Yim 



and 



Q=Q, +«Q2 +^Q3 (31) 



with the functions P and Q evaluated and substituted into Eq, (19) » 

 the wave resistance may be minimized with respect to such parameters 

 as a and Cu. 



V. OPTIMUM TRANSOM STERN AND BOW BULB 



A usual technique is employed to obtain the optimum vcdues 

 of a and cr^j for given k, B|/L, Bg/L, z,, and H/L, Namely, we 

 solve two linear simultaneous equations in a and (y^ 



aR o ,'^ 



^ = 2a{I>l + Q;) + 2cr,(P2P3 + Q2Q3) + 2(P,P2 + Q, Q^) = 



(32) 



__ PjPj (33) 



m=0 

 etc, 



from the formula of wave resistance. Cases of Bg = 0, B, ^ 0; 

 Bg =5^ , B, =0 and B, it 0, Bg ^ were calculated for each Froude 

 number F„, which will be shown later. 



VI. SLENDER BODY THEORY 



For the case of Bg = 0, the cross sectional area curve is a 

 cusp at both ends. Thus a slender body theory can easily be applied 

 here. The result will be only the change of 



E -* i (34) 



and 



(35) 



B, ^ A 



in P| and Q| in Eqs, (23) and (26) of the wave resistance of the 

 previously described Michell ship, where A is the area of the mid- 



580 



