Salvesen 



^^^^ = ^^" 2 i;^^ E,(2hsec ^) sec. 



and 



2 



(qj) = e (sec'^^).* . 



-2h sec^e .^^^2 z,n3 



* ♦ * 



REPLY TO DISCUSSION 



Nils Salvesen 



The author is grateful to the discussers for their contributions to this work. 



Mr. Giesing, Dr. Tuck, and Professor Michelsen questioned the assumption 

 of omitting the second-order contributions related to the body-surface boundary 

 condition. These very important second-order contributions have recently been 

 investigated by the author, and the results have now been included in an adden- 

 dum to this paper. 



It is interesting to note that Mr. Giesing predicted in his discussion the 

 importance of the circulation term as mentioned in the author's addendum. 



Dr. van Wijngaarden raises the question of "whether there is also a vertical 

 force on the body and of which order of magnitude." For this symmetrical body 

 at zero incidence the first-order theory will predict no vertical force, while the 

 second-order theory clearly will give a vertical force due to the nonuniform 

 flow caused by the first-order wave system. In this work only the surface waves 

 and the wave resistance were investigated; however, the vertical force can 

 easily be determined from the consistent second-order potential. 



In closing the author would like to express how pleased he was to hear that 

 Dr. Kim at the Davidson Laboratory is now applying Tuck's procedure to the 

 three-dimensional problem of a sphere and that at the University of Michigan 

 one of Professor Michelsen 's students is studying boundary layer effects for the 

 same two-dimensional body treated by the author. 



636 



