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point. When the main rope draws a set of full cars out, the tail-rope drum runs loose on the shaft, and the rope, being attached to the rear car, unwinds itself steadily. Going in, the reverse takes place. Each drum is provided with a brake to check the speed of the train on a down grade and prevent its overrunning the forward rope. As a rule, the tail rope is strained less than the main rope, but in cases of heavy grades dipping outward it is possible that the strain in the former may become as large, or even larger, than in the latter, and in the selection of the sizes reference should be had to this circumstance.

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IV. The Endless-rope System.-The principal features of this system are as follows:

1. The rope, as the name indicates, is endless.

2. Motion is given to the rope by a single wheel or drum, and friction is obtained either by a grip-wheel or by passing the rope several times around the wheel.

3. The rope must be kept constantly tight, the tension to be produced by artificial means. It is done in placing either the return-wheel or an extra tension wheel on a carriage and connecting it with a weight hanging over a pulley, or attaching it to a fixed post by a screw which occasionally can be shortened.

4. The cars are attached to the rope by a grip or clutch, which can take hold at any place and let go again, starting and stopping the train at will, without stopping the engine or the motion of the rope.

5. On a single-track road the rope works forward and backward, but on a double track it is possible to run it always in the same direction, the full cars going on one track and the empty cars on the other.

This method of conveying coal, as a rule, has not found as general an introduction as the tail-rope system, probably because its efficacy is not so apparent and the opposing difficulties require greater mechanical skill and more complicated appliances. Its advantages are, first, that it requires one third less rope than the tail-rope system. This advantage, however, is partially counterbalanced by the circumstance that the extra tension in the rope requires a heavier size to move the same load than when a main and tail rope are used. The second and principal advantage is that it is possible to start and stop trains at will without signalling to the engineer. On the other hand, it is more difficult to work curves with the endless system, and still more so to work different branches, and the constant stretch of the rope under tension or its elongation under changes of temperature frequently causes the rope to slip on the wheel, in spite of every attention, causing delay in the transportation and injury to the rope.

V. Wire-rope Tramways.-The methods of conveying products on a suspended rope tramway find especial application in places where a nine is located on one side of a river or deep ravine and the loading station on the other. A wire rope suspended between the two stations forms the track on which material in properly constructed "carriages" or "buggies" is transported. It saves the construction of a bridge or trestlework, and is practical for a distance of 2000 feet without an intermediate support. There are two distinct classes of rope tramways:

1. The rope is stationary, forming the track on which a bucket holding the material moves forward and backward, pulled by a smaller endless wire rope.

2. The rope is movable, forming itself an endless line, which serves at the same time as supporting track and as pulling rope.

Of these two the first method has found more general application, and is especially adapted for long spans, steep inclinations, and heavy loads. The second method is used for long distances, divided into short spans, and is only applicable for light loads which are to be delivered at regular intervals. For detailed descriptions of the several systems of wire-rope transportation, see circulars of John A. Roebling's Sons Co., The Trenton Iron Co., and other wire-rope manufacturers. See also paper on Two-rope Haulage Systems, by R. Van A. Norris, Trans. A. S. M. E., xii. 626.

In the Bleichert System of wire-rope tramways, in which the track rope is stationary, loads of 1000 pounds each and upward are carried. While the average spans on a level are from 150 to 200 feet, in crossing rivers, ravines, etc., spans up to 1500 feet are frequently adopted. In a tramway on this system at Granite, Montana, the total length of the line is 9750 feet, with a fall of 1225 feet. The descending loads, amounting to a constant weight of about 11 tons, develop over 14 horse-power, which is sufficient to haul ine empty buckets as well as about 50 tons of supplies per day up the line, and

also to run the ore crusher and elevator. It is capable of delivering 250 tons of material in 10 hours.

Suspension Cableways or Cable Hoist-conveyors.

(Trenton Iron Co.)

In quarrying, rock-cutting, stripping, piling, dam-building, and many other operations where it is necessary to hoist and convey large individual loads economically, it frequently happens that the application of a system of derricks is impracticable, by reason of the limited area of their efficiency and the room which they occupy.

To meet such conditions cable hoist-conveyors are adapted, as they can be operated in clear spans up to 1500 feet, and in lifting individual loads up to 15 tons. Two types are made-one in which the hoisting and conveying are done by separate running ropes, and the other applicable only to inclines, in which the carriage descends by gravity, and but one running rope is required. The moving of the carriage in the former is effected by means of an endless rope, and these are commonly known as “ endless-rope " hoistconveyors to distinguish them from the latter, which are termed "inclined " hoist-conveyors.

