Table 7 SS Esso Asheville — Distribution of Wave-Induced 

 Stress Variations for a Period of 30 Days at Sea between Sep- 

 tember 1, 1953 AND April 3, 1954 



(Average period of i 



Stiess 

 psi 



Estimated Nucnbei of Cycles of Magnitudet Greatet than the Indicated Stress 



(For a period of 30 days at sea) 



Average No. Cycles 



P and S 

 Load and Ballast 



Ship Loaded 



Ship in 



Ballast 





Starboard Gage 



Port Gage 



Starboard Gage 



Port 



Gage 



500 



181,128 



• 



188,723 



• 



188,007 



• 



174,072 



• 



173,710 



1,000 



97,640 





89,552 





97,667 





100,381 





102,958 



2,000 



33,292 



22,311 



28,237 



30.152 



33,047 



25,567 



30,508 



27,346 



41,376 



3,000 



12,170 





11,574 





12,727 





8,176 





16,204 



4,000 



4,174 



3,889 



3,889 



5,679 



5,679 



2,161 



2,161 



4,966 



4,966 



5,000 



1,139 





843 





1,020 





456 





2,239 



6,000 



566 



519 



519 



928 



928 



194 



194 



621 



621 



8,000 



61 



46 



46 



166 



166 











31 



31 



10,000 



13 











55 



55 



















12,000 







































*This estimate is based on oscillogiams taken tor a duration of 2 jnin at inteivals o( 1 li 







"Th, 

 oscillo 



s estimate is similar to the preceding one except that, for stress values less than 4,000 psi, 

 grams of 2-min duration, taken at intervals of 4 hr, were utilized in Figure 2. 



>ample 



1Pe! 



ik-to-peak variation. 











carried out for the wave-height data observed at 

 ocean station C. The method of summation given 

 by the last expression is by far the more con- 

 venient of the two choices. The computed 

 cumulative probabilities for the wave heights are 

 plotted in Fig. 13. Inspection of this figure 

 shows that the cumulative distribution of wave 

 heights derived from the distribution of significant 

 wave heights also may be represented by a log- 

 normal distribution. 



It is concluded on the basis of this analysis of 

 the extensive available wave observations, that 

 the distribution functions of both the significant 

 wave heights and the wave heights proper of 

 ocean waves are approximated by the log-normal 

 distribution. This conclusion has not been evalu- 

 ated by use of standard statistical tests of signifi- 

 cance because the data consist principally of 

 visual observations and the accuracy of these 

 observations has not been determined thus far. 



Stress Variations 



The stress and ship-motion data given in this 

 paper furnish a "truncated" or "censored" dis- 

 tribution '^ thus named because only values larger 

 than a specific lower limit are given. Fisher (16) 

 has devised a method for determining the param- 

 eters 0- and ^ which define the normal (or log- 

 normal) distribution from the measured truncated 



15 Truncated at the lower eod of the distribution. 



data. If the analytically expressed distribution, 

 thus determined, fits the measured data reason- 

 ably well, it is probable that the data follow the 

 normal distribution. The method devised by 

 Fisher will be applied here, except for the cases of 

 the Gopher Mariner and Ocean Vulcan for which 

 the degree of truncation is so large that a better 

 estimate probably can be made on the basis of the 

 estimated average periodicity of stress variation. 

 The latter two cases are given only to help sup- 

 port the conclusions based on other more exten- 

 sive tests. 



Esso Asheville 



The period covered by the data is from Sep- 

 tember 1, 1953 to April 3, 1954. Oscillograms of 

 strain, taken at hourly intervals for a duration 

 of 2 min each, were analyzed in terms of stress 

 variations (see Tables 6 and 7) and classified 

 according to the magnitude of these variations. 

 The measured number of variations were then 

 multiplied by a factor to give the estimated num- 

 ber of variations which would have been re- 

 corded if continuous measurements had been 

 made. Application of the Fisher method to the 

 truncated data yields the log-normal distribution 

 patterns shown in Fig. 16. The plotted points 

 in Fig. 16 were obtained by use of the theoretical 

 degree of truncation; their scatter from the 

 straight lines should give an unbiased measure of 

 the applicability of the assumed normal distri- 



22 



