% 9 9 9 9 9 9 16 16 16 16 16 16 2 2 3 3 24 24 6 6 6 |\w \w \w \ec \ \t od\ o*\ otfx OK otfs o!s STANDARD RIVETED PLATE FROGS FOR 30-LB. RAIL 3 11 Li General Dimensions | n "S 03 * % * "* 03 > 1 CQ^ A B C D E F G H J 04 Deg. Min. In. |"In. Ft. In. In. In. In. In. In. In. In. Ft. In. In. 3 19 12 m K 2 3 18 6 9 K 4H 9 16 24 H 3>3 16 25 IK K 2 6 21 6 8% 6 % *K 9 16 24 X 4 14 22 IK K 2 9 21 5K &K 1 5^ 9 16 2 6 X 4> 12 46 IK 3 24 5H 8 i>| 6>^ 9 16 2 6 X 5 11 30 IK K 3 3 24 4* Me 7Me IK 6K 9 16 3 X 5H 10 26 IK H 3 6 24 4 7% IX 7>^ 9 16 3 6 X 78 MINE TRACKS STANDARD RIVETED PLATE FROGS FOR 40-LB. RAIL a % 1 11 "o General Dimensions o ^ *o 0> 1 55 2 g.g 11 0> JM Q'C A B C D E F G B. J s Deg. Min. In. In. Ft. In. Ft. In. In. In. |ln. In. In. In. Ft. In. In. 3 19 12 IK H 2 9 2! 7 11 K 4% 9 16 24 H 3> 16 25 IK >S 3 24 6 2 ^J2 10K K 5K 9 16 24 K 4 14 22 IK M 3 3 24 6 9K 1 6>3 9 16 2 6 H 4H 12 46 IK M 3 6 2 3 6 9^6 IJ-i 7K 9 16 2 6 >6 5 11 30 IK H 3 9 2 3 5% 9 IK 8J-6 9 16 3 H 5M 10 26 IK H 4 2 3 4^6 8K IK 9 9 16 3 6 M STANDARD RIVETED PLATE FROGS FOR 45-LB. RAIL e | ii General Dimensions | o S5 1 2 I 9 rt M 02 -^ ll 1?; A B C D E F G|H J Deg. Min. In. In. Ft. In. Ft. In. In. In. In. In. In. In. Ft. In. In. 3 19 12 IK H 2 9 24 8 11 K 5K 10 18 2 6 }* 3H 16 25 IK % 3 24 6K 10K K 6>^ 10 18 2 6 M 4 14 22 IK % 3 6 21 6 iOH 1 7 10 18 3 M 4M 12 46 IK % 3 9 2 3 6 10 1J-^ 7K 10 18 3 6 H 5 11 30 IK % 4 2 3 5Jie 9% 6 'lK 8K 10 18 3 6 M 5>^ 10 26 IK y* 4 3 2 3 4iMe! 9K 1% IOK 10 20 4 K STANDARD RIVETED PLATE FROGS FOR 60-LB. RAIL fa General Dimensions 1 g % *" % r\ *O Q _e V a 4J OQ " M 5? "^2 3 1 JM g'C A B C D E F G H ' J s Deg. Min. | In. In. Ft. In. Ft. In. In. In. In. In. In. In. Ft. In. In. 3 19 12 2 % 3 24 8 12 K 6% 10 20 2 6 H 3M 16 25 2 % 3 G 24 12 % 7% 10 20 2 6 H 4 , 14 22 2 % 3 9 24 6 11^6 1 8> 10 20 3 H 4>6 12 46 2 % 4 2 3 6 10% IK 9K 10 20 3 6 % 5 11 30 2 4 3 2 3 5Ke 10% IK 10% 10 20 3 6 % &H 10 26 2 % 4 9 2 6 5Jf 1% 11% 10 20 4 % NOTE. Rivets to he countersunk on bottom side of bottom plate; frogs to be drilled for standard splice bars. 80 MINE TRACKS The assumption that a turnout is a simple curve from the point of switch to the point of frog is no longer tenable. By the simple curve theory, the lead was found by multi- plying twice the gage by the number of the frog; the radius of the curve by multiplying twice the gage by the square of the number. The above, of course, ignores the fact that the frog is straight and not curved, and the switch points are, especially for mine work, also straight. In standardizing the switch design, the frog numbers to be used and the length of switch point to accompany each frog should first be determined. The design of each frog and switch proposed should be gone into thoroughly and the types adopted rigidly adhered to. Local conditions will determine the frog angles and switch points most suitable. Companies purchasing their equipment from manu- facturers will find it advisable to state the frogs and switches they propose to use and have the builders of such equip- ment furnish designs of the entire turnout. For the con- venience of the companies who make their own frogs and switches, the following formulae are given. Referring to Fig. 20: Let = Angle of switch points; F = Angle of frog; G = Gage of track; B = Length of wing rail; C = Chord of connecting rail arc; S = Length of switch; L = Length of lead; R = Radius of center line of turnout curve; H = Connecting rail length; D = Distance from theoretical to actual frog point. FROGS AND SWITCHES 81 82 MINE TRACKS Then G B sin F S sin Or G-BsinF-H cos*- cos F L = (R+ y^G] (sin F- 0) + B cos F + S+ DC. Table I has been worked from the foregoing formulae the actual shape and size of the frog and switch are used a simple curve connecting the heel of the switch with the end of the frog. The dimensions in the table, of course, are only ap- plicable to turnouts having the same switch lengths and the same wing rails used in the table. As stated before, to a certain extent the frogs made from different weights of rail can be made the same dimensions, so that