Maruo 



coefficient. However Bessho has proved for the infinite strut that there is no 

 solution under such dual condition. This situation is similar for the elementary 

 ship of finite draft. 



The wave resistance of an elementary ship is expressed by a general 

 form as 



R = ^^ f(x) dx fCx') K(x-x')dx' (15) 



U J-l J-l 



where y = f(x) is the equation of the load water line and the kernel K(x - x') 

 depends upon the shape of the frame line. Change of the variables 



x= -'{•COS d , x' = -'tcos 9' 



and substitution of the expression for the solution, remembering that the opti- 

 mum form is symmetric, 



f(x) - (a + a, cos 29 + a. cos 49 + ■••) (16) 



sin 9 ° ^ ^ 



lead to the equation such as 



CO en 



'^ 'o / ■ / ■ 2n 2m 2n,2ni 



n=0 m=0 



where 



M,n 2m = d(9 COS 2n9 COS 2m0'K('{. cos 9' - -l cos 9) 69' (18) 



Jo Jo 



b being the half breadth of the ship. The condition of the constant volume is 



a^ = constant ~ C (19) 



while the half beam which is also assumed constant is 



b=b ^ (-)"a,„. (20) 



n = 



Now let us determine the coefficients a^^ in such a way that the right hand side 

 of Eq. (17) becomes minimum. Consider a function 



T(a^,a2,...,k) = 2Z Z ^2n32m^l2n,2m ^ ^ 1 " L ^-^"^2n 



(21) 



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