850 REPORT—1899, 
at 30 knots the resistance is about 174 tons; the effective horse-power is 3,600, 
and the indicated horse-power about 6,000, or 20 horse-power per ton, nearly five 
times as great as the corresponding power for the large ship. But while the 
destroyer under her trial conditions actually reaches 30 knots, it is certain that 
in the large ship neither weight nor space could be found for machinery and 
boilers of the power required for 30 knots, and of the types usually adopted in large 
cruisers, in association with an adequate supply of fuel. The explanation of the 
methods by which the high speed is reached in the destroyer has already been 
given. Her propelling apparatus is about one-fourth as heavy in relation to its 
maximum power, and her load is only about one-third as great in relation to the 
displacement, when compared with the corresponding features in a swift modern 
cruiser. j 
It will, of course, be understood that in practice, under existing conditions, 
a cruiser of 14,000 tons would not be made 765 feet long, but probably about 
500 feet. The hypothetical cruiser has been introduced simply for purposes of 
comparison with the destroyer. 
The earlier theories of resistance assumed that the resistance experienced by 
ships varied as the square of the speed. We now know that the frictional resist- 
ances of clean-painted surfaces of considerable length vary as the 1:83 power of the 
speed. This seems a small difference, but it is sensible in its effects, causing a 
reduction of 32 per cent. at 10 knots, nearly 40 per cent. at 20 knots, and 42 per 
cent. at 25 knots. On the other hand, it is now known that the laws of variation 
of the residual or wave-making resistance may depart very widely from the law of 
the square of the speed, and it may be interesting to trace for the typical destroyer 
how the resistance actually varies. 
Take first the total resistance. Up to 11 lmots it varies nearly as the square of 
the speed; at 16 knots it has reached the cube; from 18 to 20 knots it varies as 
the 3°3 power. Then the index begins to diminish: at 22 lmots it is 2:7; at 25 
knots it has fallen to the square, and from thence to 30 knots it varies, practically, 
as does the frictional resistance. 
The residual resistance varies as the square of the speed up to 1] knots, as the 
cube at 12} to 13 knots, as the fourth power about 143 knots, and at a higher rate 
than the fifth power at 18 knots. Then the index begins to fall, reaching the 
square at 24 Imots, and falling still lower at higher speeds. 
It will be seen, therefore, that when this small vessel has been driven up to 24 
or 25 knots by a large relative expenditure of power, further increments of speed 
are obtained with less proportionate additions to the power. 
Passing from the destroyer to the cruiser of similar form but of 14,100 tons, 
and once more applying the ‘ scale of comparison,’ it will be seen that to 25 knots 
in the destroyer corresponds a speed of 473 knots in the large vessel. In other 
words, the cruiser would not reach the condition where further increments of speed 
are obtained with comparatively moderate additions of power until she exceeded 
47 knots, which is an impossible speed for such a vessel under existing conditions. 
The highest speeds that could be reached by the cruiser with propelling apparatus 
of the lightest type yet fitted in large sea-going ships would correspond to speeds 
in the destroyer, for which the resistance is varying as the highest power of the 
speed. These are suggestive facts. 
Frictional resistance, as is well known, is a most important matter in all classes 
of ships and at all speeds. Even in the typical destroyer this is so. At 12 knots 
the friction with clean-painted bottom represents 80 per cent. of the total resist- 
ance; at 16 knots 70 per cent.; at 20 knots a little less than 50 per cent. ; and at 
30 knots 45 percent. If the coefficient of friction were doubled and the maximum 
power developed with equal efficiency, a loss of speed of fully 4 knots would result. 
In the cruiser of similar form the friction represents 90 per cent. at 12 knots, 
85 per cent. at 16 knots, nearly 80 per cent. at 20 knots, and over 70 per cent. at 
23 knots. If the coefficient of friction were doubled at 23 knots and the corre- 
spanding power developed with equal efficiency, the loss of speed would approximate 
to 4 knots. 
These illustrations only confirm general experience that clean bottoms are 
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