88 



THEORY OF SEAKEEPING 



suitable equipment specifications were developed, avoid- 

 ing unuecessaiy complications and costs, private in- 

 dustry maj^ be able to produce the equipment in quantity. 

 Simplicity, reasonable universality, and low cost are es- 

 sential, since much of the valuable research is expected 

 to come from many small laboratories. In general, 

 two broad types of equipment are visualized: 



(a) Magnetic-tape recorders and analyzers of the 

 (moderately broad) filtering type. 



(b) Digitizers which translate the continuous electric 

 signals from the sensing elements into the punched-card 

 or tape records suitable for direct use in universal com- 

 puting machines. This equipment is particularity ap- 

 propriate for small laboratories connected with uni\-ersi- 

 ties or other institutions possessing high-speed digital 

 computing machines. 



The author belie\'es that the most rapid progress in 

 research in oceanography and naval architecture will be 

 made if the analj^zed test data could be available to a 

 researcher while the physical obser^'ations are still 

 clear in his mind. The electronic filtering technique 

 listed under a) and recommended for project 26) gives 

 promise of such a rapid anal,vsis. B}^ u.sing transistor 

 techniques it also gives promise of a compact and rugged 

 equipment suitable for use on location in natural-wa\'e 

 observations. 



The author realizes that recorders, digitizers, and 

 analyzers have been developed by \'arious laboratories 

 and that many electronic components are available in 

 the open market. Nevertheless, no complete, compact 

 and workable instrument package appears to e.xist, and 

 the cost and the needed specialized knowledge severely 

 limit the activit.y in this field. 



37 Clarification of Confidence Limits. The con- 

 fidence limits of spectral analysis are defined with respect 

 to certain, rather narrow, filters of the digital anal.vsis or 

 electronic devices. When these limits are given in the 

 literature, as for instance in Fig. 71, it is often difficult 

 to find the frequency band widths to which they apply. 

 Furthermore, these particular freciuencj' band widths 

 may or may not be relevant to the problem at hand. No 

 distinction has been made between confidence in an 

 analysis of a particular wave record and confidence in 

 this particular record considered as a sample of the ran- 

 dom sea conditions. Finally, there appears to be some 

 confusion in the literature between expressing the con- 

 fidence in terms of wave-record-measurement subdivi- 

 sion and in terms of wa\'e lengths a\-ailable in a sample. 

 Further research to clarify the situation is recommended. 



It is emphasized that in practical use the confidence 

 limits of the spectrum must be closely connected with 

 the objective for which the spectrum is to be used. For 

 instance, confidence limits may be desired in evaluating 

 the significant wave height, i.e., the zero moment of the 

 spectrum, or the mean wave slope (the second moment), 

 or the mean wave period. A tabulation of such con- 

 fidence limits appears to the author to be more valuable 

 in practical problems than drawing the usual statistical 

 confidence-limit curves. The problem of clarifying the 



meaning of statistical confidence limits in application to 

 practical problems requires the joint work of mathema- 

 tical statisticians and oceanographers or naval archi- 

 tects. 



38 Instrumentation for the Measurement of Direc- 

 tional Wave Spectra. The need for measurement of 

 wave directional spectra on a ciuantity. i.e., .statistical, 

 basis has been indicated under project 28) and has been 

 mentioned several times before. Development of the 

 necessary instrumentation can be listed, howe^'er, as an 

 independent project. To date. Barber's methods appear 

 to be the only ones suitable for mass collection of data. 

 Barber proposed se\'eral methods, but only one of these, 

 the correlation one, was outlined in some detail in Sec- 

 tion 8.72 where references also were gi\-en to all of Bar- 

 ber's papers. A certain rather ol)\'ious development of 

 Barber's correlation method is needed for the collection 

 of the data suggested in project 28) : 



(a) The directional spectrum should be obtained for 

 several wave frequencies. 



(b) The variability of sea conditions, demonstrated by 

 Tucker, Section 8.44, requires that measurements for all 

 frequencies be obtained simultaneously. Also it would 

 be desirable to obtain simultaneouslj' the records for 

 se^'eral pairs of gages needed for correlation analysis, 

 instead of the consecutive measurements used by Barber. 



It appears to the author that available electronic tech- 

 niques will permit the following scheme: (a) The usual 

 wave-height recording can be made simultaneously for 

 several pairs of gages on the same magnetic tape thus 

 permitting a cross-spectral anal\'sis to be made later; 

 (b) the multiple record should be passed alternately 

 through se\'eral frequencA' filters, yielding several single- 

 frequency multiple-gage records; (c) each single-fre- 

 Cjuency multiple-gage record should be subjected to the 

 correlation analysis described by Barber, except that 

 electronic methods of analysis would be used instead of 

 Barber's pendulum; (d) the randoml.y distributed two- 

 dimensional correlation function, ecjuation (149), would 

 be projected on the oscilloscope screen and photo- 

 graphed ; (e) the photograph for each frequency would be 

 interpreted in the same way as Barber's photograph, 

 Fig. 87. 



It should be emphasized that sea-surface variabilit.y 

 makes it unnecessary to describe in excessive detail a 

 directional spectrum from a single observational run. 

 The spectrum is a statistical concept and the typical 

 spectrum is to be obtained as the mean of many individ- 

 ual records. This being the case, an excessive number 

 of gage pairs and of calculated wave directions should be 

 avoided. It appears to the author that four pairs of 

 gages and four wave directions will be sufficient. 



The instrumentation outlined in the foregoing may be 

 adapted to the measurements made with conventional 

 wave-height gages as well as to the wave-slope and wave- 

 acceleration measurements by floating buoys. In the 

 latter case the use of telemetering equipment will be re- 

 quired. 



