294 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 55.10 



drag, in addition to a lift force by the Magnus 

 Effect. The latter is described and discussed in 

 Sec. 37.25 of Volume I and illustrated in Fig. 

 37. Q. The shaft also generates a pressure-drag 

 force, to be described presently. Rotation of the 

 shaft surface involves tangential friction and an 

 increase in torque to keep it turning. The forward 

 motion of the ship and shaft involves longitudinal 

 friction, much the same as though the shaft were 

 covered by a casing which did not rotate. A 

 pressure drag, due to the oblique flow of water 

 past the shaft, is exerted in the general plane of 

 flow, at right angles to the shaft. This drag may 

 or may not have a longitudinal component, 

 depending upon the declivity and convergence — 

 or divergence — of the shaft axis. 



Taking the last item first, the shaft is considered 

 as a fixed appendage in the form of a 2-diml 

 circular cylinder, placed normal to a flow having 

 an effective velocity equal to that component of 

 the actual velocity perpendicular to the shaft axis 

 and in the plane of that axis. In the absence of 

 any better data, the actual streamline velocity 

 may be taken as equal to the speed of the ship, 

 and the direction of flow as parallel to the hull 

 along an appropriate diagonal flowplane, indi- 

 cated by surface (or preferably off-the-surface) 

 flow markings, described in Chap. 52. This drag 

 force will have a vertical or lifting component for 

 most ship installations, possibly having a slight 

 effect on the trim. 



The exact nature of the axial and tangential 

 components of the viscous flow around an exposed 

 rotating shaft remain unknown in the present 

 state of the art. It is customary, therefore, to 

 neglect both friction-drag components on the 

 shaft, unless the latter is excessively large and 

 rotates at high speed, or unless it is so long that 

 it has to be supported by two or more bearings, 

 external to the hull. 



To give an idea of the magnitudes involved, 

 assume two shafts, each 12 inches in diameter, 

 revolving at 400 rpm, and having an exposed 

 length of 40 ft, lying at a mean angle of 8 deg 

 to the lines of flow at a speed of 35 kt, equivalent 

 to 59.11 ft per sec. The layout of P. Mandel 

 [SNAME, 1953, Fig. 2, p. 466] shows the star- 

 board shaft of a twin-screw arrangement of this 

 kind. The tangential velocity at the surface of 

 one shaft, due to rotation only (neglecting cross 

 flow due to non-axiality), is (12/12)x(400/60) = 

 20.95 ft per sec. This is about one-third the forward 

 speed of the ship and is about 2.5 times the cross- 



flow component due to non-axial flow at the shaft 

 position, to be calculated presently. 



Neglecting rotation and considering only the 

 general flow in the vicinity, at an angle to the 

 shaft, the axial component of velocity is [(59.11) 

 cos 8 deg] or 58.53 ft per sec. The component 

 normal to the shaft is [(59.11) sin 8 deg] or about 

 8.23 ft per sec. The Co of a 2-diml circular cylinder 

 of L/D ratio 40/1.00 = 40 is, from Fig. 55.B, 

 about 0.98. The normal force expected to be 

 exerted on the shaft, neglecting the effect of 

 rotation, is then 



F = C„^Ap,„,C/= 



0.98(lf«5) 



[(40)(1)](8.23)=' 



= 2,640 lb, for the single shaft. 



The drag of locked screw propellers is discussed 

 in Part 5 of Volume III. 



55.10 Drag Data for Holes, Slots, and Gaps. 



What might be called reversed projections, in 

 the form of recesses and holes, are considered here 

 in the category of appendages, especially if they 

 have physical dimensions corresponding to the 

 appendages usually found on boats and ships. 

 S. F. Hoerner has collected drag-coefficient data 

 for holes and gaps, some based on a reference area 

 equal to that of the opening in the fair surface 

 and some based on the so-called frontal area of 

 the downstream face [AD, 1951, pp. 55-56]. 

 A stagnation point may be found here, as at Q 

 in diagram C of Fig. 7.J, but if not it may be 

 expected that some -|-Ap's are developed on the 

 downstream face. 



Because of the rather comphcated nature of the 

 drag effects, the marine architect is referred 

 directly to the Hoerner reference for such data 

 as he may need. 



The design of recesses to reduce their drag is 

 discussed in Sec. 75.13. 



55. 11 Estimated Resistance of Discontinuities. 

 The drag of any large discontinuity, invariably 

 attached to a much larger body such as a ship 

 hull, as distinguished from an appendage project- 

 ing well away from the hull, is dependent upon 

 the flow pattern around it. The latter is, in turn, 

 affected by the presence of the boundary layer 

 on the large body, with its variation in local 

 velocity across the boundary-layer thickness. 



In aerodynamics the resistance of discontinuities 

 of this type falls under the heading of interference 



