Prediction of Ship Slamming at Sea 



and green water. For the MARINER, the predictions are valid at least up to a 

 severe Sea State 7, ship speed 10 knots. 



2. The conditions leadii^ to ship slamming in rough seas are bow emer- 

 gence and a certain magnitude of relative velocity between wave and ship bow 

 (threshold velocity). It is considered appropriate to take 12 ft/sec as the 

 threshold velocity for a 520-ft ship. For a ship of different length, the above 

 given value should be modified according to the Froude scaling law. 



3. Probability of occurrence of slamming decreases with increase of 

 course angle from head seas because both the relative motion and relative ve- 

 locity decrease with increasing course angle. The probability of occurrence of 

 slamming decreases with increase of loading condition primarily because the 

 probability of bow emergence significantly decreases with increasing draft. 



4. Relative velocity between wave and ship bow at the instant of slamming 

 follows a truncated Rayleigh probability law. Truncation should be made at the 

 threshold velocity. 



5. Impact pressure applied to a ship's forward bottom when slamming oc- 

 curs follows a truncated exponential probability law. Truncation should be made 

 for the pressure induced by the threshold velocity. The law appears to be valid 

 for any course angle and loading condition, 



6. Time interval between successive slams follows a truncated exponential 

 probability law. Truncation should be made at the natural pitching period of the 

 ship. 



7. The time interval between two severe slams follows a truncated gamma 

 probability law. 



8. The probability of occurrence of deck wetness is simply the probability 

 of bow submergence. It is an exponential function of relative motion between 

 wave and ship bow and the freeboard forward. The probability decreases sig- 

 nificantly with increase of freeboard forward. 



9. Pressure associated with deck wetness follows a modified Rayleigh 

 probability law. 



ACKNOWLEDGMENTS 



The author wishes to express his appreciation to Dr. W. E. Cummins for 

 the valuable discussions and his encouragement received during the course of 

 this project. Thanks are also due to Lt. Cdr. M. C. Davis (USN) for his techni- 

 cal advice. 



The assistance of Mrs. S. R. Zoomstein and Mr. J. A. Kallio in carrying 

 out the numerical calculations is gratefully acknowledged. 



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