Figure 2 - Spheroid. Sectional-Area 



Curve A, Doublet and Source-Sink 



Distribution 



The equality ^ d = ^ is valid only 

 for the ellipsoid; see Figure 2. 

 Second , in the prismatics a differ- 

 ence arises between the length of 

 the body L and the distribution 2a, 

 2a being smaller than L. For the 

 spheroid the relative difference 



K = 



L-2a 

 2a 



D 2 _ b' 



2L' 



2a' 



where f depends on the shape of the distribution, especially at the ends. 

 (Since this problem is being thoroughly investigated by L. Landweber of the 

 Taylor Model Basin, we confine ourselves to these brief remarks. ) 



b. When complicated "abnormal" distributions like "swan necks" or 

 curves with very steep ends are investigated (for instance, Rankine's ovoid) 

 the divergence between these distributions and the sectional -area curve can 

 become appreciable even for smaller D/L. 



2.2. REPRESENTATION BY POLYNOMIALS 

 2.2.1. General Remarks 



In former reports polynomials have been used for the representation 

 of the generating doublet (source and sink) distribution along the axis. 5 ' 6 * 10 - 13 



The doublet and source-sink distributions f*(x), a[x) can be split 

 up into dimensional factors j* a and variable dimensionless parts #*(£)> 

 <r*(|); //(x) =A/ /i*U) 



<r(x) = o Q o*{S) 



with f = x/a; see Figure 3b. 



The dimensional factors will be established later; in the succeed- 

 ing discussion the f unct ions n * ( £ ) and <r*(f) will be treated in the same 

 way as ship lines and their derivatives. Generally following Munk and Weinig 

 the doublet distribution fi*( $) is identified with the sectional-area curve 

 A*(£) and the symbol r? is used for both of them. Actually the resistance 

 computations refer to given distributions for which the corresponding 



sectional-area curves can be easily calculated' 



when Munk's approximation 



is not accurate enough— as for instance in cases dealt with in Section 5. 



The first adequate representation of ship lines by polynomials is 

 due to Taylor; 11 - 12 the equations obtained are, however, suitable for a 

 separate description of the fore or afterbody only. Taylor locates the 



