Lin, Paulling, and Wehausen 



Here the variables have been made dimensionless by measuring distances in the 

 x,y,z directions by 'Ah, VzB^ and H , respectively, where B^ is not the true beam 

 but is fixed at 3h for this purpose. 



The optimum forms which were obtained for the symmetric ship for values 

 of the parameter 7^ = gL/2v^ varying from 5 to 10 were reasonably shiplike in 

 appearance except for some waviness in the lines and two small areas at the 

 waterline near the bow and stern where the ordinates became slightly negative. 

 The waviness seems almost certainly to be a result of the limited number of 

 trigonometric functions used to describe the hull. The amount of negativeness 

 was so small that these regions could be deformed to zero without significantly 

 altering the lines. The wave resistance at design speed for each of these forms, 

 as predicted by Michell's integral, was very small compared with the frictional 

 resistance, in fact, negligible for the forms corresponding to 7^ = 6 to 10. Fig- 

 ure 1 shows the wave -resistance coefficient ^m/psV for each of these optimum 

 forms as predicted by Michell's integral for Froude numbers between 0.18 and 

 0.50. 



Fig. la - Michell resistance for optimum symmetric forms 



The results obtained in the problem with the fixed afterbody were not as sat- 

 isfactory as those described above. With the exception of the forebody obtained 

 for 7^ = 5 (Fr = 0.316) the forebodies were generally unacceptable as ships. 

 Partly this was a result of the occurrence of negative offsets of substantially 



1048 



