0.05 

 0.1 

 0.2 



0.5 

 1 

 2 



S 5 

 ■| lO 



^ 20 



,3 30 

 .1" <" 



I 50 

 o- 

 ^ 60 



O- 



I 

 " 70 





























/ 









n 































/ 







































/< 



^ 







































/ 







































/ 



























o Fractiles taken from Table 10 



/ 





































/ 



< 

 / 



/ 



































/ 



/ 



































/ 



/ 





































/ 







































/ 



/ 







































/ 





















































































































/ 



y 







































/ 































































































































































99.9 

 99.8 



99.5 

 99 



5 6 7 8 9 10 20 



Roll Angle, degrees 



40 50 60 70 80 90 100 



Figure 9 - Long-Term Cumulative Distribution of Roll Angle 

 for Wartime Service, North Atlantic Ocean 



This log-normal distribution is computed on the basis of the data represented by the plotted points and it cor- 

 responds to the following parameters: 



Mean value of log.^ (variation in roll angle in degrees) = 0.4868 

 Standard deviation of log,Q (variation in roll angle in degrees) = 0.2741 

 It is probably valid up to 56 deg. 



that a ship structure is expected to experience in a given number of variations or over a given 

 period of time.* The cumulative probability functions plotted in Figure 4 (Rayleigh distribu- 

 tion) and Figures 7 through 10 (log-normal distributions) may be used to find the probability 

 of exceeding (1-P) or of not exceeding (P) a given value of the variable. 



In the preceding section a convenient formula is given for estimating the most probable 

 magnitude of the largest variation out of /V variations; this formula is applicable only when the 



♦The average number of variations expected per hour of sea operation are given in Tables 8 through 11, column 8. 



23 



