no more than a successful heuristic approach. Thus only by the introduction of the 

 irregular seaway concept can problems of average performance, especially of sustained 

 average sea speed, be handled in an appropriate manner. This fact will allow us to 

 appraise correctly the importance of seakindliness of vessels with respect to other basic 

 qualities of a ship when the necessary statistical data will be collected. Again, there 

 is a brighter outlook in this respect after pertinent research facilities have been 

 developed. 



There appear still to exist some differences in opinion on the fundamentals of 

 the irregular seaway concept and the resulting ship motions. However, for the present 

 purpose I shall assume that the principle of superposition is valid for elementary waves 

 as well as ship motions and restrict myself to the study of ship behavior in a regular 

 seaway till we later come to a discussion of design problems. 



Attempts to establish safety limits for ships by statistical observations had been 

 made long before a consistent theory of the actual seaway existed. It is evident that 

 the statistical approach is a necessary condition for dealing with the safety problem but 

 it is questionable if it is a sufficient one. Thus it is the present writer's contention that 

 the old-fashioned approach based on the investigations of transient conditions should 

 not be completely disregarded, although it is admitted that no proposal so far exists as 

 to how to formulate these conditions. 



The present theory of ship behavior in an irregular seaway as a linear theory 

 is not fit to deal with the safety problem as far as large displacements, such as those 

 in roll, are concerned. The same objection must be raised against the linear theory of 

 ship motions in a regular seaway. 



2. Preliminary Survey on the Development of the Theory of Ship Behavior 



A. Krylov's study of ship behavior, based on the undisturbed wave hypothesis, 

 remains classic because of its general character and its consistent formal approach. 

 Recently his method has been reviewed by at least six authors. It should be kept in 

 mind that Krylov's work was originally stimulated by a study of extraneous forces 

 causing bending moments and shearing forces, thus indicating the close interconnection 

 of shipbuilding science branches. 



One could surmise that Krylov, by neglecting the influence of speed of advance 

 on forces, and by rather aggressively disregarding the importance of damping in heave 

 and pitch, might have detrimentally influenced further development. However, his 

 scientific achievements have been grasped by the profession so slowly, that their weak 

 points did little harm. Indeed, by failing to use Krylov's theory as a guide for model 

 research, some experimenters were derailed into a rather sterile empiricism. Thus the 

 need for sometimes tedious computations has occasionally slowed progress in under- 

 standing basic phenomena in our field. 



The determination of exciting forces as functions of the waterline form, (to 

 some extent of the sectional area curve), of the ratio A* = X/L, and then of the heading 

 angle, was the main problem attacked by Krylov. While Krylov himself still cherished 

 the idea that he had solved the problem of ship behavior completely, his moderate 

 adepts were critical enough to consider their investigations as attempts to obtain some 

 general ideas of the phenomena. At the prevailing state of knowledge that was already 

 a useful task. 



By 1930 a standard form of linearized equations of motion for a ship in a seaway 

 was established [11]. 



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