Nowaekt and Sharma 
By evaluating ¢, ata sufficiently large number of field points 
the circumferential and disk averages of the theoretical wake can be es- 
timated. Moreover , it can be shown that the zero Froude number wake, 
the infinite Froude number wake and the bow wake (x > L) can also 
be derived from the four components of expression (B34) 
(1) (2) 
Biot Ob. Myer). apy see - ~ 
n w p x x (B54) 
ree ae (2) 
Be, oo: Wp Wee = ae he (B55) 
x >: %, (x,y,z) = ea y,z)+ ¢,,() (-x, y, z) 
+ Pes (-x, y, Z) (B56) 
This last quantity evaluated at x = -Xp yields by virtue of longitu- 
dinal symmetry the desired theoretical wake in the propeller plane 
"behind" the hull in reverse motion’. 
B.6. Wave Flow due to Propeller 
In order to calculate the perturbation flow induced by the mo- 
tion of the propeller under the free surface , we start with an alter - 
native expression for the Green's function (B33) , see formula (56) in 
Eggers , Sharma and Ward (1967) 
a2. 
] 1 2 
Go= (-s2 5 ae debice sec “6 15h eee ‘+iai) Jak 
l 2 BS 35/2 k-sec29 
n/2 2 fa 
+ Im 2 f sec’ @ exp [sec”9 (z+z'+ia) ]de 
1/2 (B57) 
with @ = (x-x') cos 6+ (y-y')sin® and r),r> as befo- 
re . Differentiating with respect to x, and taking advantage of the 
symmetry in 0 , we obtain 
x-x! x-x'! 4 m [2 
G,(x-x',y-y',z,z') = wr Rawgulsoy f se<8 de. 
ea tT? f 
= k dk 
fi exp[k(ztz') ] sin [k(x-x') cos 09]cos[ k(y-y') sin ©) aaa 
k-sec20 
0 
(contd. . ) 
1900 
