depth of the ship itself restricts the severity of the 

 buoyancy distribution. But these physical limits 

 on the external loads actually may provide the 

 key to the problem of maximum stresses, by 

 permitting the maximum loads to be determined 

 on physical grounds. Hence, it is suggested that 

 attempts be made to evaluate the maximum loads 

 on the basis of piu^ely physical consider- 

 ations. 



In this connection, the suggestions of Hazen and 

 Nims in 1940'^ may provide a promising lead. 

 They made the following suggestion, assuming a 

 satisfactory method for the computing machine 

 calculation of bending moments (a joint project 

 of the Society's S-3 and H-7 Panels is making en- 

 couraging progress here): "With a wave of any 

 given shape at any given position along the hull 

 assume a position and velocity for the ship in the 

 heave and the pitch co-ordinates. These assump- 

 tions may be considered sufficient to fix the forces 

 acting on the ship since the unbalanced force and 

 moment, and consequently the accelerations, are 

 fixed thereby. By investigating a series of such 

 conditions with the hull having a wide range of 

 positions and velocities with respect to the water 

 it is possible that an envelope for moment curves 

 would be defined which would represent the maxi- 

 mum moments that would be encountered by the 

 huU for any position and velocity to which it 

 might be subjected. . ." Once having deter- 

 mined the most extreme bending moment physi- 

 cally possible, statistical methods could be used to 

 determine the probability of occurrence of this 

 extreme condition. 



In conclusion, I feel that the statistical analysis 

 of sea and ship data presented here is of great 

 value to the profession, and the work shoiJd be 

 continued actively. I also agree with the author 

 that simple model tests can continue to be of as- 

 sistance in connection with such studies. 



Mr. J. Darbyshire.^" Visitor: The author 

 quotes data which I published in 1955 relating to 

 wave records taken by the O.W.S. Weather Ex- 

 plorer with a ship-borne wave recorder devel- 

 oped at the National Institute of Oceanography. 

 These records were taken at the positions 

 "INDIA" ■(61°00'N,15°20'W) and JULIETT 

 (52°30'N,20°00'W) and covered the period Feb- 

 ruary, 1953, to January, 1954. I have since 

 checked the logarithmic normal distribution law 

 by using all the data available from the ship from 

 February, 1953, to December, 1955. The distri- 



18 "Calculation of Motions and Stresses of a Pitching and Heaving 

 Ship," by H. L. Hazen and P. T. Nims, Trans. SNAME, vol. 48, 

 1940, p. 111. 



" National Institute of Oceanography, Wormley, Godalming, 

 England. 



bution law still appears to be satisfactory although 

 there is some departure from it at heights below 5 

 ft and above 40 ft. The relation 



p = 6.6 exp - (logx/9.0)V0.126 



was obtained where p is the probability density 

 expressed as a percentage and x is the maximum 

 wave height. 



A similar relation was found for wave heights 

 recorded at Casablanca from 1952-1955 and it 



p = 18.0 exp - (logx/3.5)V0.137 



A similar relation also could be fitted to the 

 maximum wave heights recorded at Perranporth, 

 Cornwall, England, during the year 1946-1947 

 and it was 



p = 13.0 exp - (logV4.0)V0.199 



This work has been published in greater detail.^' 



Mr. J. P. CoMSTOCK, Member: The two objec- 

 tives of this paper as stated by the author ob- 

 viously have been attained. 



I concur with the author that "there are many 

 applications in which a knowledge of the fre- 

 quency distributions of hull motions, stresses, and 

 the heights of ocean waves can be used to advan- 

 tage." However, when it comes to deducing 

 "the extreme value of the wave-induced stress that 

 can be expected over the service life of the ship," 

 I am not yet convinced that a study of statistical 

 distribution of stress can do this for us. 



To apply the example of estimating the safe life 

 of a structure to a ship's hull would require the 

 tacit assumption that ship failures are basically 

 fatigue failures. Since, in all the voluminous rec- 

 ords of ship casualties, there has been found, so 

 far as I can determine, no correlation whatever be- 

 tween age of ship and incidence of fracture, I do 

 not believe that ship fractures are basically fatigue 

 failures. I think that in most cases they result 

 from isolated fortuitous combinations of severe 

 conditions which in all probability most ships 

 never experience in their entire life, but which 

 nevertheless, if they could be known, should be the 

 basis of hull structure design. 



The author states, "In engineering applications 

 very large values (extremes) of stress and motion, 

 although they occur very seldom, may be of con- 

 siderable importance." So far as hull-girder 

 stress is concerned, this is a gross understatement; 

 they are of controlling importance. Yet, as the 

 author warns us, "theoretical distribution cannot 



" "Distribution of Wave Heights," by J. Darbyshire, Dock 

 Harbour Authority, (London), vol. 37, May, 1956, pp. 31-32. 



43 



