108 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 45.12 



cutaway in tlu' ftuefool or aftfoot, and with 

 sliort, chubby luills. For these, a value of C., is 

 tletormincil with reasonable accuracy, provided 

 the correct value of Cs is available for a prototype 

 vessel whose proportions and coefficients do not 

 differ too much from the vessel whose wetted 

 surface is sought. Suppose for example that Cs 

 from Fig. 4.").Ci is small by 0.04 for a craft of 

 abnornuil form whose Cs is known. It may be 

 taken as apjiroximately 0.04 small for the same 

 tjT>e of hull, even though the proportions and 

 coefficients are changed somewhat from those of 

 the "known" vessel. The C'., derived from Fig. 

 45.C1 by using the proportions of the given form, 

 augmented by 0.04, may be relied upon for the 

 abnormal type being developed. If it is known, 

 for instance, that the wetted surface of a twin-skeg 

 stem design is 3.2 per cent greater than that of a 

 normal-form ship, the latter as given by Fig. 45. G, 

 then this allowance may be applied rather gen- 

 erally, for any twin-skeg stern ship, to the 

 predicted result given by the formula. 



In any case, because of the present (1955) un- 

 certainty as to the correct roughness allowance for 

 any ship, it seems not necessary, when making 

 preliminary force and power predictions, to 

 calculate the wetted area to a high degree of 

 accuracj'. 



The procedure currently employed in detail 

 calculations of the friction drag on the doubly 

 curved wetted surface of a ship hull assumes that 

 the surface is flattened into a single thin plate 

 which has a DWL length equal to that of the 

 ship and a width equal to that of the half girth at 

 each station or frame. Such a plate has the general 

 .shape indicated by the 0-<liml girth curves of 

 Fig. 22.A of Volume I. The two sides of the flat 

 plate correspond to the two sides of the ship. 

 This leads to the general rule that the wetted 

 surface of the main hull, without appendages but 

 with large bo.ssings or skcgs, is the product of the 

 waterhne length and the mean wetted girth to 

 the waterline. The mean girth may be computed 

 by Simpson's first rule, using 20 e(iuully spaced 

 stations, or by any convenient e(|uivalent method. 

 The wetted surface of a large appendage, par- 

 ticularly one which is long like a bilge keel, is 

 calculated similarly from its mean wetted girth, 

 to be obtained by any convenient method, and 

 ita length as projected on the centerplane of the 

 vessel. The wetted surface of small, short append- 

 ages, which arc relatively thin and on which the 

 rcsisUincc is largely fridional, is lalciilalrd by 



the rules of solid geometry or any convenient 

 method. An appendage is considered small or 

 short when the r-Reynolds number at the trailing 

 edge is less than about 15 milUon at the given 

 speed. As an example, this occurs for a length of 

 about 7.5 ft at 15 kt, 5.G ft at 20 kt, and 3.75 ft 

 at 30 kt. If the appendages are very short, like 

 the arms of shaft struts, their wetted surfaces are 

 neglected, and their resistances are computed by 

 the rules of Chap. 55. 



The surfaces of exposed rotating shafts, rotating 

 hull plates of cj'cloidal or rotating-blade propellers, 

 and similar areas not subject to translatory 

 motion onlj', require to be handled by mcthotls 

 considered apjjropriate in each case. No logical 

 and systematic procedures have as yet been 

 worked out for these parts. Friction drag on 

 propeller-hub, fairing-cap, and blade surfaces is 

 taken into account in propeller performance. 



It has not been practicable, as described in 

 Sec. 12.3 of Volume I, to resolve the tangential 

 forces on each unit of wetted area into components 

 parallel to the direction of ship motion. The 

 summation of the actual friction forces gives 

 therefore a value slightly greater than the sum 

 of the direction-of-motion components; see Fig. 

 12. A. Effective if not e.xact compensation for this 

 inequality is achieved by using the mean girth 

 for calculating the wetted surface, without a 

 correction for obliquity, thus giving a wetted- 

 surface area slightl}' less than the actual area. 

 For those who wish to emploj' the obliquity cor- 

 rection a diagram giving the necessary factors 

 and instructions for their use is published by 

 D. W. Taylor [S and P, 1943, p. 18]. The obliquity 

 correction is of interest only for full, fat ship.s. It 

 amounts to about 0.01 for a ship having an L/H 

 ratio of 4 and a B/H ratio of 2.2. 



At the design stage where the girths are taken 

 off for the early wetted-surface calculations, 

 usuallj' onlj' the molded lines are available, 

 representing the inside rather than the outside 

 of the plating. A small plus allowance can be 

 made for the surface of the ship to the outside 

 of the plating, or the girths can be measureil 

 deliberately a little large. 



Unless circumstances indicate that the wave 

 formation along the side may be unusual at the 

 speed for which the A',, calculation is being made, 

 no account is taken of the wave priilile in altering 

 the at^rest wetted surface. The wetleil surface 

 gained in the crests of waves along the ship's side 

 is ])riibably somewhat less than that lost in the 



