Wave Data 



Observation of significant wave height' and 

 wave period, obtained over a period of 6 years, 

 have been made available by the U.S. Weather 

 Bureau. These observations were made every 

 3 hr by trained weather observers in accordance 

 with instructions prescribed by the U.S. Weather 

 Bureau (8). Only one quantitative measure- 

 ment was reported each time the sea was ob- 

 served. Darbyshire (9) obtained measurements 

 of wave heights, at Ocean Stations I and J by 

 means of a wave meter which has been developed 

 in England. Thus one set of measurements is 

 available which may be used as a check of wave- 

 height observations reported by weather ships. 



Analysis of Short-Term Distribution 

 Functions 



It is the piurpose of this section to show that, 

 on the basis of the experimental evidence, wave- 

 induced motions and stresses of ships are dis- 

 tributed according to the Rayleigh distribution 

 with a high degree of statistical significance pro- 

 vided the sea conditions, ships speed, .and head- 

 ing remain uniform throughout the period under 

 consideration. 



It has been accepted generally that the heights 

 of ocean waves passing any given point follow the 

 Rayleigh distribution, provided the associated 

 power spectrum has most of the energy con- 

 centrated in a narrow frequency band. This dis- 

 tribution is valid if measurements of wave height 

 are taken over a relatively short period of time, 

 of the order of 1 hr, during which interval the sea 

 conditions do not change appreciably. It can 

 be shown that this distribution is the same as 

 that representing all wave heights, in the area 

 under consideration, at one instant of time. The 

 statistics of the Rayleigh distribution were applied 

 by Longuet-Higgins (10) to the analysis of the 

 distribution of wave heights in a sea character- 

 ized by a narrow spectrum. This work was ex- 

 tensively applied by Pierson, Neumann, and 

 James (11) to the study of ocean waves. 



Inasmuch as hull stresses and motions are 

 caused by the passage of the waves past the ship 

 it will be appropriate to test the hypothesis that 

 the responses of the ship to the waves, i.e., stresses 

 and motions, may similarly be statistically repre- 

 sented by a Rayleigh distribution. 



For this purpose a number of tests^ were run 



Table 3 Chi-Square Test Applied to Test Goodness 

 OF Fit of Rayleigh Distribution to Test Results 







Number o[ 



Expected 







Sample Tested 



Class Limits 



Variations 

 Measured 



Number of 

 Variations 



Value ol 

 Chi Square 



Remarks 



UNIMAK 



0- 3 deg 



40 



48 



1.33 



Iy^.6.4 



Pitch Angle 



3- 6 



84 



77 



0.64 



Cood Fit 



See Fieules 2, 3 



6- 8 



49 



SO 



0.02 



P. 0.75 





8-10 



33 



33 











10-14 



27 



26 



0.04 







14-19 



5 



2 



4.5 





UNIMAK 

 Pitch Angle 

 See Figuies 4, 5 



0- 2 1/8 deg 

 2 1/8- 3 1/8 

 31/8- 41/8 



46 



25 

 31 



35 

 33 

 34 



3.46 

 1.93 

 US 



iy^.ll.? 

 Fair Fit 

 p. 0.92 





41/8- 51/8 



23 



28 



0.89 







51/8- 61/8 



It 



20 



1.80 







61/8- 81/8 



27 



19 



3.36 







81/8-101/8 



6 



6 









DESTROYER 



0- 1 deg 



14 



16 



0.25 



Sv2.4.4 



Pitch Angle 

 Sec Figures 6, 7 



1- 2 



2- 3 



34 

 55 



41 

 54 



1.20 

 0.02 



Very Good Fit 

 P - 0,30 





3- 4 



56 



54 



0.07 







4- 5 



45 



43 



0.09 







5- 6 



37 



30 



1.63 







5- 7 



18 



17 



0.06 







7-10 



11 



15 



1.07 





AIRCRAFT CARRIER 



0- 5 deg 



43 



45.96 



0.19 



Xv^.2.8 



Pitch Angle 

 See Figuies 8, 9 



5- 9 

 9-12 



76 

 36 



69.59 

 43.69 



0.59 

 1.35 



Very Good Fit 

 P . 0.30 





12-15 



32 



27.93 



0.59 







15-18 



15 



14.23 



0.04 







18-23 



S 



7.42 



0.05 





AIRCRAFT CARRIER 



0- 750 psi 



35 



28.75 



1.36 



l^.S.t 



Stress in Main Deck 

 See Figures 10, 11 



750-1500 



1500-2250 



68 

 61 



66.47 

 66.40 



0.04 

 0.44 



Good Fit 

 p. 0.75 





2250-3000 



31 



41.29 



2.56 







3000-3750 



25 



18.97 



1.92 







3750-5500 



10 



8.13 



0.f3 





on the USCGC Unimak under a wide variety of 

 combinations of sea, speed and ships heading to 

 the waves. The hull stresses, pitching, rolling, 

 and heaving motions were measured for 39 sets of 

 these combinations. The parameter E which 

 defines the Rayleigh distribution 



(x) = 



2x 



height is the average height of the upper third 



" Each test yielded a continuous Va-hr oscillogcam record of ship 

 motions and stresses applicable to a specific combination of condi- 



■ Significant 

 highest 



was compu,ted for each of the frequency distri- 

 butions of motions and stresses measured under 

 the various combinations of environmental con- 

 ditions. The individual histograms were plotted 

 and compared with the Rayleigh distributions 

 corresponding to the computed value of E. A 

 typical distribution, thus determined, is shown 

 in Figs. 2 and 3. The pattern which evidenced 

 the poorest agreement between the experi- 

 mental and the Rayleigh distribution is shown 

 in Figs. 4 and 5. 



It has been shown in the section "Statistical 

 Background," that all Rayleigh distributions may 

 be represented by a single analytic expression if a 

 new variable v is used rather than x directly. The 

 cumulative distribution function then plots as 



10 



