Beck and Tuck 
i (1) he ene Chae 
+} ddd, ( )Hy (k x- &) =a dé G(E) sin k(x- &) (6. 8) 
4 0 
; (6. 8) 
= + A, cosik= + B, sim icx « 
k 
Numerical procedures for obtaining C.,(x) and hence by solving (6. 8), 
A $, (x x) , are discussed by Taylor ( (1971) and summarized by Tuck and 
Taylor (1970). 
Figures 6.1 and 6.2 show the resulting solutions for the 
sway and yaw amplitudes respectively. At high frequencies, the 
motions tend to zero rapidly. On the other hand, as the frequency 
tends to zero (wavelength to infinity) the sway motion tends to infinity, 
as in the case of surge, because the ship is then following the hori- 
zontal fluid particle motions. 
For a fore-and-aft symmetric ship (Tog 5 0) in beam seas 
( B= 90°), the sway equation of motion simplifies to 
p ) 
. ; rie i dxA®, (x) = §5 . ikpgh I dxA¢,(x) 
i.e. the integral containing the potential jump A¢2(x) cancels out, 
leaving simply 
apes et (6. 9) 
This remarkable result shows that in this case the sway mo- 
tion equals the horizontal fluid particle motion at all frequencies, not 
just as the frequency tends to zero, The small amount of asymmetry 
in the Series 60 ship does not prevent (6.9) from giving quite close 
agreement with the curve of Figure 6.1 for B = 90° . Note that 
(6.9) predicts that sway varies in direct proportion to wavelength 
(or period), and inversely as the water depth. These qualitative pro- 
perties are also confirmed by the full computations. 
Clearly the geometry of the ship, which in general influences 
C(x) , hence A¢, (x) , has little effect on the free sway amplitude in 
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