Distribution of Hydrodynamic Forces on a Shipmodel 



DISCUSSION OF THE PAPERS BY GERRITSMA AND 

 BEUKELMAN AND BY VASSILOPOULOS AND MANDEL 



T. R. Dyer 



Technological University 

 Delft, Netherlands 



The paper by Vassilopoulos and Mandel rigorously examined seakeeping 

 theory, with valuable emphasis on practical ship design. The paper by Gerritsma 

 and Beukelman contains significant experimental results and a clear concise 

 strip theory, thus relating theory and physical phenomena. However, the paper 

 by Vassilopoulos and Mandel agrees only partially with Gerritsma and Beukel- 

 man, and with Korvin-Kroukovsky. 



The papers were examined by this discusser with the following results: 



1. Complete agreement exists as to (a) which motion derivatives appear in 

 each coefficient, and (b) the appearance of velocity dependent terms arising 

 purely from the mechanics of a fixed axis system. 



2. Disagreement exists as to the importance of the effect of forward speed 

 on strip theory, but this is the only point of disagreement. 



This disagreement led to different evaluations of some motion derivatives. 

 Direct comparison of the coefficients in the two papers does not reveal all dis- 

 agreement, because of the cancellation of terms due to strip theory by terms 

 due to the mechanics of a fixed axis system. The disagreement in the strip the- 

 ory specifically arose in two ways: (1) Gerritsma and Beukelman consider sec- 

 tional added mass to be a function of time, as suggested by Korvin-Kroukovsky. 

 This is a "three-dimensional correction" and is justified experimentally by a 

 velocity dependence in the b' term for the three-dimensional end sections of 

 Gerritsma and Beukelman's model. (2) Gerritsma and Beukelman consider the 

 distance x, between the body axis origin and the hypothetical sheet of water, to 

 be a function of time. This is independent of dimensionality. The second differ- 

 ence is confusing; for Vassilopoulos and Mandel do implicitly take x as function 

 of time when converting from movable to fixed axes, but do not when applying 

 the strip theory. 



The strip theory of Gerritsma and Beukelman was re-derived, eliminating 

 these disagreements. The results agreed completely with those of Vassilopoulos 

 and Mandel. Application of integrals quoted by Gerritsma and Beukelman showed 

 agreement between that paper and Korvin-Kroukovsky. This therefore showed 

 no errors in Korvin-Kroukovsky' s work, only disagreement with Vassilopoulos 

 and Mandel as to the role of forward speed on the strip theory. Conversion of 

 Gerritsma and Beukelman results to a movable axis system revealed no diffi- 

 culties, but clearly showed which speed terms result from mechanics and which 

 from strip theory. 



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