one turn- out design for any frog of a given number will be sufficient. Similar tables should be furnished the trackman for the various turnouts to be installed. Some trackmen, instead of using the actual length of the frog from the point to the end of the wing rail (B in the formula), prefer to have a tangent from the point of the frog for a distance not less than a few inches greater than the wheelbase of the mine cars used. This is done in order that both wheels of the car may be traveling in a straight line before the point is reached; and if this is desired, B in the formula should be made equal to this distance. Naturally, where the length of the wing rail is greater than the wheel-base, the length of the wing rail should be used. To determine the angle of the switch points or latches, the heel distance which should be 4 to 5 in., is divided by FROGS AND SWITCHES 83 i 1 * ^ 6 i \C-J CO \P5 N \CO <0 \M t^O O O N'* \^i \oo \ F-\ n\ ^\ \ w\ KJ\ rt ^ <0 \ \r< V* \ V* V* \ OOOCOCOU5O5r-l \oo \H" K5\ M\ FROGS AND SWITCHES 85 Soi 'ON V- \rt VH r4\ r-K \M \ H rt \ t-\ VH V* \ \00 \* \* \00 \00 V(l \* \-H t-\ W\ r-\ 3\ F^N i^\ PJS K5\ ooot^-ojioooeooo '-iweoo'-iN.^H rH ,H ^-f rH (N -50' Curve; then 2*-5?'t5 -49'=6 -4t'nh;ch cor- responds to an 85' Radius Curve, which will be the Radius of the Turnout if taken off the Inside of the Curve FIG. 22. Turnout off a curve. modification decimally of the standard practice for express- ing the degree of curvature, and is more fully discussed under " Alignment on the Surface." 90 MINE TRACKS The degree of the main curve may be found by stretch- ing a tape or string along one of the rails and then measur- ing the middle ordinate. From this middle ordinate, the degree of curve can be taken by referring to the table; the degree of curve corresponding to the radius of the lead curve of the turnout can also be taken from the table. The minimum radius, which has been adopted for curves, can likewise be taken in terms of degree of curve from the table. If the turnout is to lead off the inside of a curve, the degrees of curve of both the main track and the proposed turnout, as computed for turning off a tangent, are added. If this does not exceed the degree of curve of the minimum radius allowed, the frog and turnout in question may be installed. Should the degree of curve exceed that corre- sponding to the allowable radius, it will be necessary to repeat the process with longer frogs until the combined degrees of curve fall within the limit. If the turnout leads off the outside of the main curve, the degree of curve of both the main track and turnout track (as computed for on a tangent) is found similarly, the degree of turnout curve being subtracted from the degree of curve of the main track; the result will be the degree of curve corresponding, which can be found in terms of the radius by referring to the table. When this has been determined, the advisability of using a shorter frog can be considered. In every case, however, whether the turnout be off the straight or the inside or outside of a curve, the lead corresponding to a certain frog and switch points should be the same. CHAPTER VII LOCATING THE TURNOUT When the site for either the frog or switch has been decided upon, the rest of the turnout location can be taken from a standard plan. Within certain limits it will often be found advisable to place the frog at the nearest rail joint, taking care, however, that the switch points do not also come at a rail joint. If no standards are available the location of the point of either the frog or switch should be determined. The other point can then be moved along the rail, at all times keeping it in position until the tangent distance from the point of frog to the point of intersection of the line of frog and switch will equal the distance from the point of inter- section to the heel of the switch. Referring to Fig. 20, either the frog or switch must be shifted until the distance T equals the distance T l . This plan is applicable, whether the frog is on a curve or a tangent. While an experienced trackman will usually be able to lay a fair turnout under varying conditions, this cannot always be depended upon. Particularly in the case of a new trackman, some governing and easily learned rules should be given. If it is found in laying a switch point off a curve that there will not be sufficient clearance at the heel of the switch and the adjacent rail, as may occur in turning off the inside of a curve, it is well to leave a proper distance on the lead or middle rail unspiked so that when the switch is set for either track sufficient clearance will be obtained. 