84 



When the center plane contour Is a rectangle even equations with a 

 small number of terms yield satisfactory results. When dealing with more gen- 

 eral cases, it may be advantageous to introduce fractional powers. However, 

 we need not consider such procedures within the scope of the present report. 



Derivatives of dimensional and dimensionless values are connected 



by 



dy ^ B d7? 

 dx L d| 



[26] 



water lines and sectional-area curves are expressed by 



X(0 = r,{^) = 1 -27«n^" [27] 



sections by 



z(f) = vii) = 1 -Z'V'" [28] 



where generally it is assumed that 



»7(|) = for | = ±1 



[29: 



Families with two arbitrary parameters are named basic systems. 

 These parameters can be expressed by ^ or a and Taylor's t-coefficient where 



t=-||;l [30] 



We use the symbol 



{n^.n2,n^;<^: t) = 1 -J^a^.^""' [31] 



nj 712*13 



with the condition 



Z^n^ = "I 



a may be substituted for (p. 



Further form parameters are 





[32] 



I = 



(3) the dimensionless curvature at the midship section 

 of the ship line, 



[k) Length of parallel middlebody, 



(5) Position of the centroid of the fore or aft area 

 (volume), for instance 



