82 



1. Load water line 17(^,0) = X(0 = V^i^) [10] 



2. Midship section 17(0, f) = Z(^) = jj (^) [11 ] 



3. Longitudinal section »7(^f) = f = K(0 [12] 

 The area coefficients and coefficients of fineness are 



a = ^(a^ +ap) =1 [j X(Ocl| + J X(e)d|] [13] 



-1 



1 



= Jz(^)df [14] 







L-i -I 



The areas of sections are given by 



AU) = 2 j T7(^f)df 



However, we define a slightly different dlmensionless expression as sectional- 

 area curve 



k(0 



A^d) =^A(o =^ j »7(^.ddf [i6: 



Throughout the text the symbol 77 will be used for equations of surfaces as 

 well as lines. In exceptional cases we add the symbols of independent varia- 

 bles to avoid ambiguity. 



Ship lines and surfaces can be split up, with respect to the midship 

 section, into a main sjnimetrical (even) part ijAO ="^d a secondary asymmetri- 

 cal (odd) part ?7„(^). Only 77^ contributes to the total area or volume of the 

 a s 



curve or surface. 



[17] 



+1 i 



J ;7d^ = 2J 773^1 • [18] 



The asymmetrical part alone contributes to the static moment with respect to 

 the midship section 



S, = J lr,d^ = 2J|77^d^ [19] 



