Nowaekt and Sharma 
B.2. Source Representations 
All wavemaking calculations were based on the Havelock ( 1932 ) 
theory of sources moving under a free surface . It was therefore neces- 
sary to first define mathematical representations of the hull and pro- 
peller by means of source distributions . 
The standard first order (linearized) approximation in thin 
ship theory is to represent the hull by a center-plane source distri - 
bution of density 
SCOT Sx YP 2x (B3) 
fl 3 boop) (B4) 
ol; 72) 
where ; y| 
defines the hull surface (see Fig. 1) . The results obtained by Have- 
lock's theory are then identical to those of Michell (1898) 
The family of hull forms considered in the present study is defi- 
ned by (BS) 
y= ab{i = (x/f)2m\{y — «(2/7 
where b, £ and T are half-beam , half- length and draft respectively, 
while ¢€ is a flat-bottom parameter that can vary from €= 0 (wall 
sided hull with completely flat bottom) to € = 1 (sharp keeled hull 
with completely curved bottom) . By virtue of Equations (B3, B4) this 
form is represented by the polynomial source distribution 
(x2) = (m/m) (b/L) (x/L) 2" fy. 6-2/7} 
(B6) 
over the rectangular plane 
nilsson ds 5 N tg esd tout rena 
(B7) 
Following Dickmann (1938) the propeller can be represented 
by a continuous distribution of sources of (negative) density o (R, @) 
over the propeller disk 
x = Xp > Ry <R<Rp>p> -7r< O6< fF 
(B8) 
where R, 9 are polar coordinates 
= 5 = +R i 
y R4cos_6 Z Zp sin 0 (B9) 
the point (x), 0, zp) is the geometrical center of the propeller and 
1888 
