Koepe System.-In its lightest form, a drum requires a large amount of power to set it in motion, which power is absorbed by the brake and lost when it is brought to rest again. Furthermore, with deep shafts requiring long drums, the fleet, or angle that the rope makes with the head-sheave due to its traveling from one end of the drum to the other, is not only a disadvantage and possible cause of accident, but it is a source of wear. To overcome these objections and also the great cost of large cylindrical or conical drums, the Koepe system of hoisting, shown in Fig. 2, was devised by Mr. Frederick Koepe. A single-grooved driving sheave a is used in place of a drum. The winding rope b passes from one cage A up over a head-sheave, thence around the sheave a and back over another head-sheave, and down to a second cage B; it encircles a little over half the periphery of the driving sheave and is driven by the friction between the sheave and rope. A balance rope c beneath the cages and passing around the sheave d gives an endless-rope arrangement with the cages fixed at the proper points. The driving sheave is stronger than an ordinary carrying sheave, as it has to do the driving, and is usually lined FIG. 2 A with hardwood, which is grooved to receive the winding rope, the depth of the groove being generally equal to twice the diameter of the rope. Instead of being placed parallel, the head-sheaves are placed at an angle with each other, each pointing to the groove in the driving sheave, thus reducing the side friction of the rope on the sheaves. The system has been in successful operation since 1877, and experiments made on it have determined that, with a rope passing only one-half turn around the drum sheave, the coefficient of adhesion with clean ropes is about .3. If the ropes oiled, the adhesion becomes less, and sometimes slippage occurs, producing not only wear of the driving-sheave lining but giving an incorrect reading of the hoist indicator and thus possibly producing over winding, unless the are position of the cage is indicated by marks on the rope, or unless the engineer can see the cage. At the end of the hoist, if the upper cage is allowed to rest on the keep, its weight and the weight of the tail-rope are taken from the hoisting rope, and there is then not enough pull on the hoisting rope to produce sufficient friction with the drum sheave to start the next hoist. To prevent this trouble, the keeps are dispensed with, or the rope is made continuous and independent of the cage. To do this, crossheads are placed above and below each cage and connected by ropes or chains outside of the cages. The bridle chains are then hung from the top crosshead, and when the cage rests on the keeps, the weight of the winding and tail-ropes remains on the driving sheaves. With this system, only one driving sheave is necessary for the operation of two compartments, and it is light, inexpensive to build, and very narrow, admitting of a short sheave shaft and small foundations. This system permits a perfect balance of rope and cage, so that the work to be done by the engine is uniform, except for the acceleration, and consists only in lifting the material and overcoming the friction. There is no fleeting of the rope between the driving sheaves and the head-sheaves. The system has the following disadvantages, which prevent its being used to any considerable extent: Liability to slippage of the rope on the drum; if the rope breaks, both cages may fall to the bottom; hoisting from different levels cannot be well done, for, since the cages are at fixed distances from each other, the length of the rope is such that when one cage A is at the top, the other cage B is at the bottom. If hoisting is to be done from the bottom, this is satisfactory, but if hoisting is to be done from some upper level, cage B, which is at the bottom, must be hoisted to that level to be loaded before it can go to the top. Then, when cage B goes to the top with its load, cage A must go to the bottom, wait there while cage B is being unloaded, and then be hoisted to the upper level to receive its load. For each trip, therefore, the time required for a cage to go from the bottom to the upper level and be loaded is lost; and two movements of the engines are necessary for a hoist instead of one. Whiting System.-In the Whiting system, two rope wheels placed tandem are used in place of cylindrical or conical drums. As shown in Fig. 3, for a two-compartment shaft the rope passes from one cage a up over a head-sheave c, h 9 down under a guide sheave d, and is then wound FIG. 3 The drums or wheels e and ƒ are light, inexpensive, and narrow, thus permitting short sheave shafts and small foundations. They are lined with hardwood blocks, each lining having three rope grooves turned in it. The main wheel e is driven by a hoisting engine, which may be either first- or secondmotion. The following wheel ƒ is coupled to the main wheel by a pair of parallel rods, one on each side, like the drivers of a locomotive. As the rope wraps about the wheels e and f three times, there are six semi-circumferences of driving contact with the rope, as compared with the one semi-circumference in the Koepe system, and there is no slipping of the rope on the wheels. The following wheel ƒ is best tilted or inclined from the vertical an amount equal, in the diameter of the wheels, to the pitch of the rope on the wheel, so that the rope may not run out of its groove and may run straight from one wheel to the other without any chafing between the ropes and the sides of the grooves. The capacity of the wheels e and f is unlimited, while grooved cylindrical drums, conical drums, and reels will hold only the fixed length of rope for which they are designed. As shown by the dotted lines, the fleet sheave g is arranged to travel backwards and forwards, in order to change the working length of the rope from time to time to provide for an increased depth of shaft, and for changes in the length of rope due to stretching and when the ends are cut off to resocket the rope. The fleet sheave g is moved a distance equal to one-half