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'.
[Illustration: 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.