f; (26) 



Prediction of Ship Slamming at Sea 

 Prob {Deck Wetness} = Prob {r > D} = t 



where 



D = freeboard at FP, 



R^ = twice the variance of relative motion at FP. 



It is noted that R^ in the above equation has a different value from that in 

 Eq. (5), since the relative motion between wave and ship bow at the forward 

 perpendicular is considered for this case. 



The number of occurrences of deck wetness per unit time, N , is given by 



-^ (27) 



N = ^^ 1/ — - e '' . 



^ 277 I' r; "^ 



Table 3 shows comparisons between predicted and observed probability of 

 occurrence of deck wetness per cycle of wave encounter and number of deck 

 wetnesses in a 30-minute operation of the MARINER in a moderate Sea State 7 

 at a 10-knot speed. Variance of the relative motion at the forward perpendicular 

 used in the computation of the probability was evaluated by the method given in 

 Appendix 1. Although satisfactory agreement between the predicted and observed 

 values can be seen in Table 3 for full loading condition, agreement for moderate 

 and light loading conditions is poor. However, this is not surprising since only 

 12 occurrences were observed for the moderate and 4 occurrences for the light 

 load condition as compared to 34 occurrences for full draft condition. It is 

 noted that a comparison of the predicted value with the observed value which 

 was obtained from a small number of samples is not statistically proper. How- 

 ever, the comparison is included in the table to provide some indication of how 

 significantly the probability decreases with decrease of loading condition. 



It is of interest to discuss the effect of freeboard forward on the probability 

 of occurrence of deck wetness. Newton, based on his experimental study on a 

 destroyer-type vessel, concluded that the freeboard forward had a most impor- 

 tant influence on the degree of wetness [10]. Newton's conclusion derived from 

 tests in regular waves is valid in irregular waves also since the probability of 

 occurrence of deck wetness decreases significantly with increase of freeboard 

 forward [see Eq. (26)] and since the severity of wetness also decreases as will 

 be seen later in Eq. (30). 



As a practical example of the effect of freeboard forward on the probability 

 of occurrence of deck wetness per cycle of wave encounter. Fig. 18 was pre- 

 pared. The figure shows the probability of deck wetness of the MARINER for 

 various heights of freeboard forward. The probability was computed for a 10- 

 knot speed in a moderate Sea State 7 for full load condition. The actual height 

 of the freeboard forward on the MARINER is 36.7 feet. As can be seen in 

 Fig. 18, if the freeboard were increased by 10 percent, the probability of deck 



573 



