58 



To eliminate the trivial answer that the wave resistance vanishes 

 for vanishing displacement some additional "restraint" must be introduced; the 

 most Important condition is to assume a constant displacement. Also, the con- 

 ditions of a fixed midship section A„ = ^xBxH = const, and of least specific 

 resistance are of theoretical interest. Thus, a number of Isoperlmetric 

 problems in wave resistance are formulated. 



Frbm an inspection of Michell's Integral as well as from physical 

 reasoning, it is obvious that a rather trivial answer exists as to the best 

 vertical distribution of the displacement. Since the influence of the wave 



_ 2jL£ 



making decreases with e ^ the displacement should be concentrated as far 

 below the water line as possible or the draft should be Infinite. Thus, even 

 when the volume is fixed, additional restrictions on the draft and the shape 

 of the transverse sections are necessary. The essential remaining problem to 

 be solved is the optimum longitudinal distribution of displacement. 



A plausible simplification is to substitute an Infinite draft as 

 long as only general information is desired; but such an approach is not suit- 

 able when detailed practical results are needed. 



Some results have been found by applying Rltz's method which, how- 

 ever, are valid only for the restricted kind of functions used (Figure 31). 



To quote from an earlier paper 



'As a further difficulty It may be mentioned 



that the assumption of the type of surface equation Involves a highly arbi- 

 trary element, and very advantageous forms can remain outside the scope of our 

 considerations by lack of knowledge of their analytical representation;" 



Figure 31 - Sectional Area Curves for Ships of Least Resistance 



