Computatton of Shallow Water Shtp Mottons 
beam seas, since the integrals involving 4¢) (x) tend to cancel out. 
We may expect a similar conclusion for other headings, and for yaw 
motions. On the other hand, as indicated by Tuck and Taylor (1970), 
if the swaying motion is to be restrained, by moorings, fenders, etc. 
a knowledge of C(x) and henceA¢d > (x) is vital for computation of 
the required restraining forces. 
The yaw motion is plotted in Figure 6.2 as horizontal bow 
motion, analogously to pitch. Note that yaw vanishes identically in 
both head and beam seas, irrespective of fore-and-aft symmetry, so 
that maximum yaw occurs at some intermediate heading angle. 
As the frequency tends to zero, the yaw motion tends toa 
finite limiting value which may be estimated for a fore-and-aft sym- 
metric ship as follows. We also assume that we can neglect the second 
term of (6.5) , which is true if the radii of gyration of displacement 
and mass are nearly equal. Thenas k— +0, we have 
Xf 
{ jikegh sna f dxx Ad, (x) [1 +ikx cosB +.. | 
ay 
t 
ve ; roa [exes 
f 
af Ok pgh sin B eh dacx“Ag, (x) 
Again the integrals involving 4¢, (x) cancel out, leaving 
¢ sin8 cos8 
6 = fe (6. 10) 
However, this result is of much more limited validity than (6.9), in 
particular being valid only for low frequency. Note again an inverse 
dependence on depth, and a maximum at 45° heading. 
VII. CONCLUSION 
In the present age of offshore mooring facilities for super- 
tankers and giant ore carriers, the usefulness of a shallow water ship 
motion theory is obvious. However, the results presented in this 
paper are purely theoretical. To the author's knowledge there is very 
little experimental verification available. Until there are experiments 
with which to compare the theory, we are forced to rely on the good 
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