422 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 62.2 



The weight displacement of the ship is 16,400 t. 



The block coefficient Cb of an elUptic ellipsoid 

 (or of half such an elUpsoid) is [(4/3)7ra6c]/(8a?)c) 

 = 7r./6 = 0.5236. The block coefficient Cb of the 

 fifth approximation to the preliminary design 

 of the ABC ship is, from Table 66.e, 0.593. 



The mass moment of inertia of the liquid 

 displaced by the buoyant elliptic ellipsoid is: 



For rotation about the x-x or a-axis, 



■^pahcib'^ + c') 



For rotation about the y-y or 6-axis, 



-x%Trpabc{a' + c^) 



For rotation about the z-z or c-axis, 



■rsT'pabcia + b'). 



The British Shipbuilding Research Association 

 has collected, and S. L. Smith has published 

 added-mass data for prolate spheroids, for bodies 

 of other shapes, and for surface ships having a 

 rather wide range of @ or L/V^^^ values [INA, 

 1955, pp. 525-561, esp. Fig. 12 on p. 542]. The 



Length- Volume Ratio L/V'^ or (M) Value 



Fig. 62. C Added-Liquid-Mass Data fob Submerged 



Prolate Spheroids, and for Other Floating 



Streamlined Bodies and Ship Forms 



This figure has been adapted from one published in INA, 



1955, Fig. 12, p. 542. 



data are for axial or surging motion, either 

 acceleration or deceleration, parallel to the axis 

 of symmetry of the body or the principal axis of 

 the ship. Fig. 62. C is adapted from the reference, 

 with an added scale of fatness ratio ^/(O.IOL)^. 

 The spots on the original graph, indicating the 

 source and kind of data, are not reproduced here. 

 It is assumed that all the surface-ship data are 

 for hulls without propulsion devices of any kind. 

 L. Landweber and A. Winzer have computed, 

 by potential theory, the added-mass coefficients 

 Cam for a series of streamlined bodies of revolution 

 having fore-and-aft asymmetry [ETT, Stevens, 

 Rep. 572, Jun 1955]. The typical body, shown 

 diagrammatically in Fig. 62. D, has its x-axis 



Midlenqth Posit 



J Sidlinq on 

 I Transverse 

 ' Axis 



Fig. 62.D Definition Sketch of Body of Revolution 



OF L. Landweber and A. Winzbb, with Fore-and- 



Aft Asymmetry 



coinciding with the axis of revolution. In this 

 case, however, the y-axis lies at x = 0, that is, 

 at the nose. With L as the length of the body, 

 and D its maximum diameter, the nondimensional 

 coordinates become x' = x/L and y' = y/D. Of 

 the seven body characteristics, using notation 

 corresponding to that employed elsewhere in 

 this book: 



771 is the 0-diml abscissa occurring at (/' = 0.5. 

 In other words, m = x/L where y = D/2. 



Ro is the 0-diml radius of curvature at the nose. 

 It is equal to RoL/D', where Ro is the absolute 

 radius of curvature at the nose. 



