Lifting -Surface Theory 



The questions which now rise are 



1. What is the use of this computer program for design purposes? 



2, What kind of improvement is desirable for improvement of its applica- 

 bility and which effects would be expected to be included in the near future ? 



Professor Weissinger (Technische Hochschule Karlsruhe) gives a contribu- 

 tion on the improvement of the treatment of the singularity in lifting- surface 

 theory. [M. Borja and H. Brakhage, Z.F.W. 16 (1968), pp. 349-356]: 



a(x,y) 



4-V Jj (y-y' 



1 + 



(x-x')2 + (Y-y')2 



k(x',y')dx'dy' 



where a (x,y) is the local angle of attack and k the vorticity on the lifting sur- 

 face. Through partial integration, the equation is transformed into 



^('^•y) '- 4^1/ 



(x-x') + [(x-x')2 + (y-y')2] 

 (x-x') (y-y') 



ky' (x',y')dx'dy' , 



where the form for the kernel 



Kp(x,x'xy,y') 

 (x-x') (y-y') 



is essential for the method. 



Introducing Glauert coordinates x'. - -cosi9'., x. = -cosi?. 



(2j-l)77 



N 



!?• = 21 — , n - 

 ^ N 



N + 1 



, j = l(l)n, i = l(l)n -1 



or 



^■> - ^-^ — , &. = (2i-l) — , n 



N + 2 



where the first set of points are pivot points and the second set are collocation 

 points. 



These configurations give the approximation formulas 



u(x') dx' 2 -^ "(^'j' ) 



J_ r ' U(x') dx' ^ y. "'-^i' > 



1 r' dx' 2 V" 



u(x') = - 2. "(^j' ) , 



1594 



