374 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.10 



continue unceasingly until a logical and reliable 

 prediction procedure is available. 



60.10 Finding the Relative Rotative Efficiency. 

 The physical and analytical basis for relative 

 rotative or thrust-torque efficiency, as applied to 

 a screw propeller working behind a model or ship, 

 is described in Sec. 34.7 of Volume I. Further 

 comments on this factor are embodied in Sec. 

 34.16. 



It is necessary to estimate or predict the prob- 

 able value of the relative rotative efficiency riji 

 when the expression [rio{vH)vR] is used to estimate 

 the propulsive coefficient r/p . This prediction, 

 however, is much more easily mentioned than 

 made. 



K. E. Schoenherr gives a few comments con- 

 cerning this factor. In the absence of any more 

 reliable and authoritative information these 

 comments have acquired the nature of a pre- 

 diction rule. He states that: 



"The average values of the relative rotative efficiencies 

 determined in the tests worked out to be 1.02 for the single- 

 screw models and 0.985 for the twin-screw models. 



"It should be emphasized that the foregoing formulas 

 are valid only for merchant ships of normal form operating 

 at speed-length (T,) values below unity" [PNA, 1939, 

 Vol. II, p. 150]. 



More recentb^ L. C. Burrill and C. S. Yang 

 have calculated the overall thrust and torque, 

 including the K^ and Kq values, for a group of 

 screw propellers operating in certain assumed wake 

 distributions over the propeller disc, corresponding 

 to the conditions behind several hypothetical 

 ships [INA, 1953, Vol. 95, pp. 437-460]. By 

 calculating the same quantities for the same 

 propellers working in a uniform flow, simulating 

 open-water tests, they are able to predict the 

 thrust-torque factors ToD/Qo and TD/Q for the 

 "open-water" and the "behind-ship" conditions, 

 respectively. From the discussion of Sec. 34.7 in 

 Volume I, the relative rotative efficiency is then 



T„D 



TD 

 Q 



where D is the propeller diameter, the same behind 

 the ship as in open water. 



As a result of their analysis Burrill and Yang 

 conclude that: 



". . . the quantity designated relative-rotative-efiiciency 

 has a real meaning, in terms of the method of analysis 

 usually adopted, and its value can be estimated by calcu- 

 lation, in the manner described in the paper [pp. 440-441 

 of the reference cited]. The numerical values obtained 



agree reasonably well with the experimental data" [INA, 

 1953, Vol. 95, pp. 446, par. 8(4)]. 



However, the calculations involved are laborious, 

 at least with desk-type computers, and the values 

 derived are generally in line with the empirical 

 values previously used. 



If a condition is assumed in which the torque 

 Q behind the ship is the same as Qo , then a value 

 of 77fi greater than unity indicates that the thrust 

 T exerted by the propeller behind the ship is 

 greater than To in open water. The service con- 

 ditions are such, therefore, as to make the pro- 

 peller more efficient in pushing the ship than 

 when it is just pulling itself along in open water. 



Additional information concerning the values 

 of 7?B to be expected on single-screw ships is found 

 in the following reports of self-propelled models: 



(a) Ten tanker models; SNAME, 1948, Fig. 32, 

 p. 416 



(b) TIMB Series 60 parent models and related 

 models; SNAME, 1954, Figs. 12(a) and 12(b) on 

 pp. 141-142. The values of rjR range from 1.04 

 to 1.01, with an average of about 1.02. 



(c) Todd, F. H., and Pien, P. C, "Series 60— 

 The Effect upon Resistance and Power of Varia- 

 tion in LCB Position," SNAME, 1956. Tables 18 

 through 22 list the relative rotative efficiency 

 (as e„ in that text) for a wide range of speeds on 

 all the models tested. 



For the reader who wishes to undertake some 

 of this analysis on his own, the value of the relative 

 rotative efficiency tjb is derived from the self- 

 propelled test of a ship model by the following 

 procedure. The case used as an example is that 

 from the self-propelled test of TMB model 4505-1, 

 representing the arch-stern design of the ABC 

 ship undertaken in Chap. 67: 



(1) The basic data are: 



(a) The propeller diameter D, in this case 

 24.22 ft 



(b) The wake fraction w, indicated on 

 Fig. 78.1 as 0.072 for 20.5 kt 



(c) The thrust-deduction fraction /, taken 

 from the same figure as 0.175 



(d) The rate of propeller rotation n, of 

 90.1 rpm or 1.502 rps 



(e) The propulsive coefficient vp of 0.686 



(f) The hull efficiency j;„is (1 - /)/(l - if) 

 or (1 - 0.175)7(1 - 0.072) = 0.889. 



