THE CRANE.
331. We have already explained ([Art. 38]) the construction of the lifting crane, so far as its framework is concerned. We now examine the mechanism by which the load is raised. We shall employ for this purpose the model which is represented in [Fig. 48]. The jib is supported by a wooden bar as a tie, and the crane is steadied by means of the weights placed at h: some such counterpoise is necessary, for otherwise the machine would tumble over when a load is suspended from the hook.
332. The load is supported by a rope or chain which passes over the pulley e and thence to the barrel d, upon which it is to be wound. This barrel receives its motion from a large wheel a, which contains 200 teeth.
The wheel a is turned by the pinion b which contains 25 teeth. In the actual use of the crane, the axle which carries this pinion would be turned round by means of a handle; but for the purpose of experiments upon the relation of the power to the load, the handle would be inconvenient, and therefore we have placed upon the axle of the pinion a wheel c containing a groove in its circumference. Around this groove a string is wrapped, so that when a weight g is suspended from the string it will cause the wheel to revolve. This weight g will constitute the power by which the load may be raised.
333. Let us compute the velocity ratio of this machine before commencing experiments upon its mechanical efficiency. The effective circumference of the barrel d is found by trial to be 14"·9. Since there are 200 teeth on a and 25 on b, it follows that the pinion b must revolve eight times to produce one revolution of the barrel. Hence the wheel c at the circumference of which the power is applied must also revolve eight times for one revolution of the barrel. The effective circumference of c is 43"; the power must therefore have been applied through 8 × 43" = 344", in order to raise the load 15"·9. The velocity ratio is 344 ÷ 14·9 = 23 very nearly. We can easily verify this value of the velocity ratio by actually raising the load 1', when it appears that the number of revolutions of the wheel b is such that the power must have moved 23'.
Fig. 48.
334. The mechanical efficiency is to be found as usual by trial. 56 lbs. placed at f is raised by 3·1 lbs. at G; hence the mechanical efficiency deduced from this experiment is 56 ÷ 3·1 = 18. The percentage of useful effect is easily shown to be 78 by the method of [Art. 323]. Here, then, we have a machine possessing very considerable efficiency, and being at the same time economical of energy.
Circumference of wheel to which the power is applied, 43"; train of wheels, 25 ÷ 200; circumference of drum on which rope is wound, 14"·9; velocity ratio, 23; mechanical efficiency, 18; useful effect, 78 per cent.; formula, P = 0·0556 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs. | Difference of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 14 | 0·9 | 0·8 | -0·1 |
| 2 | 28 | 1·6 | 1·6 | 0·0 |
| 3 | 42 | 2·4 | 2·3 | -0·1 |
| 4 | 56 | 3·1 | 3·1 | 0·0 |
| 5 | 70 | 3·8 | 3·9 | +0·1 |
| 6 | 84 | 4·5 | 4·7 | +0·2 |
| 7 | 98 | 5·3 | 5·5 | +0·2 |
| 8 | 112 | 6·2 | 6·2 | +0·0 |
335. A series of experiments made with this crane is recorded in [Table XXI]., and a comparison of the calculated and observed values will show that the formula P = 0·0556 R represents the experiments with considerable accuracy.
336. It may be noticed that in this formula the term independent of R, which we frequently meet with in the expression of the relation between the power and the load, is absent. The probable explanation is to be found in the fact that some minute irregularity in the form of the barrel or of the wheel has been constantly acting like a small weight in favour of the power. In each experiment the motion is always started from the same position of the wheels, and hence any irregularity will be constantly acting in favour of the power or against it; here the former appears to have happened. In other cases doubtless the latter has occurred; the difference is, however, of extremely small amount. The friction of the machine itself when without a load is another source for the production of the constant term; it has happened in the present case that this friction has been almost exactly balanced by the accidental influence referred to.
337. In cranes it is usual to provide means of adding a second train of wheels, when the load is very heavy. In another model we applied the power to an axle with a pinion of 25 teeth, gearing into a wheel of 200 teeth; on the axle of the wheel with 200 teeth is a pinion of 30 teeth, which gears into a wheel of 180 teeth; the barrel is on the axle of the last wheel. A series of experiments with this crane is shown in Table XXII.
Table XXII.—The Crane for Heavy Loads.
Circumference of wheel to which power is applied, 43"; train of wheels, 25 ÷ 200 × 30 ÷ 180; circumference of drum on which rope is wound, 14"·9; velocity ratio, 137; mechanical efficiency, 87; useful effect, 63 per cent.; formula, P = 0·185 + 0·00782 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs. | Difference of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 14 | 0·30 | 0·29 | -0·01 |
| 2 | 28 | 0·40 | 0·40 | 0·00 |
| 3 | 42 | 0·50 | 0·51 | +0·01 |
| 4 | 56 | 0·60 | 0·62 | +0·02 |
| 5 | 70 | 0·75 | 0·73 | -0·02 |
| 6 | 84 | 0·85 | 0·84 | -0·01 |
| 7 | 98 | 0·95 | 0·95 | 0·00 |
| 8 | 112 | 1·05 | 1·06 | +0·01 |
The velocity ratio is now 137, and the mechanical efficiency is 87; one man could therefore raise a ton with ease by applying a power of 26 lbs. to a crane of this kind.