384 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.14 



propellers. If the propeller diameter D is not 

 tentatively fixed, several solutions may be worked 

 out, each for a different diameter. 



The necessary formulas for this calculation are 

 taken from Sec. 34.11: 



F., = V{\ - w) T = 



Ttq 



1 - t 



= «'(l^) 



Pe = RtV 



1 - t 



\ — w 



Ctl = ^2t^3 ^ in 0-diml form (34.xxvii) 



Ctl = 290.68 



pD VaVii 



PcChorses) 



p[Z>=(ft)][Fj(kt)]„„ (34.xxviii) 



in dimensional form. 



When several propellers are to be used, D^ is 

 replaced by 2Z)' = Dl + Dl + Dl + Dl , as 

 appropriate. The effective power P^ is always 

 the total ship figure. 



With the calculated 0-diml value of Ctl , the 

 curves of Figs. 34.B, 34.C, or 34.E are entered 

 and a value is found for the 0.8-ideal efficiency. 

 This is taken to be the actual operating efficiency 

 of the propeller, as yet not designed, and is 

 equal to the open-water efficiency r]„ of some 

 propeller at some advance ratio / = VA/inD). 



The position of the Ctl point along the 0.8- 

 ideal-efficiency curve of Fig. 34. G indicates, by 

 reference to the efficiency curves of the three 

 Wageningen propellers, an approximate value of 

 the pitch ratio P/D which may be expected to 

 produce the most efficient propeller under the 

 circumstances. Consulting the open-water charac- 

 teristic curves of some "stock" propeller which 

 has this pitch-diameter ratio, and entering the 

 open-water efficiency curves with the rjo value 

 from the 0.8-ideal-efficiency curve, give at once 

 the advance ratio / = F^/(nZ>). With the values 

 of Va and D previously used, the rate of rotation 

 n is found. A nomogram for solving Eq. (34.xxviii) 

 is embodied in ETT, Stevens, Technical Note 

 145; this facilitates working out a number of 

 solutions for a different combination of assump- 

 tions. 



A portion of this problem is worked out for an 

 early design of the ABC ship in Sec. 66.27, 

 sufficient only to derive a value of Ps . A some- 

 what more complete example is worked out here, 



using the basic values from the self-propulsion 

 test of the ABC transom-stern model, to deter- 

 mine the agreement (or otherwise) with the self- 

 propelled model predictions for the 20.5-kt trial 

 speed. The basic conditions assumed are: 



Rt = 160,120 lb, from Fig. 78.Nb 



D = 20.51 ft, for stock propeller actually used, 



from Fig. 78.Ma 

 V = 20.5 kt = 34.62 ft per sec 

 Wt = 0.190, from Fig. 78.Nb 

 t = 0.070, from Fig. 78.Nb; vht = 1.148 

 Va = F(l - w) = 34.62(1 - 0.190) = 28.042 



ft per sec 

 T = Rt/{1 - t) = 160,120/(1 - 0.070) = 



172,170 lb 

 p^ = R^V = 160,120(34.62) = 5,543,350 ft-lb 



per sec. 



Then, from Eq. (34.xxvii), 



Ctl — 



2.546Pb 



pD VaVh 



^ 2.546(5,543,350) 



~ (1.9905)(20.51)'(28.042)'(1.148) 



= 0.666 



It may be simpler and quicker for the user to 

 calculate the thrust-load factor by 



T 



C TL ^ 



AoVl 



172,170 



(0.99525)(20.51)'(0.7854)(28.042)' 

 = 0.666 



This is somewhat smaller than the 0.700 of 

 diagram 3 of Fig. 59.1 because the latter is cal- 

 culated for a final-design wheel diameter of 

 20.0 ft. 



From Table 34.a, or Fig. 34. B, the correspond- 

 ing ideal efficiency r], is 0.873 and the 0.8-ideal 

 efficiency or real efficiency r/Re„i is 0.698. This is 

 the working efficiency of the propeller at 20.5 kt. 

 Consulting the open-water curves for the stock 

 propeller in Fig. 78. Mc the advance coefficient 

 J for 7,0 = 0.698 is 0.769. Then J = VA/inD), 

 whence 



JD 



28.042 



(0.769)(20.51) 



= 1.778 rps or 106.7 rpm. 



