Application of Wavemaking Resistance Theory 



DISCUSSION 



K. Eggers 



Institut fUr Schiffbau 



University of Hamburg 



Hamburg, Germany 



I have to make a general remark concerned with the method by which Dr. 

 Pien and other colleagues find hull forms for which certain singularity distribu- 

 tions are considered representative for calculation of wave resistance. 



We know that by the Hess-Smith procedure we can determine source distri- 

 butions on surface of these hull forms, and that wave resistance for such distri- 

 butions then can be calculated along the lines developed in the paper of Breslin 

 and Eng. 



I declare that there is definitely no convincing argument for the assumption 

 that resistance calculations for these alternative singularity distributions should, 

 precise numerical methods assumed, lead to identical values. 



Furthermore, we can create systems of arbitrary high wave resistance, 

 which still generate the same flow around the'double body under infinite gravity, 

 just by proper linear combination of both kinds of distributions ! 



Which wave resistance then is to be considered the 'correct' one, assuming 

 now the form to be given ? We could select the lower limit from the class of all 

 distributions representing the form under infinite gravity and constant speed at 

 infinity. But probably this value is not attained by a single distribution over the 

 whole range of Froude numbers. 



It is easily shown that for any form of nonzero volume there must exist 

 more than one distribution to represent it in infinite fluid. We can, for instance, 

 at any interior point add a source layer of constant strength on a surrounding 

 sphere, compensated by a corresponding sink layer on an exterior concentric 

 sphere such that there is no resulting flow outside. 



In case of a submerged body this will not change the wave resistance. In 

 case of a floating body, however, only the part of the additional system below 

 the undisturbed free surface will contribute within linear theory. The flow due 

 to this lower part only will in general not vanish outside and will thus induce 

 additional waves. 



Take the case of a semi-submerged spheroid. This can be represented by 

 volumetric dipole distributions in any confocal spheroid, equivalent to source 

 layers on the surfaces. As a limiting case we get a line dipole distribution be- 

 tween the foci. This latter gives the largest, i.e., infinite resistance. 



For a singularity distribution found by analytical methods to be optimal 

 within a certain class, we may determine some associated body form by tracing 



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