Ochi 



(b) Probability distribution of impact pressure associated with slamming, 

 and magnitudes of the average one-third and one-tenth highest impact pressures. 



(c) Probability distribution of the time interval between successive slams 

 and between two severe slams. Probability that a time, T (or more), elapses 

 between severe slams. 



(d) Probability of occurrence and severity of deck wetness caused by ship- 

 ping of green water, i.e., application of the theory to the deck wetness problem. 



The above subjects are evaluated theoretically, and the results are com- 

 pared with statistically analyzed experimental results obtained in tests con- 

 ducted on a 13-ft MARINER model. 



PREDICTION OF OCCURRENCE OF SLAMMING 



Basic Concept 



Prediction of the occurrence of slamming is made from two viewpoints: 

 one being the prediction of slamming occurrence per cycle of wave encounter, 

 the other being that per unit time. The question pertaining to how many times a 

 ship will slam during a certain period of time belongs to the latter prediction. 

 The basic concepts used for development of the theory for these two predictions 

 are, however, essentially the same. 



First, the conditions leading to slamming will be discussed. Szebehely has 

 shown that three conditions should exist for slamming to occur [2]. They are: 

 (a) bow (forefoot) emergence, (b) certain magnitude of vertical relative velocity 

 between ship bow and wave, and (c) unfavorable phase between bow motion and 

 wave motion. The present author has also arrived at the same conclusion 

 through his tests [3]. Tick considered three conditions in the development of 

 his theory for predicting the number of slams per unit time. These are: (a) 

 bow emergence, (b) relative velocity, and (c) angle between keel line and wave 

 surface at the instant of impact [l]. 



All of the above conditions were inferred from results of model experiments 

 conducted in regular waves. The question then arises as to whether or not these 

 are necessary and sufficient conditions leading to slamming in rough seas also. 

 To answer this question, data obtained from slamming tests conducted in irreg- 

 ular waves were carefully analyzed, and two conditions leading to slamming in 

 rough seas were obtained. They are: (a) bow (forefoot) emergence, and (b) a 

 certain magnitude of relative velocity between wave and ship bow. In other 

 words, the probability of occurrence of slamming is the joint probability that 

 the bow emerges and that the relative velocity exceeds a certain magnitude at 

 the instant of reentry. 



Bow emergence is prerequisite for slamming. Results of the tests revealed 

 that slamming never occurred without bow emergence. This was found to be 

 true irrespective of sea state, ship speed, course angle or loading condition [4]. 

 However, bow emergence is not a sufficient condition for slamming. There 



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