Prediction of Ship Slamming at Sea 



theory will not be described here, but the formula which meets our require- 

 ments ( r = H, I r i > f^) is given instead. 



The number of slams per unit time, N^ is given by 



(6) 



The definitions of r;., r'^, h, and f^ are the same as those used in Eq. (5). 

 It is noted that Eqs. (5) and (6) are related by the formula for the expected pe- 

 riod, T^ , for a narrow-band random variable having a normal distribution with 

 zero mean. 



(7) 



Table 2 shows the predicted probability of occurrence of slamming per cy- 

 cle of wave encounter and the number of slams in a 30-minute operation of the 

 MARINER for various conditions. Included also in the table are the experimen- 

 tal values observed in tests conducted on a 13-ft model [4]. To evaluate the 

 predicted values, the response amplitude operators of the relative motion at 

 Station 2 were obtained for various course angles and ship drafts by conducting 

 tests in regular waves, and the superposition technique was used for estimating 

 the variance of the relative motion. The variances of relative velocity were 

 obtained from the energy spectra of the relative motion [7]. Examples of the 

 response amplitude operators of the relative motion and the computed energy 

 spectra of relative motion and velocity are shown in Fig. 4. 



As can be seen in Table 2, the predicted values show satisfactory agree- 

 ment with the observed values; there being approximately a 10 to 15 percent 

 discrepancy, except for moderate and full draft conditions. For the deep draft 

 condition, however, the discrepancy of 25 percent is not surprising since the 

 probability is small. Thus, the application of superposition principle for evalu- 

 ation of relative motion and velocity appears to be adequate to obtain realistic 

 engineering estimates of the probability of occurrence of ship slamming at sea. 



It is of interest to discuss the effects of course angle and loading condition 

 on the probability of occurrence of slamming. It was found experimentally that 

 the probability decreases with increase of course angle and with increase of 

 loading. In other words, the probability of slamming is highest when a ship 

 navigates in head seas at light draft condition [4]. The occurrence of slamming 

 becomes less with increasing course angle because both the relative motion and 

 velocity between wave and ship bow significantly decrease as can be seen in 

 Table 2. For example, the computed R^ and r! (twice the variances of relative 

 motion and velocity, respectively) for a 45 degree course angle both decrease to 

 60 percent of their values in head seas. On the other hand, the occurrence of 

 slamming becomes less with increase of loading primarily because ship draft 

 deepens and thereby bow emergence is less frequent. As can be seen in Table 2, 



553 



