Page 248 - Practical Design Ships and Floating Structures

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where eq. (2) is for shallow water depth, and eq. (3) is for deep water depth. Thus, the velocity
potential at infinity field from the floating structure is expressed in the foilowing equations.
for shallow water;

for deeD water:

Now, if Kochin hction is defined as follows,
for shallow water;

for deep water;
H(K,a) = jj(*-ba)e-imds, an (7)
Sn
a final equation of the steady wave drifting force of a surge mode is obtained as following equation,

While the drifting force of a sway mode is expressed as follows:

The variables in the above equations are; ‘p’ is fluid density, ‘g’ is gravity acceleration, ‘w’ is circular
fiequency, ‘h’ is water depth, ‘i’ means a complex value (fi). But, subscript i stands for the
component wave of ‘i’ and superscript ‘*’ means a complex conjugate. And, K, k and R are defined as
follows:
,
02
K = - K = k tanh kh , R = J(x - XI)+ - y’)+ (Z - 9).
g
When the wave drifting forces are computed, the effect of the elastic motion is considered due to
including or not including the radiation component in the velocity potentials.
2.2 Theory for a zero- draft body
The pressure distribution method is applied to the analysis of the hydrodynamic forces and the wave
drifting forces under the zero-draft assumption. The velocity potential is obtained in the following
equation:
4, (x.Y) = - 16 pi (x‘, Y‘). Ga@’ . (10)
Where G is the Green’s fbction [l] for the shallow draft theory and SH means an area of a body’s
bottom of a zero draft floating structure.
The steady wave drift forces in regular waves are given by the momentum theory, i.e. the far field
theory as follows.
In this theory, Hi defined as the Kochin function and can be expressed as follows:
is
.
Hi(ki,ai)= 16 n pi (~,y~)e-&(x’cosa,+Y’sina,)dSH (11)
Using this Kochin function, steady wave drift forces of surge and sway modes in regular waves are
given as follows: