= To show the application of this formula, the following calculations of an actual instance are given:-2900 tons of coal have to be raised from a depth of 600 yards in eight hours. Each tub contains 16 cwts. of coal, so that 2900 × 20 3625 tubs of coal will have to be drawn, and as from the experience of the neighbourhood it is known that in this particular seam 1 tub of dirt is produced to each 20 tubs of coal, the engine will also have to raise 181 tubs of waste, or a total = 16 3625 20 = 3806 = of 3625 + 181 3806 tubs in eight hours or 480 minutes. The complete journey, including raising the coal, changing the tubs on the cage, and all allowances for hindrances, must be made in one minute, and, consequently, the cage will have to hold 7'93, say 8 tubs. There will be four decks in the cage, each carrying 2 tubs, and, in order to prevent overloading, the inset must be so arranged that never more than one deck can be filled with dirt tubs, which hold 24 cwts. each. The gross weight of mineral on each cage will never exceed 6 tubs of coal at 16 cwts. each and 2 tubs of waste at 24 cwts. 144 cwts. = The actual weight of a steel four-decked cage with disengaging hook and coupling chains is 80 cwts., and each tram weighs 8 cwts. The total weight at the end of the rope is-cage, 80 cwts.; 8 tubs, 64 cwts.; and coal and dirt, 144 cwts. 288 cwts. A plough steel rope, 5 inches circumference, weighs 16 lbs. to the yard, and as the shaft is 600 yards deep and the pit frame 35 yards high, the weight of rope hanging in the shaft is 635 × 16 I 12 = 90'7 cwts. The maximum weight hanging on the rope is consequently 288 + 90'7 = 378.7 cwts., and as such a rope has a breaking strain of 160 tons, the factor of 160 x 20 safety is 378 7 = 8.5 nearly. This is sufficient for such depths and loads, because the margin between the load (18.93 tons) and the breaking strain (160 tons) is 141'1 tons. The drum will have a slightly coned part at each end, and be cylindrical in the centre. Each cone will commence at 161 feet at the edge, and rise to a maximum of 17 (see Fig. 402a). There will be several spare coils of rope on the drum, and, consequently, the diameter of the drum at the first moment the engine starts to lift will be 165 feet 52.88 feet circumference. If we assume that the engine attains its maximum speed in 5 revolutions, as the rope during this period has travelled up the slope, the diameter of the drum will then be 17 feet 53'40 feet circumference, and the space passed through by the cage will be 52.88 + 53′40 = = 2 × 5 revs. = 265.7 feet. If full speed is attained in 10 seconds (t in formula), the average velocity will be 26:57 feet per second, and as the acceleration is uniform from zero, the maximum velocity will be double this figure, or 53'14 feet = v. As the rope starts to coil on the drum when its diameter is 165 feet (52.88 ft. cir.), and the cone ends at 17 feet diameter (55'75 ft.. cir.), the average circumference of the coned part is = 52.88 + 55'75 2 54'31 feet. For the complete wind half the rope will coil on the cone and half on the flat (55'75 ft. cir.), so that the average circum54°31 +55 75 ference during the centre part of the run will be = 55 feet. The engine must stop in 4 revolutions, in 9 seconds of time, equal to 4 x 55 75, or 223 feet. The actual wind is, therefore, performed as follows: 2 This leaves a margin of 16:32 seconds under the minute allowed. As the four decks of the cage will be changed simultaneously in 10 seconds, 6.32 seconds per wind are available for contingencies, equal in 480 winds to 50 minutes during the complete working day. The steam pressure in boilers is 150 lbs., but a drop of 10 lbs. should be allowed between boilers and stop valve on engine making the absolute pressure there 155 lbs. = p'. If it is decided to use a pair of single-cylinder direct-acting engines and cut off steam at 80 per cent. of the length of the stroke during the five revolutions in which acceleration is taking place, the theoretical number of expansions will 125, but the actual expansions will be less, owing to the effect of steam left in the clearance spaces of the cylinder. In this class of engine a factor of 0.85 may be taken, and, consequently, the actual number of expansions is 125 × 0·85 = 1'06, say I'1 = r. The theoretical mean steam pressure (p") be 100 80 = pressure = but the actual mean pressure is always lower on account of steam condensing on the cylinder walls, &c., and the figure so obtained must be reduced by multiplying by 0.85, which gives the actual mean 154'2 × 0·85 = 131 lbs. The effective pressure on the piston is the mean pressure less back pressure, and if the engine works non-condensing this can be taken as 5 lbs. above the atmosphere —i.e., 20 lbs. absolute-but condensing it will only be 5 lbs. absolute. These engines will be connected to a condenser, and, therefore, the effective pressure will be 131 5 P in formula. = 126 = The two cases for consideration are when the engine runs with and without the load being balanced. I. When the load is balanced by a rope beneath the cages:— * Boiler pressure plus that of the atmosphere. The hyperbolic or Naperian logarithm of the ratio of expansion. The total length of rope to be set in motion = twice the depth of shaft (600 yds.) + height of headgear (35 yds.) + distance to drum (35 yds.) = 2 x 670 = 1340 + the rope coiled on drum, which is equal to the depth of the shaft, or a total of 1940 yards. yard = 31,040 lbs. The total weight, W, to be set in motion Rope, * 2 cages, hooks, &c., 80 cwts. each, 16 tubs, full and empty ones, 8 cwts. each, Half-weight of drum (26 tons) and half-weight of 2 pulleys (8 tons) = 340 cwts., . At 16 lbs. to the The stroke of the engine may be taken at 5 feet, one-third the diameter of the drum, and as the maximum velocity is attained in five revolutions, S 5 × 2 × 5'5 = 55 feet. The unbalanced load in = this case is minerals only. With two cylinders this gives 707 square inches for each, but a further allowance of from 15 to 25 per cent. has to be made for friction, If 25 per cent. be added the area becomes 884 square inches, and the diameter of each cylinder will consequently be : 2. Where the load is unbalanced : The weight set in motion for tubs, coal, &c., will be as before, but as the length of balance rope (600 yds.) is taken away, this reduces the weight by 9600 lbs., and W becomes 116,864. During the time acceleration takes place the load is lifted 265'7 feet in five revolutions of the drum, and this length of rope, weighing 1417 lbs., is taken off the ascending rope and added to the descending one. The unbalanced rope at the commencement is 600 yards, or 9600 lbs., and at the end of the ten seconds is 9600 2 × 1416, or *The winding rope in the shaft and the balance rope. + Foot-lbs. of work done in ten seconds. This multiplied by 6 and divided by 33,000 gives 1780 horse-power. 