Free Surface Effects tn Hull Propeller Interactton 
multiplied, such that the calculated thrust coefficient equalled the 
measured K-ypy;,. The primary output of the program was the distri- 
bution of bound circulation along the radius. In addition, it also fur- 
nished a calculated torque coefficient K and a mean effective wake 
Wo (based on thrust average rather than volume average) from which 
followed the equivalent open water advance coefficient Jp. This 
elaborate analysis was done only for three selected Froude numbers 
corresponding to y_=4.0, 7.0 and 12.5. The results are shown 
in Fig. 26 and 27. The effect of wake on circulation distribution is 
quite evident in Fig. 26 where the circulation maxima have been shift- 
ed toward smaller radii as compared to the open water condition of 
Fig. 11. Turning now to Fig. 27, the good agreement between cal- 
culated and measured advance coefficient J, is a confirmation of the 
realistic simulation of thrust generation in ine theoretical model, 
while the lack of agreement between calculated and measured torque 
coefficient Kp ;; points up the shortcomings of the theoretical model, 
specially the total neglect of all circumferential nonuniformities and 
the associated lack of any simulation of the relative rotative efficiency. 
However, we would not expect these defects to have any serious effect 
on the intended calculation of thrust deduction. 
Before passing on to the evaluation of thrust deduction we 
pause to consider briefly the issue of nominal wake versus effective 
wake. Conceptually, the distinction is clear : Nominal wake is the 
flow perturbation created by the hull in the propeller plane with the 
propeller removed, while effective wake is the flow perturbation due 
to the hull in the propeller plane with the propeller in place and oper- 
ating. In practice, however, the relative magnitudes of these two 
wakes have been a topic of considerable controversy and confusion in 
the literature on hull propeller interaction. It is generally agreed 
that there are two fundamentally different reasons why these two wakes 
need not be identical. First, there is a genuine physical effect of the 
propeller on the flow perturbation caused by the hull. This has three 
partially counteracting components. a) The potential component, 
which may be understood as the additional flow induced by the image 
of the propeller in the hull, tends to increase the effective wake com- 
pared to the nominal wake, since this image consists predominantly 
of sinks in the afterbody. b) The viscous component, which results 
from a contraction of the viscous wake, is specially pronounced if the 
line of boundary layer separation is shifted rearward by propeller 
suction and generally tends to decrease the effective wake compared 
to the nominal wake by bringing more undisturbed flow into the pro- 
peller disk. c) The wave component, referred to as a pseudo-non- 
linear effect of the propeller on the wavemaking properties of the hull 
in Section 3.5, can act in either direction depending upon Froude 
number. Second, there is a spurious computational effect due to dif- 
1865 
