Data for Ships of Minimum Resistance 



° 0.05 — 



Fig. lb - Michell resistance for optinnum symmetric forms 



larger amount than for the symmetric bodies, partly it was the result of exces- 

 sive waviness in the waterlines. In the present context the latter was objection- 

 able not because of the practical difficulty of fabricating such shapes but be- 

 cause of the great liklihood of boundary -layer separation behind the bellies. As 

 was stated in the cited paper, imposition of restraints like < f(x,z) < m, 

 -C < f^(^,g)< D, which would have prevented the excessive waviness, presents 

 a much more difficult problem in computation. The wave resistance for these 

 forms, again as predicted by Michell's integral, is no longer negligible compared 

 with the frictional resistance for comparable forms. For example, at the design 

 speed the coefficient R^,/pgV for the form corresponding to /^ = 5 is approxi- 

 mately half the coefficient R/pgV for the equivalent ship from Taylor's Standard 

 Series, and about one third the frictional resistance coefficient R^/pgV. 



Following the obtaining of these results, several courses of action seemed 

 open: there were mathematical questions to be resolved; the effect of increasing 

 the number of Fourier components upon the waviness of the waterlines could be 

 studied; a feasible method of incorporating inequalities among the constraints 

 could be devised. However, more important than any of these seemed having 

 some experimental evidence that the optimum forms derived from theory did, 

 in fact, have good resistance characteristics. The main purpose of this paper 

 is to report the results of testing two of the forms. 



1049 



