Free Surface Effects tn Hull Propeller Interaction 
by the program for the shallow submergence. However, this refine- 
ment is considered unnecessary. 
Second, for evaluating the propeller performance in the behind 
hull condition again the same procedure was used, with the measured 
nominal wake w(R) substituted in Equations (C4) and (C7). However, 
the calculated thrust and torque were found to deviate substantially 
from the measured values. Since the primary purpose of this calcula- 
tion was to obtain a realistic simulation of actual propeller perfor- 
mance by a mathematical lifting line, it was decided to enforce a 
thrust identity. However, this was accomplished not by further mani- 
pulating the assumed foil characteristics but by multiplying the input 
wake w(R) with a constant wake corrector k,, whose final value was 
determined by iteration. Thus the program was here used not only to 
determine the equivalent circulation distribution but also to simulate 
the physical difference between the nominal and effective wake through 
the factor k,. Moreover, the program also calculated a mean effec- 
tive wake wT which was based on a thrust average rather thana 
volume flux average. This was defined as 
R 
ne alee) {Rag} {re ¢ tan 6, } r(R)dR 
are 
w. = R (C18) 
Uh {oR : ugh {t- « tan 6, | T(R)AR 
Ru 
where not only the nominal wake w and the circulation [ but also 
the quantities up ,8; , and e€= Cp/Cy, vary with radius, even though 
this has not been explicitly indicated in the formula. The numerical 
values obtained for k,, and wr and their practical significance have 
been discussed in Section 3, 6.2. 
1911 
