Goodrich 



It has been assumed that the short term distribution of the variation of rela- 

 tive vertical motion of the bow will have a Rayleigh distribution. With this dis- 

 tribution the probability of exceeding a specific value of relative bow motion S. 

 is 



2 , 2 

 e 



In order to obtain the long-term distribution of S, a weighting factor for weather 

 distribution must be included. As was stated earlier no weighting factor has been 

 included in this analysis to take account of variations in the sea direction. The 

 probability of exceeding a specific value of S- is therefore: 



2 



v -(s./s y 



where P . is the weighting factor for the general weather probability distribution. 

 The weather distribution used is given below over the range of weather groups 

 1 to 5. 



The mean value of S^ for each group has been used in the calculation of Q., 

 with values of S- of 10, 20 and 30 ft for all lengths of ships. From the calculated 

 values of Q^ for specific values of s. probability curves can be drawn such as in 

 Fig. 5. If freeboard at the fore perpendicular is substituted for S- then these 

 curves show the probability of the water rising above the freeboard. A non- 

 dimensional freeboard ratio can be used, (defined as the ratio of the freeboard 

 at the fore perpendicular to the ship length) rather than absolute freeboard and 

 the results for the 0.60, 0.70 and 0.80 Cg ships are given in terms of this ratio 

 in Figs. 6, 7 and 8. The curves for the 0.80 Cg ships include lengths of up to 

 1000 ft since there is a growing interest in the behaviour of bulk cargo carriers 

 of such lengths. 



Figures 9, 10 and 11 show the freeboard ratio required for various ship 

 lengths for equal probability of wetness. 



DISCUSSION OF RESULTS 



The results show that for equal probability of occurrence the freeboard ratio 

 decreases with increasing ship length. The results for the 0.60 and 0.80 Cg ships 

 are similar but the analysis shows that the 0.70 Cg ships require a greater free- 

 board. This result is a direct consequence of the higher responses obtained for 



602 