The general arrangement of the eadless-rope hoist-conveyors consists of a main cable passing over towers, A frames or masts, as may be most convenient, and anchored firmly to the ground at each end, the requisite tension in the cable being maintained by a turnbuckle at one anchorage.

Upon this cable travels the carriage, which is moved back and forth over the line by means of the endless rope. The hoisting is done by a separate rope, both ropes being operated by an engine specially designed for the purpose, which may be located at either end of the line, and is constructed in such a way that the hoisting-rope is coiled up or paid out automatically as the carriage is moved in and out. Loads may be picked up or discharged at any point along the line. Where sufficient inclination can be obtained in the main cable for the carriage to descend by gravity, and the loading and unloading is done at fixed points, the endless rope can be dispensed with. The carriage, which is similar in construction to the carriage used in the endless-rope cableways, is arrested in its descent by a stop-block, which may be clamped to the main cable at any desired point, the speed of the descending carriage being under control of a brake on the engine-drum. Stress in Hoisting-ropes on Inclined Planes. (Trenton Iron Co.)

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The above table is based on an allowance of 40 lbs. per ton for rolling friction, but an additional allowance must be made for stress due to the weight of the rope proportional to the length of the plane. A factor of safety of 5 to 7 should be taken.

In hoisting the slack-rope should be taken up gently before beginning the lift, otherwise a severe extra strain will be brought on the rope.

A Double-suspension Cableway, carrying loads of 15 tons, erected near Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury in Trans. A. I. M. E. xx. 766. The span is 733 feet, crossing the Susquehanna River. Two steel cables, each 2 in. diam., are used. On these cables runs a carriage supported on four wheels and moved by an endless cable 1 inch in diam. The load consists of a cage carrying a railroad-car loaded with lu

ber, the latter weighing about 12 tons. The power is furnished by a 50-H.P. engine, and the trip across the river is made in about three minutes.

A hoisting cableway on the endless-rope system, erected by the Lidgerwood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in length, with main cable 21⁄2 in. diam., and hoisting-rope 134 in. diam. Loads of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute.

Another, of still longer span, 1650 ft., was erected by the same company at Holyoke, Mass., for use in the construction of a dam. The main cable is the Elliott or locked wire cable, having a smooth exterior. In the construction of the Chicago Drainage Canal twenty cableways, of 700 ft. span and 8 tons capacity, were used, the towers travelling on rails.

Tension required to Prevent Slipping of Rope on Drum. (Trenton Iron Co.)-The amount of artificial tension to be applied in an endless rope to prevent slipping on the driving-drum depends on the character of the drum, the condition of the rope and number of laps which it makes. If Tand S represer respectively the tensions in the taut and slack lines of the rope; W, the necessary weight to be applied to the tail-sheave; R, the resistance of the cars and rope, allowing for friction; n, the number of half-laps of the rope on the driving-drum; and f, the coefficient of friction, the following relations must exist to prevent slipping:

T= Sefn", W=T+S, and R=T-S;

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in which e = 2.71828, the base of the Naperian system of logarithms. The following are some of the values of ƒ :

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Wet.

Greasy.

.120

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235

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.495

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The importance of keeping the rope dry is evident from these figures.

The values of the coefficient

efnπ +1
efnt 1

, corresponding to the above values

of f, for one up to six half-laps of the rope on the driving-drum or sheaves, are as follows:

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When the rope is at rest the tension is distributed equally on the two lines of the rope, but when running there will be a difference in the tensions of the taut and slack lines equal to the resistance, and the values of T and S may be readily computed from the foregoing formulæ.

Taper Ropes of Uniform Tensile Strength.-The true form of rope is not a regular taper but follows a logarithmic curve, the girth rapidly increasing toward the upper end. Mr. Chas. D. West gives the following formula, based on a breaking strain of 80,000 lbs. per sq. in. of the rope, core included, and a factor of safety of 10: log G = F/3680+ log g, in which Flength in fathoms, and G and g the girth in inches at any two sections F fathoms apart. The girth g is first calculated for a safe strain of 8000 lbs. per sq. in., and then G is obtained by the formula. For a mathematical investigation see The Engineer, April, 1880, p. 267.

TRANSMISSION OF POWER BY WIRE ROPE.

