642 



IIYDROnYNAMICS IN SHIP DESIGN 



Sec. 71.5 



calculation of Eq. (Tl.iii) into agreement with 

 corresponding values calculated from observed 

 ship data. There are several difficulties here. The 

 published data available to the analyst lack one 

 or more of the important values necessary for a 

 logical calculation. The simple formula of Eq. 

 (71.iii) takes no account of velocities induced by 

 adjacent blades, spillover around the edges of the 

 blades, motion of the blades in a loop-shaped path 

 as worked out in the early years of paddlewheel 

 propulsion [S and P, 1943, Figs. 168 and 169, 

 p. 149], and changes m the elevation and shape 

 of the. water surface in way of the blades. Further- 

 more, it assumes that not several but only one 

 blade at a time, on each paddlewheel, is acting 

 upon the water. The rectangular area of the 

 stream tube in which momentum is being imparted 

 to the water, when so derived, is undoubtedly 

 larger than the rectangular area of one blade. It 

 may be more nearly the area of the thrust- 

 producing segment indicated by the hatched rec- 

 tangles on each side of diagram 2 of Fig. 15.G. 



Purely as a means of working out a numerical 

 example it is assumed here that a reduction 

 factor may be applied to the calculated blade 

 area, because of the conditions described in the 

 preceding paragraph. This factor is established 

 arbitrarily for the moment as 0.90. The necessary 

 area per blade on the ABC paddlewheel is then 

 only 163.4(0.9) = 147.06 ft^ A better reduction 

 factor may be taken when it is found. For paddle 

 tugs it is possible that no reduction in calculated 

 effective area should be made. 



The next step is to select the proportions of 

 the blades. The narrower and shallower they are, 

 the smaller can be the wheel diameter and the 

 higher its rate of rotation, but at the expense of 

 shaft and paddlewheel length and overall beam 

 of the vessel. The deeper and shorter the blades, 

 the less can be the wheel width and the overall 

 beam but at the expense of greater wheel diameter 

 and a slower rate of rotation. The slower the rate 

 of rotation the larger and heavier is the propelling 

 machinery. 



The average value of length-height ratio s/h 

 -of a blade in Bragg's referenced table is slightly 

 in excess of 3.0, with a maximum blade width 

 for the nine vessels hsted of 5.0 ft. Assuming a 

 blade width of 6.5 ft for the ABC ship, developing 

 nearly twice the power of the fastest vessel 

 tabulated there, the blade length is about 22.6 

 ft and the length-height ratio is just under 3.5. 



This length is within the limit given by D. W. 



Taylor [S and P, 1943, p. 150], who states that 

 good practice requii'es the blades for a seagoing 

 vessel to be no longer than one-third the beam. 

 A blade length of O.iB is a good figure for any 

 type of smooth- water ship; a maximum value for 

 any design, except paddlewheel tugs, is 0.5B. 



The average pitch ratio, illustrated in Fig. 

 32. B and defined as the circumferential distance 

 between adjacent trunnions of a feathering paddle- 

 wheel divided by the blade height, is of the order 

 of 1.5 for the most modern designs in the Bragg 

 table. This gives a circumferential spacing on the 

 trunnion circle, assumed for the moment as 

 equal in diameter to the circle passing through 

 the midheights of the blades, of 1.5(6.5) = 9.75 ft. 

 Taking 10 blades as a starter, the circumference 

 of the ABC trunnion circle is 9.75(10) = 97.5 ft; 

 its diameter is 97.5/7r = 31.03 ft. 



The outside diameter of the paddlewheel, 

 assuming no circumferential rings external to the 

 blades, is approximately 31.03 -{■ 6.5 = 37.53 ft, 

 giving a blade-height ratio of 6.5/37.53 = 0.1733. 

 This is somewhat larger than the largest value of 

 0.168 (for the Tashnwo) in Bragg's table. It could 

 be reduced by using 11 blades instead of 10 but 

 with the selected pitch ratio of 1.5, this would 

 increase the overall wheel diameter to about 

 40.7 ft. The blades could be narrowed to 6.0 ft, 

 giving a blade-circle diameter of [11(6.0)1.5]/ 

 X = 31.5 ft and a blade- height ratio of only 

 6.0/(31.5 -I- 6.0) = 0.16. However, this would 

 increase the blade length to 147.06/0.6 = 24.5 ft. 

 While still of the order of one-third of the beam 

 of 73 ft for the ABC ship, the length-height ratio 

 of each blade is 4.09, which is considerably too 

 large for actuation by one feathering crank at 

 one end. 



71.5 Alternative Methods of Determining 

 Paddlewheel Blade Area. Other methods of 

 calculating the effective area per blade, such as 

 that described by D. W. Taylor [S and P, 1943, 

 p. 150], are based upon the same combination of 

 the engine power (possibly determined previously 

 by the owner or operator), the ship speed, the 

 slip ratio, the wheel diameter, and the rate of 

 rotation. Taking the formula given by Taylor 



A = K 



V 



(71. iv) 



where A is the area of two blades, in ft", one on 

 each side of the ship 



K is a coefficient depending primarily upon 

 the apparent-slip ratio and secondarily upon 



