Beek and Tuck 
the resonant frequency of the mooring. 
The actual variable tension in the cable resists only a small 
fraction of the exciting force under these circumstances, which is 
just as well, since these exciting forces on large ships are generally 
enormous, The ratio between the amplitude of variation of the cable 
tension and the exciting force is 
ko 
at 
k 
(4. 12) 
2 
k-Mo 
: | 
ni eg ee 
Ibs 
WSs 
which is also shown in Figure 4.2. For example, if oa >5eR (i. e. 
the wave period is less than one fifth of the mooring resonant period), 
the mooring bears less than 4% of the exciting force, and the motions 
are not more than 4% higher than the free motions. 
V. THEORETICAL CONSIDERATIONS ON HORIZONTAL PLANE 
MOTIONS 
The developments of the theory of Tuck (1970) and Tuck and 
Taylor (1970) on horizontal plane motions were confined in effect to 
computation of the sway exciting force. The resulting formula for the 
total exciting force is 
i 
i =e a ipghk sin | Sees $08 Eig. (x) (5,1) 
f 
where Ag; isa "potential jump" across the ship section, computable 
from purely near-field considerations, Although (5.1) was only deriv- 
ed for i=2 (sway) itis also valid for i= 4 (roll) and i=6 (yaw). 
In the case of yaw, there is no need to obtain Ag, separately, since 
Ag, = x A¢,. The computation of A b> and Ad, will be discussed 
later. 
Tuck (1970) also suggested a connection between the integral 
(5.1) at B= 0 and the added mass and damping coefficients. For 
instance we have 
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