630 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.38 



■ By way of comparison, as discussed in Sec. 

 70.22, Prohaska's logarithmic chart for the 

 Wageningen propeller series B.4.40, Fig. 70.B, 

 indicates a P/D ratio of 1.2 and a propeller 

 efficiency t/o of 0.72. The same parameters as 

 calculated by Lerbs' short method are P/D = 

 1.193 at the 0.7 radius and t/o = 0.733. This 

 shows satisfactory agreement with a good stand- 

 ard propeller series. 



70.38 Summary of Design Steps for Lerbs' 

 Short Method ; Schoenherr's Combination. Sum- 

 marizing the procedure of Sees. 70.21 through 

 70.37: 



(1) Determine the number of blades Z, the rake, 

 the propeller diameter D, the hub diameter d, 

 and the rate of rotation n 



(2) Calculate the thrust-load coefficient Ctl , 

 the coefficient {Ctl)s , and the absolute advance 

 coefficients X and Xs 



(3) Determine the ideal efficiency with jet rota- 

 tion riK from Fig. 70. D 



(4) With successive approximations, determine 

 the hydrodynamic pitch angle ^i , and the thrust 

 distribution over the blades which will allow the 

 propeller to develop the required thrust; use 

 Eqs. (70.i) through (70.vi) and Fig. 70.G 



(5) Determine the hft-coefficient product 

 Cl{c/D), apply the lifting-surface correction, and 

 calculate the hydrodynamic pitch-diameter ratio 

 P/D for each blade section; use Eqs. (70.vii) 

 through (70.bc) 



(6) From strength considerations, calculate the 

 blade-thickness fraction to/D, and the maximum- 

 blade-thickness distribution ratio tx/c; use Eqs. 

 (70.x) and (70.xi) and Fig. 70.J 



(7) Choose the type of meanline and thickness 

 form to be used for the blade sections 



(8) Using cavitation criteria, determine the maxi- 

 mum camber of the meanhne nix , the chord 

 lengths c of the blade sections, and the Uft co- 

 efficients Cl of the sections; use Eqs. (70.xii) 

 through (70.xiv) and Fig. 70.K 



(9) Draw and fair the blade outline and determine 

 the final chord lengths, maximum cambers, and 

 lift coefficients; use Fig. 70.M if necessary 



(10) Apply the curvature correction to the camber 

 ratio; use Eq. (70.xvi) and Fig. 70.N 



(11) Apply the viscous-flow correction and cal- 

 culate the final pitch distribution; use Eqs. 

 (70.xvii) and (70.ix) 



(12) Determine the amount of skew-back and 

 lay out the skew-back fine 



(13) Draw the propeller 



(14) Calculate the final propeller efficiency; use 

 Eq. (70.xbc). 



The Lerbs 1954 method, described here, is con- 

 sidered neither too long nor too intricate for the 

 final design of a screw propeller to go on an 

 important or costly ship, especially as it gives the 

 designer more flexibility in taking account of 

 unusual conditions than a method based solely 

 on empirical or experimental data. The calcula- 

 tions proper can be made by anyone who knows 

 arithmetic, algebra, logarithms, and elementary 

 trigonometry. The several correction factors 

 involved in this procedure, some of them semi- 

 empirical, will disappear with increasing knowl- 

 edge. The analytic framework of this method 

 should serve well for the insertion of results of 

 future research and the presentation of additional 

 useful data for the propeller designer, especially 

 when more is known of the flow in and around 

 the propeller position. 



K. E. Schoenherr has recently [SNAME, 1955, 

 p. 366] outlined a logical, workable combination 

 of the propeller-design chart and analytic method 

 embodying the following steps, adapted from the 

 reference: 



(a) The problem is first solved by the use of 

 design charts and the methods described in 

 PNA, Vol. II, Chap. Ill 



(b) The method of Th. Theodorsen in his 

 book "Theory of Propellers" [McGraw-Hill, 

 New York, 1948] is then applied to obtain the 

 lift-grading curve 



(c) The blade area, blade width, and blade- 

 thickness distribution are chosen to keep the 

 propeller out of cavitation, to meet strength 

 requirements, and to give good thickness ratios 



(d) Lift-coefficient curves for the sections are 

 calculated, if not already available, by the method 

 of L. C. Burrill, explained in reference (39) of 

 Sec. 70.20 



(e) The angle of attack is read from the lift- 

 coefficient curves and the final pitch distribution 

 is obtained by smoothing out the calculated 

 results 



(f) The effective pitch obtained from the fore- 

 going calculations is compared with the pitch 

 obtained from the design chart as a check on the 

 accuracy of the solution. 



According to Schoenherr, "... variable wake 

 can be introduced readilj'" into this design 

 procedure. 



