The transformation is given by 



§= -2(x - 0.5) or 



The resulting equation is 



y 2 = A n + A § + A £ 2 + A £ 3 + A ? 4 + A t 5 + A f 6 [3] 



1 2 3 4 5 6 



where 



a =r-5. A = - t— 5. a = r n ( n - 1 1 -^ 



4 2 n x 4 2 n 2 4 2 2 n 



A ■./• n(n-1)(n-2) 

 3 4 2 x 3 x 2 n 



Equation [3] can be split up into a symmetrical and an antisymmetrical part 



Y s = A o + V* + V 4 + A 6^ [4a] 



y 2 - Y - Y s + y a 



Y a = AJ + kj 3 + kj 5 [4b] 



The obtained form [3] has definite advantages when calculating the wave re- 

 sistance since the latter is the sum of the wave resistance corresponding to 

 the symmetrical and antisymmetrical part computed independently. 



Going further, we derive from [3] the following simple properties 

 of the Landweber bodies: 



i" *rf -z v n 



The coefficient A Q can be factored out and merged into a dimensional constant 

 which defines the midship section. Thus, the normal form of our polynomial 

 is obtained 



1 " A i 

 with a . = — r± 



1 A o 

 The symmetrical part of [4c] is a two-parameter family 



H B '(«) = T - a 2 * 2 - aj* - a g * 6 = 1 - ? 6 - a^ 2 - § 6 ) - a^. (**-«•) 

 because from the boundary condition 



n s 0) - 



a = 1 - a - a 



6 2 4 



