Free Surface Effects in Hull Propeller Interaction 
The results showed that the arrangement with 125 elements yielded 
adequate accuracy for our purposes. Moreover, the average wake 
was practically identical to that calculated by thin ship theory. (This 
gave us, of course, more confidence in applying the thin ship theory 
also to the finite Froude number case where no such accuracy control 
was possible. ) 
Potential wake Wp averaged over the propeller disk 
Thin Ship 
Theory 
Hess and Smith Program 
N =100 N =125 
2x,,/L 
0.1785 0.1769 
OTrSazu 0.1502 
0. L307 DE 1Z9IS 
0.1136 OTL 27 
0.0998 0.0990 
Next, a series of effective wake calculations was conducted 
with the propeller located in its proper position (xp = -0.51 L) and 
assumed operating at the advance coefficients J,,; = 0.733,0.889 and 
1,131 corresponding to the ship self-propulsion points at Y, = 4.0, 
7.0 and 12.5 respectively, see Section 3.6. This involved two extra 
complications compared to the previous nominal wake calculations. 
One, the presence of the propeller destroyed the longitudinal symme- 
try of the flow so the number of significant hull surface elements had 
to be doubled from 125 to 250. Two, the flow induced by the propeller 
(and its mirror image about the plane z= 0) onthe hull surface had 
to be given as an additional input to the Hess and Smith program. For 
this the Hough and Ordway source disk representation of the propeller 
(see Fig. 29) was used. The algorithm for computing the flow induced 
by source rings at arbitrary field points was taken from Ktiichemann 
and Weber (1953), pp. 310-316. The results are summarized in the 
following table. 
1913 