the change in the length of rope. Hoisting from intermediate levels can be readily done with the Whiting system; for instance, if the cage a is at the top and cage b at the bottom, and hoisting is to be done from some upper level, it is only necessary to run the fleet sheave g out, and thus shorten the working length of the rope until cage b comes up to the upper level. It can then be loaded and go to the top. While cage b goes to the top, cage a descends to the same level, where it can be loaded while cage b is being unloaded, and can then go directly to the top without any lost time, as is the case in the Koepe system. The system permits a perfect balance of rope and cage, so that the work to be done by the engines is uniform, except for the acceleration, and consists only in lifting the material and overcoming the friction. There is no fleeting of the rope, so the rope wheels can be placed as close to the shaft as may be desired. This system was tried as early as 1862 in Eastern Pennsylvania, but it was not used extensively because hoisting from great depths was not necessary, since, for depths of less than 1,000 ft., cylindrical and conical drums are quite satisfactory. Two of the Whiting hoists in the Lake Superior copper region are among the largest hoisting plants in the world. Each of these consists of a pair of triple-expansion, vertical, inverted-beam engines, driving direct a pair of 19-ft. drums. The high-pressure cylinders are 20 in. in diameter, the intermediate cylinders 32 in., and the low-pressure cylinders 50 in., and all six of them have a 72-in. stroke. The rope used is a 24-in. plow-steel rope and hoists 10 T. of material at a trip, in one case from a depth of 4,980 ft. Modified Whiting System.-A modification of the Whiting system is sometimes used in which a large drum keyed to the crank-shaft replaces the small tandem drums, and even the slight probability of the rope slipping in the Whiting system is thus obviated. One rope is fastened to one end of the drum, and the other rope to the other end in such a way that while one is winding on the other will be winding off the drum. One rope passes directly to the head-sheave while the other passes first around a fleet sheave, similar to that used for the Whiting system, but preferably placed horizontal, and thence to the head-sheave. This system possesses the same advantages as the Whiting system except that the depth of hoist is limited by the size of the drum, and that there is a fleet of the rope. Up to the limiting depth, as determined by the size of the drum, this system can be used with equal economy for any depth. This hoist, as well as the Whiting, is therefore especially suitable for a place where one mining company operates several mines, for it enables the company to select one size for all their permanent work, with all the advantages that come from duplicate machinery. Empty Load FIG. 4 Despritz System. The general arrangement of the Despritz system is shown in Fig. 4. A drum with a radius T is keyed to the same shaft as the rope drum with a radius R, and carries a small rope to which is attached a chain whose length N is one-half of the distance between landings H. The small rope is so wound on to its drum that at the commencement of the hoist the chain is suspended at full length in a small compartment specially provided. Immediately the hoisting commences, the small rope starts to unreel, piling up the chain at the bottom of its compartment until the cages reach their point of passing midway of the shaft, at which instant the hoistingrope loads balance, the piling up of the entire chain length is complete, and its load moment on the main shaft is zero. At this instant, also, the small rope, carrying the chain, has all unreeled from its drum and its point of fastening is about to pass around underneath and take the rope into the position shown by the dotted line. Hence, as soon as the cages have passed each other the chain rope begins to reel up again, extending the chain upwards until, at the termination of the hoist, it again hangs at full length, giving a load moment of opposite sign to that which it had at starting of the hoist. That is, during the first half of the hoisting period the load moment of the chain on the drum shaft is plus, while during the second half of the period it is minus. If W weight of hoisting rope per foot; Monopol System.-The system outlined in Fig. 5 is known as the Monopol. An auxiliary drum of diameter equal to the winding drums, is keyed to the main shaft and is of sufficient width to carry two relatively small ropes, one of which is underwound and the other overwound. These ropes support a length of heavier balancing rope in the position shown; this balancing rope is usually a length of old hoisting rope of the size used in the hoisting operations and which has been discarded on account of wear. A glance at the diagram makes it evident that if this balancing rope is adjusted at the outset, so that each of its ends is in position opposite one of the cages, as shown, they will so remain whatever the position the cages take during a hoisting period, and the load moment on the drum shaft, so far as the hoisting ropes are concerned, will be equalized throughout. As in the former case, the weight of the small rope can be neglected. Load FIG. 5 Empty In practice either of the foregoing systems requires that a small compartment be provided for the accommodation of the balancing device. This is usually partitioned off from one end of the pump compartment of the main shaft at a nominal expense. As for the rest of the arrangements, almost any mechanic at the mines will find little trouble in providing whatever may be required for the installation. CALCULATIONS FOR FIRST-MOTION HOISTING ENGINES General Considerations.