The ship will be considered as rigid and the fluid as ideal. In fact, according 

 to our present ideas viscosity plays an important part almost only in the damping of 

 roll. The insight that viscosity effects can be disregarded in most cases represents in 

 itself an important achievement. 



A large part of current investigations deals with forced motions of ships in calm 

 water; effects due to wave action are added using the principle of superposition. 



3.1. Dimensionless Parameters 



In the absence of a consistent theory the determination of similitude parameters 

 is a necessary prerequisite for research and application; in a later stage appropriate 

 expressions are indispensible working tools. At the same time, this absence of theory 

 hinders discovery of the most advantageous and significant similitude parameters for a 

 particular problem. Up to the present time, varied experiences and personal preferences 

 have produced a rather wide variety of dimensionless parameters for the study of ship 

 mechanics, and some kind of standardization appears desirable. Once these parameters 

 will have been standardized, it should become customary to characterize a vessel's 

 oscillatory properties by them in the same way that this is being done for the resistance 

 by the Froude number. (The author's preferences in choice of parameters is indicated 

 in the list of symbols and throughout the remaining text.) 



For purposes of any general discussion, it is convenient to have in mind some 

 standardized ship geometry or series of shapes. Submerged elongated vessels can be 

 approximated by bodies of revolution (especially their most distinguished of such — the 

 spheroid), even a moderate departure from axial symmetry being permissible; and it 

 appears that in the case of surface ships a two-dimensional treatment can be founded 

 with success upon the well-known class of F. Lewis sections [27] which have been used 

 independently by Grim and Haskind. 



B 



A section of the Lewis class is determined by the ratio and the area co- 



2 H 

 efficient fi. 



The velocity potential which governs fluid perturbations caused by motions of 

 such bodies has been established also in the presence of a free surface. 



3.2. Added Masses 



The determination of added masses has become a central problem in the study 

 of ship behavior, since the computation not only of inertia but also of exciting and even 

 damping forces depends upon it. 



To my knowledge, Haskind [28] was the first to establish theoretically the 

 influence of a frequency parameter, say cd b * — u\/B/g, upon the magnitude of added 

 mass values m ri (co B *) already found experimentally by Holstein [13]. Unfortunately, 

 our information rested on a part of Haskind's publications only, so that the method by 

 which he obtained his important results in the three-dimensional case remains unknown, 

 although further details of his work have become available [25].* In the meanwhile 

 contributions have been made by Ursell, Grim, and Havelock. Japanese authors [29] 

 investigated the submerged spheroid under the free boundary condition $ - 0, while 



the other extreme case — =0 has been treated by Eisenberg [30]. 



dz 



There are several methods in use to formulate dimensionless added mass co- 

 efficients; the most popular are those found in Lamb and those proposed by F. Lewis. 

 However, especially in the case of rotational motions there is still a wide variety of 

 definitions. 



* In the two-dimensional case of heaving the result m n (0)— >oo is obtained while 

 Haskind's investigation yielded a finite value supported by experiments. 



67 



