Free Surface Effects tn Hull Propeller Interactton 
with 
Deg te) 
2m-1 
a Sas aif ad] ae ! -e(-2'/7)™h 
x 
cy a es Me 
(B34) 
vy! 
eee dz' 
3/2 
{(xc-x1 )2 + (y-ys2+( 2-2")? } 
(B35) 
etc . It turns out that in the resulting integrals the x', z' integrations 
can be carried out in closed form , while the u,w integrations must 
be performed by numerical quadrature . 
It takes some algebra to reduce the expressions to a form 
suitable for computer programming . We will show this for one exam- 
ple . Substitute in (B35) 
Bis/l, t= x'/l, nay/h, b22/l, 0% =2° fk, r= 7T/h 
(B36) 
Then 
Wy ee Alehee) [ ¢ ] 
bar ( tie be Wola (2k) athe 
Px ar xf dé! VA Digi, Lbs eter se) =e ee) 
Now put (B37) 
(een ae oa fee ie st 
(B38) 
Then ; 
oy fai f (eCepeie elt aint; Vie Hm fat 
ee = ae ak MiG, Pe eee 
: es ftr ees ce tale 
Now factor out the constants and apply the binomial theorem to get 
2m -1 : 
at} SB (-) i ( 2m-1 ) ee, 
i 
i=0 
1895 
