year, will exceed each given level are obtained by summing the product of column 9 with col- 

 umns 10 through 18 over all environmental conditions. The last line in the table gives the 

 probability of exceeding any one of the given magnitudes, for the long-term distribution. The 

 latter values are plotted on the cumulative probability distribution charts in Figures 7 through 

 10. 



The straight lines shown on these charts have not been drawn by eye through the plot- 

 ted points but have been computed directly from the percentages represented by the plotted 

 points under the assumption that the long-term distribution is of the log-normal type. A sample 

 calculation is given in Appendix B. The rather good fit of the computed line to the plotted 

 points indicates that this assumption is reasonable. One would expect tJiat the points corres- 

 ponding to the more extreme values would lie above the theoretical line because by far the 

 greatest contribution to the computed probability for these extreme values derives from the 

 more severe sea conditions. It is apparent that if data had been available for more severe 

 seas than State 5, the probabilities of exceeding the higher values would have been increased 

 whereas the plotted points representing probabilities of exceeding low or medium large values 

 would not have been affected to any noticeable extent. 



The value of E corresponding to any short-term distribution may readily be used to pre- 

 dict the most probable maximum value of the motion or stress expected in any given number of 

 oscillations. LonguetrHiggins^ has shown that the largest probable value out of A' measure- 

 ments is -/fi^ times a constant if the population is of the Rayleigh type, where the constant is 

 a function of N only. For large values of N, the constant is nearly equal to yJlog^N. Table 7 

 gives the value of the constant by which ^'^must be multiplied. A comparison of predicted 

 and measured maximum values, utilizing this method, is given in Tables 2 through 6. There 

 appears to be a satisfactory agreement. 



The wave-induced hull-girder stresses can be converted to the corresponding vertical 

 bending moments amidships by making use of the midship section modulus which is applicable 

 to the strain-gage location (23.8 ft above baseline, 10 ft above the location of the neutral 

 axis). Tests have indicated ^'^ that the deckhouse of the AVP vessel is fully effective in 

 resisting bending, thus resulting in a section moment of inertia of 761 ff* which corresponds 

 to a section modulus applicable to the strain-gage location of 11,000 ft-in^. This value of 

 the section modulus has been used to convert wave induced stresses to wave-induced bending 

 moments. 



10 



