Ochi 



the computed r; decreases only slightly with increase of loading. However, the 

 probability of bow emergence is an exponential function of the square of the 

 draft at the bow [Eq. (5)], and thereby the probability decreases drastically with 

 increase of the draft. 



For a better understanding of the above statement, Fig. 5 was prepared to 

 show the computed probability of slamming as well as the probability of bow 

 emergence and the probability that the relative velocity exceeds the threshold 

 velocity for the MARINER in head seas of a moderate Sea State 7 at a ship speed 

 of 10 knots. The probability of occurrence of slamming, is, of course, the prod- 

 uct of the other two probabilities. It is clear in the figure that the probability of 

 bow emergence, Prob {r >H}, is responsible for the rapid decrease in the prob- 

 ability of slamming. 



25 "^ 50 r75 



Cargo Loading in Percent 



[Light I iModerotel 



Fig. 5 - Probabilities of occurrence 

 of slamming and bow emergence, and 

 probability that the relative velocity- 

 exceeds the threshold velocity 



100 



PREDICTION OF SEVERITY OF SLAMMING 



Ship slamming is always accompanied by an impact pressure on the flat 

 bottom, and the magnitude of the pressure is indicative of the severity of slam- 

 ming. The impact pressure is approximately proportional to the square of the 

 magnitude of relative velocity at the instant of impact as was shown in Fig. 1. 

 The same conclusion was obtained from results of tests conducted in regular 

 waves [3]. Hence, this basic relation of the impact pressure and relative veloc- 

 ity will be considered in the development of the theory. Prior to a discussion 

 on the prediction of slamming severity, a statistical consideration of the magni- 

 tude of relative velocity will be given. 



556 