91 92 MINE TRACKS The switch points are sometimes bent, to accommodate this clearance, but this expedient for light rail frequently results in having the points break after a little wear at the place where the rail bender has been applied. LADDER TRACKS A ladder track is one from which a number of parallel tracks branch, the frogs being located at intervals, depend- ent upon the centers required between tracks and the frog number used. In Fig. 23, A is the ladder track, and B, C and D are the branches. Angle of Trog- : \ \ MfllN rff/7C FIG. 23. Ladder tracks. The distance required between frog points is found by dividing the distance desired between track centers by the sine of the frog angle. The ladder track should be on an angle to the main tracks, equal to the frog angle to be used. The ladder track makes a better and more symmetrical layout where several turnout tracks are to be laid, than having each turnout track branch off the one adjacent, the usual method, used around mines. CHAPTER VIII BOOK OF RULES It is obvious that in order to secure any high degree of perfection in the standardization and installation of track it will be imperative to have definite instruc- tions and plans to govern and guide the workman in its construction. The instructions should be concise and easily understood ; the routine work should be covered fully; and the duties of the trackman, and those indirectly concerned, clearly specified. This will preclude any evasion of responsibility; and, on the other hand, by prescribing the course to be pursued under different conditions, remove to a great extent the burden of decision from the workman. This policy will help to develop more quickly young and in- experienced trackmen and tend to conserve material and time with the more efficient. Able trackmen are not pro- duced over night, and there is a vast waste of time and many inferior layouts made before any great proficiency is acquired. Those concerned in any way with the track installation and the preliminary work on which it is to a great extent dependent, should be furnished with copies of the rules, plans and all information in reference to them, and care taken to insure that they are thoroughly familiar with these instructions. It will be conceded that more efficie'nt and uniform results will be obtained if such a course is pursued 93 94 MINE TRACKS than if the workmen are all left to depend upon their own judgment. The engineering department should lay out the work in a manner that will utilize the standard equipment supplied to the trackman. The curves should be of a radius to correspond to the regulation frog to be used, so that the turnout can be installed with the frog fitting the curve and requiring no compromising in its installation. To do this, a radius that will be tangent to the end of the frog that joins the curve, and at the same time conform to the portion between the switch and the frog, should be used. . The mine foreman, or his assistants, should see that their work is symmetrical and conforms to the plans. A failure on the part of either will compel a distortion of the trackwork. The following book of rules is here given as a skeleton or model around which the many rules demanded by local conditions can be built. This plan is an adaptation of the practice of many standard-gage roads that regulate their maintenance-of-way employees with instructions governing their various duties. Some of the rules have been carried to a refinement which it is realized will be