Ming-Shun Chang 
The directional spectra obtained from the pentagonal arrange- 
ment were not good and are not shown here. The measured phase lags 
between the probes had the same accuracies as those obtained by the 
linear array. However, as previously mentioned, the relations bet- 
ween the Fourier coefficients and cross spectra are more complicat- 
ed and thus, the results were not as good as those obtained from the 
linear array method. 
DISCUSSION 
The result of the study on the idealized unidirectional spec- 
trum indicates the need for improvements in recommended spectral 
forms in order to obtain a better prediction of long term ship motions, 
The two-parameter spectral form underestimates the wave energy for 
both high and low frequencies and overestimates the wave energy over 
the wave frequency range of 0.1 cycle/sec. to 0.14 cycle/sec. 
This has been illustrated in Figures 1 and 5, 
For applications, one has not only to be aware of this limita- 
tion associated with the idealized spectrum but also the varieties of 
ocean wave spectra. Fora better representation of the ocean environ- 
ment, one needs to know not only the averaged wave period and wave 
height but also other parameters, With more measured spectra a 
data bank of wave spectra can be established on a digital computer 
and stored on tapes for direct access. Such a data bank would even- 
tually make idealized spectra obsolete. It would certainly be more ac- 
curate than the idealized spectra and would contain samples of all of 
the various ocean wave spectra. 
The experiment on the directional waves suggests that the ac- 
curacy of a measured directional spectrum depends more on the di- 
rectional compositions of a wave field than on frequency compositions 
of the waves. This is demonstrated in Figures 11, 12 and 13. In order 
to accurately measure the spectrum of a swell and wind waves combin- 
ed sea, one has to use a technique which can estimate a sharp peaked 
cross-spectrum accurately, such as the narrow band process or the 
time shift process|'4 . However, it will require much longer re- 
cords of surface elevation. 
The linear array is a better probe arrangement than a penta- 
gon arrangement for the wave fields generated for this paper. How- 
ever, a linear array does not allow one to separate the waves propa- 
gating in the direction left of the array from those of the right. Two 
linear arrays may be needed for the measuring of an actual wave field 
in which waves propagate in an angle of more than 90 degrees. 
1346 
