Surfaces of a more general character than these elementary ships 

 can be deduced in various ways. For rectangular contours surface equations 

 can be derived immediately from the expression [25]. However, it seems pref- 

 erable to begin with simple geometrical concepts. 



A. Consider for instance 



r, = [X(|) - y{^)f^{i)] Z(^) [41] 



where the "fining function" v(^) complies with the condition 



v(1) - v(-T) = v(o) = 



fglo) = 



[k^ ] can be interpreted as an elementary ship minus a layer v{^)f^{^)Z{,^) 

 which assumes zero values on the center-line contour. The equation of the 

 sectional-area curve becomes 



A^l) = X(^) -A v(|) [42] 



with 



Putting for instance f(f) = ^ we get an inclination of sections at the LWL. 

 When v(0 ^ 0, >ff > 0, Equation [42] expresses the fact that the sectional" 

 area curve becomes finer than the water line towards the ends. The local sec- 

 tional-area coefficients are expressed by 



ySd) = ys - ^^ III] [45] 



i.e., they are smaller than /S when > 0,v{^) > d. 



B. An additional effect is obtained by substituting for Z(f) 



Z(^0 = 1 - bn Ulf"^'... [44] 



By suitably choosing the functions b (O and exponents n the fullness and max- 

 imum curvature of sections towards the ends can be reduced. 



When a parallel mlddlebody is inserted in the forebody of length !„ 

 an appropriate expression for a water line is 



