Sec. 73.16 



FIXED-APPENDAGE DESIGN 



cm 



on Fig. 73. M, where the included angle between 

 the two adjacent tangents to the hull is 100 to 

 120 degrees. The distance between the point K 

 and the hull gives an acceptable hydrodynamic as 

 well as practical width for the keel. For a per- 

 fectly square-cornered bilge this gives, as it 

 should, a width of zero. The maximum width is 

 for a semi-circular midsection, where it is 0.302 

 (B/2) for a 100-deg angle and 0.154(5/2) for a 

 120-deg angle. 



The length of the keel is determined partly by 

 the area required, assuming that the average 

 width has already been determined, and partly by 

 the length of that portion of the ship for which an 

 adequate lever arm for the keel can be obtained. 

 When the transverse sections have narrowed or 

 contracted so that the lever arm, i^^ , as meas- 

 ured by the distance OB on Fig. 73. M, be- 

 comes less than a certain fraction of the lever 

 arm at the maximum bilge-diagonal offset, the 

 keel is terminated. Since the effectiveness of the 

 keel varies about as Rk , there is little to be 

 gained by making the minimum Rk less than 

 about 0.8 the maximum. At this point (0.8)^ = 

 0.512. For vessels of rather full midsection, say 

 Cx > 0.90, this fraction may be kept larger than 

 0.85. For vessels of slack section, where Cx < 0.90, 

 a minimum value of 0.75 might be justified. 



The midplane of the roll-resisting keel may 

 change angle with the horizontal, at a gradual and 

 moderate rate from amidships to either end, as 

 may seem appropriate when considering the flow 

 of water in its vicinity, at a distance from the 

 shell. Use of the "tangent rule" set down at the 

 beginning of this section produces a narrow keel 

 alongside the sharp-bulged sections of a form and 

 a very wide keel alongside the narrow or slack 

 sections. For the same total area, however, a 

 more efficiftnt keel is obtained by making it as 

 wide as possible amidships and keeping it of 

 approximately constant width. This is because 

 the additional width amidships has a much 

 greater lever arm than at the ends of the keel. 



All too frequently the maximum width or the 

 amidships width of a roll-resisting keel is limited 

 by working clearances around the keel edges. 

 This prevents damage when lying alongside quay 

 walls and when entering graving docks. The 

 clearances are expressed generally as (1) a distance 

 inboard of the point of extreme beam at any 

 section and (2) a clearance above the baseplane 

 throughout the length. The latter is desirable 

 when hauling bilge blocks, especially when the 



/Assumed Position of Rolling Axis 



An(^le Between Rodiol Line OB^ 

 and Tanqent to Shell 



^\ Qt Inner Edge of Bilge 



Keel Should Lie ^^ "^X\\ 

 \Betwean 80 ond IOO^eg\ 



Distance KE Should Be Such 

 That the Angle Between the ■ 

 Vertical MNE and the Tangent KN, 

 f> More Than 3 dea 



-Lines 

 Through K 

 Tangent to5hell- 



FiG. 73. M Bilge-Keel Design Diagram at 

 Midsection 



bilge-block bearers slope slightly downward 

 toward the centerline of the dock. In some cases 

 it may be necessary to provide this clearance 

 above the floor line rather than above the base- 

 plane. In fact, this requirement may be expected 

 for all vessels which are to have bilge blocks 

 hauled under them when drydocking. To obtain 

 the required clearance it is often necessary to 

 shave off the bilge-keel width amidships. 



The forward and after ends of the keels are 

 tapered gradually to practically zero width. A 

 gradual taper occupies a length at least 3 times 

 the keel width, with a maximum slope of about 

 40 deg. For any leading edge lying forward of 

 about 0.5L from the FP, the taper should occupy 

 at least 5 times the keel width, with a maximum 

 slope of 20 deg for medium-speed and 10 deg for 

 high-speed ships. This taper avoids fouling or 

 catching ropes and cables on the ends and 

 ehminates sharp structural discontinuities where 

 the keels terminate. 



It is possible that ships with sections projecting 

 beyond the limits of waterline beam, where 

 Cx > 1-0, hardly need roll-resisting keels at all' 

 A flat, shallow raft with a deep fixed keel, having 

 a Cx approaching 0.0, likewise needs no additional 

 appendage because of the powerful roll-damping 

 effect of the keel. Yachts, with deep fixed keels, 

 no bilge keels, and values of Cx less than 0.5 

 behave much like the raft, except for the addi- 

 tional steadying effect of their sails. Of all the 

 intermediate forms, the craft which needs the 

 maximum roll damping is one having a B/H 



