1 - P{xt) = e-"' 



Therefore if the variable under study is expressed 

 in terms of the standardized variate v then the 

 function [1 — e""^] will represent the cumulative 

 distribution of all Rayleigh distributions. This 

 cumulative-distribution function will plot as a 

 straight line if the logarithm of [1 — P(x^)], 

 that is, the probability of exceeding Xi, is plotted 

 against v'^ as has been done in Fig. 3. 



It should be noted that the methods of sta- 

 tistics are strictly valid only if the measured val- 

 ues are independent samples. The physical 



5 The USCGC Unimak, a former U.S. Navy 

 AVP class vessel, now fitted as a weather ship, 

 operating at weather station B in the North 

 Atlantic Ocean. Some data also were obtained 

 for a sister ship, the USCGC Casco. These 

 vessels are approximately 300 ft long and displace 

 about 2500 tons. 



6 A destroyer approximately 380 ft long oper- 

 ating in the Atlantic Ocean. 



7 An aircraft carrier approximately 900 ft 

 long operating in the Atlantic Ocean. 



The actual measurements of strain obtained 



Fig. 4 USCGC Unimak, Distribution of Variation in Pitch Angle — Sample 2 



(This sample represents the poorest fit to the Rayleigh distribution of 129 samples that were an- 



data are not, in general, independent of one an- 

 other. However if the tests of significance indi- 

 cate, on the basis of assumed independence of all 

 observations, that these data reasonably can be 

 assumed to derive from the distribution speci- 

 fied by the hypothesis, then this conclusion is 

 even more sound than the tests of significance 

 indicate. 



Sources of Data 

 Stresses 



Service stresses were obtained for the following 

 ships : 



1 The SS Esso Asheville, a T-2 Maritime Com- 

 mission design tanker, which operated in coast- 

 wise service between the United States, Central 

 and South America. 



2 The SS Gopher Mariner, a C-4 Maritime 

 Commission design dry-cargo vessel, which oper- 

 ated in the transatlantic service. 



3 The SS Ocean'Vulcan (7), a dry-cargo vessel. 

 No specific data are available to the author as to 

 its area of operation. 



4 The USS Fessenden, a destroyer escort, oper- 

 ating in coastal waters off the U.S. East Coast. 



for these ships, excepting the Ocean Vulcan (7), 

 were made by the U.S. Navy's David Taylor 

 Model Basin. In many cases these measure- 

 ments were obtained by means of automatic 

 instrumentation which did not require the pres- 

 ence of an operator aboard the ship. The strain 

 gages were installed on the strength deck, near 

 amidships, see Fig. 1. The tests of six of these 

 ships {Gopher Mariner, Esso Asheville, Unimak, 

 Fessenden, Destroyer, Carrier) covered a period 

 of about 3 to 8 months, predominantly in the 

 winter season; the Ocean Vulcan data however 

 cover a period of 2}^ years. 



Motions 



Ship motions were obtained by Taylor Model 

 Basin personnel on the £550 Asheville, Casco, 

 Unimak, a destroyer, and an aircraft carrier. 

 The motions were recorded by means of an auto- 

 matic recorder which took a record at preset 

 intervals of time for a predetermined duration of 

 time. The complete tests on the Esso Asheville, 

 Casco, and Unimak are described in references 

 (3, 1 and 4), respectively. 



