But this cannot be done. It is a fact, on the contrary, that the work
wasted on the water increases in a very rapid ratio with its speed.
The work stored up in the moving water is expressed in foot pounds by
the formula
W v squared / 2g
where W stands for the weight of the water, and v for its velocity.
But the work stored in the water must have been derived from the
engine; consequently the waste of engine power augments, not in the
ratio of the speed of the water, but in the ratio of the square of its
speed. Thus if a screw sends 100 tons of water astern at a speed of 10
ft. per second per second, the work wasted will be 156 foot tons per
second in round numbers. If a hydraulic propeller sent 10 tons astern
at 100 ft. per second per second, the work done on it would be 1,562
foot tons per second, or ten times as much. But the reaction effort,
or thrust on the ship, would be the same in both cases. The waste of
energy would, under such circumstances, be ten times as great with the
hydraulic propeller as with the screw. In other words, the slip would
be magnified in that proportion. Of course, it will be understood that
we are not taking into account resistances, and defects proper to the
screw, from which hydraulic propulsion is free, nor are we considering
certain drawbacks to the efficiency of the hydraulic propeller, from
which the screw is exempt; all that we are dealing with is the waste
of power in the shape of work done in moving water astern which we do
not want to move, but cannot help moving.
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