64 



THEORY OF SEAKEEPING 



0.20^ 



0.15 



0.10 



0.05 



-0.05 



2 4 6 8 10 12 14 le 16 20 22 24 26 28 30 



h 



Fig. 70 "Raw" or unfiltered power spectrum (from Pierson and Marks, 1952) 



Area under Solid Line 

 Equals 601.5 CM^ 



1 2 3 4 5 6 

 2Trh. TT TT TT TT 7T IT 



22 23 24 25 26 h 

 TT TT TT TT TT 



120 60 30 20 15 12 10 8.6 15 6.7 £ 5.5 5 4.6 43 4 3.8 3.5 3.3 3.2 3 



il°00 120 60 40 30 24 20 171 15 133 12 109 10 9.2 8.6 8 7.5 71 6.7 6.3 6 

 h 



p in sec 



2S 27 26 2.5 ?.4 2.3 



S.7 5.5 5.2 5 48 4.6 Tsec 



Fig. 71 Best estimate of pressure-power spectrum of autocorrelation function plotted in terms of l^pfffju)' 

 versus fi]. True spectrum lies between dashed boundaries 90 per cent of time (from Pierson and Marks, 



1952) 



in the literature involves weighting coeifficients of 0.23, 

 0.54, 0.23 and is called Hamming (after Hamming). 

 There are any number of other smoothing functions that 

 can be u.sed and some are li.sted by Fleck (1957). 



The procedure for numerical computation of spectral 

 density given here is thoroughly discussed by Blackman 

 and Tukey (1958) and clearly outlined by Fleck (1957). 



Fig. 68 shows a normalized autocovariance function, 

 R{t)/R{0) computed from wave records obtamed by a 

 pressure transducer. The "raw" spectrum, appropriate 

 to this function is shown in Fig. 70 and the "smoothed" 

 spectrum obtained by ecjuation (125) is shown by the 

 solid Ime m Fig. 71. These graphs are from Pierson and 

 Marks (1952). This paper also contains an important 

 section dealing with the extrapolation of the subsurface 



pressure-wave record to the free surface. These two 

 spectra, superimposed, are shown in Fig. 72. 



8.42 Choice of computational parameters — inter- 

 pretation of spectrum. The discus,sions on measurement 

 of the seawa}' so far gi\-en in Section 8 would ordinarily 

 suffice for the purposes of this monograph on seaworthi- 

 ness and we would be tempted to go on with a brief de- 

 scription of the statistics deri\'able from the sea spec- 

 trum plus some qualifying remarks on the statistics and 

 then close the issue. It turns out however (as will be 

 seen in Chapter 3, Section 3) that wave records and ship 

 motion records have the same basic property of random- 

 ness. This suggests that the same treatment given wave 

 data, to extract certain information, will apply in the 

 same way to ship motion data obtained at sea or in the 



