Table 4 



USCGC Unimak — Pitch Angle — Comparison of Predicted 

 AND Measured Maximum Values 



Sea 

 SUIe 



Sign Wave 



HeiiM 



II 



Heading ol 



Waves Relative 



loShip 



Ship 

 Speed 

 knots 



Sampling 

 Time 



Tiital Nool 

 Variations in 

 Sample, N 



Computed 



Value ol E, 



(deg)2 



Measoied Ma> 

 Value 

 deg 



Predicted Max 

 deg 



2 



e 



Head Seas 



10 

 14 



30 

 32 



240 



296 



4.00 

 4.48 



4.3 

 5.3 



4.7 

 5.1 



Quailel 

 Head Seas 



10 

 14 



37 

 3Z 



249 

 274 



1.97 

 1,86 



2.9 

 3.3 



3.3 

 3.2 



Beam Seas 



10 

 14 



1% 

 32 



276 

 343 



5.40 

 3.75 



6.3 

 5.1 



5.5 

 4.7 



Qiiarlei 

 Following 



14 



29 



282 



1.68 



3.9 



3.1 



Following 

 Seas 



14 



32 



308 



1.86 



3.8 



3.3 



3 



7-9 



Head Seas 



10 

 14 

 17 



26 

 32 

 27 



253 

 321 

 277 



10.35 

 9.S2 

 9.59 



7.3 

 7.3 

 6.3 



7.6 

 7.5 

 7.3 



Qoa.le. 

 Head Seas 



10 

 17 



27» 

 37 



269 

 365 



1.79 

 2.02 



3.1 

 3.9 



3.2 



3.5 



Beam Seas 



10 



29 



262 



3.52 



4.3 



4.4 



Qoarler 



Followmg 



Seas 



17 



31 



270 



1.15 



3.9 



3.2 



Following 

 Seas 



17 



23 



193 



1.28 



2.4 



2.6 



4 



16 



Head Seas 



14 



30 



289 



26.12 



10.3 



12.2 



5 



Zl 



Hud Seas 



7» 

 14 



2714 

 24 



236 

 235 



47.32 

 56.00 



18.0 

 15.5 



16.0 

 17.5 



Qiaiter 

 Head Seas 



714 

 14 



3814 

 2814 



347 

 274 



35.13 

 47.14 



13.5 

 16.5 



14.3 

 16.6 





Beam Seas 



Tk 



30 



182 



16.78 



8.8 



9.3 



gnader 



Following 



Seas 



10 

 14 



2814 



29 



27 



175 

 143 

 136 



20.24 

 28.00 

 17.2 



9.8 

 11.5 



8.3 



10.4 

 11.8 

 9.2 



Following 

 Seas 



n 



14 



33 

 31 



160 

 HO 



31.12 

 20.54 



12.5 



10.8 



12.6 

 10.1 



Piocedure for Prediction ol 

 Probable Maximjm Value 

 from a Rayleigh Disltibulion 



Let X ^3^ = most probable maximij 



sample containing N 



Then iccording lo Longuel-Higgin 



fl=log,N-log,[l--^(l-e-«)] 



Sample Size 



Et 



1 



0.707 



2 



1.030 



5 



1.366 



10 



1.583 



20 



1.778 



50 



2.010 



100 



2.172 



200 



2.323 



500 



2.509 



1000 



2.642 



2000 



2.769 



50O0 



2.929 



10,000 



3,044 



20,000 



3.155 



50,000 



3.296 



100,000 



3.400 









Thesh 

 Thete 



ip pitched at a rate of about 400 variations per hour. 

 >t sample consisted of 270 variations in pitch angle. 



/ 



/^^ 



Test Conditions 



Significant Wave Height, 14 ft 



N 





Head Seas 



Ship Speed, 15 knots 





1 



^ 



1 ID 1 I. n . >, .- 



/ 







N, 



. = 17.1(degree)2 

 j.^Exptrimentai Histogram 







V 



1 







1 





1^^ 







3 



4 







8 9 10 U 



Variation in Pitch Angle in degrees 

 Fio. 6 Distribution of Variation in Pitch Angle, Destroyer 



a straight line on the type of probabiUty chart 

 that was devised in the section mentioned (see 

 Fig. 3). 



A statistical test of significance was applied 

 to the hypothesis: "The variations of the meas- 

 ured sample from the assumed population, 

 specified by £, are no larger than may be ex- 

 pected according to the laws of chance." 



Aside from the deviations attributable to chance 

 it was necessary to consider the expected vari- 



ations due to the inaccuracies of the measurement 

 process. The variances of the fractiles for the 

 sample under consideration were computed ac- 

 cording to the theorem stated in the section cited. 

 Fig. 3 which represents the results for a typical 

 test indicates that the measured data fall well 

 within the 90 per cent limits ; a second set of curves, 

 the 67 per cent limits also was computed and the 

 data satisfy this more restrictive test. Thus a 

 high degree of confidence can be placed in the hy- 



11 



