Nowaekt and Sharma 
The disk average lw, increases steadily with loading (i.e. decreas- 
ing J) as one would naturally expect. 
The next and final step in our propeller analysis was aimed 
at an indirect verification of the entire theoretical model by compar- 
ing the calculated performance at shallow submergence (based only on 
theory and the known performance at deep submergence) with actual 
measurements. For this purpose the calculated self-induced free- 
surface wake w,(R) was used in two ways, First, following Dickmann 
(1939), its disk average value wy was used simply to define a virtual 
advance coefficient 
De mo 
£ ei (14) 
f 
at which the thrust and torque values were read off from the known 
deep submergence characteristics (Figure 8) and replotted against J 
(see squares in Figure 13) as the predicted characteristics at shallow 
submergence. Second, the radial distribution w (R) was fed into the 
computer program for off-design performance which then calculated 
the thrust and torque by vortex theory (see crosses in Figure 13). 
Since this program matched perfectly with the deep submergence cha- 
racteristics (see Figure 10) and since w,(R) was practically constant 
over the radius (see Figure 12), the net effect was the same as in the 
first method, namely a loss of thrust and torque owing to the negative 
value of self-induced wake and increasing steadily with loading. The 
actually measured characteristics, replotted from Figure 9 as the 
dashed curves in Figure 13, indeed confirm that the calculated effect 
is in the right direction and of the right magnitude. 
Encouraged by this success of the theory, we repeated the 
above calculation for the entire range of advance coefficients J = 0.10 
step 0.05 until 1.10. However, for the sake of simplicity, we now 
estimated the source strength directly from the thrust coefficient by 
Dickmann's relation (i.e. substituting Equation (B10) instead of (B13) 
into (B61)) and applied only the simple method of virtual advance coef- 
ficient J; explained above. The result is represented by the conti- 
nuous curves in Figure 13. Although not as accurate as the previous 
calculations, which made use of vortex theory, even this simple ap- 
proach leads to fairly reasonable predictions of the effect of wave- 
making on propeller performance, Of course, at very high loadings, 
especially for advance coefficients below the "'critical'' value of 0.41, 
ventilation rather than wavemaking is the decisive factor, and hence 
wavemaking theory alone fails to predict the behavior found in the ex- 
periment. 
1858 
