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_.
+-----------+--------+--------+----------+--------------+
| | | | P. |Difference of |
| Number of | R. |Observed|Calculated| the observed |
|Experiment.| Load | power | power |and calculated|
| | in lbs.| in lbs.| in lbs. | values. |
+-----------+--------+--------+----------+--------------+
| 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.