Ochi 



On the basis of the above discussion, it is expected theoretically that the 

 time interval between two successive slams follows an exponential probability 

 law. However, one condition must be considered for the present problem. That 

 is, the shortest time interval between successive slams is very close to the 

 natural pitching period as was mentioned earlier. With this modification, a 

 truncated probability density function is derived for the time interval between 

 successive slams as follows: 



f(t) = N e 



■N rt-t,) 



t > t. 



(20) 



where 



Ng = number of slams per unit time, 



t^ = minimum time interval between two successive slams (natural pitch- 

 ing period). 



Results of numerical calculations using Eq, (20) are shown in Fig. 14 along 

 with the histogram obtained in the experiment. 



I 



A further comparison between theory and experiment was made for the time 

 interval between successive slams in bi-directional waves. The bi-directional 



Fig. 14 - Sample histogram and the 

 predicted probability density function 

 for time interval between successive 

 slams (severe Sea State 7, ship speed 

 10 knots, light draft, head seas) 



568 