impossible to obtain in actual practice; however, they furnish a standard which ex- perience will determine how close it is required to approach. The underlying reason for the rules should be explained to those concerned, and meetings held at intervals where any suggestions or revisions can be discussed. This policy will instill enthusiasm and a spirit of rivalry among the trackmen, which if fostered should be productive of the most beneficial results. It may be pertinent to state here that, to produce the most efficient transportation, careful attention must be BOOK OF RULES 95 likewise given to improving the running parts of the rolling stock, so that the results to be expected from well-installed track may not be nullified by poor cars. There are many ways of performing almost any task. Scientific management (so-called) has shown the advantages to be derived in selecting and perfecting one method and performing in their logical sequence the various operations involved. The considerations or formulae which determine the following rules will be found in the preceding articles. In conclusion I would say that even though the best practice may not be achieved in the first set of rules, an inferior practice well carried out will accomplish more than a good system indifferently followed. (A) GENERAL RULES 1. The foreman of each colliery must supply copies of these rules and standards to the trackmen and repairmen; and the assistant foreman must enforce obedience to them and report to the district superintendent all violations and the action taken thereon. Every employee with duties in any way prescribed by these rules must be conversant with them. 2. The fact that any person enters or remains in the service of the company will be considered assurance of willingness to obey its rules. 3. In the event of any doubt as to the meaning of any plan, or if additional data is required, application should be made to the .* 4. Meetings will be held at least once every 3 months by the , where a review will be taken of the various 1 Where blanks occur in these rules they should be filled with the title of the proper official, or necessary data, in this case probably the division engineer. 96 MINE TRACKS rules, and suggestions for alterations, improvements or additions to the existing standards received. 5. Safety is of prime importance in the performance of any duty; every precaution must be taken .to avoid accident to the workmen themselves or others. 6. Workmen are responsible for the care and condition of their tools. 7. All work must be left in a safe condition. 8. Any work that interferes with the safe passage of trips at their normal speed is an obstruction, and except in emergencies should be attempted only after working hours. 9. Material must not be piled along the sides of haulageways. 10. Only such an amount of material must be stored inside as is required for immediate use, and care must be taken to place this so as to permit free passage on the ditch side of the gangway. 11. Tools and special material must be kept under lock and key and not given out or loaned without proper authority. (B) ROADBED 1. The roadbed on all new work, or wherever roadbed is re- newed, should conform to the standard plan. 2. The drainage ditch should be driven full width and depth at the same time as the heading or tunnel, and maintained clear within 25 ft. of the face by the party driving same. 3. The will determine what material shall be used for roadbed, and see that same is adhered to. Ballast is graded as follows: (1) Broken stone, excellent. (2) Ashes, good. (3) Breaker slate, fair. (4) Coal and refuse, poor. 4. Where rock is used for ballast, it must be broken to a size that will pass through a 3-in. ring. 5. All main haulage roads should have at least 2 in. of ballast beneath the tie, wherever possible. (C) TIES 1. Ties must be laid 16 to a 30-ft. rail and 18 to a 33-ft. rail. They must be placed at right angles to the rail and properly and evenly spaced. BOOK OF RULES 97 2. Whether or not ties are of uniform lengths, the ends of the ties on the ditch side of the track should be aligned at an even distance from the rail. 3. Selected ties should be used on all main haulageways. 