Free Surface Effects tn Hull Propeller Interaction 
any element E; ; can be constructed by recurrence , for example 
os vg ¥ Pp 
3 3 3 
E> 2 = 3 + In (z+r) acy In(xt+r ) +4 arctan (xz/yr) 
an ae? 
E33 re os y* (2 +2% -2y*) + 2 (xt+2%) - 222} 
(B43) 
For a computer algorithm , however , it is not necessary to develop 
the analytical expressions explicitly since the recurrence formula 
(B41) can be applied numerically to each of the four summands (cor- 
ner values) of the definite integral (B39) . 
A similar analysis can be applied to the second term of (B34) , but 
but the final result is obtained more easily by considerations of sym- 
metry < 
o ex, y,z)= = e Moxy, -z) (B44) 
Restricting our attention to field points behind the hull 
(x <-1), the third and fourth terms of (B34) can be simplified as 
follows . 
gle) 4 Peeping te Jeg pee none e(-2'/T) 4h. 
ice Mgt ce a 
w exp [w(x-x') tiuy +i a au“ (z+z' i} 
ne 
w -u- -liw 
bre 
=" af Parx2L,min, ¢ 7) cos(uy) du (B45) 
0 
where 
Pn Os [u(x+ZL) 4 Nap agg i exp(iz one an, < ei ee 
“hice a ao dan alia a 8 
exp(-t) dt 
(B46) 
1897 
