Lin, Paulling, and Wehausen 



Some preliminary comments with regard to possible expectations seem in 

 order. As noted above, for the symmetric forms the Michell wave resistance at, 

 and for some interval below, the design speed is generally negligibly small 

 compared with the frictional resistance. If the "real" wave resistance does in 

 some sense approximate this, any attempt to observe it experimentally will be 

 plagued by the uncertainty in estimation of the "viscous part" of the total resist- 

 ance. In particular, a region of boundary-layer separation or even an excessive 

 form drag may have the effect of masking completely the quantity being meas- 

 ured. In addition, one must bear in mind that Michell' s integral is based upon 

 linearization of the boundary conditions and represents the first term in a per- 

 turbation series in B/L . However, the fact that this first term is very small for 

 a particular form does not imply that the second-order term is also very small 

 for this form. Under such circumstances it may, in fact, be considerably larger, 

 although still of second order. Consequently, there may exist an appreciable 

 wave drag in an inviscid fluid even though the linearized theory predicts prac- 

 tically none. 



CHOICE AND CONSTRUCTION OF MODELS 



One hull form was selected from each of the two series. For each, the form 

 optimum for /^ = 5 (Fr = 0.316) was selected. As has been mentioned above, 

 the choice y^ = 5 for the hull with prescribed afterbody was hardly a free one. 

 For the symmetric ship this form was chosen because 0.316 was the largest 

 Froude number for which the corresponding optimum ship had waterlines of 

 small enough slope so that boundary- layer separation did not seem likely to 

 occur and thus render invalid the fundamental assumptions underlying the com- 

 putation. Figure 2 shows the section curves, waterlines and area curve for the 

 optimum symmetric ship for 7^ = 5. Figure 3 shows the prescribed afterbody, 

 both as designed and as represented by the Fourier series. Figure 4 shows the 

 optimum forebody for 7^ = 5. 



The models as actually constructed differed slightly from those designed by 

 the computer. For the symmetric model the lines in the neighborhood of the 

 regions of negative ordinates were modified slightly so that the ordinates were 

 zero in these regions. In effect, this created a submerged protruding bulb, as 

 in some of Inui's optimum forms, but not as deeply submerged. The optimum 

 forebody as shown in Fig. 4 has rather noticeable wiggles in the midship section 

 and in the section just ahead of it, a result of trying to fit a U-shaped section 

 with only six terms of a Fourier series. In this case the afterbody was built as 

 originally designed and not as approximated, and the forebody was modified 

 slightly near the midsection to make it join smoothly to the afterbody. Figure 5 

 shows photographs of each model. 



CRITERIA AND STANDARDS OF COMPARISON 



One way to judge the performance of a proposed hull form is to compare it 

 with others of acknowledgedly good performance. Of the usual measures of per- 

 formance the dimensionless ratio R//ogV at and near the design Froude and 

 Reynolds numbers seems most appropriate and has been used in this paper. The 



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