Mr. R. p. Erickson,^* Visitor: The excellent 

 statistical description of ship data, discussed in 

 the paper, has as a major application the establish- 

 ment of design criteria. Because the data are 

 empirical they fit ideally only the ship on which 

 the data were gathered and must be extrapolated 

 for new ship designs. If these new designs are 

 not distinctly different from the tested design it 

 follows that the extrapolation would be satisfac- 

 torily accurate. The purpose of this discussion is 

 to mention a problem where previous similar ex- 

 perience is not available and thereby point out a 

 need for the statistical description of derived, as 

 well as empirical, data. 



This problem arises in the specification of en- 

 vironmental conditions encountered during the 

 shipboard handling and launching of large ballis- 

 tic missiles. The structural loads imposed on the 

 missile by the motion of the ship is one of a number 

 of similar problems that represents a critical de- 

 sign criteria. Minimum structural weight is abso- 

 lutely essential to the effective utilization of the 

 missile as a weapon. Minimum weight implies 

 minimum acceptable structural strength. The 

 emphasis on weight reduction is so strong that 

 missile designers are prepared to accept a statis- 

 tical risk of structural failure if a known statistical 

 risk can be defined. 



The establishment of a statistical design criteria 

 for ship-launched ballistic missiles must be based 

 upon an intelligent specification of the maximum 

 operational sea conditions in which the weapon 

 must be utilized. Then attempts must be made 

 to determine the statistical description of the sea, 

 or preferably of the ship motions, encountered 

 under this assumed steady environmental condi- 

 tion. Thus far the attempt to define a design ap- 

 proach can benefit significantly from the work of 

 the author. Now, however, because of a lack of 

 previous experience, additional information as to 

 missile structural loads must be derived by en- 

 gineering analysis and the statistical properties of 

 the derived information must be determined. 



To date, with the co-operation of the Navy, 

 especially Bu Ships, the Hydrographic Office, and 

 the David Taylor Model Basin, we have been able 

 to define statistical wave-height and wave-length 

 distribution based on constant underlying param- 

 eters. We have been forced to extend this in- 

 formation to the statistical definition of missile 

 loads by relatively crude graphical methods. 

 This technique can be improved by additional ex- 

 perimental data on ship response which is now 

 being gathered. The eventual goal of this pro- 

 gram is to be able to describe derived data in a 



M Supervisor, Applied Mechanics Group, Missile Operations, 

 Chrysler Corporation, 



convenient statistical form similar to that sub- 

 stantiated by the author for experimental data. 



Mr. Harry Press,^^ Visitor: The author is to 

 be congratulated in making a valuable contribu- 

 tion to the problems of ship behavior in disturbed 

 seas by his collection and analysis of statistical 

 data on ocean waves and ship responses. The 

 paper is of particular interest to me in that it 

 closely parallels some of our recent studies on the 

 analogous problem of the airplane behavior in 

 rough air published in the National Advisory Com- 

 mittee for Aeronautics Technical Notes 3362 and 

 3540. 



The paper considers two major points : The first 

 point is concerned with the demonstration of the 

 applicability of the Rayleigh distribution for de- 

 scribing the probability distribution of ocean 

 wave heights and ship responses for steady ocean 

 conditions. The second point is concerned with 

 the probabihty distribution of wave heights and 

 such ship responses as disturbed motions and 

 structural stresses under broader operating con- 

 ditions, presumably over-all ship operations. The 

 author claims that such distributions are well 

 represented by a log-normal probability distribu- 

 tion. In both cases, the evidence presented is al- 

 most entirely empirical and the conclusions 

 reached based on statistical tests on the data of 

 these hypotheses. 



A few comments on the two major points of the 

 paper appear warranted. In regard to the Ray- 

 leigh distributions for steady ocean conditions, 

 the statistical evidence presented in most cases 

 seems to be quite convincing. It is unfortunate 

 that the author didn't more closely tie the present 

 statistical evidence to the closely related recent 

 work on the response of linear systems to Gaussian 

 random processes. Results obtained in the theory 

 of stationary processes indicate that the distri- 

 bution of peaks for a Gaussian process having a 

 narrow power spectrum should tend to adhere to a 

 Rayleigh distribution (Rice). The work of Pier- 

 son and St. Denis has served to demonstrate that, 

 to a very good first approximation, the disturbed 

 sea under given conditions may be considered a 

 stationary Gaussian random process. Conse- 

 quently, if the ocean wave power spectrum is 

 narrow and peaked, which appears to be the case 

 frequently, the distribution of ocean wave heights, 

 either peak to trough or mean value to peak, may 

 well be expected to approximate a Rayleigh dis- 

 tribution. This approximation would tend to 

 deteriorate as the spectrum broadens. 



In regard to the distribution of peaks of the ship 



" Head, Gust Loads Branch, NACA, Langley Field, Va. 



51 



