Wrought iron screw, square thread, diameter
1"·25, with 3 threads to the inch, length of
arm 10"·25; nut of cast iron, bearing surfaces
oiled, velocity ratio 193, useful effect 36
per cent., mechanical efficiency 70; formula
_P_ = 0·0143 _R_.
+-----------+-------+-------------+-------------+----------------+
| | | | P. | Difference of |
| Number of | R. | Observed | Calculated |the observed and|
|Experiment.| Load | power | power | calculated |
| |in lbs.| in lbs. | in lbs. | powers. |
+-----------+-------+-------------+-------------+----------------+
| 1 | 28 | 0·4 | 0·4 | 0·0 |
| 2 | 56 | 0·8 | 0·8 | 0·0 |
| 3 | 84 | 1·2 | 1·2 | 0·0 |
| 4 | 112 | 1·6 | 1·6 | 0·0 |
| 5 | 140 | 2·0 | 2·0 | 0·0 |
| 6 | 168 | 2·4 | 2·4 | 0·0 |
| 7 | 196 | 2·7 | 2·8 | +0·1 |
| 8 | 224 | 3·3 | 3·2 | -0·1 |
+-----------+-------+-------------+-------------+----------------+
283. The results of the experiments are shown in Table XVI. If the
motion had not been aided by a start the powers would have been
greater. Thus in experiment 6, 2·4 lbs. is the power with a start, when
without a start 3·2 lbs. was found to be necessary. The experiments
have all been aided by a start, and the results recorded have been
corrected for the friction of the pulley over which the rope passes:
this correction is very small, in no case exceeding 0·2 lb. The fourth
column contains the values of the powers computed by the formula
_P_ = 0·0143 _R_. This formula has been deduced from the observations
in the manner described in the Appendix. The fifth column proves that
the experiments are truly represented by the formula: in each of
the experiments 7 and 8, the difference between the calculated and
observed values amounts to 0·1 lb., but this is quite inconsiderable in
comparison with the weights we are employing.
284. In order to lift 100 lbs. the expression 0·0143 _R_ shows that
1·43 lbs. would be necessary: hence the mechanical efficiency of the
screw is 100 ÷ 1·43 = 70. Thus this screw is vastly more powerful
than any of the pulley systems which we have discussed. A machine
so capable, so compact, and so strong as the screw, is invaluable
for innumerable purposes in the Arts, as well as in multitudes of
appliances in daily use.
285. It is evident, however, that the distance through which the screw
can raise a weight must be limited by the length of the screw itself,
and that in the _length of lift_ the screw cannot compete with many of
the other contrivances used in raising weights.
286. We have seen that the velocity ratio is 193; therefore, to raise
100 lbs. 1 foot, we find that 1·43 × 193 = 276 units of energy must
be expended: of this only 100 units, or 36 per cent., is usefully
employed; the rest being consumed in overcoming the friction of the
screw. Thus nearly two-thirds of the energy applied to such a screw is
wasted. Hence we find that friction does not permit the load to run
down, since less than fifty per cent. of the applied energy is usefully
employed (Art. 222). This is one of the valuable properties which the
screw possesses.
287. We may contrast the screw with the pulley-block (Art. 199).
They are both powerful machines: the latter is bulky and economical
of power, the former is compact and wasteful of power; the latter is
adapted for raising weights through considerable distances, and the
former for exerting pressures through short distances.
[Illustration: FIG. 44.]