Sec. 70.29 



SCREW-PROPELLER DESIGN 



619 



^0.2 0.3 0.4 05 0.6 0.7 0.8 



Radius ffotiox; = o- 





Fig. 70.H Variation with Radius Fraction op 

 Thkust-Load Coefficient Based on Ship Speed 



Ratio. Having found the values of the hydro- 

 dynamic pitch angles /3i and the radial thrust 

 loading which allow the propeller to develop the 

 required total thrust, it is possible to proceed 

 with the next phase of the calculation. This 

 consists of finding the lift-coefficient product 

 Ci(c/D), applying the lifting-surface correction 

 factor, and calculating the corrected hydro- 

 dynamic P/D ratio. The lift-coefficient product is 

 determined from the following formula: 



Cl{cID) = Y (x'K) sin /3, tan {fi, - fi) (70.vii) 



where c is the chord length of the blade sections 

 and Ct is the lift-coefficient of the blade section 

 at each radius. 



Next, using the tangential induced-velocity 

 ratio Ujt/V found in Table 70. f of the previous 



section, it is possible to compute the lifting- 

 surface correction factor. This factor is needed 

 because the propeller-design problem is a bound- 

 ary-value problem, which at present is not amen- 

 able to exact solution. This solution would lead 

 to a curvature of the flow which is different at the 

 different stations along the chord length. The 

 curvature correction by Ludwieg and Ginzel, 

 introduced later in Sec. 70.33 and appUed to the 

 camber ratio, takes into account only the curva- 

 ture at the midlength of the section. This flow 

 curvature requires a corresponding additional 

 curvature of the section to maintain its properties. 

 The additional change of curvature over the chord 

 length requires for its correction the addition of 

 an angle of attack. This angle of attack has been 

 determined by Lerbs on a basis of Weissinger's 

 simplified hfting-surface theory [NACA Tech. 

 Memo 1120, Mar 1947]. Even in the framework 

 of this simphfied theory, the calculation of the 

 additional angle of attack is rather laborious. 

 Fortunately, a sufficiently close approximation is 

 obtained by using the expression: 



tan 13 tc 

 tan Pi 



1 + 



1 [UjT X^l 



2 1 V'x'j 



(70.viii) 



where tan Pre is the corrected hydrodynamic 

 pitch angle [Lerbs, H. W. E., "Propeller Pitch 

 Correction Arising From Lifting-Surface Effect," 

 TMB Rep. 942, Feb 19.55]. 



Design experience indicates that, for destroyer- 

 type propellers, 0.75 times the term inside the 

 bracket of Eq. (70.viii) gives a better pitch 



TABLE 70.g — Determination of Lift-Coefficient Product, Lifting-Surface Correction, and 

 Hydrodynamic Pitch-Diameter Ratio 



Col. B From Col. E, Table 70.f 



Col. C From standard tables, using (/3; — 0) from Col. D, 



Table 70.f 

 Col. D = [4,r (Col. N, Table 70.f)]/Z 

 Col. E Using Eq. (70.vii) = (Col. B)(Col. C)(Col. D) 



Col. F Lifting-surface correction factor 



= 14- (Col. J, Table 70.f) (Col. C, Table 70.e) 

 Col. G Using Eq. (70.viii) = (Col. F)(Col. B, Table 70.f) 

 Col. H Using Eq. (70.ix) = ^(Col. A) (Col. G) 



