894 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 78.17 



(c) A centerline skeg that was unusually thin and 

 narrow, in a deliberate effort to cut down the 

 thrust deduction. 



A designer may well question the usefulness or 

 the validity of an estimating procedure, recom- 

 mended for use in the paper stage of a preliminary 

 design, which says (in Sec. 66.27) that 16,930 

 horses will be required at the shaft at the designed 

 speed while the test results of a self-propelled 

 model, from Fig. 78.Nb, indicate that the shaft 

 power need not exceed 13,250 horses. Allowing 

 say 2 per cent for the resistance of a scoop not 

 fitted to the model, and for power to drive the 

 circulating water through the condenser of the 

 main propelling plant, the model prediction cor- 

 responds to a reduction of some 19 per cent in 

 the estimated power. Conversely, the calculation 

 represents an increase of about 25 per cent in the 

 shaft power predicted by the self-propelled model 

 test. It must be remembered, however, that Uttle 

 or nothing was known of the shape or details of 

 the hull when the first and larger estimate was 

 undertaken. 



Actually, a third approximation or estimate 

 of the shaft power should have been made for the 

 transom-stern ABC ship after the hues had been 

 drawn, the appendages designed, and the stock 

 propeller selected. This could have been done 

 while the model was being built. With data 

 available as hsted hereunder, the procedure and 

 results are outlined briefly in the following: 



(i) When the manner of plating the hull has 

 been decided, the roughness allowance ACf 

 (for the clean, new hull) of 0.4(10"') of Sec. 

 66.9 is reduced to the value of 0.3(10"') of 

 Sec. 78.6. This means that C^ + ^Cp is (1.470 + 

 0.3)(10"') = 1.770(10"'). Adding the value of 

 C„ of 1.246(10"') from Sec. 66.9, Ct is (1.246 4- 

 1.770)(10"') = 3.016(10"'). Then 



Rr = ip/2)V'SCT 



= (0.99525) (34.62)'(46,231) (3.016) (10"') 

 = 166,322 lb. 



(ii) With the appendages designed, and with no 

 condenser scoops to be added or cooling water to 

 be circulated in the model, there is no longer any 

 reason for doubling the calculated appendage- 

 resistance increase of 4 per cent or for adding the 

 full scoop resistance, as was done in Sec. 66.9. 

 The augment of resistance for the appendages is 

 then taken as 5 instead of 10 per cent, 

 (iii) Applying the 1.05-factor from (ii) to the 

 Rt oi (i) preceding. 



^r(App) = (1.05) (166,322) = 174,638 1b. 



(iv) The thrust-deduction fraction t, using the 

 area factor 0.172 from Fig. 67.V and entering the 

 upper graph of Fig. 60.P, is 0.135. This procedure 

 takes account of the presence of the rudder in 

 each case. The estimated value of the propeller 

 thrust T is 



174,638/(1 - 0.135) = 174,638/0.865 = 



201,894 lb. 



(v) The wake fraction w predicted from the 

 Schoenherr formula, using Eq. (60.ii) and the ship 

 and propeller dimensions at this stage, is 0.254. 

 The speed of advance at 20.5 kt is 20.5(1 - 0.254) 

 = 20.5(0.746) = 15.29 kt or 25.82 ft per sec. 

 (vi) The ram-pressure load over the disc area of 

 the 20-ft ship propeller is (p/2)AoFi = qAo = 

 0.99525(25.82)'(0.7854)(20)' = 208,609 1b. 

 (vii) With a thrust T from (iv) preceding of 

 201,894 lb, the thrust-load factor Ctl = T/{qAo) 

 = 201,894/208,609 = 0.968. This is somewhat 

 less than the value of 1.287 predicted in Sec. 66.27. 

 It means that the real efficiency of the propeller 

 will be somewhat higher than previously esti- 

 mated. 



(viii) The rate of rotation of the ship propeller is 

 not known at the stage at which this approxima- 

 tion is made. It is therefore assumed that its real 

 efficiency will be O.Srji , based upon the reasoning 

 of Sec. 34.4. Consulting Fig. 34.B with the Ctl 

 value of 0.968, the predicted real efficiency tjo 

 is 0.665. 



(ix) With a w-value of 0.254 and a i- value of 0.135, 

 the corresponding rjn is (1 — i)/il — w) = 

 (1 - 0.135)/(1 - 0.254) = 0.865/0.746 = 1.160. 

 Assuming an i/K-value of 1.02 from K. E. Schoen- 

 herr [PNA, 1939, Vol. II, p. 150], the estimated 

 propulsive coefficient ijp is 'r}o{vH)vR = 0.665 

 (1.160)1.02 = 0.787. 



(x) The predicted shaft power is i2j-(App)F/ 

 (550) (0.787) = 174,638(34.62) /432.85 = 13,968 

 horses. 



This is only 5.5 per cent greater than the Ps of 

 13,243 horses derived from the model self-propul- 

 sion test. The r;^ of that test, at 20.5 kt, was 0.761 

 and the t/s only 0.968. The real efficiency of the 

 stock propeller used was 0.685 instead of the 

 0.665 predicted by the estimate of (viii) preceding. 



Values of the propulsive coefficient tjp derived 

 from the self-propelled test of the ABC transom- 

 stern model, for a range of ship speed from 9 to 

 23 kt, are plotted in Fig. 78.P. For comparison 



