5 
with the velocity according to a certain exponential func- 
tion, namely, 
5 WV? 
peer ig é ) ; : : ‘ (2) 
where A and v! are constants as regards v. 
Before examining this relation we change the variables in 
certain manner. Instead of the speed v, we use the speed- 
length ratio ¢ defined as (speed of ship in knots)//(ength in 
feet); further, the resistance R is expressed in lbs. per ton 
displacement of the ship. The advantages of these changes 
are found in calculating from the results of model experl- 
ments similar quantities for a ship of any dimensions on the 
same lines as the model; R is the same for equal values of ¢ 
in the two cases. 
400 
EY) 
ys 7) 
Fig. 1 represents the type of curve given by R=Ae x : 
The slope of the curve increases up to the value c!, and 
then falls off for higher values of c. I increases continu- 
ally with ¢, and approaches a limiting value equal to the 
coefficient A. If we compare Fig. 1 with any experimental 
curve of residuary resistance we find that the general 
features are the same, but if we wish to obtain a close agree- 
ment over a large range of values of ¢ there are two ways in 
which the formula must be extended. 
63 