6766 lbs. Half of these two, or 9600 + 6766 = 2 8183 lbs., is the weight of unbalanced rope lifted on the average during the time in which the maximum velocity is being obtained. The average unbalanced load is consequently 16,128 lbs. of mineral +8183 lbs. of rope 24,311 lbs. = Each piston should, therefore, have an area of 833 square inches +25 per cent. for friction, or 1041 square inches, and a diameter of— The Position of Engine-House.-In nearly every case the direction of the inset governs the position of the winding engine, the drum shaft being generally at right angles to the axis of the inset and cages. choice, therefore, appears to be limited to two positions, either A or B (Fig. 402). Such, however, is not the case; the cages may still be kept in the same line by placing the pulleys obliquely, shown by dotted lines, and, by doing so, the enginehouse may be situated at, say, either C or C1, or practically anywhere; indeed, by putting one pulley over the other, the engine may be placed at right angles, D, to the axis of the inset. VB Fig. 402. Drums.-The winding rope is coiled on a drum, which may be of various forms. The first division is produced by the type of rope adopted. The ropes are flat ones and coil on themselves; the drum consists of a narrow cylinder of small diameter fitted with horns on each side. Its weight is small and its construction simple. The other main division is caused by the employment of round ropes. It has been tried to make round ropes coil on themselves, and employ a drum similar to that used for a flat rope, but the experiment did not meet with success. Three types of drum for round ropes are in use: (1) the ordinary cylindrical form, parallel throughout; (2) the conical; (3) the spiral. # Foot-lbs. of work done in ten seconds; equal to 2098 horse-power. The parallel form is obviously the simplest, cheapest, and least liable to accident. Its only disadvantage is the side friction resulting from the angling of the rope. The successive coils lie side by side, and as they lap on the drum are constantly moving relatively to the centre line of the pulley. An attempt is made to equalise this strain, by placing the drum in such a position that at the commencement of a wind the rope is at the same distance on one side of the centre line as it is on the other side at the conclusion-that is to say, the centre line of the pulley coincides with the centre line of half the drum. The result, however, is that at first the coils do not lie against each other, but have spaces between, as the rope tries to get into the same plane as the pulley, but after the central point is passed, the rope still tries to keep in the same plane as the pulley, and the successive coils not only lie very close against each other, but a grinding action is set up between them. This disadvantage is removed in some cases by turning shallow grooves in the circumference of the drum for the rope to coil in. It then winds evenly and grinding is avoided. A cheaper plan, and an equally satisfactory one, is to make the drum slightly conical instead of cylindrical, a slope of 1 in 10 being sufficient. The tendency of the rope to get into the same plane as that of the pulley, is thereby counterbalanced by its disinclination to climb the slope, and each coil winds evenly against the other. With either system, and a cylindrical drum, it is impossible to avoid side friction altogether. What is done is to make the side friction of one lap equal to that of another, and not throw all the grinding action upon one or two coils. If the drum is kept of reasonable diameter, its width increases to an objectionable amount when the depth of the shaft is great, and consequently the usual practice is to wind the incoming rope on the same space that the out-going rope has just previously uncoiled from. In this way the width of the drum can be reduced by nearly one-half and excessive angling of the rope prevented. A rope, however, cannot be wound on a drum down a slope, and consequently if any portion is coned, the total width of such a drum must be greater than the space occupied by the full complement of rope belonging to one cage. The better-designed drums of this class consist of a short-coned piece at each end and a parallel portion in the centre (Figs. 402a and 402b), and unlike older forms are made of rolled-steel plates and channels, and are built as light as possible. Indeed, a good many err in not being strong enough. Lightness is most desirable, but must not be obtained by the sacrifice of stiffness. The central bosses should be light, the castings cored out wherever possible, and strength obtained by ribs instead of by increasing the thickness of metal. The pockets for the channel steel arms, n, twelve in number, are machined out to obtain a good fit, and the arms are secured thereto preferably by turned bolts fitting into bored holes, which give better results than rivets, extra bearing surface for these being obtained by the introduction of short lengths of flat bars, a, which are riveted to the webs of the channels near to the central boss. The outer rims of the drum are formed of steel plates, b, connected together by butt straps, and riveted to the channel arms. On the outside of these plates a channel steel ring, c, is attached by countersunk rivets to form the brake rim; |