Free Surface Effects tn Hull Propeller Interactton 
As explained in Appendix B. 6, the wavemaking resistance of 
the propeller follows directly from its self-induced wake, see Equa- 
tion (B62). Hence opportunity was taken to compare the three differ- 
ent source representations of the propeller, defined by Equations 
(B10), (B11) and (B13), by plotting for each the ratio of calculated 
wavemaking resistance to measured thrust as a function of advance 
coefficient, see Figure 14, Since the source disk is not a valid model 
for calculating forces acting on the propeller, the wavemaking resis- 
tance Rwyp is not necessarily equal to the loss of thrust experienced 
by a propeller operating near the free-surface as compared to an 
equivalent deeply submerged condition. More appropriately, the ratio 
Rywp/T should be regarded as a measure of the loss of propeller ef- 
ficiency due to the expenditure of energy for maintaining its steady 
wave pattern, 
IlI,5. Wave Analysis 
Ithasalready been stated that longitudinal wave profiles were 
measured at a fixed transverse distance (Yo = 0.134 L) from the 
model center plane in two conditions : 1) model with propeller runn- 
ing at the ship self-propulsion point (for an arbitrarily assumed model 
scale of 1:80), and 2) model with propeller replaced by a dummy 
hub, each at two selected speeds corresponding to the two values of 
speed-length parameter Y, = 7.0 (F, = 0.267) and ¥, = 4.0 (F, = 
0.354). Two pairs of corresponding profiles are reproduced in suitable 
nondimensional form in Figures 15 and 16 respectively with the verti- 
cal scale magnified 100 times for the sake of clarity. 
Evidently, the propeller exercised a measurable influence on 
the wave pattern of the model, the transverse wave amplitude behind 
the stern being higher with the propeller running in the cases shown. 
Even within the linearized wave theory two significantly different ex- 
planations can be offered for this effect. First, it might be a purely 
linear effect due to a superposition of the propeller wave on the hull 
wave. Second, it might be a pseudo-nonlinear effect due to a modifi- 
cation of the wavemaking properties of the hull itself as a result of 
propeller suction. 
Another point of interest to note is the slight breaking of the 
bow wave clearly visible at the leading peaks in Figure 16. It shows 
that the wave pattern was in places steep enough to introduce truly 
nonlinear effects, at least locally. This should be kept in mind when 
making comparisons with the calculations based on strictly linearized 
theory. 
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