172 



THEORY OF SEAKEEPING 



O L 



t 20. 



i 60 



>^ 40 

 c (J" 



o-S 20 



-1.0 1.0 2.0 



Devia+Ions from Mean, In. on Tape 



Normal Curve 



Th-T^^-^ 



-:o -10 1.0 2 



revia+ions from Mean Value, In, on Tape 



Fig. 1 3 Frequency of occurrence of deviations from mean val- 

 ues of points on wave record (upper) and on pitching record 

 (lower) (from Lewis and Numata, 1956). Series 60-0.60- 

 block-coefficient model 5-ft long at 2 fps in high irregular head 



waves 



frequency-response function is evaluated and the phase 

 relationships remain unknown. Complete determina- 

 tion of the amplitude and phase responses is made po.s- 



sible by cross-spectrum analysis which will be discussed 

 shortly and by the method of Fuchs and MacCamy (1953) 

 described in Section 3.2. 



3.5 Analysis of Ship Motions Data — Single Param- 

 eter. In Section 1-8.1, the random jiroperties of 

 wa\'es were discussed. Ship motions, caused by wave 

 motions, are likewise random and never repeat. Fig. 

 12(a) is an example of wave and pitch motions recorded 

 in the model tank. From the striking similarity between 

 the wave and pitch records it is not difficult to conclude 

 that both of these phenomena may be analyzed and in- 

 terpreted in the same way. However, many observed 

 wave and ship motions are cjuite dissimilar in appearance 

 as evidenced by Fig. 12(6). In such cases, like treat- 

 ment of ship and wave records is predicated on the hy- 

 pothesis that a stationary random process (waves) excit- 

 ing a linear system (ship) produces a stationary random 

 process (ship motions). To further validate this hy- 

 pothesis, some ship-motion records, made in irregular 

 waA'es in a towing tank, were analyzed to determine 

 whether points chosen at random were distributed ac- 

 cording to the Gaussian law and whether the peak-to- 

 peak oscillations in the shijj motions were distributed ac- 

 cording to the Rayleigh distribution, these properties hav- 

 ing already been assigned to wave records in Chapter 1. 

 The results appear in Figs. 13 and 14. It is fairly well es- 



20 _ 



Experimental Histogram 



a 



30_ 



30^ 



20 _ 



c 



<v 



Jheoretical Rayleigh 

 Dis+ribu+ion 



\A 2.8 ^, 4.2 ^^ 5.6 



Double Wave 'Ampli+ude" In. 



Experimental Histogram 



.-TheorG+'ical Rayleigh 

 Distribu+lon 



7.0 



3G __ 54 



Double Bending Moment Ampli+ude" !n-Lb 



12 



Double Pitch Amplitude, Deg 



0.6 1.2 1.8 ^^ 2.4 3.0 3.6 

 Double Heave Amplitude. In. 



Fig. 14 Distribution of wave, pitching, heaving, and bending-moment amplitudes in towing-tank tests of 

 Series 60-0.60-block-coefl5cient model at 2 fps in high irregular head seas (from Lewis, 1956) 



