Statistical Distribution Patterns of 



Ocean Waves and of Wave- Induced Ship 



Stresses and Motions, vv^ith 



Engineering Applications' 



By N. H. Jasper,^ Member 



Little is known about the frequency of 

 occurrence of the various magnitudes of 

 ocean waves. Even less is known about 

 the severity of the wave-induced motions 

 and stresses which ships experience in 

 service. The intent of this research effort 

 is to show that, by utilization of statistical 

 methods, it is possible to describe and 

 predict service conditions for ships in an 

 orderly and relatively simple manner de- 

 spite the general complexities of the prob- 

 lem. Wave observations taken continu- 

 ously over a period of 6 years at several 

 weather stations in the Atlantic Ocean 

 were studied. Wave-induced motions and 

 stresses in ships obtained under a wide 

 range of operating conditions were studied 



for seven different ships. On the basis of 

 an analysis of voluminous experimental data 

 it is concluded that the probability dis- 

 tributions of wave height, wave length, 

 wave-induced pitch, roll, and heave mo- 

 tions of ships, and wave-induced ship 

 stresses may all be approximated by a one- 

 parameter-type distribution function when 

 the environmental conditions are steady, 

 whereas these variables will tend to follow 

 the two-parameter logarithmically normal 

 distribution when the environmental con- 

 ditions are allowed to vary over a wide 

 range. Applications of the results of this 

 study to the solution of engineering prob- 

 lems are described with the help of perti- 

 nent illustrations. 



Introduction 

 It is probably correct to state that the ship- 

 building industry knows less about the service 

 conditions under which its product must operate 

 than does any other major construction industry. 

 In contrast to the aircraft builders, shipbuilders 

 have made only a small effort to establish actual 

 service stresses and motions or in incorporating 



^ The paper given here was originally submitted to the School of 

 Engineering and Architecture of the Catholic University of America, 

 Washington, D. C., in partial fulfillment of the requirements for the 

 Degree of Doctor of Engineering. 



2 Engineer and Deputy Division Head, Vibrations Division, 

 David Taylor Model Basin, Navy Department, Washington, D. C. 



Presented at the Annual Meeting, New York, N. Y., November 

 15-16, 1956, of The Society of Naval Architects and Marine 

 Engineers. 



the results of such studies into methods of ship 

 design. A deterrent to progress in this direction 

 has been the complexity of the problem as evi- 

 denced by the extensive variability of the sea 

 and of the response of the ship to the sea. The 

 intent of this paper is to show that, by utilizing 

 statistical methods, it is possible to describe and 

 predict service conditions for ships in an orderly 

 and relatively simple manner, even though the 

 problem appears formidable. 



The experimental approach taken in this paper 

 should complement the theoretical work of St. 

 Denis and Pierson although the present study 

 was developed independently of theirs and is not 



