THE SHIP SURFACE COORDINATE SYSTEM 

 The hull surface coordinate system that is used in the boundary layer 

 calculation method described in the previous section stems directly from the 

 hull surface representation of von Kerczek and Tuck. This hull surface 

 representation utilizes conformal mapping onto a unit circle of the cross 

 sections of the hull and polynomial interpolation along the length of the 

 hull of the individual mapping coefficients. Let s be the longitudinal 

 coordinate, x the lateral coordinate, and y the vertical coordinate of the 

 ship hull. Tnese coordinates are made dimensionless by the half length L 

 so that the bow and stern perpendiculars lie at s = + 1, respectively. The 

 load water-line is located at y = and the keel at midships is located at 

 y = -D. 



The hull surface representation of von Kerczek and Tuck results in a 

 parametric surface equation of the form 



N M 



> > A i(3-2n)e m-1 

 Y. + -Ly = y y k e s (22) 



n=l m=l 



where the matrix (A ) of coefficients specifies the hull form and is 

 mn 



computed from a set of defining hull offsets by an algorithm given by 

 von Kerczek and Tuck. 



The surface coordinate system used in the boundary layer equations 

 consists of the 6 = constant lines, obtained from Equation (22) and their 

 orthogonal trajectories, here denoted by cj) = constant lines. It is not 

 necessary to specify the variable (j) since the arclength along the (}) = 

 constant lines will be used directly. 



Equation (22) can be written in real form as 



X = x(s,e) = ^ J^\n ^" ^ cos(3-2n)e (23a) 



n=l m=l 



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