Prediction of Ship Slamming at Sea 



From Eqs. (A. 10) and (A.ll) 



A'-r; i^gj 



(A.12) 



Next, let the average of the one-third highest values be rj/3, and consider 

 their moment about the origin of the probability density function. Then 



3 1/3 J_ 



i- f(f) df = — e 





2e ^ df 



where 



r: 



r: 



+ sA«y Jl-4.h/^r,^3 



(A. 13) 



(D( 



"^ =7^1 



dt 



(A. 14) 



Thus 



• 2 



r: 



3 e 



(^/3) 



+ x/ttRT Jl- $ 



(A.15) 



where r j/3 is given in Eq. (A. 12). 



The above equation gives the average of the one-third highest values of the 

 relative velocity for the truncated Rayleigh distribution. 



Similarly, the average of the one-tenth highest of the relative velocity for 

 the truncated Rayleigh distribution is given by 



1/ 10 



r! 

 10 e ' 



where 



<^^i/ioV 



R.' 



+ yfrrR: Jl- 



(A.16) 



1/10 



r: (log 10 



(A. 17) 



587 



