SEAWAY 



65 



EpHMa«."601.5CM2 

 EMax.= l2e3CM^ 

 Equivalent to a Pure 

 Sine Wave 35.5 CM High 



Fig. 72 Comparison of pressure-power spectrum with free-surface power spectrum. Note the much greater 

 amplification of the low-frequency components (from Pierson and Marks, 1952) 



towing tank (in irregular-wave tests). Since motion 

 measurement is a vital part of seaworthiness studies, it 

 will be worth while to study in detail the nature of the 

 statistics derivable from a sample record and hence from 

 the parent population from which the sample was drawn. 

 In this connection, all that has preceded in this section 

 and all that will follow applies equally well to ship-mo- 

 tions records as to wave records. 



At this stage of discussion, there is available a wave re- 

 cord and a means (theoretical and numerical) of reduc- 

 ing this wave record to an energy spectrum of the sea- 

 way. The question ari.ses: What is the best way of 

 utilizing the means available for going from the record to 

 the spectrum, in order to obtain the most reliable re- 

 sults? This is not easy to answer and is, in fact, com- 

 plicated by our failure to specify a particular problem, 

 which in turn implies something of the nature of the re- 

 sults we are seeking. As will be seen, the specification of 

 the problem plays an important part in the choice of 

 computational parameters. However, it will be most 

 profitable to keep the discussion as general as it will per- 

 mit. 



Three questions may be posed at the outset that will 

 have profound effects on the ultimate estimate of the 

 energy spectrum. They are: 



1 How long a record shall be taken? 



2 How large shall the sampling interval (At) be? 



3 How many lags shall be computed? 



The last two cjuestions relate directly to the accuracy of 

 the spectral-density estimates; the first question relates to 

 the sampling variability; i.e., it determines whether 

 the sample, from which the spectrum is determined, 

 truly represents the population from which it was drawn. 



"FromTukey (1949). 



It turns out however, that these three questions cannot 

 be treated independently; they must be considered to- 

 gether in order to design the analysis procedure properly. 

 As was .stated in Section 8.3, the work of Tukey (19-19) 

 combined the effects of finite-record length and com- 

 putational procedure into a compact expression that de- 

 fines the confidence criteria which may be applied to the 

 estimated spectral densities. A Cfuote from Pierson and 

 Marks (1952) will introduce the expression for the con- 

 fidence bands on the spectrum: "The final results are 

 estimates. Estimates can be in error, and the important 

 part of this method of analysis is that it also yields a 

 .statistical analysis of how much in error the estimates can 

 be. Tukey (1949) and Tukey and Hamming (1949)* 

 have shown that the errors are distributed according to a 

 chi-squared distribution with / degrees of freedom where 

 / is given by 



*See reference p. 105. 