The following notes have been furnished to the author by Mr. Wm. Hewitt, Vice-President of the Trenton Iron Co. (See also circulars of the Trenton Iron Co. and of the John A. Roebling's Sons Co., Trenton, N. J.: "Transmission of Power by Wire Ropes," by A. W. Stahl, Van Nostrand's Science Series, No. 28; and Reuleaux's Constructor.)

The force transmitted should not exceed the difference between the elastic limit of the wires and the bending stress as determined by the following tables, taking the elastic limit of tempered steel, such as is used in the best rope, at 57,000 lbs. per sq. in., and that of Swedish iron at half this, or 28,500 lbs. (The el. lim. of fine steel wires may be higher than 57,000 lbs)

Elastic Limit of Wire Ropes.

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Section

The working tension may be greater, therefore, as the bending stress is less; but since the tension in the slack portion of the rope cannot be less than a certain proportion of the tension in the taut portion, to avoid slipping, a ratio exists between the diameter of sheave and the wires composing the rope, corresponding to a maximum safe working tension. This ratio depends upon the number of laps that the rope makes about the sheaves, and the kind of filling in the rims, or the character of the material upon which the rope tracks.

The sheaves (Fig. 165) are usually of cast iron, and are made as light as possible consistent with the requisite strength. Various materials have been used for filling the bottom of the groove, such as tarred oakum. jute yarn, hard wood, India-rubber, and leather. The filling which gives the best satisfaction, however, in ordinary transmissions consists of segments of leather and blocks of India-rubber soaked in tar and

of Rim,

Section of Arm.

FIG. 165.

packed alternately in the groove. Where the working tension is very

great, however, the wood filling is to be preferred, as in the case of long-distance transmissions where the rope makes several laps about the sheaves, and is run at a comparatively slow speed.

The Bending Stress is determined by the formula

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k

bending stress in lbs.; E

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modalus of elasticity gregate area of wires, sq. ins.; R = radius of bend; d= For 7-wire rope d = 1/9 diam. of rope; C = 27.54.

d = 1/15

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66

; C = 45.9.

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19-wire From this formula the tables below have been calculated.

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2,692 1,822 1,877 1,106 9:25
4,243 2,878 2,178 1,751
5.962 4,053 3.070 2,470 2,067 1,777: 1,558 1,387 1,250 1,138
8,701 5,915 4,486 3,613 3,025 2,601 2,282 2,032 1,831] 1,667
8,267 6,278 5,060 4,239 3,646 3,199 2,849 2,569 2,339
10,535 8,008 6,459 5,412 4,657 4,087 3,641 3,283 3,059
13,655 10,392 8,388 7,032 6,053 5,314 4,735 4,270 3,888
21,585 16,465 13,309 11,168 9,620 8,449 7,532 6,795 6,189
24,492 19,824 16,651 14,354 12,613 11,249 10,151 9,249
34,721 28,144 23,661 20,411 17,986 16,011 14,453 13,172
38,472 32,374 27,945 24,582 21,942 19,814 18,062

42,962 37,110 32,661 29,164 26,344 24,021
55,595 48,054 42,314 37,799 34,155 31,151

Bending Stresses, 19-Wire Rope.

794

696

620

558

508

1,465 1,259 1,104

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4,546 2,389 1,620 1.226
6,609 3.495 2,376 1,800 1,448 1,212 1,042
5,089 3,468 2,630 2.118 1,773 1,525 1,338 1,191
7,095 4,847 3,680 2,967 2,485 2,137 1,876 1,671
9,257 6,201 4,818 3,886 3,257 2,802 2.459 2,191 1,976
11,807 8,101 6,165 4,977 4,173 3,591 3,153 2,809 2,534
18.183 12,528 9,556 7,724 6,481 5,583 4,886 4.371 3,943
27,612 19,113 14,614 11,830 9,937 8,566 7,528 6,714 6,059

26,566 20,357 16,500 13,872 11,966 10,523 9,387 8,474
35,683 27,400 22,239 18,713 16,153 14,209 12,682 11,452
48,109 37,028 30,096 25,350 21,897 19,272 17,209 15.545
61,238 47,229 38,436 32,403 28,008 24,662 22,030 19,906
59,094 48,152 40,629 35,140 30,95727,664 25,005
74,565 60,844 49,919 44,476 39,203 35,048 31.689
90,325 73,795 62,379 54,022 47,659 42,606 38.534
88,409 74,795 64,814 57,183 51,160 46,285
92,203 81,428 72,908 66,002
99,951 96,540

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