Sec. 70.27 



SCREW-PROPELLER DESIGN 



6L5 



0.85 



°-™a4 05 06 077 OB 09^ 



Thrust-Load Coefficient Cj|_ 



Fig. 70. E Vaeiation of Ideal Efficiency yik with 

 Thrust-Load Coefficient 



determination of tjk for the exact Ctl is shown in 

 Fig. 70.E. Thus r,K = 0.783 for C'tl = 0.730. 



70.27 First Approximation of the Hydro- 

 dynamic Pitch Angle and the Radial Thrust 

 Distribution. The next step is to calculate the 

 hydrodynamic pitch angle /3/ , using the following 

 formula, which represents Lerbs' approximate 

 optimum condition for a wake-adapted propeller: 



tan /3j = -7 • — -; (70. i) 



Here x' is the ratio of the local radius R to the 

 tip radius i?Ma:i of the propeller, namely x' = 

 ^/■Bmsi , and Wx- is the corrected average wake 

 at each radius, to be explained presently. 



The average local wake fraction w,- at each 

 0-diml radius, obtained from the wake survey, 

 is shown in Fig. 60.N. It is found that the average 

 wake fraction over the propeller-disc position 

 obtained by pitot-tube measurements with the 

 model propeller not mounted, called the nominal 

 wake fraction, rarely agrees with the wake fraction 

 obtained from the model self-propulsion test at 

 the same speed, known as the effective wake 

 fraction. This is a common occurrence in model 

 testing. It indicates that the action of the pro- 

 peller and the presence of the rudder have a 

 definite influence on the wake velocities. For the 

 ABC ship, the nominal wake fraction over the 

 propeller disc, obtained from the wake survey 

 and shown in Fig. 60.N, is 0.1735 at 20.5 kt, as 

 compared to the effective wake fraction of 0.195 

 from the model self-propulsion test. To compen- 

 sate for this difference, the local wake fraction at 

 each radius is multiplied by the ratio of (1) the 

 effective wake from the self-propulsion test to 

 (2) the nominal wake from the pitot-tube survey. 

 The method thus makes use of the wake-fraction 

 distribution found by the wake study, with the 

 numerical values modified so that its average 

 over the propeller is the same as that derived 

 from the self-propulsion test. In the ABC pro- 

 peller design, the local nominal wake fraction at 

 each radius is increased by the factor 



0.195 

 0.1735 



= 1.1239 OTW,. = 1.1239 iZi,- 



TABLE 70.d — Calculation of Hydrodynamic Pitch Angle 



Col. B = X/x, where X = 0.2738 

 Col. C = (Col. B) (1/vk) where vk = 0.783 

 Col. D; Wx- is obtained from Fig. 60,N, which was deter- 

 mined from the wake survey with the pitot tube 

 Col. E; Wx' = l,1239uJx' 

 Col, F = 1 - Col. E 



Col. G = Col. F/(l - w), where (1 - w) = 0.805 at the 



designed speed, obtained from self-propulsion test 

 Col. H = (Col. G)i« 



Col. I Using Eq. (70.i) = (Col. C) (Col. H) 

 Col. J From standard tables 



