BOW WAVES BEFORE BLUNT SHIPS AND 

 OTHER NON-LINEAR SHIP WAVE PROBLEMS 



Gedeon Dagan 



Teohnion- Israel Institute of Technology 



Haifa^ Israel 



and 



Marshall P. Tulin 



HydronautiaSf Incorporated 



Laurel^ Maryland 



NOTATION 



a Draft at bow of a completely blunt shape 



(dimenslonless) 



b, b Outer and inner coordinates of point B in the 



^ and X planes 



^1. '^t. '<^|. '<^9. » 



Arbitrary constants 



Cq Drag coefficient 



D' Drag force; D = D'/pU'^T' 



f = <►' + i^\>' Complex potential; F = f'/gi/2T'V2; f = f'g/U'^ 

 f = f'/U'T' 



1/2 



Fr^ = U'/(gL') Length Froude number 



Fr^= U'/CgT')*^^ Draift Froude number 



h'(x') Function describing the body shape; H = h'/T'; 

 h = h'g/U'2 



i,' Forebody length; if = -tf' g/U' 



i' Characteristic length; i = i 'g/U'^ 



N= t|'/T' Dimensionless free-surface elevation 



P = P'/pU'^ Dimensionless pressure 



t' Jet thickness; t = t'g/U'^ t = t'/T' 



T' Draft 



w' = u' + iv' Complex velocity; w = w = w'/U'; W = w'/CgT')'^^ 



607 



