Page 505 - Practical Design Ships and Floating Structures

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from the figure, the wave angle is about 35’. We can see both transverse and divergent wave systems.
But the divergent wave systems are dominant. For Fig 10, 4 is equal to 1.2. The wave angle is about
SO’ measured from the figure. We can only see the divergent wave systems. The wave angles are in
good agreement with the results in Fig 1. Wash has a close relationship with the corresponding wave
resistance. We can therefore get some information on how to minimize wash from Figs 4 and 5. The
shallow water wave resistance ratio r is about 1.5 for Fh = 0.9 , HIL = 0.1 and is about 4 for
Fh = 1.2, HI L = 0.1. This means that the wash at Fh = 0.9 is favorable. By using Figs 4 and 5 we
could minimize wash by changing 6. For Fh = 1.2, we should actually increase 6. If we increase
the speed by -lo%, r will decrease from -4 to -2. But for Fh = 0.9, the change of 6 will not
improve the wash problem. Both increase and decrease of 4 will increase the value of r if the change
of 4 is confined to It 10%. We should note that a large value of shallow water wave resistance ratio
r is not necessarily corresponding to large value of wave resistance if there is a large difference
between F, . It should also be noted that r can be less than 1 which means that shallow water can have
a positive effect on wash.

4 CONCLUSIONS
Steady forward ship motions in finite water depth are numerically investigated by thin ship theory and
steady Green’s function satisfying classical linear free surface condition in finite water depth. Both the
wave part and the local disturbance of the Green’s function are studied carefully. The local disturbance
is numerically difficult to handle. The longitudinal force 4, vertical force 4, pitch moment 4 and
wash are calculated. The local disturbance part of the Green’s function is important in calculating 4
and 4. The present methods have been tested for a Wigley hull, and the results are compared with
experiments and Tuck’s shallow water slender body theory. The shallow water theory is limited to
small water depth while the present theory applies to any water depth. Wash is discussed by
systematically presenting results for the wave resistance.

References

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