Sec. 70.6 



SCREW-PROPELLER DESIGN 



595 



Then Schoenherr's K, = K„i{J)~. For a range of 

 values of the advance coefficient J from O.GO to 

 0.80, the calculated values of K, are listed in 

 Table 70. b. The parabola corresponding to these 



TABLE 70.b — Data for Plotting Auxiliary 

 Curve on Schoenhbrr Chart 

 From the text, K,^ = 0.371245 = 0.371. 



A', = K,,J^ 



0.1336 

 0.1569 

 0.1819 

 0.208S 

 0.2376 



values is then drawn lightly in pencil on Chart L 

 At the intersection of this pencil parabola with 

 the heavy broken line marked "eMax (or rjuax) for 

 Ktd Const." the following optimum values are 

 picked off: 



J = 0.748 

 P/D = L02 



7/0 = 0.683. 



Since rpm = V^{QO)/iJD), where ,/ = 0.748, 

 the rate of rotation is found to be 102.6 rpm. 

 Except for the slower rate of rotation, the pitch- 

 diameter ratio and the efficiency are close to 

 those obtained from the Prohaska chart for the 

 Wageningen B.4.40 series. The latter have a 

 mean-width ratio of 0.189 and a blade-thickness 

 fraction of 0.045. The EMB propellers upon 

 which Schoenherr's Chart 1 is based have a 

 mean-width ratio of 0.20 and a blade-thickness 

 fraction of 0.05. The difference in rate of rotation 

 is undoubtedly due to the airfoil blade sections 

 of the Wageningen propellers and the ogival 

 sections of the EMB propellers, with zero-lift 

 lines at different angles to the base chords, where 

 the nominal pitch is measured. 



Since the mean-width ratio of the ABC ship 

 propeller may exceed 0.20, Schoenherr's Chart 2 

 is used to obtain an alternative solution for a 

 mean-width ratio of 0.25 and a blade-thickness 

 fraction of 0.05. This gives the values: 



J = 0.740 vo = 0.673 



P/D = 1.02 rpm (by calculation) = 103.7 



The narrower-blade propeller appears to be the 

 better of the two. 



Using the Lewis charts for the same given 

 values, and following the procedure described 

 [SNAME, 1951, pp. 614-615 and Type 3, pp. 

 619-620], it is noted that Lewis' coefficient Ka is 

 the same as Schoenherr's K,j , except that the 

 wake fraction used is that derived from what is 

 known as thrust identity only. Lewis' Ku , defined 

 as T/{pD'Va), has the form of a thrust-load 

 coefficient; it is equal to (t/8)Ctl ■ Taking 

 Lewis' published chart for the Wageningen 

 B.4.55 series propellers, and drawing a curved 

 line lightly in pencil for a constant value of 

 K[/ = 0.371, the corre.sponding values of the 

 parameters sought are as listed in Table 70. c. 

 From this table the best values appear to be: 



/ = 0.702 7,0 = 0.665 



P/D = 1.00 rpm (by calculation) = 109.3 



TABLE 70. c — Data for Plotting Auxiliary Curve 



ON Lewis Chart 

 Here Lewis' Ku = Schoenherr's Kui = 0.371245 = 0.371. 



Except for the lower efficiency, because of the 

 too-wide blades of this series, the values are very 

 nearly equal to those obtained from the Prohaska 

 chart. 



The stock model propeller for the ABC ship 

 model should thus have the following charac- 

 teristics: 



(a) The ship to model scale ratio X(lambda) is 25.5 



(b) Z>Modei = -DsLip/X = 20/25.5 = 0.7843 ft or 

 9.412 in 



(c) The P/D ratio is about 1.00 or 1.02 



(d) The mean-width ratio should be about 0.20 



(e) The blade-thickness fraction is about 0.045 to 

 0.050 



(f) The proper expanded-area ratio Ae/Ao is 

 about 0.40. 



The actual selection of the stock model pro- 

 peller is discussed in Sec. 78.4. 



Subsequent to the selection of this propeller, 

 J. D. van Manen published a paper in which he 