-Owing to the fact that many of the resistances that have to be overcome can only be estimated approximately, the determination of the horsepower required to hoist, as well as the dimensions of the engines required for that purpose, cannot be made exactly. The usual procedure is to calculate an average or minimum horsepower by means of some simple formula and then to add to this an amount that experience has indicated to be necessary to provide for uncertainties both in resistances to be overcome and in the future demands for power. The horsepower having been obtained, the actual design of the engines should be left to a skilled mechanical engineer; in fact, the entire matter, even including the calculation of the horsepower, is more properly the work of the engine builder than the mine superintendent. The methods involved in the solution of hoisting-engine problems are best explained by the working out of the following example. EXAMPLE.-What should be the horsepower and dimensions of a firstmotion engine to hoist 1,500 T. of coal per da. of 8 hr. from a shaft 1,000 ft. between landings under the following conditions: One-half hour is allowed for delays of various kinds, 7 sec. for caging each trip, and 5 sec. each for acceleration and retardation; the car holds 5,000 lb. of coal and weighs 2,500 lb.; the cages weigh 4,000 lb. each; the drum is cylindrical, 8 ft. in diameter and 8 ft. wide; the head-sheaves are 8 ft. in diameter; the mean effective pressure of the steam in the cylinder is 100 lb. per sq. in., the plant has an efficiency of .85%; and the resistance of friction is taken to be the same as that required to move a weight equal to 5% of the total load? SOLUTION.-1. Hoisting Period. The operation of hoisting through a shaft may be divided into three periods. First, a period of acceleration, during which the load, rope drum, sheaves, moving parts of the engine, etc., are brought from rest to full speed. Second, a full- or constant-speed period during which the load is hoisted at the uniform velocity attained at the end of the period of acceleration. Third, a period of retardation, during which the load and moving parts are brought from full speed to rest. In practice, the time required for acceleration is variously estimated as being equal to one-seventh of the net time of hoisting, as from 3 to 7 sec. depending on the depth of the shaft and speed of hoisting, as the time required for the drum to make, say, three revolutions, as the time required to hoist the cage 50 or 150 ft. starting from rest, etc. The period of retardation is usually taken to be equal in time to that of acceleration, although it may be a little shorter. The full-speed period is the longest of the three, and consumes about three-fourths of the net time of hoisting. Because, in addition to raising the load, it as well as the drum, sheaves, and moving parts of the machinery must be accelerated or brought up to full speed from rest, the power required to hoist is very much greater during the period of acceleration than at any later time; and hoisting engines should be designed with this fact in view. 2. Net Time of Hoisting.-The gross time actually devoted to hoisting is 8-7.5 hr. The weight of coal hoisted per hour=1,500÷7.5=200 T. As 5,000 lb. = 2.5 T., the number of hoists per hour is 200÷2.5-80. As there are 3,600 sec. in 1 hr., the gross time of hoisting per trip is 3,600÷80=45 sec. As 7 sec. is allowed for caging, the net time of hoisting is 45-7-38 sec. 3. Speed of Hoisting.-Assuming that the acceleration, that is, the increase in velocity of the cage, is uniform, the speed attained at the end of the period of acceleration may be found from the formula, in which V= H 1,000 in-t 38-5 30.3 ft. per sec v=full speed of hoisting, in feet per second; As the cage starts from rest and attains a velocity of 30.3 ft. per sec. at the end of 5 sec., the space traversed during acceleration is Xt=75.75 ft., because the average velocity is one-half the final. The acceleration, a is found from the formula a=v÷t=30.3÷5-6.06 ft. per sec. per sec. The space passed over during acceleration is not the same for each of the 5 sec. In the first second, the cage is raised a distance of but a, or 3.03 ft.; during the second second, it is raised a+a-9.09 ft.; and during each succeeding second it is raised a distance a=6.06 ft. more. The distances passed over in the single seconds making up the period of acceleration, are, respectively, 3.03, 9.09, 15.15, 21.21, and 27.27 ft., the sum of which is 75.75 ft. as determined before. The velocity attained at the end of any particular second is found from the formula vat. Thus, at the end of the fourth second, the velocity of the cage is 6.06X4 24.24 ft. per sec.; that is, if the accelerating force ceased to act at the end of the fourth second, the cage would enter the fifth second with sufficient velocity to carry it 24.24 ft. But during the fifth second, the accelerative force still acts, and adds a or 3.03 ft. to the distance traveled. Similarly, at the end of the fifth second, the cage, after traveling 27.27 ft. begins the sixth second with a velocity sufficient to carry it 27.27+a=30.3 ft. during that second without further acceleration. 4. Revolutions of Drum per Minute.-If D is the diameter of the rope drum, in feet, the number of revolutions per minute made by it during the fullspeed period may be found from the formula, rev. per min. vX 60 30.3 X 60 1,818 =72.33, say, 72.5 The total number of revolutions made by the drum during acceleration or retardation is 75.75÷25.13=3, very nearly. The number of revolutions, or fractions of a revolution, made by the drum during the individual seconds of the acceleration period is found by dividing the distance passed over in any second by the circumference of the drum. In the problem, the approximate number of revolutions in each of the 5 sec. will be, respectively, t.. t. t. 1. 5. Friction in Hoisting.-In well-designed and well-built first-motion hoisting engines, the resistance due to friction should not exceed that due to raising a weight equal to 5% of the total load including the weight of the ropes, but in second-motion or geared hoists this resistance may amount to 7.5 to 10%. The method of allowing for the effects of friction varies. By some, the friction is added to the load and treated as part of it; by others, the area of the steam cylinders is calculated on the basis of there being no friction and from |