Page 71 - Practical Design Ships and Floating Structures

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S, and Si are the real and imaginary parts of the far-field spectrum function S = S(a, fl where a is
defined in terms of the Fourier variable pas

a (B )=JRo/F (14
This relation and expression Eqn. IC follow from the dispersion relation F 'a'=k.
The wave spectrum function S = S,+i Si in the Havelock integral (Eqn. la) is approximated here by
the zeroth-order slender ship approximation defined in Noblesse (1 983) as
s = Insex z+w .+a Y)
dA + FZ j(nr)Ztyer(s y'dL (2)
E r
Here, dA and dL stands for the differential elements of area and arc length of the mean wetted hull
surface Z and the mean waterline r, and n * and t are the x and y components of the unit vectors,
n' = (nr,ny,n") and f = (tr,tY,O), normal to the ship hull surface Zand tangent to the ship waterline
r; points inside the flow domain (i.e. outside the ship) and 7 is oriented clockwise (looking down).
n'
Thus the wave spectrum function S in the Havelock formula for the wave drag is defined explicitly in
terms of the ship speed and the hull form in the zeroth-order slender ship approximation.
The present wave cancellation multihull ship (see Wilson et. al. (1993) and Yang et. al. (2000))
consists of one main center hull centered at (0, 0, 0) and two identical outer hulls centered at (a, &b, 0).
In the first step of the optimal design process, the wave drag for each individual hull is evaluated using
Eqns. 1-2, and the center hull and the outer hull are optimized independently for the purpose. of
minimizing the wave drag of each hull.

In the second step of the optimal design process, the total wave drag CW for the optimal center and
outer hull forms obtained form the first step needs to be computed so that an optimal arrangement of
the outer hull with respect to the center hull can be determined. The total wave drag CW for such a
wave cancellation multihull ship can be expressed as (see Yang et. al. (2000))
c, =c; +2c; +c; (34
where C& and C; are given by

and represent the wave drags of the center hull and of an outer hull, respectively. The spectrum
functions S' = S,C + iS;C and So = S,O + iSso are defined by Eqn. 2 in which Z: rare taken as Z;, & or Zo
r, i.e., the wetted surface and waterline of the center hull or the outer hull. The component
Ca accounts for interference effects and is defined as

where A, AR and A' are defined as

(3e)

It is noted that the wave spectrum functions S' and So are independent of the parameters a and b
within the current approximation. Therefore, the wave spectrum functions s' and S" defined by Eqn.