Computatton of Shallow Water Shtp Mottons 
been made above that the clearance (water depth minus ship draft) 
is not small compared with the water depth. In the case of small 
clearances, the order of magnitude of the horizontal self and diffrac- 
tion forces is increased above that shown, in the ratio ''water depth/ 
clearance", 
We now consider the effect of these order of magnitude esti- 
mates on the equations of motion (2.2), supplementing the hydrody- 
namic estimates (2. 9) with the information 
a” = 0(e) 
M = 0(<*) 
“Gr ma (2. 10) 
14 = 0(€) 
Cy32 Ogg» Cog» Cg = O(€) 
Crs, = 0(e) 
Note that (2.8) requires ae = O(€) , restricting attention to low fre- 
quencies or long waves, and at least in principle ruling out resonance 
in any mode. The order of magnitude of C,, is an upper bound, on 
the basis that the metacentric height is at most O(e) ; in fact it be- 
comes a crucial question for roll to assess correctly the minimum 
order of magnitude of C,,. 
The significance of the various forces in the equations of 
motion (2.2) may now be summarized for each mode in turn as fol- 
lows. 
SURGE, ieee motion 
Z 
Important Forces, O(e ) : natural inertia, F-K exciting 
foriee. 
3 : " : ; 
Small Forces, O(e ) : added inertia and damping, coupling 
from heave and pitch, diffraction 
exciting force. 
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