692 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 73.16 



diagonal offset on the midsection is a maximum. 

 There is a further condition that the diagonal 

 should make an angle with, the tangent to the 

 shell at the diagonal intersection which is at 

 least 80 dog. The angle that counts is the one at 

 the shell, not with the horizontal. 



For negligible pressure resistance and minimum 

 friction resistance, the keel should lie along the 

 lines of flow in its region. It forms in effect a 

 diagonal stream surface, parallel to the lines of 

 flow at the ship hull and for the entire width of 

 the keel away from the hull. These lines of flow, 

 especially on a fast or a high-speed ship, change 

 position and shape with speed because of the 

 influence of the surface-wave profile. A trace 

 conforming to the flow at one particular speed is 

 therefore selected. This is generally the service 

 speed or the highest speed at which the ship is 

 to run for the greater part of its time in service. 



For slow-speed vessels with nearly square 

 sections in the middlebody, it may be assumed 

 that the flow is approximately parallel to the 

 bilge corner for the region where the bilge- 

 diagonal ofl^set is 0.9 or more of the maximum 

 bilge-diagonal intercept amidships. It is vastly 

 preferable, however, to check a proposed trace 

 with surface lines of flow on a model. It is still 

 better to double-check the position with tufts or 

 flags mounted on pins and extending for at least 

 0.9 the maximum width of the bilge keel from 

 the hull. 



Occasionally it happens that when laying out 

 a trace from the optimum position amidships, 

 the keel leads up too close to the free-water surface 

 or down too close to the floor line or the baseplane. 

 One portion of the keel may then be terminated 

 when it moves out of optimum position and 

 another portion started in an offset position, 

 reckoned girthwise, where it may be placed to 

 better advantage for performing its function. The 

 keel endings at this offset may, in fact, overlap 



longitudinally by the length of the taper on each 

 keel but no overlap is preferred, shown in the 

 lower profile of Fig. 73. L. There may, of course, 

 be a fore-and-aft gap of any desired length 

 between them. In general, the girthwise offset 

 should be at least 1.5 times and preferably 2 

 times the full width of each keel near the gap, 

 shown by the middle diagram of Fig. 73. L. 



For ships of such full sections that working 

 clearance is not available for keels in way of the 

 midship bulge, the roll-resisting keel may be 

 omitted there. Separate shorter keels are then 

 laid out, forward and aft, where the clearance is 

 adequate. Such a design is illustrated in the upper 

 profile of Fig. 73. L. 



For a vessel with a large but exceptionally slack 

 midsection, and a limit to the width of the 

 excrescences that can be applied to it, such as a 

 motor lifeboat, it is possible to fit two roll-resisting 

 keels abreast on each side of the hull. In such a 

 layout the spread between the adjacent keels is 

 made at least 6 times the maximum width of 

 each keel to insure its proper functioning. On 

 the Dutch liner Oranje of the late 1930's, which 

 was built with discontinuous bilge keels of the 

 picket-fence type, a second partial row of such 

 keels was added below the main row [WRH, 15 

 Jan 1939, p. 21]. The transverse spacing was, with 

 justification, less than that prescribed in the 

 foregoing for solid bUge keels abreast. 



73.16 Bilge-Keel Extent, Area, and Other 

 Features. Because of its greater lever arm, 

 and possibly also because of its width with refer- 

 ence to the thickness of the boundary layer, a 

 keel on a sharp bulge, designed to give a certain 

 degree of roll-quenching, may be relatively 

 narrow. It must be wider, however, as the bulge 

 radius is increased. 



Having determined the girthwise position of 

 the roll-resisting keel, a point is selected on the 

 exterior portion of the diagonal, indicated at K 



■x^A\^^ "Offset Should Be- of the Order of 



k^After Section Offset Upward Here; 

 ■^^^ It Can Be Offset 



I Jownword 



1.5 to 2,0 Times 



I the Bilge-Keel Width Near the Gap 



Fig. 73. L Bilge-Keel Arrangements With Gap and Offset Amidships 



