646 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 71.7 



position of the wheel. The pitch ratio of 1.5 and 

 blade spacing of 9.75 ft previously adopted for 

 the ABC wheel appear not too small. 



The average position of the center of pressure 

 CP on each moving blade, in the course of its 

 travel through the water, is somewhat below its 

 geometric center, possibly only 0.4 times the 

 blade width from the bottom. It is customary to 

 place the blade trunnion at a point somewhat 

 below the midheight point H in Fig. 71. A. This 

 means that the blade-circle or trunnion-circle 

 diameter is somewhat greater than twice the 

 radius to the midheights of the lowest blade, at 

 the 6 o'clock position. For the nine vessels listed 

 in Bragg's table, reference (14) of Sec. 59.6, this 

 diameter ratio varies from 1.00 to 1.04. The 

 ratio of the height of trunnion above the lower 

 edge of the blade in the 6 o'clock position to the 

 blade height varies from 0.40 to 0.50. For the 

 ABC ship of Fig. 71.B it is taken as 3.0/6.5 = 

 0.462. Thus in the elevation from starboard, at 

 the left of Fig. 71. B, GH is 3.0 ft and HF is 

 3.5 ft. The trunnion circle passing through H 

 has a diameter of 2 (AH) = 2 (AG - GH) = 

 2(18.75 - 3.0) = 31.5 ft. 



Having determined the trunnion-circle diam- 

 eter, the blade width, and the blade spacing, the 

 number of blades becomes approximately ir times 

 the trunnion-circle diameter divided by the blade 

 spacing, CJ in Fig. 71.B, to the nearest whole 

 number. There is no particular advantage in 

 using an odd or even number of blades but the 

 minimum practical number is about 6, preferably 

 not less than 7, although paddlewheels have been 

 built with only 5 blades. The number 10, selected 

 for the ABC ship in Sec. 71.4, is a good average 

 value from the Bragg table. 



There is undoubtedly an advantage in mounting 

 the port and starboard paddlewheels on their 

 shafts at an offset or phase angle corresponding 

 to half the angular distance between adjacent 

 blade trunnions, so as to have the water entry 

 of the port blades taking place midway between 

 those of the starboard blades. This would depend, 

 however, on the torsional-vibration characteristics 

 of the paddlewheel shaft. 



Even with feathering blades, it is almost never 

 possible to use a wheel diameter (or trunnion- 

 circle diameter) large enough to cause the blade 

 edges to enter and leave the water in a direction 

 parallel to the resultant-velocity vectors at those 

 points. For instance, in Fig. 7 LA the lower edge 

 of the entering blade TS is almost exactly tangent 



to the resultant-velocity vector PiQ on the forward 

 side of the wheel. However, on the after side, the 

 leaving edge of the blade XjYi is far from tangent 

 or parallel to the vector QiPj . The blade would 

 have to shift angularly about its trunnion to the 

 position XY to comply with this condition. 

 Furthermore, if one wishes to make a compre- 

 hensive analysis, the position of the wave profile, 

 the direction of flow within the wave, and the 

 known component velocities of Fig. 71.A all 

 require to be taken into account. 



The practical solution is to make the lower 

 edge of an entering blade meet the water surface 

 with the blade tangent to the resultant velocity 

 vector. Curving the blade radially, with its 

 concave and +Ap side aft, helps to accomphsh 

 this. However, this very curvature can be said 

 to impart a greater upward component of velocity 

 when the blade leaves the water than would be 

 the case if its surface were flat. The major source 

 of noise and vibratory forces in a paddlewheel 

 drive appears to be the periodic impact of the 

 entering blades. This involves a sufficiently heavy 

 blow, for example, to render a paddle vessel 

 audible before it appears around a bend in a river. 

 It is important, therefore, to favor this condition 

 and to provide as nearly shock-free entrance as ■ 

 possible at this point. It is the excessive lifting 

 of the water as the blade leaves the surface which 

 raises the high crest abaft most paddlewheels, > 

 pictured in Fig. 73.J, and which makes it possible 

 to use a fixed contra-vane abaft the wheel to 

 such good advantage. 



There is no fixed value, nor are there very 

 definite limits, for the radius of curvature of the 

 blade faces. This may be as large as 1.5 times the 

 blade-circle radius, AC in Fig. 7 LA, or as small 

 as 1.0 times that radius. The latter ratio is used 

 in the layout of Fig. 71. B, where it is taken as 

 15.5 ft. 



If feathering wheels are fitted to a double- 

 ended ferryboat or other craft which must run 

 equally well in either direction the blades are 

 made flat rather than curved. The feathering 

 mechanism can be so designed that they enter 

 and leave the water at about the same angles 

 when going astern as when going ahead. 



To provide plenty of leverage for the unbalanced 

 forces acting on the entering and leaving blades 

 the lengths of the crank arms are made from 0.5 

 to 0.7 times the blade width. This length is 4.0 

 ft, or 0.615 times the blade width of 6.5 ft, for 

 the layout of Fig. 71. B. 



