Ochi 



2a -^ 



i7(Qo^-c.^) 



(29) 



Since q^ in the above equation is the pressure corresponding to the peak of 

 the relative motion, and q* is that corresponding to the freeboard forward, the 

 pressure due to the green water on the deck q, is the difference between them. 

 Thus, the probability density function of the pressure due to green water can be 

 derived from Eq. (29): 



2a 2 R 



f(q) = ^ (q + q*) e ^ 



7{(q+q*)^-q*} 



(30) 



q > 



where 



q = pressure due to green water on the deck (psi), 

 R^ = twice the variance of relative motion between wave apd ship bow (ft^), 



q* = D/a (psi), 



D = freeboard at the ship bow (ft), 



a = constant =2.32 (ft/psi). 



Equation (30) is essentially a truncated Rayleigh distribution. However the 

 base line is shifted, so it may be considered as a modified Rayleigh distribution. 



The average of the one-third highest (significant), qj/j, and one-tenth high- 

 est qi/io pressures are given by the following formulae respectively: 



li/3 e "■ + V^]/^- e ' 1 1 - $ 



where 



Rl 



.2 1 l^^g Jl- q^ 



- (qi/3 + q*) 



(31) 





(D(u) = —^— I e ' dt 



576 



