Ming-Shun Chang 
a measured spectrum from an idealized spectrum. By use of the dif- 
ferent definitions of T, one will thus obtain the different correspond- 
ing idealized spectra. The use of T, (1) is recommended by ITTC 
Figure 5 indicates that all of the idealized spectra under- 
estimate the wave energy for the high and low frequency band by a 
factor of 1/2 and overpredict the wave energy for the middle fre- 
quency band. The use of different definitions of T, has not altered 
the result significantly , calculation base on T(-1) is slightly better 
than that of the others, but is not significantly better. The probabi- 
lity diagram was not constructed for measured spectra because of 
the small number of the samples. 
These differences in the energy distribution of the idealized 
spectra and that of the measured spectra are consistent with the dif- 
ferences found between the energy distribution of the idealized spec- 
tra and the average hindcast spectrum shown in Figure 1. In both 
cases the energy in the high and low frequency bands is underestimat- 
ed by the idealized spectra, and in the middle frequency range it is 
overestimated. This leads one to suspect the usefulness of the two- 
parameter spectrum for approximating the ocean environment, es- 
pecially in studying the motions of platforms and buoys. 
In spite of the bias described above, the parameterized spec- 
trum approach has simplified the prodedured in calculating the sta- 
tistical properties of the ship responses. The probability diagram 
representation is a good tool to engineers, if the idealized spectrum 
form is improved and the statistical bias is tolerable. 
DIRECTIONAL WAVE SPECTRA 
The motion of a ship in a seaway depends not only on the fre- 
quencies of the waves, but also on the directions of the component 
waves, The unidirectional spectrum discussed previously has little 
use when the ocean waves do not propagate in a dominant direction. 
Unlike the unidirectional wave spectrum, a directional wave spectrum 
can not be obtained from a continuous record of wave elevation at a 
single location on the sea surface. It requires knowledge of wave 
elevations over an area of the sea. Due to this requirement Apo) 
few measured directional ocean wave spectra are available [7 
The rapid growth of techniques for seakeeping analysis re- 
quires a more accurate description of a ship's environment, In order 
to make meaningful comparisons between the analytic results, basin 
experiments, and full scale trials one has to establish the capability 
£338 
