EXPERIMENTS ON THE FROUDE. 115 
Completing the square gives, 
inst — AX wit , tf yt y 
R gaint K with (V+V'0) (V— V'u) = {((V+ V1.) +(V— Vu) } 
KA 
eset V?—2 Vu" =(2V)? 
=4V" 
a V?=2Vu" 
Vro= a{Rassioe Re win against SR: with MY: 
2KA 
To illustrate the use of this method, in the case of the experimental 
model Froude, 2 KA = . 34. 
On the runs of August 23 at 7 knots the thrust with the wind was 286 
pounds and against the wind was 322 pounds. Whence, 
oe V2 49 
Vien [P= 28S, —49= ey ya os) 
Therefore the speed of the idl V'w=7.5 knots. 
With the velocity of the wind known it is now possible by using Froude’s 
formula to figure the wind resistance of the boat at any speed in either 
direction, as for instance at 7 knots. 
Ry against — O.17 (14.5)°= 35-7 
non SON Of S On 
Now the total divergence between the two curves at 7 knots should be 
equal to the sum of these quantities. 
35-7 +0.4 = 36.1 pounds. 
As a matter of fact, the difference was actually 36 pounds. 
Subtracting the wind resistance from the curve with the wind, will 
give a curve for zero air resistance; that is for a ship always accompanied 
by air going at the same velocity that the ship is. 
Now to the curve of zero air resistance should be added the normal air 
resistance due to the speed of the ship through the still air which gives 
the heavy full line curve of Fig. 32, and this is a curve from which wind 
influence has been eliminated. 
It is interesting to note that the speed of the wind as solved by the 
above method agreed closely with that speed of the Froude where the entry 
in the log reads “ V of Froude same as V of wind.” 
