54 



THEORY OF SEAKEEPING 



4 8 12 16 20 24 28 32 3S 40 

 Wind Speed in Kno+'s ►- 



Fig. 60 Deviations of hindcast wave heights from observed 



ones in per cent for different methods of hindcasting (from 



Walden and Farmer, 1957) 



with an anemometer on the ship'.s mast at the height of 

 oO ft. Hindcasts were made on the basis of weather 

 maps. The percentage deviations of the hindcasts from 

 the obser\-ed significant waves are shown in Fig. 60, 

 and the average deviations in Table 1 1 . 



It will be observed that although there is a hopeless dis- 

 parity between Neumann's and Darbyshire's spectra 

 shown in Figs. 45 and 51, the disparity in the results of 

 practical applications of their methods to normal sea 

 conditions is much less. 



6.6 Descriptive Spectrum of Voznessensky and 

 Firsoff (1957). The spectra outlined in tiic foregoing .sec- 

 tion describe an irregular sea as a function of wind 

 speed, duration and fetch. They ha\'e been developed 

 for the purpose of forecasting sea conditions and usually 

 I'eciuire the perusal of weather maps for their evaluation. 

 There is, howe\-er, another problem, that of describing 

 an observed sea regardless of the wind and fetch condi- 



tions which caused it. Such a description is needed, for 

 instance, when a comparison of a ship's motions and 

 stres.ses with wave conditions is called for. 



The foregoing parts of Section 6 have dealt with pre- 

 diction of wave spectra. The last section (8) of the 

 monograph will be concerned with the analysis of a wave 

 record which will give a description of a sea .state without 

 resort to its pre\ious history. However, everything per- 

 taining to the irregular sea must be handled by statistical 

 methods, and a standardized (but flexible) sea descrip- 

 tion is desirable in this connection. Voznessensky and 

 Firsoff de\'eloped one such form of wa\'e-energy spectrum 

 in connection with their study of a ship's rolling. 



It will be shown later in Section 8 that the first result 

 of a digital analysis of a wave record is the "auto-co- 

 variance function," the plot of which is called a "cor- 

 relogram." Fig. (i5 shows nine correlograms obtained 

 by the analysis of instrumental wave records. All cor- 

 relograms are similar in three aspects: the maximiun 

 ordinate is at zero on the abscissa scale, there are peri- 

 odic oscillations and a decay in the amplitudes of oscilla- 

 tion. Such functions are approximately expressible by 

 an eciuation of the form 



/?(, 



R(0)e-''U-os liT 



(103) 



where, for the time being, r can be considered simply as a 

 number (designating time) on the abscissa scale of a cor- 

 relogram. It will be shown in Section 8 that at r = 0, 

 the function H{0) represents the area of a spectrum, and 

 is therefore a measure of the wave height. The symbol 

 E will therefore be substituted for R{0). The parameter 

 a is a measure of wave irregularity. The autoco variance 

 or correlation function of a regular sinusoidal wa^-e is also 

 a sinusoidal wa\'e, and therefore a = in this case. 

 The rate of attenuation of oscillations increases with 

 broadness of spectrum; i.e., when the distribution of the 

 spectral energy of the irregular sea is over a wider band of 

 freciuencies. This is indicated by increasing values of a. 

 The parameter /3 is the circular frequency of oscillations. 

 In the limiting case of a sinusoidal wave, l3 is the fre- 



30 

 Seconds 



40 



10 20 



Fig. 61 Definitions of apparent wave heights and periods in measurements from a wave record (from Neumann, 1954) 



