Wave Forces on a Restratned Shtp tn Head-Sea Waves 
indicate that this is true for a wave length which is half of the length 
of the ship, but that it is not true for a wave length which is three- 
fourths of the length of the ship. 
By integrating the pressure in an appropriate way over the 
submerged part of the ship, we are able to predict the exciting force 
and moment on the ship. For the zero-speed case there is another 
way to obtain the exciting force and moment on a ship, namely to use 
the Khaskind relation (see Newman (1962) ). The disadvantage of the 
Khaskind relation is that it cannot predict the pressure distribution 
along the ship. Further it is a formula derived on the basis of a gene- 
ral mathematical relationship, and so it does not give us much insight 
into the physical problem. 
We are in this paper considering both the forward-speed and 
the zero-speed problem. They are separate problems and are handled 
as so. Both problems are solved by using the method of matched 
asymptotic expansions. We then introduce a farfield description which 
is valid in a distance of order one from the ship and a near-field des- 
cription which is valid in a distance whichis of order e€ from the 
ship. Here e is the usual slenderness parameter which is a measure 
of the transverse dimensions of the ship compared with the longitudi- 
nal dimensions of the ship. The shipis slender so ¢€ isa small 
quantity. The length of the ship is a quantity of order one. It is the 
diffraction potential we solve for, and it is found that the far-field 
picture can be described by a line distribution of sources of density 
oscillating in the same way as the incoming waves and located on the 
x-axis between -L/2 and L/2 (see Figure 1). It is, however, the 
near-field solution that has the main interest. But the inner expansion 
of the far-field solution is giving us necessary boundary conditions on 
the near-field problem. It is found for both the zero-speed and the 
forward-speed problem that a first approximation to the diffraction 
potential in the near-field (not near the ends of the ship) is just minus 
the incident wave. So a first approximation to the total potential (in- 
cident + diffracted wave) will be given by the second approximation to 
the diffraction potential. Writing the total potential as 
it is found that ¥ satisfies the following equations in a cross-sectio- 
nal plane of the ship. 
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