The Wave Generated by a Ftne Shtp Bow 
ACKNOWLEDGEMENTS 
The analysis described in this paper developed during and out 
of discussions that I had in the spring of 1971 with several students in 
the Department of Naval Architecture and Marine Engineering at the 
University of Michigan : Eiichi Baba, Odd M. Faltinsen, Miguel H. 
Hirata, Arthur M. Reed, and William S. Vorus. It was a unique expe- 
rience for me to have these students together, working as a group, 
analyzing problems without inhibitions even while criticizing one an- 
other. Each of them contributed in some way to this paper, and I de- 
dicate it to them, scattered as they now are over four continents. 
This research was carried out under the Naval Ship Systems 
Command General Hydromechanics Research Program, Subproject 
SR 009 01 01, administered by the Naval Ship Research and Develop- 
ment Center (Contract No. N00014-67-A-0181-0033). 
NOTATION 
b(x,z) hull offset (half-width) 
b(x) special case of b(x,z) (the wedge problem) 
g gravitation constant 
H(x) draft of the section at x 
H special case of H(x) (the wedge problem) 
L transform variable 
L ship length 
r (y* + z2)1/2 
U forward speed 
V's 2 coordinates 
D4 xVK/H 
a b'(0) , half-angle of the wedge 
€ slenderness parameter 
(x,y) free-surface elevation 
Z(X) nondimensional $(x,0) ; see Equation (17) 
g/u4 
p perturbation velocity potential 
W(x, y) o (x, y, 0) 
Fez 1 
