640 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 71.3 



certainl}' greater than V. Since so little is known 

 of these velocities for the paddlewheel positions 

 on ships, especially as the wheels extend outward 

 from one-third to one-half the beam, it is cus- 

 tomary to assume that the speed of advance V a 

 and the ship speed V are the same. 



There has been in the past some difference of 

 opinion among commentators and designers with 

 regard to the radius at which the tangential 

 velocity of a paddlewheel blade is to be measured, 

 for the purpose of determining the slip ratios. 

 By some this velocity is measured at a radius 

 corresponding to the distance from the wheel 

 center to the bottom of a blade in its lowest 

 position. Twice this radius is roughly the overall 

 wheel diameter, leaving out of account the angu- 



Blade Lent^th is 

 Normal to Paae 



FeQtherino 

 Link and Blade 

 Foul Here 



Blade Dip- WG 

 Biometer of Trunnion 

 Cirde-A|C°2AC 



Actual Sli| 

 Velocity 



Positive Wave- Wake Speed I 



<?Ne(jQtive Potential-Flov« Woke 



Shtp Speed V- 



u.auii 

 r*— '<j^Speed V plus Induced U- 



sj^ ■ 



H-n-n(AC) 



Fig. 71. a Definition and Design Sketch for 



Feathering Paddlewheels 

 For the wheel shown here, the trunnions are placed at 

 midheights of the blades. 



larity of feathering blades as they swing around 

 the circle and the presence of external rings 

 serving as guards and as ties between the arms. 

 "The actual slips can only be determined by 

 careful analysis of the path of the paddles at 

 given speeds of boat and wheels" [Taylor, S., 

 SNAME, 1908, p. 245; Stevens, E. A., Jr., 

 SNAME, 1908, p. 246]. It appears customary, 

 however, to measure the tangential blade velocity 

 at the midheights of the blades for a radial 

 wheel, and at these positions or at the trunnion 

 centers for a feathering wheel [SNAME, 1926, 

 p. 187]. The difference usually is not appreciable. 

 Fig. 32. B indicates that the circle corresponding 

 to these trunnion positions is in this book called 

 the hlade circle. The tangential velocity of this 

 circle is represented by the symbol V° (vee circle). 

 The vector diagram in the lower right corner 

 of Fig. 71. A indicates all the velocities known to 

 be acting in the case of a paddlewheel drive, with 

 their correct ahead or astern directions. Their 

 magnitudes in this diagram are, however, purely 

 schematic. The}^ will remain so until more data 

 are made available, covering the flow across the 

 entire width of a paddlewheel (length of a blade), 

 from its inboard to its outboard end. When the 

 curved paths of the blades and the waves on the 

 surface of the adjacent water are taken into 

 account, the velocities are not all horizontal, nor 

 do they remain the same in various parts of the 

 field swept by the blades. In the past, as previously 

 described, this situation has been simplified at one 

 stroke by assuming that V a. = V. The apparent- 

 slip ratio is then 



V of blade circle — Va 



V of blade circle 



_ V of blade circle — F of ship _ V° — V 

 V of blade circle v° 



For radial wheels the ratio Sa ranges from 0.2 

 to 0.3. For feathering wheels on ships of relatively 

 fine form it varies from 0.1 to 0.2, averaging about 

 0.15. E. M. Bragg gives values of Sa for nine 

 passenger ships, ranging from 0.146 to 0.223, 

 when reckoned on a basis of the tangential speed 

 of the midheight of the (feathering) blades 

 [SNAME, 1916, PL 90]. For paddlewheel tugs 

 O. Teubert gives a range of s^ values from 0.3 

 to 0.5 ["Binnenschiffahrt (Inland-Waters Ship 

 Operation)," 1912, p. 445]. For operation in 

 shallow and restricted waters, Teubert adds 0.1 

 to all the apparent-slip ratios mentioned. 



