A New Appraisal of Strip Theory 



REPLY TO THE DISCUSSION 



L. Vassilopoulos and P. Mandel 



Massachusetts Institute of Technology 



Cambridge, Massachusetts 



* Professor Grim has pointed out that the algorithm we have been using was 

 originally intended to be valid only for the frequency range of waves which se- 

 verely excites pitching and heaving. The new information which he has supplied 

 to us privately has been used by Professor Porter to make the comparisons 

 shown in his discussion, which for normal type ship sections show excellent 

 agreement. There are two main reasons for pursuing comparisons between 

 Professor Grim's work and that of Professor Porter. First, there is the natu- 

 ral urge to make a comparison between two well-founded theoretical approaches 

 to a question; especially in view of the fact that the first section of the paper 

 still showed disagreement between theory and experiment for resonant condi- 

 tions. In this regard Professor Porter's program does indicate higher damping 

 in heave than the 1959 Grim data which was used in the first part of this paper. 

 This would tend to reduce the gap between theory and experiment shown there. 

 Secondly, Professor Porter's approach allows for the effect of changes in ship 

 section shape which is important for sections found at the ends of the ship, 

 whose contribution to pitch damping should be significant. Whether this refine- 

 ment is of importance in the final answer as far as motion amplitudes are con- 

 cerned we do not yet know. At the moment we would point out that Professor 

 Grim's subroutine is very much faster than that of Professor Porter, but the 

 latter program has not as yet been optimized with respect to time consumed in 

 the machine. 



Mr. Gale's contribution supplements the objectives of the first part of the 

 paper. His correlations are related to a family of destroyer forms and hence 

 agreement appears better than in our results because of the wallsidedness of 

 the ship sections in the vicinity of the designed waterline. In the M.I.T. pro- 

 gram, a ship can be defined by any number of sections up to and including 20; 

 nevertheless, it appears that computations using 10 sections yield approximately 

 similar results. With respect to added mass computation, we prefer either the 

 Grim or the Porter data to the Ursell-Prohaska data even though the differences 

 according to Mr. Gale's calculations do not seem to be large. 



The comments of Professor Abkowitz are particularly welcome because he 

 is an acknowledged leader and teacher in the United States in this field. A 

 point on semantics was mentioned by Professor Abkowitz. The differences be- 

 tween the approach of this paper and that of Korvin indicate that the newer ap- 

 proach may be regarded as a "pure strip" theory, whereas the Korvin approach 

 should properly be referred to as a "modified-slender body" theory. The first 

 part of the paper demonstrates the practical utility of the Korvin- Kroukovsky 

 and Jacobs theory. Indeed, this was our primary objective. The fact that we 



'•'See comments by Dyer on paper by Gerritsma and Beukelman, 



405 



