Computation of Shallow Water Shtp Mottons 
Consider for example a linear elastic cable of spring constant k 
and length R, attached to the bow and initially nearly parallel to the 
calm water line and nearly lying in the centre plane of the ship. 
Small angular deviations from this equilibrium configuration have no 
effect on the restoring coefficients. We suppose there is a mean cable 
tension Ty at equilibrium due to wind, wave (mean stress) and cur- 
rent effects. 
The displacements of the bow as a result of small vertical 
plane motions are $, longitudinally and f5 - £5 upwards, and 
from Figure 4.1 we see that the new cable length is 
a 
Lene agers Ae oe eee a LO 
(4. 1) 
~ Re LG 
at adil 2 <<R, and the new cable tension is thus 
Br =9) Ty qo(Ri ye) 
(4. 2) 
=i mibbsy 
Thus heave and pitch have no effect on cable tension in this case, 
However, this does not mean that there is no vertical restoring force 
in these modes, 
In fact the surge restoring force due to the mooring is 
PF Poeeuee Top 
; cos 0 
oe 
= — k§ > 
the heave restoring force is 
F. een 2S 1 
(4. 4) 
2-1 Doi te =£¢.) 
e557 
