Free Surface Effects tn Hull Propeller Interaction 
where pl) and p) are the functions already defined in (B24) 
The integrals (B45) and (B49) can be truncated at a sufficiently 
large value of u and approximated by the known recurrence for- 
mulas for Fourier series . Suppose 
co 
Cc. + is =m I(u) {cos(uy) + i sin(uy) } du 
: N 
~ Au = (u, ) { cos(u,y) + isin(u vy) be, ie 
with 
1 
i = vou, €, sco ae e, = "Itor 9S! 116 
where Au isa suitable step size and N is sufficiently large . Then 
cat 
C= 2. (Uj-U 
and 
S = U, sin(y Au): Au (B51) 
where the U, are defined by the sequence 
Pitas UN NM Ge Se yO 
U, = I(u,) + 2cos(y a ak PE rach ete | (B52) 
This completes the wanted algorithm for all four terms of (B34) . 
By our definition , g¢ evaluatedin the propeller plane is iden- 
tical to the total potential wake fraction , 1.e. the sum of the so-called 
potential wake (zero Froude number effect) and the wave wake (finite 
Froude number effect) . Thus 
(B53) 
wp(R, 6) + wy (R,0) = x(x, y, 2) 
if | | x = Xp» y = R cos®, 24= 2, +R sin © 
1899 
