694 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 73.17 



ratio of 2.0, a semi-circular maximum section, 

 a Cx of 7r/4 or 0.785, and a rolling axis in the 

 waterplane, at the center of the circular-arc 

 section. 



A design curve or lane to give suitable values 

 of the roll-resisting keel area Ak with relation to 

 some other suitable term should therefore have 

 a maximum at a Cx value of about 0.785, cor- 

 responding to a semi-circular midsection, and two 

 minimums at values of Cx approximating 1.0 

 and 0.0. P. Mandel has given such a design lane 

 for the range of Cx from 0.7 to 1.0 [SNAME, 1953, 

 Fig. 25, p. 492], based upon the ratio 10A^:/(LH), 

 where Ak is the bilge-keel area on one side of the 

 vessel. The graph should in fact diminish toward 

 zero at Cx values of 0.4 or less, corresponding to 

 those of deep-keel yachts. 



73.17 Structural Considerations in Bilge-Keel 

 Design. The pubhshed literature and reference 

 books on the structural design and construction 

 of ships overlook many of the important features 

 of bilge-keel design. Some of these are closely 

 related to hydrodynamics and are accordingly 

 discussed briefly here. 



The roll-resisting keels are in effect principal 

 longitudinal members of the ship structure, re- 

 sembhng stringers. As such they must diminish 

 gradually in section so that the shell connection 

 at any point may carry the increment of shear 

 load appUed at that point. In other words, the 

 keel and the hull must stretch and compress 

 together. The securing angles attaching the keel 

 to the shell should project well beyond the end 

 of the keel proper, about as diagrammed in Fig. 

 7.3.N of Sec. 73.18. 



If the roll-resisting keels extend forward to the 

 vicinity of the quarter point, and if they rise to 

 points above the baseline greater than about 0.3 

 the draft in any operating condition, the forward 

 ends require strengthening against wave slap 

 and water impact. 



The transverse shape of a roll-resisting keel 

 should remain relatively sharp and pointed at 

 its outer edge. If it needs lateral stiffening, such 

 as is often afforded by a half-round bar, this is 

 best provided by an outer-edge flange such as 

 that on an I-beam with the outer flange trimmed 

 down. This construction gives increased damping 



I ! 



U-: 



Roll- Resisting Keel 

 is Coniinuous in [-e 

 This Interval | 



End of Toper Cul at 

 Toes of Shell Angles 



Terminal Plate Forward 

 o'2_5^ , Riveted to Shell Plating 



hl.'O^J — ^-^^ U-r 



I f 

 0.75 



Rivets as Close 

 to Heel of Anqle 

 QS Practicable 



Section B-B Section A-A 

 Fio. 73. N Structural Layout for Roll-Resisting Keels for the ABC Ship 



