Sec. 46.2 



DATA ON SEPARATION, EDDYING, AND VORTEXES 



135 



zone is deepest at the centerline and it diminishes 

 in depth toward Ep and Eg . The transverse 

 extent of the zone is rather easily determined by 

 attaching tufts to that portion of the model and 

 watching the behavior of these flexible indicators 

 in the moving water of a circulating-water channel. 

 A considerable amount of non-systematic but 

 reasonably reliable modern data indicates that 

 the slope of a ship waterline at which separation 

 begins, at the air-water interface, is of the order 

 of 13 to 15 deg. This is reckoned with respect to 

 the relative direction of motion of the ship and 

 the water and is based upon a surface along the 

 ship's side that is more vertical than horizontal. 

 The critical slope given here is somewhat lower 

 than the values of 18 or 20 deg previously quoted 

 in the literature but it has been well checked on 

 ship models. It may be assumed that a separation- 

 free horizontal slope in the run, at the water 

 surface, is in the range of 11 to 12.5 deg, as shown 

 in diagram 1 of Fig. 46. B. 



No Separation at Surfaoa 

 if lf^ is Leas Than 12.5 



Discontinuity 



■ y 



No Separation at Surface 

 f Cornar Angle is more 

 than 165 deq 



1 



'Separation at Surface Definitel\y Occurs at Ep 



if Corner Anqle is less than about 160 



or 165 deq, provided W/aterline. Slope 

 Anqle Does Not Exceed 12.5 deg 2 



Waterline/ 



1^^.^ Transom 



r"^ Corner Anqle / 3 



Separation at Surface Definitelvj Occurs at Ep and Es if 

 Tronsom Corner Angle has a Value Between 90 and 165 deg 



Fig. 46.B Sketch Indicating Typical Separation 

 Criteria for Waterlines 



Regardless of the waterline slope with reference 

 to the longitudinal ship axis or direction of motion, 

 separation is almost certain to occur at any dis- 

 continuity along that line, where a sharp knuckle 

 exists with a horizontal obtuse angle less than 



165 deg. This may be either at the after end of a 

 blunt entrance, indicated at the right in diagram 1 

 of Fig. 46. B, or at a discontinuity in the run, 

 pictured at the left in diagram 2. Considering the 

 pointed stern of diagram 2 as a form of transom 

 stern, separation is definitely to be expected at 

 the corners Ep and Eg in diagram 3 of Fig. 46. B 

 if the values of the corner angles lie between the 

 limits of 90 deg and about 165 deg. 



There is, unfortunately, a serious lack of in- 

 formation upon which to base an estimate of the 

 rate at which the critical slope in a flowplane that 

 is generally horizontal increases with hydrostatic 

 pressure, at levels below the free surface. In the 

 absence of analytic studies or systematic experi- 

 mental data it may be said tentatively that the 

 separation-free slope increases at the rate of 

 0.6 deg per ft submergence, on a full-size displace- 

 ment-type vessel, up to an estimated critical 

 slope of about 36 deg at a depth of 40 ft. The 

 limiting waterUne slope for freedom from eddying 

 abaft a skeg, placed ahead of a single propeller, 

 is given by W. P. A. van Lammeren as 20 deg 

 [RPSS, 1948, p. 94]. The corresponding depth is 

 not stated but it is at least as far below the 

 surface as the tip submergence. 



The indications are that there is a corresponding 

 variation on the model of such a ship, so that the 

 separation zones and their boundaries are geo- 

 metrically similar. This is to be expected of a 

 pressure phenomenon which is a function of F^, 

 when the model is run at corresponding speed. 



Fining the trailing edges of sternposts, skegs, 

 and rudders to conform to these critical or limiting 

 horizontal slopes is not always achieved, hence 

 separation abaft them is by no means unusual. 

 In some ships with full runs, like the Magunkook 

 of Sec. 23.1 of Volume I, separation has been 

 known to occur abaft the whole underwater hull. 

 In many of these cases there is not only a greatly 

 increased drag but a seriously diminished rudder 

 effect. 



On the stern contour or profile, the separation 

 zone begins at the point Ek , marked on diagrams 

 1 and 2 of Fig. 46.C. When the flow is predomi- 

 nantly in the vertical plane, as it is under the 

 run of the wide, flat barge of diagram 1 of that 

 figure, the maximum separation-free slope appears 

 to be of the order of 14 to 15 deg [Dawson, A. J., 

 SNAME, 1950, p. 9]. This is for a region not more 

 than 2 or 3 ft below the waveline on a ship-size 

 craft. When the flow is both inward and upward, 

 as under the canoe or whaleboat or "cruiser" 



