102 EXPERIMENTS ON THE FROUDE. 
The question of direct interest to the shipbuilder and the naval architect 
is the power which should be given to a certain ship to give a desired speed. 
In the end all tests and trials should be made to tend toward an answer to 
this question. As a contribution to the answering of this question a com- 
parison will be made of the actual observed power of the Manning with an 
estimation of power from the resistance of the 23.5-foot model as determined 
in the Model Basin, together with an estimate of the wake and the thrust- 
deduction from the tests on the Froude. 
Thus, in the analysis on page 100, the residual power estimated from 
the 23.5-foot model is 850, while the surface friction power is 539, so that 
the effective horse-power can be estimated to be 1,389 instead of 1,200 as 
set down. Consequently an estimate of the power for the Manning from 
the 23.5-foot model would be in excess in the ratio 
1389 +1200=1.155; 
that is, the excess appears to be 153 per cent. 
At first blush this discrepancy appears to be distressing, but those who 
have experience in this matter come to look upon it as normal instead of 
exceptional. 
In the first place we must remember that the power varies rapidly with 
speed and that the comparison just made is very sensitive. Commonly the 
power of a ship is assumed to vary with the cube of the speed; but this relation 
is proper only when the speed-length ratio is less than unity. In the case 
in hand the speed-length ratio is 1.17 which indicates an abnormally high 
speed for a ship of the type of the Manning, and the power probably increases 
as the fourth-power of the speed if not more rapidly. If the fourth-power 
be taken in this case then an overestimate of 16 per cent. in the power 
would give only 4 per cent. excess in speed. So much for an attempt at 
quieting the apprehension of the shipowner. As for the naval architect 
if he can satisfy himself that a certain method habitually overestimates the 
power by a known per cent. he is nearly as well pleased as he would be with 
an accurate method. 
For our present purpose the most desirable thing if possible would be 
an analysis of the discrepancy with the object of distributing it among the 
various elements that may influence it. 
Through an inadvertence on our part the 23.5 model as tested at the 
Washington Model Basin was 3 per cent. light compared with the Manning 
on trial. It has been pointed out by Naval Constructor Taylor that the 
resistance of a ship does not increase with the displacement but at a slower 
