CONICAL DRUMS
12. In hoisting in balance from deep shafts with cylindrical drums, if no tail-rope is used, or in hoisting from a single shaft with an unbalanced cage, the hoisting engine is not loaded equally at different points of the hoist owing to the gradually changing weight of the unbalanced rope. The following illustrations will further explain this.
13. Hoisting With a Cylindrical Drum.—Suppose that, from a single-compartment vertical shaft 1,000 feet deep, it is required to hoist each trip a load, including friction, of 11,000 pounds made up as follows:
| Pounds | |
| Weight of material | 4,000 |
| Weight of car | 3,000 |
| Weight of cage | 3,000 |
| Friction, 10 per cent. | 1,000 |
| Total | 11,000 |
If a 1⅜-inch cast-steel rope weighing 3 pounds per foot is used, winding about a drum 7 feet in diameter, the weight of rope is then 3 × 1,000 = 3,000 pounds and the load on the rope, when the cage is at the bottom, is 11,000 + 3,000 = 14,000 pounds, while at the top the load on the rope is only 11,000 pounds. The moment of the load at the bottom is then the load 14,000 multiplied by the radius 3½, or 14,000 × 3½ = 49,000 foot-pounds; and at the top, 11,000 × 3½ = 38,500 foot-pounds. This shows that the load against the engine is much greater at the beginning than at the end of the hoist.
14. Take now a double-compartment vertical shaft of the same depth as in [Art. 13] and assume the same amount of material hoisted at a trip, in the same mine car and on the same cage; but that an empty car and cage are lowered in one compartment while the loaded car and cage are hoisted in the other. The two cars and the two cages will balance each other, and the loads will be as follows: At the beginning of the hoist, when the loaded car and cage are at the bottom, the gross load is 14,000 pounds, made up as follows:
| Pounds | |
| Weight of material | 4,000 |
| Weight of mine car | 3,000 |
| Weight of cage | 3,000 |
| Friction, 10 per cent.of above | 1,000 |
| Weight of rope | 3,000 |
| Total | 14,000 |
Multiplying this by the radius of the drum, the gross turning moment is 14,000 pounds × 3½ feet = 49,000 foot-pounds, as before, but there is a counterbalancing load of 6,000 pounds, made up as follows:
| Pounds | |
| Weight of mine car | 3,000 |
| Weight of cage | 3,000 |
| Total | 6,000 |
| Less friction, 10 per cent. | 600 |
| 5,400 |
This means a counterbalancing load moment of 5,400 pounds × 3½ feet = 18,900 foot-pounds. The net load moment to be overcome by the engine at the beginning of the hoist is, therefore, 49,000-18,900 = 30,100 foot-pounds.