Statistical Society, vol. 47, September, 1952, pp. 

 425-441. 



18 "A New Method of Analyzing Extreme 

 Value Data," by J. Lieblein, NACA Technical 

 Note 3053, January, 1954. 



19 "Statistical Theory of Extreme Values and 

 Some Practical Applications," by E. J. Gumbel, 

 National Bureau of Standards Applied Mathe- 

 matics Series No. 33, February, 1954. 



20 "The Application of the Statistical Theory 

 of Extreme Values to Gust Load Problems," by 



H. Press, NACA Technical Note 1926, November, 

 1949. 



21 "SS Ocean Vulcan, ' ' Admiralty Ship Weld- 

 ing Committee Report R-8, H. M. Stationery 

 Office, London, England. 



22 "On the Stabilization of Roll," by J. H. 

 Chadwick, Jr., Trans. SNAME, vol. 63, 1955, pp. 

 237-280. 



23 "The Outlook on Airframe Fatigue," by 

 W. Tye, Journal of the Royal Aeronautical Society, 

 vol. 59, May, 1955, pp. 339-348. 



D 



iscussion 



Mr. E. V. Lewis, Member: The author has 

 carried out an ambitious program of assembling 

 data on ship motions and stresses at sea and has 

 demonstrated that statistical methods can bring 

 them into some kind of order. It is particularly 

 encouraging that he finds the short-term ampli- 

 tudes (from peak to hollow) follow the Rayleigh 

 distribution. Other writers have indicated that 

 this should be so, but the author has made a dis- 

 tinct contribution in assembling such an impres- 

 sive weight of evidence to prove that the Ray- 

 leigh distribution does apply to waves, ship 

 motions, and hull stresses — over a wide range of 

 ship types and conditions. Thus the great value 

 of this paper is believed to be the way in which it 

 adds to and fills out a growing knowledge of the 

 sea and ship behavior. 



It may help to see better how his work fits into 

 the broad picture, by noting, for example, that 

 the Rayleigh distribution is the same as that 

 referred to as the "target or chi-square" distribu- 

 tion by St. Denis-Pierson (reference 15 of the 

 paper). The author's E is in principle the same 

 as the R of St. Denis-Pierson — both are pro- 

 portional to the mean square value of the record 

 or the area under an energy spectrum. But the 

 author's E is numerically 4 times R. It is the 

 writer's understanding that the "variation in 

 pitch angle" and other quantities plotted — as in 

 Fig. 2 of the paper — refer to the successive double 

 amplitudes or peak-to-trough distances on the 

 record. It should be noted that the Rayleigh 

 distribution of amplitudes is entirely consistent 

 with a normal or Gaussian distribution of points 

 on the record, chosen either at random or at 

 equal intervals of time. Since theoretically the 

 Rayleigh distribution applies only for "narrow" 

 spectra, it may be concluded from the author's 

 work that most sea and ship response spectra are 



narrow, in this sense. It is only necessary then 

 to know one parameter, E (or for practical 

 purposes a^), to define the distribution. 



Model research at the Stevens E.T.T. in irregu- 

 lar head seas has shown that E for motions and 

 for external bending moment (hence stress) can 

 be predicted accurately from a knowledge of the 

 sea spectrum and of the characteristic response of 

 the model to different wave lengths (frequencies), 

 which easily can be obtained experimentally. 

 Hence, it is comparatively simple to predict the 

 distribution patterns, as noted by the author. 

 (Model results on motions were presented before 

 the Society last year, and work on bending 

 moments sponsored by the S-3 Panel of the Hull 

 Structure Committee is to be published soon.) 



Actual distribution curves for amplitudes of 

 model response have not been published, and 

 therefore it may be of interest to show some 

 typical plots we have just worked out for com- 

 parison with the author's full-scale data. 



Fig. 24 shows distribution of wave, pitch and 

 heave amplitudes for the Series 60 model re- 

 ported on last year; speed 12 knots in high 

 irregular sea (5 runs). The wave spectrum and 

 the motion spectra were quite narrow and very 

 good agreement is shown. It should be added 

 that a typical case of 18 knots in a more moderate 

 sea — with a broader spectrum which according to 

 Pierson and Neumann is not so realistic — did not 

 show such good agreement. 



Fig. 25 shows distribution of bending moment 

 for T-2 Tanker model reported in 1954. Again 

 good agreement is shown at a speed of 14^-^ knots 

 in a high irregular sea (3 runs) . 



The author's finding that long-term sea and ship 

 data follow a log-normal distribution is also of 

 interest, since it makes it possible to characterize 

 a mass of accumulated data by two parameters — 



41 



