Wave Forces on a Restratned Ship tn Head-Sea Waves 
assume that the rate of change of ¥ in the transverse plane is go- 
verned by the order of magnitude of the transverse dimensions of the 
body and that the rate of change of y in the x-direction is governed 
by the order of magnitude of the longitudinal dimensions of the body” 
Sointhe yw -problem we stretch the coordinates 
y =¢ ys Zia @zi 4 n Set og. x = 5% (24) 
Here nz2p is the unit normal out of a cylinder with the same cross- 
section as the ship at a given section. 
We will assume an asymptotic expansion of yw of the form 
yv~> $C, 72, <9 (25) 
where yy ., =o(y,) ase 0 for fixed X, Y, Z. 
We introduce 
k = ve (26) 
and 
ep SS (27) 
w 
Since the problem is linear in C, we shall not be bothered with the 
order of magnitude of C. 
* Note that the rate of change in the x-direction of the diffraction 
potential, $), as given by (20) is of the same order of magnitude 
as the rate of change of $p in the transverse dimensions, 
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