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 |