B. V. Korvin-Kroukovsky 



In this valuable paper, Dr. Weinblum has presented a very comprehensive review 

 of the entire subject of the analysis of ship motions. It is not feasible to present a 

 discussion of such a broad field; a discusser must single out a few aspects in his par- 

 ticular sphere of interest. This discusser appreciates the clear definition of two basic 

 directions of ship theory development as given by the author: a. to state the practical 

 conditions as completely as possible and to look for an approximate solution (the 

 vigorous approach), and b. to simplify to the utmost the problem presented by prac- 

 tice (i.e., substitute a simple mechanical model), and to apply rigor in the mathematical 

 solution. 



The family tree of the first method is easily traced from the initial work of 

 Kriloff (1896) through the work of Weinblum and St. Denis (1950) and St. Denis 

 (1951) to Korvin-Kroukovsky (1955). During the past year it has received important 

 additional development (as yet unpublished) by Prof. M. Abkowitz and Prof. Fay of 

 M.I.T. and by Miss W. R. Jacobs (this discusser's associate). Valuable contributions 

 for the elements of this theory appeared also in the more mathematical works of 

 Havelock (1955, 1956). Were all these developments taken into account, the general 

 tone of the author's outline would appear to be too reserved. The successful com- 

 parison of calculations with experimental data for several models in several wave 

 lengths could well call for more enthusiasm. Unfortunately, a certain amount of time 

 will have to elapse before these latest developments can be published. 



The author points correctly to the fact that calculation of the exciting forces 

 for a submerged body are simpler and appeared earlier than those for a surface ship. 

 This discusser cannot agree with the author, however, that the calculation of the latter 

 was made by "analogy". The technique was first developed for a submerged body, 

 and then was applied to a surface ship, but this latter application was made inde- 

 pendently without resort to analogy. The striving for simplicity required that the basic 

 solution be developed for a semi-circular ship section; the results were subsequently 

 generalized to apply to any form of cross section by introducing the coefficient of 

 accession to inertia in view of the basic work of G. I. Taylor (1928) as well as Have- 

 lock's (1954) work on submerged spheroids. The word "analogy" is therefore partly 

 applicable only to this final step. The computed exciting forces for a ship model were 

 found to agree very well with the experimental data. 



The cross-coupling damping terms which appear in the work of Haskind and 

 Havelock (1955) deserve additional comments. It should be observed that these 

 "damping" terms result from the calculations based on the inviscid fluid, and in Have- 

 lock's case, without wave formation. They do not involve, therefore, any energy dissipa- 

 tion, and can be termed "dynamic" damping, in distinction to the wavemaking damping 

 defined by the works of Holstein, Havelock, Ursell and Grim. This wavemaking 

 damping must be added as a separate step to any calculation in which the surface 

 wave formation is not included in the initial setup of the problem, as, for instance, 

 that of Korvin-Kroukovsky (1955). 



"Dynamic" damping terms of the general form 



Ak 2 mVz and Bk 2 mVd (31) 



appear in the work of Korvin-Kroukovsky (1955), as well as in the yet unpublished 

 work of Prof. Abkowitz and Prof. Fay. It is gratifying to see that with regard to these 

 terms the simplified work of these authors is in agreement with the more rigorous 

 mathematical work of Haskind and Havelock. While there is an agreement in regard 

 to the form, the coefficients A and B have different values with each author, and 

 apparently depend on the assumptions made as to the nature of the free boundary and 

 of the ship surface. In particular, comparison of the work of Korvin-Kroukovsky 

 (1955) and of Fay (not yet published) brings out the difference between the assump- 

 tions of cylindrical or conical form for an element of ship length. 



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