Prediction of Ship Slamming at Sea 



waves were composed of two wave systems corresponding to a moderate Sea 

 State 7 and Sea State 5 coming from directions at 90 degrees to each other. In 

 this case, the frequency of occurrence of slamming is higher than that in the 

 long-crested waves (moderate Sea State 7 alone); however, the severity of the 

 slams for the former is considerably less than that for the latter [4]. A total of 

 164 slams were observed in a 57.7 minute observation, hence N^. in Eq. (20) is 

 equal to 0.0475 per sec. By using this value, the predicted curves shown in 

 Fig. 15 were obtained. The actually observed minimum time interval between 

 successive slams was 6.2 sec in this case, a value somewhat lower than the 

 natural pitching period. Nevertheless, good agreement can be seen between the 

 predicted probability density function and the experimental histogram. Thus, it 

 may be concluded that the time interval between successive slams follows a 

 truncated exponential probability law. 



Fig. 15 - Sample histogram and the 

 predicted probability density function 

 for time interval between successive 

 slams (bi-directional waves, ship 

 speed 10 knots, light draft) 



40 60 80 



Time in Sec 



Prediction of the Time Interval Between Two Severe Slams 



In the foregoing discussion, the severity of slamming was not introduced. 

 Here, the discussion will be expanded to include the probability problem of time 

 interval between two severe slams. In other words, the time interval between 

 two slams, both of which cause an impact pressure of magnitude greater than a 

 certain value will be considered. The method of approach is as follows: Eq. (20) 

 is the probability density function of the time interval between two successive 

 slams. We may now evaluate the time interval between m slams considering 

 that every mth time the slam is severe, and that the magnitudes of impact pres- 

 sure for these slams exceed a certain value. Here, m can be determined by 

 taking the inverse value of the probability given by Eq. (16) since that equation 



569 



