Some Hydrodynamic Aspects of Ship Maneuverability 



trailing edge. Thus its applicability to a conventional ship hull with a long hori- 

 zontal keel profile is open to question, and it certainly would not be applicable 

 to ships with cut-away stern profiles. 



The principal feature of the slender-body theory and low aspect-ratio wing 

 theory, in the context of the lateral force and moment, is that the differential 

 side force acting on each transverse section of the body depends only on the 

 geometrical characteristics of that section. This (steady) side force can be ex- 

 pressed in terms of the added mass of the same two-dimensional section for 

 horizontal motions, in accordance with the formula 



Y2D= -V'^ £m(x) 



which has been derived by Lighthill (1960). Here V is the forward velocity, /S is 

 the drift angle, and m(x) is the two-dimensional added mass of the section. In- 

 tegration of this differential force over the length of the hull gives the total side 

 force and moment in the form 



Y = -V2/3 I £ m(x) dx = v2/3m (- |] 



J-L/2 ^ ^ ' 



N= -V2/3 r' x^dx 

 dx 



J-L/ 2 



= V2 /? m(x) dx - V2^|m (- ^^ 



= \^fi 



V 2 \ 2 



Note that we have allowed for the possibility of a non-zero added mass at the 

 stern, as would be the case for a finite trailing edge or vertical deadwood on the 

 hull, whereas we have assumed that the bow is sufficiently pointed that the added 

 mass vanishes at the forward end of the hull. 



If the body is pointed at the stern, m(-L/2) = and the classical potential- 

 flow results are obtained: 



Y = 



N = V^/SY. 



215 



