Ochi 



where 



<!>_ C^e) ~ energy density of cross- spectrum between wave and vertical 

 ""^ ship motion, 



'!'_..( c^e^ - energy density of cross-spectrum between wave and vertical 

 ^^ acceleration. 



The variance of relative velocity between wave and ship bow can be obtained 

 by the same procedure as that for the relative motion. 



Numerical examples of the evaluated correlation coefficients, p^^^, p^^ (for 

 relative motion) and p. ., p. . (for relative velocity) are tabulated in Table 4. 

 These were evaluated from experimental results obtained on MARINER in Sea 

 State 7. As can be seen in Table 4, the correlation coefficients Pgb ^"*^ /^ab ^^® 

 very small in this case, since point A is located near the forward perpendicular 

 and point B is located at the center of gravity. 



From this table, the coefficients required for evaluating the relative mo- 

 tion and velocity at an arbitrary point along the ship length can be estimated by 

 either interpolation or extrapolation. i 



Appendix 2 



DERIVATION OF THE AVERAGE OF THE HIGHEST ONE-THIRD 

 AND HIGHEST ONE-TENTH VALUES FOR THE TRUNCATED RAY- 

 LEIGH AND EXPONENTIAL PROBABILITY DENSITY FUNCTIONS 



(A) TRUNCATED RAYLEIGH PROBABILITY DENSITY 

 FUNCTION 



It was mentioned in the text that the probability of the relative velocity be- 

 tween wave and ship bow follows a truncated Rayleigh probability law. The 

 probability density function in this case is given by Eq. (11) in the text. That is, 



Hi) = 



2f «r *^ . _ (A.10) 



The average of the one-third highest values for this probability density 

 tion is evaluated as follows: Let fj/, 

 highest values of relative velocity. Then 



function is evaluated as follows: Let r^^^ be the lower limit of the one-third 



Prob {r > fj/3} = I f(f) df = |. (^-^^^ 



586 



