By E. van Spiegel
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Extra resources for Boundary Value Problems in Lifting Surface Theory
Example text
Oit can easily be derived along the same lines that a a The downwashes WXmcl , which correspond to the potentials y12,,,+, can be determined with the sane method and the result is . a %tl (I+) I 4m+3p 4% 4 m t i (9) . 12 Numerical evaluation of the coefficients i n the linear systems. These formulas read The properties expressed ,by (2,12,1) are well-known and will therefore not be proved here. However, the proof of the formulas (2,12,2) will be given. 2) : 1tx w ,Q (XI= '/a P, (XI% l-x - ,,-,(X) , with -l Hence The last r e l a t i o n h o l d s f o r every downwash d i s t r i b u t i o n W (X,L)) we may conclude t h a t t h e i d e n t i t y (2,7,10) remains v a l i d by omission o f t h e i n t e g r a t i o n over t h e wing s u r f a c e . Thus -8 Determination o f 5% QV,o,s,, i t h e Fourier c o e f f i c i e n t s of the function . I n o r d e r t o be a b l e t o e v a l u a t e t h e F o u r i e r c o e f f i c i e n t s o f the BIW we start w i t h t h e d e r i v a t i o n of t h e f o l l o w i n g theorem: function If U a n d % a r e a r b i t r a r y r e a l o r complex numbers n o t s i t u a t e d on t h e r e a l a x i s between -00 and +1 and i f t h e i n e q u a l i t y ! 0 Sn 5 4, o,i,z, . . 5'' C n S The coefficients p and$' will be evaluated in section 12. The system (2,10,17) represents an infinite set of linear algebraic equations In order to arrive at numerical results for the unknown coefficients an it is necessary to truncate the infinite series in (2,10,17) to get a finite system of linear equations, which can be solved. The mathematical treatment of the anti-symmetric problem follows the same lines as in the symmetric case. The weight-functions @)and %(a) are written in the form .
