732 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 74.16 



accomplish this imposes lift loads which increase 

 the thickness ratio and make it more difficult to 

 lay out hydrofoil sections of suitable shape. 



With these considerations m mind a compromise 

 solution employing a leading-edge offset on the 

 rudder -v'aryiug as sin^ <^, utUized previously for 

 the design of the contra-guide skeg ending dis- 

 cussed in Sec. 67.22, is employed here for the 

 contra-rudder as well. The offset taken as a 

 reference may be based, as before, on a value of 

 about 0.85 times the propeller hub radius d/2 

 opposite the 0.1 propeller radius. A graph for 

 selecting the angle which the median luie at the 

 leadmg edge of a fixed contra-propeUer blade is to 

 make with the fore-and-aft plane is given by 

 R. Wagner [STG, 1929, Fig. 44, p. 224]. This 

 graph could be used as well for the leading edge 

 of a contra-rudder, whether this edge were the 

 fixed portion of a compound rudder or the leading 

 edge of a balanced rudder. It calls for an angle 

 of 45 deg at O.lSfi (of the propeller), 19 deg at 

 0.48fi, and 9 deg at O.SOi?. 



Whatever rule is used, some asymmetry in 

 the form of leading-edge angle does and should 

 remain abaft the propeller-blade tips, as for the 

 contra-guide skeg endmg, at vertical distances 

 above and below the shaft axis equal to the pro- 

 peller radius R^^^ . 



A transition is necessary from the maximum 

 twist toward the trailing edge of the propeller 

 blades at the 12 o'clock position to the maximum 

 twist in the opposite direction (but also toward 

 the trailing edges) at the 6 o'clock position. This 

 should be made gradually, not abruptly, across 

 the "shadow" of the propeller hub. In fact, one 

 good way to make it is to use a cylindrical pro- 

 peller hub and to Avork a large hub fairmg into 

 the contra-rudder in this region. By this means 

 abrupt and harmful discontinuities m the rudder 

 structure abaft the hub are avoided. A variation 

 of this method is to work a bulb into the rudder 

 at the transition pomt, extending well aft on the 

 rudder [Maritime Reporter, 1 Feb 1954, p. 23]. 



If all the rotation is to be taken out of the 

 propeller-outflow jet, the median lines of the 

 trailing edges of the contra-rudder sections should 

 be parallel to the mean plane of the rudder in its 

 zero or neutral position. It may possibly be better 

 to make the face, on the -|-Ap side of the trailing 

 edge, parallel to this mean plane. Also, if an 

 appreciable forward component of the lift or 

 lateral force on the rudder is to be realized as 

 thrust, it is advantageous to place the base chord 



of each of the rudder sections at an appreciable 

 angle to the mean plane of the rudder blade. All 

 this may require that, not only must the leading 

 edge be directed and offset one way from this 

 plane, but the trailing edge must be offset the 

 other way. The transition takes the form of a 

 crossover from one side to the other, abaft the 

 propeller hub, in both the leading and trailing 

 edges, but in opposite directions. As a means of 

 avoiding sharp corners and coves along which 

 the water must flow, and of structural discon- 

 tinuities in the rudder as well, an easy transition 

 is also called for when the trailing edges are 

 offset from the mean plane of the blade. 



In one of the earliest descriptions of the contra- 

 propeller, for installation abaft a screw, R. Wagner 

 mentions that: "A particularly good result is 

 obtained by shaping the trailing edges of the 

 blades eccentrically to the hub center" [transl. 

 of Schiifbau, 14 Feb 1912, pp. 365-366]. He does 

 not, unfortunately, give specific reasons for this 

 statement. The diagram accompanying the refer- 

 ence has the trailing-edge offset marked by a 

 symbol, not mentioned in the text. Incorporating 

 this offset gives the designer somewhat more 

 freedom in shaping the vane or blade which is to 

 convert some of the rotational energy into thrust, 

 and places the base chord at a greater angle to 

 the ship axis. If other conditions are right, a 

 somewhat greater forward-thrust component is 

 derived from a given lift force. 



For the single rudder of the ABC transom- 

 stern ship it is decided not to incorporate any 

 offset in that part of the blade lying abaft the 

 rudder stock or in its trailing edge. When, as 

 described in Sec. 74.17, a contra-shape is incor- 

 porated in the fixed horn ahead of the rudder 

 stock, there will be an appreciable lift force 

 acting to starboard on the unsymmetrical hydro- 

 foil assembly composed of this horn and the tail 

 of the rudder. Combined with the Hovgaard 

 Effect, described in Sec. 33.17, there wA\ be a 

 continual lateral force acting to push the stern 

 to starboard when the ship is going ahead. This 

 swinging effect can be counteracted only by giving 

 a contra-shape to the underhung foil and exerting 

 a hydrofoil lift force to port. The preponderance 

 of force to starboard may still require carrying 

 more than the usual amount of right rudder to 

 maintain a straight course. This is another reason 

 for not working a contra-guide ending into the 

 upper portion only of the centerline skeg ending. 

 It too would exert a lateral force to starboard and 