4. The standard square ties in graded lengths, conforming with both the turnout and main tracks, should be used at all turnouts and switches. 5. Joint ties should be selected and be as near the same size as possible. 6. When a spike is drawn from a tie, the hole should be plugged before a spike is again driven in this tie. 7. As ties become unfit for service, they should be removed in the manner known as " spotting" and not in continuous sections. 8. Ties removed that cannot be used for any other purpose should be loaded and taken out of the mine at once. 9. All ties must be well tamped and particular attention given to tamping under the rail. 10. On account of drainage and tamping considerations, the practice known as corduroying that is, inserting new ties between those partially rotted without removing the rotten ties must not be employed except in cases where mule haulage only is in service. 11. Steel ties alone should only be used in locations where the roof is low and no acid water abounds. 12. Where fishplates are used, a selected tie should be placed directly under the rail joint. 13. Where angle bars are employed, the rail joint should be suspended with a selected tie under the angle bar on each side of the joint so as to give the angle bar a good and sufficient bearing. 14. Ties not up to specifications should not be laid until the foreman's attention has been called to them and his instructions received. 15. Tie Specifications: (a) Mine ties, ft. long, must be first-class sound timber and stock well manufactured, not less than nor over in. thick, with not less than in. faces at small end. Such ties may be of 98 MINE TRACKS either oak, chestnut, hemlock, ash, soft maple, ironwood, locust, hickory or pitch pine. They must be hewed or sawed on two parallel faces. (6) Outside ties, ft. long, must be first-class sound timber and stock well manufactured, to in. thick, with not less than in. faces at small end, and be of either oak, chestnut, locust or pitch pine, and hewed or sawed on two parallel faces. (c) Notched ties, ft. long, must be not less than in. in diameter under bark at small end, and of the same kinds of timber as (a) mine ties. 16. (a) Mine ties (a) should be used for general work inside. (6) Ties ft. long should be used for outside work, (c) Notched ties may be used only for chamber work where wood rail is in service. (D) RAIL AND SPIKES 1. Rails must be laid with broken joints; that is, the joints of one line should be as nearly opposite as is practicable the centers of the rails on the opposite line. 2. Short rails are only advisable for temporary work. No rail under 10 ft. in length is permitted on main-haulage roads. 3. Rails must be spiked in full and each spike driven home perpendicularly with full hold on the rail. The last blow should be a light one, to avoid breaking the spike under the head. 4. The shall see that not more than enough spikes to last days are given out at one time to any workman. 5. Spikes should be staggered; that is, the outside spikes of both rails must be toward the same side of the tie and the inside spikes toward the opposite side. 6. Rails should be laid true to gage. No deviation from this rale may be made except on curves as shown. 7. The gage on all curves whose radius is less than ft. should be widened 1 in. The gage on all curves whose radius is 200 ft. should be increased in.; for 250-ft. radius, in.; for 300-ft. radius, in., etc. BOOK OF RULES 99 8. On straight track both rails must be on the same level, except on approaches to curves, where the proper elevation must be given the outer rail. 9. The superelevation for the outer rail for maximum speed allowed must be: Gage . Underground, On the surface, in. in. For a 30-ft. radius curve For a 40-ft. radius curve For a 50-ft. radius curve For a 60-ft. radius curve . For a 80-ft. radius curve For a 100-f t. radius curve For a 150-ft. radius curve ........ For a 200-f t. radius curve ........ 