70 



THEORY OF SEAKEEPING 



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15.00 h 



15 May 1955 



20.00 h 



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 5 



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20.00 h 

 21 May 1955 



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 ZZ May 1955 



Fig. 80 Values of mean square wave-height averaged 



over 10-min intervals. Mean value of each group of 



twenty is shown (from Tucker, 1957) 



have a low probability of describing the seaway, a 20-min 

 sample will be a better estimate, and a 30-min sample is 

 bound to be very good. 



The lower graph in Fig. 80 is essentially the same, ex- 

 cept that the waves are somewhat higher and the state of 

 the sea not nearly so stationary OA'er the 10-hr recording 

 period. The 10-min samples are even more inadequate 

 in this case. An extension of the experiment of Tucker is 

 suggested to provide more information on sampling vari- 

 ability versus sea state. This will lend itself to intelli- 

 gent plamiing of any seakeeping measurement. 



8.5 Scalar Sea Spectrum — Calculation by Electronic 

 Analog Filter Method. Section 8.4 discussed a computa- 

 tional procediu'e for obtaining the energy spectrum by 

 numerical methods. The particular method, that of 

 calculating the autocovariance function and l-'ourier co- 

 sine transform, is not exclusive to digital computation 

 but may be done electronically as well (Brooks and Smith, 

 1956). A more direct electronic method for obtaining 

 the energy spectrum is the use of filter techniques. Of 

 course, the filter method may be adapted for numerical 

 use as well. 



This introductory comment is meant to point up the 

 possibility of confusion among naval architects (and 

 others) on the notion of which kinds of equipment and 

 which methods may most efficiently be used to compute 

 spectra. In principle, whate\'er can be done electronic- 

 ally (analog) can be done numericall.v (digital). Further, 

 there are general and special purpose digital computers 

 as well as general and special purpose analog computers 

 so that no distincti(jn can be made on that account. 

 Still further, there is little to choose in speed and accuracy 

 in so far as the requirements of the spectrum are con- 

 cerned. It is possible to produce a spectrum almost as 

 soon as the data are collected by either analog or digital 

 means. If accuracy implies high resolution, then there is 

 still little difference considering that "ultra-high" resolu- 

 tion of a finite sample defeats the purpose of describing 

 the ensemble average or population. Certainly, large 

 masses of data can be handled both ways, and again 

 there is a practical upper bound beyond which additional 

 data add little to tlie description of a stationary process. 



The fact is that choice of analog or digital methods de- 

 pends largely on what is available to the investigator. 

 The choice of either autoco\'ariance-transform or filter- 

 squaring is dependent on what is convenient for the 

 machine. Most investigators involved with relatively 

 few spectra are content to use available general purpose 

 digital computers, because it only involves .supplyhig a 

 list of numbers and a decision on the number of lags. 

 The computational equations are available and program- 

 ming is done by the custodians of the ecjuipment. Also, 

 there is no capital investment. General purpose analog 

 cominiters are not as readily a^■ailabl(>. ^^'hen the num- 

 ber of spectra is lai'ge so that computing time is involved 

 and the program desires frequent changes for special 

 treatment of each record to be analyzed, a special pur- 

 pose computer may be a W(jrth-while in\'estment. The 

 analog computer lends itself well to specialization be- 

 cause the components necessary for amplification, filter- 

 ing, and squaring are commercially available. A special 

 purpose digital computer would have to be built from the 

 ground up. 



For the reasons gi\'en here, there have developed 

 lately in seakeeping analysis, two primary techniques for 

 spectrum analysis: a) Autoco\'ariance-Fourier trans- 

 form-digital, and h) filter-square-analog. The first of 

 these has been treated thoroughl}^ in Section 8.4; the 

 second will be discussed here. 



Unlike the digital input of equally spaced ordinate 

 values, the input to the analog computer is a continuously 

 varying signal either recorded on film (or paper) and 

 scanned by a photocell or recorded on magnetic tape and 

 fed into the analyzer as a variable voltage. 



The theory and practical operation of photocell-type 

 analyzers have been described by the following authors: 

 Barber, Ursell, Darbyshire, and Tucker (1946); Tucker 

 and Collins (1947) (see ref. p. 105); Barber and Ursell 

 (1948?)); Barber (1949); Tucker, Pierce, and Smith 

 (1950); Tucker (1955); Klebba (1949); Rudnick (1949). 



The principles of the analog-filter type analyzer have 



