Prediction of Ship Slamming at Sea 



30 35 40 45 



Freeboord ot FP in Ft. 



50 



Fig. 18 - Effect of freeboard forward 

 on the probability of occurrence of 

 deck wetness (moderate Sea State 7, 

 ship speed 10 knots, full draft) 



derivation of the probability density function for the pressure due to green water, 

 the following conditions will be considered. These are: (1) magnitude of relative 

 motion is greater than the freeboard forward (bow submergence condition) and 

 (2) magnitude of peak pressure during one cycle of deck wetness is equal to the 

 static water-head corresponding to the difference between the maximum value 

 of relative motion and the freeboard forward. 



Now, the double amplitude distribution of the relative motion follows the 

 Rayleigh probability law. Since deck wetness occurs only when the bow is sub- 

 merging, the relative motion in one direction is taken instead of the peak-to- 

 peak value. Then, analogous to Eq. (9), the probability density function of the 

 amplitude of the relative motion r^, when r^ is greater than the freeboard for- 

 ward, D, is given by 



2r„ 



■7(r 2-d2) 



> D 



(28) 



It is convenient to express the above formula in terms of pressure units 

 (psi). For this, let q^, = r^/a and q* = D/a. Here, a = 2,32 ft/psi if r^ and D 

 are expressed in the foot-unit. Then, the probability density function given in 

 Eq. (28) becomes 



575 



