Salve sen 



Last, I should make it clear that my use of the word "true" corresponds to 

 the author's use of "exact," as defined by his footnote. That is, by the "true 

 wave resistance" of the circular cylinder is meant the x component of force on 

 the body in the "exact" potential flow of an inviscid fluid past it, irrespective of 

 whether this flow is a good representation of reality or not. For a circular 

 cylinder there is no question that this flow does not represent reality, but in the 

 present case of a streamlined body there is plenty of evidence to suggest that it 

 is a good approximation. 



It would seem from this fine paper that the mild warnings I gave at the end 

 of my paper have been strengthened a little, and it is now clear that it was not 

 the bluffness of the circular cylinder that caused free-surface nonlinearity to be 

 so important. The question remains —was it the two-dimensionality ? The 

 analogous results for three-dimensional bodies now become even more interest- 

 ing, and I understand some work is being done at Stevens Institute on a sub- 

 merged sphere. If the nonlinear effect persists for submerged three-dimensional 

 bodies, it can hardly be less important for nonsubmerged bodies. 



DISCUSSION 



F. C. Michelsen 



University of Michigan 

 Ann Arbor, Michigan 



It has become increasingly evident that research on second-order wave 

 theories should be increased in magnitude and scope in an attempt to answer 

 some of the basic questions raised when applying the linearized first-order 

 theory to the study of wave resistance of ships. In the past the linear theory 

 has required a major part of our attention. Besides, we may be guilty of some 

 reluctance in tackling the second-order theory because of its complexity when 

 applied to three-dimensional ship shapes. Furthermore, one should demand 

 that basic theoretical results be verified experimentally, which in view of the 

 difficulties in defining the measured wave-resistance of ship models is not par- 

 ticularly encouraging to the researcher contemplating investigations of second- 

 order effects. 



It can be concluded that a much simpler model should be studied, and this 

 is exactly what the author has done. He selected a two-dimensional submerged 

 strut which was shaped in such a way that a flow separation as well as viscous 

 boundary layer would hopefully have a negligible influence on the results. 



Because of close contact with the research described in this paper I find 

 myself at a handicap in the role as a critical reviewer. On the other hand, I do 

 not believe there is much I could have said anyway. Research objectives are 

 well formulated and only in one or two cases does the author express ideas 



632 



