Free Surface Effects tn Hull Propeller Interaction 
nominal wake w. This was available at three speeds only (compare 
Fig. 7). 2) The disk average of the potential wake w_,, calculated by 
thin ship theory, see Appendix B.5, especially Equation (B 54). This 
is a zero Froude number approximation. 3) The disk average of the 
sum of potential and wave wakes (w, + w,,) also calculated by thin 
ship theory, see Appendix B.5, especially Equation (B 53), 4) The 
quantity (wp -wp-wWy) as an approximate estimate of the viscous 
component w,, , see Equation (1). The striking correlation between 
the measured effective wakes and the calculated wave wake certainly 
suggests that the observed oscillations of wake with Froude number 
are indeed free-surface effects and that the thin ship wavemaking 
theory despite all its weaknesses does give a reasonable estimate of 
this phenomenon, Even the quantity (wp-wp-w,,), which as the dif- 
ference of a measured effective wake and calculated nominal wake 
components must be regarded with due caution, gives a credible im- 
pression of the magnitude of viscous wake w,. However, one cannot 
put much faith in its observed oscillations, 
III. 6.3. Thrust Deduction 
We now turn to our final goal of calculating the thrust deduc- 
tion fraction and its components. This was done to two different de- 
grees of approximation, At the three selected Froude numbers, where 
the calculated circulation distribution was available (see Fig. 26), the 
Hough and Ordway relation, Equation (B 16) in conjunction with the 
simulated effective wake k,,w(R) , was applied to generate the equi- 
valent sink disks. At all other Froude numbers we had to be content 
with Dickmann's approximate relation between thrust coefficient and 
source strength, Equation (B 15) in conjunction with the measured ef- 
fective wake wp. The numerical difference between these two ap- 
proximations is illustrated in Fig. 29. Evidently, the Hough and 
Ordway approximation yields slightly higher mean values and, in ac- 
cordance with the distribution of bound circulation, effects a concen- 
tration of sink strength toward the inner radii. It is believed to be 
more accurate than Dickmann's uniform sink disk since the vortex 
model yields a more realistic flow pattern than the simple momentum 
theory. 
In either event, the sink disk was used to calculate first the 
wavemaking resistance of the propeller alone and of the system hull 
and propeller as explained in Appendix B. The wavemaking resistance 
(and free-wave spectrum) of the propeller in the behind hull condition 
calculated in this way were found to be in reasonable agreement with 
the corresponding results of measured wave profile analysis at two 
Froude numbers as already discussed in Section 3.5. Given the wave- 
making resistances of the hull Rwy» propeller Rywp., and total 
system Rwy, only one additional quantity 5;4Rwp =, see Eq. (B 64), 
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