Nowaekt and Sharma 
IlI.4. Propeller Analysis 
Measured propeller performance characteristics for three depths 
of submergence are plotted in Fig.8 in the usual nondimensional coeffi- 
cient form. The largest depth (h/R, = 3.47) was the maximum attainable 
with the propeller boat available for open water tests, andthe smallest 
(h/Rp= = 1.50) corresponds exactly to the immersion selected for self- 
propulsion tests (Zp = -0.5T) describedlater. Apart from verifying the 
measurements eaiactea previously ataneven lager depth (h/Rp = =\4'.0) 
in the Hamburg Ship Model Basin (HSVA), the principal conclusion from 
these tests was that free-surface effects are negligibly small for depths 
h/Rp 21. 50. 
At the shallowest depth investigated , however , with the pro - 
peller disk just touching the static water level (h/Rp = 1.0), pronounced 
free-surface effects were measured , see Fig.9 . The observed loss 
of thrust and torque as compared to the deeply submerged condition , 
the steady accentuation of the effect with increasing loading (i.e. de- 
creasing advance coefficient) , and a slight drop in efficiency are to be 
naturally expected from the combined effects of ventilation and wave - 
making at the free surface . It is not intuitively obvious , however , 
why the thrust and torque should suddenly break down at some "'critical" 
advance coefficient , here Jx0.41 . Similar discontinuities have been 
measured by others, notably by Shiba (1953) . Flow observations reveal 
that the discontinuity is accompanied by a sudden transition from partly 
ventilated to fully ventilated condition . A satisfactory theoretical ex- 
planation of this phenomenon would certainly require an intricate ana- 
lysis of the stability of partly ventilated flow . It is also intriguing to 
note that the drop in thrust and torque is nearly proportionate so that 
the discontinuity is hardly perceptible in the curve of efficiency, This 
lends some credibility to Dickmann's (1939) simplified treatment of 
propeller ventilation as a mere reduction in the density of the medium 
due to a mixture of air with water! 
For the sake of completeness it should be reported that ventila- 
tionalsooccured to some extent at two ofthe deeper immersions,namely 
h/Rp =1.5 and 2.0, especially in the bollard condition and at the low- 
est advance coefficients. It was distinctly audible and often visible as 
a vortex from the free surface to the propeller tip, but its effect on 
thrust and torque was obviously too small to be measurable (see Fig.8). 
The measured thrust and torque characteristics (in the deeply 
submerged condition) were transformed into an equivalent vortex model 
of the propeller by means of a computer program based on lifiting line 
theory and using assumed (or adjusted) two-dimensional foil characte- 
1856 
