Figure 3a - Landweber's Axes Figure 3b - Present Axes 



Figure 3 - Systems of Axes 



origin at the bow or stern. The present writer has proposed 13 ' 14 other sets 

 of polynomials referred to a system of axes with an origin located midships. 

 This approach has definite advantages when investigating the wave resistance. 



Landweber 2 has generalized Taylor's equation by adding one more 

 term and by introducing appropriate boundary conditions; he uses the ex- 

 pression obtained as the equation of the sectional-area curve of a four- 

 parameter form. 2 The parameters are interpreted geometrically as the pris- 

 matic coefficient, the location of the maximum section along the axis and 

 the nose and tail radii of curvature. It will be immediately shown that 

 Landweber's equation transferred to an origin at the midship section can be 

 split up into a two-parameter symmetrical and a two-parameter skew part with 

 respect to this section; thus expressions are obtained for which the wave 

 resistance can be calculated in a simple way. 



2.2.2. The TMB (Landweber) Class of Bodies and Some Generalizations 



The TMB (Landweber) class of bodies of revolution is given by the 



equation of the sectional-area curve 



y 



a'x + a'x* + a'x J + a'x* + a'x 3 + a'x" 



11 21 31 41 51 61 



[1] 



referred to axes, as shown in Figure 3- We transform the equation of the 

 body by shifting the origin to the midship section x = 0.5, reversing the 

 direction of the axes, and putting the length of the body equal to 2. 

 Thus for 



x = 



i 



x = 0.5 

 1 



X = + 1 



$ = + 1 



I = 

 * - - 1 



