370 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.9 



[PNA, 1939, Vol. II, Eq. (112), p. 149], for twin- 

 screw vessels with: 



(a) Bossings and outward-turning propellers 

 w = 2iC^Yil - Ce) 



-1-0.2cosMy) - 0.02 



(eO.iii) 



where jS(beta) is the slope of the bossing termina- 

 tion, measured in degrees 

 (b) Bossings and inward-turning propellers 



(60. iv) 



w = 2{Cb)\1 - Cs) 



+ 0.2 cos' [1(90 - /?)] + 0.2 



(c) Propeller shafts supported by struts 



w = 2(Cb)'(1 - Cs) + 0.04 (60.V) 



For the single-screw ABC ship, the data re- 

 quired for the Schoenherr formula (60.ii) are, 

 from the SNAME RD sheet of Figs. 78.Ja and 

 78.Jb and the drawings of Chaps. 66 and 67: 



Cpv = 0.822 

 Cp = 0.621 

 Bx = 73.08 

 L = 510 



H = 26.163 ft k' = 0.6 

 Rake = 0. 



E = 10.5 ft 



D = 20.51 ft for the stock 

 propeller used on 

 TMB model 4505 



Setting down the SchoenheiT equation and 

 substituting: 



w = 0.10 



+ 4.51 



CpvCpB\ 1 



L 7(7 - 6Cpy){2.8 - l.SCp) 



+ 



= 0.10 + 4.5[2:^??(|f)^3^] 

 1 



[7 - 6(0.822)] [2.8 - 1.8(0.621)] 



1 r 10.5 _ 20^ _ "1 



2 [26.163 73.08 ^■'^^^^j 



+ 



= 0.255 



This value of 0.255 for the 20.51-ft stock pro- 

 peller compares with the value of about 0.24 

 from Fig. 60.O, where Cb is taken, from the 

 fifth approximation in Table 66. e, as 0.593. As 

 a matter of interest, the wake fraction determined 

 from the model self-propulsion test with this 

 propeller, at a speed corresponding to 20.5 kt, is 



0.190; see Fig. 78.Nb. This is Wt , derived from 

 thrust identity with the open-water test. The 

 value of Wo , derived from torque identity with 

 that test, is 0.200. 



For vessels with tunnel sterns, there are little 

 or no published data on the wake fractions to be 

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

 Ships," 1950, p. 117]. For the arch-stern design 

 of the ABC ship of Part 4, the self-propulsion 

 curves of Fig. 78.1 indicate a wake fraction w at 

 the designed speed of only about 0.072. 



In this connection it is of interest to note, from 

 the statements of L. Troost, that: 



"Wake factors (based) on thrust identity depend on 

 propeller loading (thrust-load coefficient). The more 

 heavily loaded the propeller, the smaller is the wake 

 factor we find [6th ICSTS, 1951 (SNAME, 1953), p. 143].' 



The comments in parentheses are those of the 

 present author. 



60.9 Prediction of the Thrust-Deduction Frac- 

 tion. It has been customary since the 1860's, 

 when W. J. M. Rankine and W. Froude both 

 worked on this problem [INA, 1865, pp. 13-39], 

 to base predictions of the thrust-deduction frac- 

 tion of screw-propelled vessels upon the estimate 

 of the wake fraction [PNA, 1939, Vol. II, pp. 

 149-150]. So far as known this procedure has 

 been limited generally to single-screw vessels. 

 In any case, it gave little or no credit to efforts, 

 put forward by D. W. Taylor and others, to 

 decrease the thrust deduction by thinning the 

 ship sections or "straightening" the surfaces of 

 the hull and its appendages ahead of the propeller 

 disc, so that less transverse area is acted upon by 

 the —Ap's ahead of the disc. These efforts were 

 based upon the hope that the thrust-deduction 

 fraction would be reduced at a greater rate than 

 the wake fraction, so as to hold the hull efficiency 

 to as high a value as possible. 



W. J. Luke was among the earliest to give 

 empirical values of the thrust-deduction fraction 

 that were of practical use to the ship designer. 

 D. W. Taylor and others quoted these values 

 [S and P, 1933, p. 117; S and P, 1943, p. 120; 

 PNA, 1939, Vol. II, Table 9, p. 148; RPSS, 1948, 

 pp. 177-178]; they are plotted in diagram 2 of 

 Fig. 60.O, together with more recent data from 

 TMB model tests. They, hke the wake-fraction 

 graphs in diagram 1 of that figui'e, suffice for 

 rough estimates in the preliminary-design stage 

 of a ship of normal form. 



C. H. Peabody, in his 1910 tests of the large. 



