26 



and hollows of the resistance curve. ^"^ Thus, using Michell's integral, the 

 concept of dimensionless form seems to be quite appropriate. We shall go even 

 a step farther by splitting up the resistance due to longitudinal and vertical 

 displacement distribution and investigating them independently. 



Matters become more complicated for wholly submerged bodies, but 

 even here the character of the resistance curve is only slightly influenced 

 for small changes in the depth of immersion. 



It is a wholly different question how far the dimensionless form can 

 be treated independently of proportions when dealing vfith actual ship forms 

 to which Michell's theory does not rigorously apply. Let us put the ques- 

 tion in a rather special but practical way: Can we assume that the merits of 

 dimensionless forms tested at definite L/B and L/H ratios (for instance for 

 slender bodies) remain the same for other ratios of L/B and L/H? This problem 

 involves a critical investigation into the validity of Michell's integral. 



Lindblad^* points out that the optimum shape of the sectional-area 

 curve depends to some extent on the B/H ratio. D.W. Taylor's experiments with 

 variants of the "YORKTOVJW" Indicate a slight dependence of the shape of the 

 resistance curve upon B/H. More systematic work dealing with this problem is 

 urgently needed . 



A qualitative estimate can be obtained from a study of bodies of 

 revolution. V/hen their diameter/length ratio d/L is very small the sectional- 

 area curve is proportional to the doublet distribution.*^ By reducing the 

 speed of the generating uniform flow larger d/L ratios are obtained; dimension- 

 less sectional-area curves are no longer affine to the distribution and do not 

 coincide with each other. For a spheroid the deviation is characterized by 

 a decrease in the "length of distribution" with increasing d/L, the prismatic 

 obviously remaining constant <z> = |-. 



The following statement, can be proved for a class of bodies of revo- 

 lution: a. When the fineness coefficient of doublet distribution M., > 2/3, 

 the fineness coefficient of the resulting body decreases with increasing 

 d/L (example: Rankine's oval), b. and when <^, < 2/3, the fineness coefficient 

 increases with d/L. Thus one must infer that the image system suitable to 

 generate a ship form depends on the ratio of principal dimensions. Hence, 

 even the shape (and not just its magnitude) of a resistance curve derived for 

 a dimensionless form varies in principle with these ratios. 



Some additional information is given in the next chapter. We antic- 

 ipate the conclusion: The assumption that the wave resistance of hulls can 

 be treated independently as a function of the dimensionless form and the 



