Sec. 71.6 



DESIGN OF MISCELLANEOUS PROPULSION DEVICES 



643 



many other factors. For apparent-slip ratios 

 ranging from 0.10 to 0.30, K = [212.5 - 375(s^)] 



P is the shaft or indicated power; unfortunately 

 a rather loose definition 



V is the ship speed in kt. 



Assuming for the bare-hull ABC ship an 

 effective power of 10,816 horses, from Sec. 66.9, 

 and a propulsive coefficient rjp of as high as 0.55 

 for a modern design, the value of P for Eq. (71.iv) 

 is about 19,660 horses. That of K, for an assumed 

 apparent-slip ratio of 0.16, is [212.5 - 375(0.16)] 

 = 152.5. Substituting in Eq. (71. iv) 



Ct. 



T 



A = 



Kyz = 152.5 ^^^ = 347.9 ii\ 



The effective blade area on each side of the vessel 

 is half of this value or 173.9 ft^. This is a somewhat 

 larger area per blade than the value of 163.4 ft^ 

 calculated by Eq. (71.iii) but the discrepancy is 

 perhaps not too large, considering the assumptions 

 made. 



The additional formulas given by W. F. Durand 

 [RPS, 1903, pp. 198-201] and by 0. Teubert 

 ["Binnenschiffahrt," 1912, p. 446] are dimensional, 

 as is the formula given by D. W. Taylor. They 

 require in addition an estimate of the wheel 

 diameter and the rate of rotation, or both. 



Another method of approximating a suitable 

 blade area, if complete and reliable reference data 

 were available, is to make use of the thrust-load 

 coefficient and to work backward to find the 

 equivalent thrust-producing area Ao by the 

 following formulas, assuming as before that 

 Vj, = V: 



Cr 



T 



Q.bpAaVl 0.5p(equivalent ylo)F' 

 Equivalent area ^o , for both sides, 



CrL(0.5p)F' 



For example, taking the total resistance Rt oi 

 the Commonwealth, derived earlier in this section 

 as 89,876 lb, and assuming that it equals the 

 thrust T of both paddlewheels, with a thrust- 

 deduction fraction t of 0.0, it is possible to derive 

 the thrust-load factor Ctl for this vessel. The 

 speed is 20 kt, or 33.78 ft per sec. The apparent 

 dip of the blades, so called by Bragg because it is 

 measured to the at-rest WL, is 7.58 ft and the 

 length of each blade is 14.5 ft, so that Ao = 2(7.58) 

 14.5 = 219.82 ft'. Then 



Q.bpAoV 



89,876 



0.9953(219.82)1,141.1 



= 0.3599, say 0.36 



Assuming the same value of Ctl for the ABC 

 ship at a speed of 20.5 kt or 34.62 ft per sec, and 

 using the value of 72r = T = 176,400 lb mentioned 

 earlier, 



Equivalent area 



^0 = 



T 



C'rL(0.5p)F- 



176,400 



0.36(0.9953)1,198.5 



= 410.8 ft' 



This is the estimated thrust-producing area on 

 both sides of the vessel; on one side it is 205.4 ft'. 

 With a tentative dip ratio of 1.35, the estimated 

 area of one blade is 205.4/1.35 = 152.1 ft'. This 

 value is only slightly larger than the estimated 

 area of 147.06 ft', derived previously in this section 

 by using the momentum method, with a reduction 

 factor of 0.9. 



The usefulness of the Ctl method obviously 

 depends upon knowledge as to proper thrust-load 

 coefficients for design purposes. For instance, the 

 value of Ctl for the Tashmoo from Bragg's table, 

 using a mechanical efficiency of 0.9 and a propul- 

 sive efficiency of 0.55, is only 0.26 as compared to 

 the 0.36 of the Commonwealth. For a paddle tug, 

 pulling heavy loads at slow speeds of advance, 

 the thrust-load coefficient might reach or exceed 

 10 times these values. 



71.6 Relation of Paddlewheel Diameter and 

 Position to Ship Hull Design. Taking account 

 of general design considerations, the selection of 

 paddlewheel diameter is one rather closely related 

 to the overall ship design, because it concerns the: 



(a) Space which can be allowed for the wheel 

 boxes or recesses 



(b) Overall beam of the vessel, measured to the 

 guards outside of the wheels 



(c) Type of engine, and of reduction gear if fitted 



(d) Rate of rotation n of the paddlewheel drive 



(e) Speed of the vessel 



(f) Probable values of wake fraction w and real- 

 slip ratio Sr . 



In general, the greater the wheel diameter the 

 more efficient is its propulsive action. With a 

 larger diameter the blades enter and leave the 

 water more nearlv tangential to the resultant- 



