368 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.S 



fraction w is (F — Va)/V. This is known in some 

 quarters as the "analysis" wake fraction. That it 

 can be considerably different from the arithmetic 

 mean of the several wake fractions derived from 

 a 3-diml wake-survey diagram, when averaged 

 over a complete revolution of the propeller, is 

 indicated by the short-dash horizontal line in the 

 upper right-hand corner of Fig. 60. N. Here the 

 mean nominal wjake fraction, representing the 

 arithmetic mean of the values of the average 

 wake fraction for the nine 0-diml radii from 0.2 

 through 1.0, is 0.1735. For comparison, the wake 

 fraction Wt (for thrust identity with the open- 

 water test), for the transom-stern ABC model, 

 when self-propelled at a speed corresponding to 

 20.5 kt, is 0.190, indicated on Figs. 78. Nb and 

 78.Nc. 



This single value of the wake fraction, either 

 estimated analytically or derived experimentally, 

 is the value required for the shaft-power predic- 

 tions of Sees. 60.4 and 60.14. 



60.8 Estimating the Ship-Wake Fraction. 

 The discussion in this section concerning the 

 prediction of wake fractions for ship propulsion, 

 as well as that in Sec. 60.9 for predicting thrust- 

 deduction fractions, is limited strictly to proce- 

 dures used in the early stages of a ship design, 

 before any self-propelled model tests are run. 



W. J. M. Rankine was among the first if not 

 the first naval architect to establish a procedure 

 for estimating the wake fraction for a ship 

 propelled by a single screw. His method, published 

 in his 1866 book "Shipbuilding: Theoretical and 

 Practical," page 249, was based on the expanded 

 length of a curved line drawn on the body plan 

 of the ship in question. This curved line began at 

 the center of the propeller and crossed the lines 

 of successive sections forward of the propeller at 

 right angles to those lines until it reached the 

 maximum-section line. The ratio of the expanded 

 length of this curved line to the length of the run 

 was the approximate wake fraction desired. 



Many other procedures for predicting the wake 

 fraction in advance of model tests have been 

 devised and used since then, as listed in the partial 

 bibliography of Sec. 52.20. Among these proce- 

 dures is one of D. W. Taylor, published in tabular 

 form [S and P, 1933, Table XXV, p. 118; 1943, 

 Table XXV, p. 121; PNA, 1939, Vol. II, Table 10 

 on p. 149]. The data in these tables, as well as 

 the data mentioned subsequently in this section, 

 were taken from special wake measurements on 

 models or from wake-fraction values derived by 



model self-propulsion tests. Taylor's values are 

 plotted in graphic form in diagram 1 of Fig. 60. 0, 

 together with more recent data from TMB model 

 tests. They suffice for a rough estimate of w for 

 the designed speed at an early stage of a pre- 

 liminary design, despite the inconsistency of some 

 of the values. Taylor's data, for both single-screw 

 and twin-screw ships, are taken from S and P, 

 1943, Table XXV, page 121. Data from self- 

 propelled tests of the 10 tanker models are from 

 SNAME, 1948, pages 360-379; those for TMB 

 Series 60, the tanker Pennsylvania, and the 

 Schuyler Otis Bland are from SNAME, 1954. 



J. Lefol in his paper entitled "Les Interactions 

 entre la Carene et le Propulseur (Interactions 

 Between the Hull and the Propeller)" [ATMA, 

 1947, Vol. 46, pp. 221-251], gives in Part VIII, 

 on pages 235-236, nine formulas for wake fraction, 

 taken from the published literature. Recently, in 

 his discussion of the 1956 SNAME paper by 

 F. H. Todd and P. C. Pien on the TMB Series 

 60 model tests, A. Q. Aquino proposes for single- 

 screw vessels a formulation 



Wr = (A constant) 



Lxi)'L(6.5 - 5.5CpyA)iS - 2Cp^)J 

 - k[f(LCB)] 



where D is the propeller diameter. 



A comprehensive summary of existing pub- 

 lished data on wake at screw-propeller positions, 

 as well as some not published, has been made by 

 S. A. Harvald ["Wake of Merchant Ships," 

 Danish Tech. Press, Copenhagen, 1950]. This is 

 accompanied by a careful, studied analysis. The 

 paper is replete with graphs and plots but un- 

 fortunately it lacks the flow and other diagrams 

 that would have assisted the reader, and that 

 might also have changed some of the author's 

 ideas and conclusions. It is based solely on the 

 longitudinal or axial component of the relative 

 and the true-wake velocities, in the form of the 

 customary speed of advance and Taylor wake 

 fraction, and almost exclusively upon wake as 

 affecting one or more stern screw propellers. 



It is considered most significant that Harvald 

 achieves his only major correlations with practice, 

 and his only really consistent ones, when he uses 

 predictions based on theoretical analyses. In the 

 comparisons with empirical data, employing 

 orthodox form coefficients and parameters, it 

 becomes almost necessary at times to force 



+ 



