Analyses of Multiple-Float-Supported Platforms in Waves 



The results have been given for a range of dimensionless sea 

 states Hwg/v 1 / 3 up to 1.0, so that for a craft of 30000 long tons 

 displacement the corresponding significant wave height is 102 feet. 

 This corresponds to a high Sea State 9 and, according to the recom- 

 mendations of the ITTC [16] , the approximate wind speed in the open 

 ocean would be well above 80 knots. For a 10 -ton craft, however, the 

 significant height would be 7.05 feet, or Sea State 4. 



Dimensionless statistical response data are presented in tabul- 

 ar form for all of the model tests reported by Mercier [5] , in Tables 

 5a-5y. Large values of Hj/3/ v 1 / 3 , U p to 4 . (H^ i% « 75 ft for a 

 3000-ton craft), are covered in these tables but because the transfer 

 functions derived from the basic tests are not precisely defined at low 

 frequencies, which are strongly excited by extremely high sea states, 

 the results above Hwg/v ' = 1.0 are somewhat less reliable. This 

 is especially true for the pitch motions which have very low but un- 

 defined natural frequencies. The transfer functions were extrapolated 

 "by eye" to lower frequencies to permit these calculations for 1.0 < 

 H 1 / 3 /v 1 / 3 < 4.0 to be undertaken. 



Extreme Response 



Ochi [2l] has adapted order statistics with a given probability 

 of being exceeded, for evaluating long-term statistical behavior which 

 may be more appropriate for evaluating limiting sea state operating 

 conditions. His equation, which is applicable to Rayleigh probability 

 distributions, may be expressed non-dimensionally as 



1/3 



J-2 E^ in |l-(l-Prob) ly/N o( (9) 



where x = extreme value (amplitude) (for examples : heave, z ; 

 pitch, 6 V ' j acceleration, (A/g)v ' , etc.) 



v -^ T ime ffi ^rjir 



Time = Duration time in hours 



Prob = Probability of computed value, x , being 



exceeded 



E = Dimensionless response variance, Eq.(6) 



x 



E. = Dimensionless response velocity variance 



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