ssc-367 - Ship Structure Committee

0.2.3 Wave Spectra
The wave spectrum used in the spectral analysis may be an idealized
mathematical spectrum or a set of data points derived from the
measurement of real waves. When a set of data points are used, a
linear or higher order curve fit is employed to create a continuous
function. Custom wave spectra for specific regions are often
provided as one of the conventional idealized spectra with parameter
values selected to match a set of measured wave data. For areas
where there is little wave data, wave height characteristics are
estimated from wind speed records from the general area.
B.2.3.1 Wave Slope Spectra
For certain responses, particularly the angular motions of pitch and
roll, the RAO is often presented as response angle per unit wave
slope angle. For these cases the wave spectrum in amplitude squared
must be converted to a wave slope spectrum. The maximum slope of any
constituent wave of the spectrum is assumed to be small enough that
the wave slope angle in radians is approximately equal to the tangent
of the wave slope. The water depth is assumed to be deep enough (at
least one-half the longest wave length) that the wave length is
approximately equal to:
(g/2~)*T2 or 2~g/~2.
By using the Fourier series representation of the wave spectrum,
selecting one constituent wave, and expressing the wave equation in
spatial terms instead of temporal terms, the wave slope is derived as
follows.
rI=a*cos(2rx/L) = a*cos(x~2/g)
dq/dx = -(a~2/g)*sin(x~2/g)
B-8
LJt Y