Sec. 13.15 



FIXED-APPENDAGE DESIGN 



691 



and cavitation are not liable to occur alongside 

 it except for short periods. For example, the horn 

 supporting the rudder under a ship with a broad, 

 fiat stern runs normally at angles of attack varying 

 from zero to a few degrees on either side. However, 

 when the stern swings around and skids over the 

 water in a turn, the angle of attack on this fixed 

 appendage may rise initially to 15 or 20 deg. The 

 angle of attack is, as explained in Sec. 36.10, 

 applied in the wrong direction to facilitate the 

 turn. 



Separation is almost certain to occur on the 

 inside of the turn. Cavitation may occur as well, • 

 if the top of the horn is sufficiently close to the 

 water surface. By making the leading edge of the 

 horn reasonably blunt this separation or cavitation 

 is at least confined to a limited region. It would 

 otherwise, on a thin section with a sharp entrance, 

 extend all the way forward to the leading edge. 

 The skeg section is usually combined with the 

 rudder section to make a streamlined whole. 

 Section shapes found satisfactory on high-speed 

 vessels are similar to the strut sections dia- 

 grammed in Fig. 73. C. Their coordinates are 

 given by P. Mandel [SNAME, 1953, Fig. 3, p. 468]. 



Horns supporting rudder tails and forming 

 compound or flap-type combinations require 

 special shapmg and recessing for the tail. This is 

 to give the minimum clearance and pressure- 

 leakage area between the fixed and movable 

 portions, for the reasons stated in Sec. 37.3. It 

 is easily and simply achieved by providing one 

 or more fixed lugs on the inside of the rudder 



Rudder Post or 



Fixed Portion of 2. 



Compound Rudder 



Fig. 73.K Hrr^GE-GAP Closures fob two Types of 

 Rudder 



recess, directly forward of the stock axis. If the 

 forward edge of the movable tail of the rudder is 

 finished to form a surface concentric with the 

 axis, the mechanical clearance between this sur- 

 face and the fixed lug may be quite small. The 

 manner in which this may be accomplished is 

 illustrated in Fig. 73. K. 



73.15 Selecting the Position, Type, and 

 Number of the Roll-Resisting Keels. The first 

 step in the design of roll-resisting keels is to deter- 

 mine whether or not they are actually needed. If 

 required, what are the operating conditions, and 

 what are the keels called upon to do? It is pointed 

 out in Sec. 36.13 that the discontinuous or multi- 

 fin t3Tpe of keel is advantageous only when the 

 vessel is moving through the water. A continuous 

 or sohd type is indicated if roll-quenching charac- 

 teristics are required at low or creeping speeds or 

 when at anchor. 



Assuming that the continuous type of keel is 

 selected, the next step is to determine its general 

 proportions, dimensions, and location on the hull. 

 The total area is to some extent governed by the 

 degree of roll damping expected or demanded and 

 the inherent roll-quenching characteristics of the 

 underwater form. A hull shape approaching a 

 circular form, as on some submarines, requires a 

 high degree of quenching from the keels, compared 

 to the rolling moments apphed by surface waves. 

 A hull with nearly square sections in the middle- 

 body calls for a smaller degree of quenching 

 moment. Practically all roll-resisting keels involve 

 some increase in appendage resistance. 



The best transverse location for the keels is 

 on the corners of the bulge between side and 

 bottom or at positions having the greatest radius 

 from the rolling axis. The position must insure 

 practically if not definitely continuous submer- 

 gence under all operating conditions. If the rolling 

 axis is not known from model or full-scale tests, 

 it may be assumed at the intersection of the center- 

 plane and the waterplane, or at a parallel line 

 through the center of gravity CG for the particular 

 weight distribution assumed. 



A. Caldwell ["Steam Tug Design," 1946, p. 42] 

 states that "the bilge keels will answer their 

 purpose most effectively if placed at that point 

 on the shell which is farthest from the meta- 

 center." He does not explain his reasoning in 

 this matter. 



A first approximation to the midsection position 

 is obtained by drawing on the body plan a diagonal 

 from the rolling axis to the point where the 



