19 by a' 



31 



The resistance curves in Figure 19 corresponding to £ - £ 5 and I* 



are somewhat similar in the range of the large hump and the ratios of their 

 absolute values are of the order of 0.5. In the range of the second hump the 

 ordinates of both curves are small, but it is characteristic that here a much 

 lower resistance corresponds to the finer line I*, rather than to £ - £ 5 . 



We return now to the four TMB models designated by I, II, III, I? 

 shown in Figures 14 and 15. In these figures the line A*(£) shows the sym- 

 metrical part of a body. The resistance results are plotted on Figures 16, 17 

 and 18;* in them the lower set represents the contribution due to antisymmetry 



R a 



r oa ^TrpgC 2 b 4 /a ' 



the upper set the total wave -resistance coefficient 



R a + R s 

 r o = knpgC* b 4 /a* 



The computations are made under the assumption that the doublet distribution 

 //*(£) = A*(£). With the model number rising from I to IV the prismatic in- 

 creases and the asymmetry decreases. In the important range of Froude numbers 

 0.50 > F > 0.35 the finer models are extremely unfavorable because of the 

 low prismatic as well as because of the very pronounced asymmetry. 



When comparing the total resistance values a slight departure from 

 symmetry generally is advantageous because of viscous effects. It has also 

 been pointed out that small asymmetric terms do not increase appreciably the 

 wave resistance even in the most sensitive range of Froude numbers, say 

 0.45 ^ F > 0.35; this is well supported by our present results, for instance 

 by Curve IV. Further, the obvious fact must be once more emphasized that an 

 immediate comparison between symmetrical and asymmetrical bodies— as to their 

 wave -resistance properties— is only feasible when the sectional area of the 

 former A*(£) is the even part of the sectional area of the latter 



A*U) = A*U) + A»(£) 

 It is entirely possible to obtain asymmetrical forms with wave-resistance 

 properties which are superior to the corresponding ones of a poorly chosen 

 symmetrical form, equal prismatics and principal dimensions being assumed. 



Similar computations have been performed for other depths of im- 

 mersion; some results are listed in Table 2 of Appendix III. Obviously it 

 is not difficult to investigate the wave resistance corresponding to any 

 curve of the family defined by Equation [4e] at the three depths of immersion 

 for which the integrals have been tabulated. 



*There is a slight error in the resistance curves R of Model III due to inaccuracy in computations, 

 but it does not invalidate the comparison. 