10. The track level should be tested frequently and always used when surfacing track. 11. (a) Ib. rail shall be the lightest rail laid and be used only for buggy work. (6) Ib. rail shall be the lightest rail used where the regular mine cars run. (c) Ib. rail shall be the lightest rail used where locomotive haulage is employed, (d) to Ib. rail may be used on main-haulage roads, and for heavy outside traffic by special arrangement. 12. "Dead" steel rail that is, old rail unfit for regular haulage shall be used wherever possible for chamber work. 13. Wood rail shall be used only for heavy pitching chambers and slants where the "dead" rail cannot be utilized. 14. Wood rail not conforming to specifications should not be used until the foreman's attention has been called to its defects and his permission to lay it obtained. 15. Specifications for wood rail: Wood rail should be first- class sound timber and stock well manufactured and sawed by in. and in to ft. lengths; it must be square edged and sound, of beech, birch, maple, oak or ash. 16. Steel rail must not be dropped from the sides of railroad cars. 100 MINE TRACKS 17. The size of spikes should be for ties inches. 18. The size of spikes should be for ties inches. 19. The track gage must be placed square with the track, and the rail held tight against it, until the spikes are driven. 20. The locomotive engineer or driver shall report the location of any poor roadbed, and all derailments and the .cause thereof to the . 21. Spikes in abandoned ties or track must be reclaimed by (E) CURVES 1. Lines will be given by the engineers for all tunnels and rock curves, and no tunnel or curve shall be started without such a line. 2. It is the duty of the mine foreman to see that all lines are rigidly adhered to. 3. A ft. radius curve is the minimum curve allowed. 4. When curves are necessary in following the irregularities of a bed, the curve offset for a chord should not be greater than ft. (F) ANGLE BARS, TIE-PLATES AND RAIL BRACES 1. All rail 25 Ib. or over should be laid with joint fastenings. 2. All rail joints where mechanical haulage is in service should be laid with angle bars. 3. All joint fastenings must be applied with the full number of bolts, washers and nuts, screwed up and kept tight. 4. The ties at joint fastenings should be laid as indicated in Rules C 13 and C 14. 5. Where heavy locomotives are in service and the flange of the rail cuts the tie, requiring frequent notching, tie-plates may be used by permission of the . 6. Tie-plates may be used where the traffic wears out the flange of the rail before the head has given full service, and where the rail cuts the spikes by applying to the . 7. Rail braces may be used on curves where it is hard to main- tain the gage by applying to the . BOOK OF .&J.LES 101 8. Rail braces, when used, should be applied to both rails. 9. Rail braces must not be applied where tie-plates are used. (G) FROGS AND SWITCHES 1. A No. cast frog shall be used on all new chamber switches of Ib. rail. 2. A No. builtup frog shall be used on all new chamber switches of Ib. rail or over. 3. A No. frog shall be used for general use. 4. A No. frog may be used in cases where the traffic is fast and heavy. 5. A No. frog may be used outside by special arrangement where the locomotives are large and the traffic is unusually fast and heavy. 6. A ft. tongue switch should be used with the cast frog. 7. A ft. split switch should be used with the No. and No. builtup frogs. 8. A ft. split switch should be used with the No. and No. frogs. 9. Frogs inside the mine must be placed to conform to the ribs of the curve and not the nearest rail joint. . 10. The lead of a frog to be located on a curve should be the same as the number of frog adopted calls for that is, no difference should be made in the lead whether the turnout is off a tangent or a curve. 11. When the frog is located on a curve, the sum of the degree of curve of the main track and the degree of curve corresponding to the frog should not exceed deg. The degree of curve of the main track may be found by measuring the ordinate of a 10-ft. chord and referring to Table , page . The degree of curve corresponding to the turnout radius may also be taken from the same table. 