68 R. Timman and G. Vossers 
where L is the length of the ship and T the draft. The ship is moving in the x direction with 
constant velocity c. The disturbance potential 9, from which the disturbance velocities 
u=—d9/dx, v=—09/dy, w=-09/dz are derived, is determined by the condition that at 
the hull of the ship | 
2 _. Of 
Ape ee 
The linearization, introduced by Michell consists in applying this condition at the plane of 
symmetry y = 0, in which case the potential, satisfying the Laplace equation V7 = 0 and 
the free surface condition at the plane z= 0: 
Px ~ KO, = O 
where 
& 
K = — e 
'c2 
The solution of this boundary value problem is then 
9(X,¥,2Z) 
2 
a 
en OsezD i a. 
Ic ante z Of(x,, 21) fe e * *” sin [<x Xt y oa? 13] 
Seek dx, [ 2 ax, ; ; a da. 
-L/2 0 K USK 
2 Oy 
Fe To aay abuse 
Le pes Pe (a posers Cag ipa: d 
= xX, Zy ae cos a(x-x,) da 
-L/2 0 4 0 Kk? - a? 
L 
2c ae f Of(x,,2,) 
er | dx, | dz, ax J cos @(x-x,) da 
DS 2 0 : 0 
0 
[2,2 
x | eo" *” cos (nz-€) cos (nz,-€) dn 
0 a? + n? 
where 
ne 
tan —— 
An 
The pressure is determined by Bernoulli’s equation 
1 i 2 Dp 
-9, + 5|(-'c+ 0) Paget o2| rE eR oho as 
