57 



Fig. 65 Sample autocovariance diagrams obtained from an analysis of waves recorded at sea (from 



Voznessensky and Firsoff, 1957) 



where //, — His the deviation of an indi\i(hial wave where log i?, denotes the mean vahie of the logarithms of 



height from the mean value 

 Mean square E = - ^H,- 



(109) 



Three frequency distrilnition laws have been formu- 

 lated : 



1 The "normal distrilnition": 



p{H,) = -\^ oxp [-(//, -77) V2a^l (110) 



2 The "log-normal tlistribution," a normal ilistrihu- 

 tion of the logarithm of //.; 



. „ . 1 



expf-(log//,-log//,)V2<7=] 



(111) 



//.. 



3 The "Rayleigh distribution" defined as 

 p{Hd = =1^ exp (-H.V/i) 



(112) 



v'here 



//, > 



Fig. 64 shows the histograms of the wave heights in an 

 irregular sea test in a towing tank and the corresponding 

 Rayleigh distribution. A simple derivation of this dis- 

 tribution, equation (112), will be found in the Appendix 



to Williams" (3 ICr^) ,.^^ . G a' .:;,■. -.l::o.: ;f the 



foregoing and numerous samples of sea and ship motions 