12. The rail connecting the frog and the heel of the switch should conform to the length shown on the standard layout draw- ings. One rail should be bent to the required radius and should be drilled, and a supply kept constantly in stock. 102 MINE TRACKS 13. The distance from the switch to the frog must agree with the standards, so as to make the connecting rails interchangeable. 14. Where possible, the switch lever should be placed on the ditch side of the gangway, or heading. 15. Switch stands must be used at all switches where mechanical haulage is employed. 16. The switch with spring should be used at all main switches; for general use, the type without the spring must be employed. 17. The switch and spring must be kept clean and well oiled. 18. When a turnout is to be laid, a complete set of parts should be delivered to the proper location in ample time. 19. Bills of material for each turnout design used are as follows : These bills of material to be prepared for standard turnout installations. The standards adopted, of course, will be pe- culiar to each mine or company. INDEX Acid water, 5, 23, 24 Angle bars, 23, 26, 27 Ballast, 29-30 corrosion of rail, 29 drainage, 29-30 Cinders, 29 Corduroying, 24 Crystallization, 9 Curves, alignment of, 31-39 compensation for, 36-37, 54- 60 formulae, 40-44 increase of gauge, 63-66 radii, 34-36, 41-44 resistance, 36-37, 65 superelevation of, 61-63 surface, 38-44 symbols, 38-44, 40-41 underground, 31, 38 Drainage ditches, 46-47 Draw bar pull, 36-37, 48-54 Elevation of outer rail, 61-63 Expansion of rail, 10 Fish plates, 23, 26, 27 Friction, coefficient of, 11 curvature, 36-37, 48-51, 54- 60, 63-66 journal, 52-55 Frogs, 68-74, 76-79 cast, 70, 71 determination of number, 69-70 guard rails, 71-72 movable points, 73, 74 rail, 70, 72 shrouds, 70-72 - standardization 68, 69, 76-79 tables, 76-79 track crossing, 74 Gauge on curves, 63-66 Grades, boards, 56-58 car journal resistance, 52-55 compensation, 55-60 construction, 55, 57, 58 designation of, 45 determination on surface, 45 drainage, 46, 47, 51 gravity, 59-63 mining disadvantages, 51, 54 tables, 56-58 theoritic, 48-50, 58 track resistance, 48-51 underground, 45-46, 48-50, 52-55 Guard rails, 66-67, 71-72 shrouds, 70-72 Ladder tracks, 92 Latches, 74-75 103 104 INDEX Projection of haulage roads, 31-34 curve alignment, 31-34, 38-39 formulae, 40-44 radii, 34-36 short, 43-44 resistance, 36-37 economic considerations, 34- 37 geologic considerations, 31 preliminary location, 38-40 surface, 38-44 underground, 31-38 Rail, 1-11 acid water, 5, 23-24 annealing, 9 benders, 8 bending moment, 14-15 braces, 27-28 coefficient of friction, 11 corrosion, 5, 23, 24, 29 creep, 10 crystallization, 9 deflection, 19-20 dimensions, 5, 6 dishes, 6, 22 durability, 3, 4 expansion, 10 impact stresses, 13 joints, 6, 7, 23 spikes, 25 stiffness, 2, 13, 19 strength, 3, 14, 15 wear resistancy, 4, 27, 28 weight required, 1, 16, 17, 25 wood, 10, 11, 24 Rail bender, 8 Rail braces, 27-29 flange preservation, 28 Roadbed, 29-30 Rules for trackmen, 92-100 advantages, 93 angle bars, 100 coordination of work, 93, 94 curves, 99, 100 frogs, 100 general rules, 95 rail, 98 rail braces, 100 roadbed, 96 spikes, 98 standardization, 93 superelevation, 98, 99 switches, 100 tie plates, 100 ties, 100 Shrouds for frogs, 70-72 Spikes, 25-26 Superelevation of rail, 61-63 Switches, 66, 74, 82 angle of, 76, 82, 87 spring, 75 stub, 75 ties, 24 underground, 75 Tie plates, 27-29 rail flange preservation, 28 Ties, 12-24 ballast, 12, 13, 18 corduroying, 24 dimensions, 12, 21, 22, 25 failures, 21, 27, 28 INDEX 105 Ties, notched, 24 Turnouts, ladder tracks, 92 plates, 27, 28 location of, 91 spacing, 12-14, 16-18, 21, 23 off curves, 87-89 spikes, 25 radii, 88-90 steel, 24 standardization, 80, 82, 86, switches, 24 87 wood preferred, 12, 24 tables, 83-85 Turnouts, 80-92 formulae, 80-82, 87 Wood rails, 10, 11, 24 IYERSITY OF CALIFORNIA LIBRARY