A General Theory for Marine Propellers 



DISCUSSION 



T. Y. Wu 



California Institute of Technology 

 Pasadena, California 



After we have worked for a number of years on a difficult subject such as 

 the general theory of propellers, with more and more untractable problems ac- 

 cumulating in practice, it is always refreshing, and sometimes rewarding, to 

 lean back and take a new look or try a new approach. This paper, I think, offers 

 such a refreshing point of view. It is encouraging to hear the authors' experi- 

 ence that their theory, equipped with the simplifying assumptions they intro- 

 duced, has made the numerical calculations noticeably simpler than the other 

 existing methods. — 



In the case of the linearized theory the difference between the method of ve- 

 locity potential and that of the Prandtl acceleration potential is nothing more than 

 a personal preference, since they always yield the same result. I believe that 

 another linearized theory in terms of a different function, such as the linearized 

 version of the present theory, must bear a definite correspondence with the 

 former two. It should be valuable if Dr. Pien and Dr. Strom- Tejsen could clarify 

 further these correspondences, including the boundary conditions. 



It is in the context of the authors' claim of the exactness and completeness 

 of this theory that I wish to make a minor observation here. If I may put the 

 formulation in a little different way, the relationship between the "exact accel- 

 eration potential" ^ - p/p + q^/2 defined by the authors and the velocity potential 

 X, q = Vx is Simply . , ... ^ , ., ^_^^^. ^ . 



'^^ ^ 



+$ = const . , .■ 



3t 



which is the Bernoulli equation for inviscid, irrotational flows. For steady flows 

 in particular, <l> must be identically a constant and hence cannot be represented 

 by a distribution of singularities. This situation may be changed if the calcula- 

 tion is based on a perturbation of the linear quantities caused by a weak dis- 

 turbance of a moving body, which may be replaced by a force system. Since this 

 theory is new, its potential usefulness can be greatly enhanced when the exact 

 significance of the approximations introduced here is fully understood. 



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