25 



More detailed information will be given in the next chapters, which 

 are intended to give a clear idea of what can and cannot be expected from the- 

 ory. Anticipating these results we assert that theory even in its present 

 condition yields a powerful tool in resistance research and that an endeavor 

 should be made to use it as a guide in developing closer approximations. 



5. WAVE RESISTANCE AS A PIMCTION OP THE SHIP FORM 



5.1. PROPORTIONS AND SHAPE 



When treating Ship Forms 1.1.2 we made a fundamental distinction 

 between the proportions of a hull and its dlmensionless form. The discussion 



of wave resistance will be based on this division, since by it it appears pos- 

 sible to introduce a scheme into the manlfoldness of dependencies of the re- 

 sistance upon the form. 



Therefore, our next task will be to estimate how far the resistance 

 of a given form can be investigated independently of its proportions. The 

 estimate will be performed by two steps: Within the validity of Michell's 

 integral and outside of it. 



The wave resistance formula denoted by Michell's integral is repro- 

 duced In Appendix 2. For our present investigation we substitute for the 

 rather complicated integral a symbolic formula 



R = pg ^^ Eg ,r?,p) [13] 



In principle, as has been pointed out before, this expression which is equiv- 

 alent to Michell's integral holds only for narrow wedgelike ships. The dl- 

 mensionless factor E{H/L, t? ,P) in which we are primarily interested is a com- 

 plicated function of H/L, the dlmensionless equation of the surface rj and 

 Froude number; it does not depend on the beam. 



Thus we see at once that within the range of validity Michell's 

 integral the dependence of the resistance upon the dlmensionless form 77 is not 

 Influenced by the beam, and that no rigorous separation can be made between 

 the Influence of the surface equation 77 and the draft H (H/L). 



Fortunately, the ratio H/L influences primarily the absolute value 

 of R and only to a slight extent the character of interference effects. Thus 

 comparison between different forms can be made for a definite H/L and the qual- 

 itative results (within the validity of Michell's integral.') safely extrapo- 

 lated to other ratios of H/L. Havelock has shown that even calculations based 

 on infinite draft give reliable results with respect to the position of humps 



