Sec. 60.8 



SHlP-POWERlNG DATA 



369 



0.05 QIC 0.15 OZO 

 Thrust-Oeduction Fraction t 



Fig. 60.O Graphs fob D. W. Taylor's Predictions 



OF Wake Fraction and W. J. Luke's Prediction 



OF Thrust-Deduction Fraction 



agreement. At their best, the relationships so 

 established are complicated, confused, and often 

 conflicting. 



The use of the known features of the boundary 

 layer abaft a flat plate accounts for most of the 

 radial and tangential (peripheral) wake variations 

 observed abaft normal forms of single-screw 

 sterns. The derivation of the potential-flow wake 

 abaft bodies formed by various combinations of 

 sources and sinks in an ideal liquid gives a reason- 

 ably consistent picture of the potential-wake 

 Variations abaft ship forms of varying fullness, 

 proportions, and size. B. V. Korvin-Kroukovsky 

 Uses this approach in his paper "On the Numerical 

 Calculation of Wake Fraction and Thrust 

 Deduction in a Propeller and Hull Interaction" 

 [Int. Shipbldg. Prog., 1954, Vol. 1, No. 4, pp. 

 170-178]. However, an understanding of this 

 paper requires a thorough knowledge of source- 

 and-sink phenomena and stream functions, La- 

 gally's theorem, friction resistance, and the 

 various kinds of flow around bodies of revolution 

 and ship-shaped forms. 



In a still later paper S. A. Harvald carries on 



this analysis somewhat further ["Three-Dimen- 

 sional Potential Flow and Potential Wake," 

 Trans. Dan. Acad. Tech. Sci., 1954]. Applied 

 Mechanics Reviews, May 1955, page 206, has 

 this to say of it: 



"The Rankine bodies generated by various combina- 

 tions of sources and sinks, situated at isolated points or 

 distributed over lines and surfaces, are computed. The 

 purpose of the work is to compute by this means the 

 velocity field due to the ship's hull in the neighborhood of 

 the propeller. Since the effect of the ship's boundary layer 

 on the potential flow is neglected, the results should be 

 only roughly applicable for this purpose." 



There is as yet nothing approaching a formula or 

 routine step-by-step procedure which a naval 

 architect can use while his ship design is progress- 

 ing. 



Despite these intense analytical studies, S. A. 

 Harvald comes to the conclusion, in the 1950 

 reference cited earlier in this section, that the 

 empirical formula of K. E. Schoenherr [PNA, 

 1939, Vol. II, Eq. (110), p. 149] is, with slight 

 modifications, the naval architect's best known 

 method of predicting the wake fraction for a 

 given design, when the hull shape has been 

 delineated and the screw-propeller position (s) 

 determined. The Schoenherr formula, without 

 modifications but with standard symbols, as 

 employed for single-screw vessels of normal or 

 nearly normal design, is 



w = 0.10 



+ 4.51 



\j pyiu plJ 



1 



(7 - 6Cpv)(2.8 - l.SCp) 



+ 



1 r^ 



2\_H 



— — fc' {Rake) 



(60. ii) 



where E is the height of the propeller axis above 

 the baseplane at the disc position, 



D is the propeller diameter, 



{Rake) is the rake angle of the propeller blade, 

 measured in radians, and 

 k' is a coefficient that has values of: 



(1) 0.3 for a normal stern 



(2) 0.5 to 0.6 for a stern with aftfoot cut 

 away. 



This formula, despite its intricacy, is non- 

 dimensional. An example of its application, to the 

 transom-stern single-screw ship designed in Part 

 4, is worked out presently. 



K. E. Schoenherr gives a second set of formulas 



