386 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.15 



that the wake fraction w has increased from the 

 0.190 of Fig. 78.Nb to 0.210. The thickening of 

 the boundary layer, and the increase of viscous- 

 wake velocity due to fouling are assumed to have 

 a greater effect on increasing w than the augmented 

 Ctl has on reducing it, as described by L. Troost 

 in Sec. 60.8. It is assumed further that the thrust- 

 deduction fraction t has increased from 0.070 to 

 0.115, because of the greater thrust-load coefficient 

 Ctl at which the propeller must operate. At this 

 increased Ctl the inflow jet will have a somewhat 

 larger diameter in way of the skeg, so that the 

 — Ap's will act on more of the stern area; this is 

 another reason for increasing t. 



For the clean ship, at 19.7 kt, tj^ from Fig. 

 78.Nb is 1.148 but for the fouled ship it is 



, ^ _ (1 - Ofou. _ (1 - 0.115) _ , ,„„ 

 U^JFoui - ^^ _ ^^^^^^ - (^ _ Q 210) - ^-^^^ 



The speed of advance V a for 19.7 kt, fouled, is 

 7[(1 - w)f„„,] = 33.27(0.79) = 26.28 ft per sec. 

 By interpolation from the values of 10~^ T 

 from Fig. 78.Nb, the thrust T at 19.7 kt, for the 

 clean ship, is 152,600 lb. Then for a ship carrying 

 a propeller of 20.51-ft diameter, corresponding to 

 the stock model propeller, V a = VO- — w) = 

 33.27(1 - 0.190) = 26.95 ft per sec, and 



T 



the same when the bottom is both clean and foul, 



A,Vl 



152,600 



(0.99525)(20.51)'(0.7854)(26.95)' 



0.639 



For the fouled ship at 19.7 kt, T = Rr/(l - t) 

 = 193,640/(1 - 0.115) = 218,800 lb. Then 



Tfou, 



\S^TLJ-i 



I A„[(F^)P„„,]^ 



218,800 



(0.99525)(20.51)'(0.7854)(26.28)' 

 = 0.963 



From a larger-scale version of Fig. 34. G or 

 from Fig. 70.B, for a PjD ratio of 1.0, the value 

 of the real efficiency ijReai for a Ctl of 0.639 is 

 0.717. For a Ctl of 0.963 on the fouled ship, and 

 a P/D ratio of 1.00, the value of the real efficiency 

 '/Real is 0.677. It is not possible to pick the latter 

 value from the open-water characteristic curve 

 of Tjo because the J-value and the rate of rotation 

 n in the fouled condition are not known. 



If the relative rotative efficiency t\R is assumed 



{■<\^\ 



('?o)Foul('?/r)Foul 



VoViT 



(0.677)(1.120) 

 (0.717)(1.148) 



= 0.921 



R. W. L. Gawn states, on page 247 of his paper 

 "Roughened Hull Surface" [NECI, 1941-1942, 

 Vol. LVIII, pp. 245-272], that "Relative rotative 

 efficiency is less when the surface is rough, 

 . . . ," but he gives no numerical values. 



Interpolating from the r)p = EHP/SHP 

 values in Fig. 78. Nb, the value of rip for the clean 

 ship at 19.7 kt is 0.769. For the fouled ship at the 

 same speed it is estimated to be 0.769(0.921) = 

 0.708. Hence 



Ps = 



11,713 

 0.708 



= 16,540 horses. 



This is about 3,290 horses more, or about 25 

 per cent in excess of the 13,250 horses required to 

 propel the clean ship at 20.5 kt, as predicted by 

 the self-propelled model test. It is not much less 

 than the whole clean-bottom power margin 

 required to provide the speed differential from 

 18.7 kt (predicted Ps of 9,320 horses) to 20.5 kt 

 (predicted Ps of about 13,250 horses), namely 

 3,930 horses. It corresponds to an average increase 

 in shaft power Ps of only about 2.5 per cent per 

 month, or about 0.08 per cent per day, yet when 

 considered as an additional power expenditure it 

 seems large. 



For the designer who is to recommend a 

 definite amount of shaft-power reserve to the 

 owner, the situation definitely calls for an investi- 

 gation of the use of hot plastic anti-fouhng paint 

 instead of the older type of self-leveUng paint. 

 From Table 45.f of Sec. 45.18: 



ApCp for the plating is taking as 0.0, since any 

 plating roughness is obscured by the hot- 

 plastic paint coating and the fouling 



A.sCf for structural roughness is assumed to be 

 0.1(10"'), as before 



AcCp to cover the initial roughness of the hot- 

 plastic paint is taken as 0.5(10"'), from the 

 left margin of Fig. 45. L 



ApCp for fouhng only, from the dot-dash fine of 

 Fig. 45.L, is 0.11(10"'). 



Then 2ACf is (0.0 + 0.1 + 0.5 -1- 0.11)(10"') = 

 0.71(10"'). 



The values of Cr and Cp for the clean ship at 

 19.7 kt are 0.94(10"') and 1.48(10"'), respectively. 



