p r o p e r t i e s o f t h e f o r c e d i s t r i b u t i o n p such as t h e behav io r n e a r s u r f a c e edges are b u i l t i n t o t h e approximation by a p p r o p r i a t e cho ice o f t h e func- t i o n s i n t h e s e r i e s.
LATTICE METHOD SERIES
The t r a d i t i o n a l m e t h o d - f o r o b t a i n i n g approxi- mate s o l u t i o n s f o r p when w i s g iven is t o a s s m e a series approximationĪnd t o determine t h e c o e f f i c i e n t s aij by s a t i s f y i n g no rma l -ve loc i ty c o n d i t i o n s on t h e surf_ace. The t h a t t h e i n t e g r a l i n Eq. *At the time of this writing, the authors learned that a similar extension had been developed fnde- u1 = (MR - 2 rl, kl =wrl/U, (1 - n 2 % ) - pendently by Stark.(19) ( 4 ) The linearized formulation of the oscillatory subsonic lifting surface theory relates the normal velocity at the surface Rodemich'') has given a derivation of the kernel function for a nonplanar surface, and Landahl(2) has presented a relatively concise formula:Į-ik1U11R2(1 + u1 2 % ) 1 K = -312 - iklM r 2 Where (x,s) are orthogonal coordinates on the sur- face S such that the undisturbed stream is directed parallel to the x-axis. P(x,s,t) = Re p(w,s) e 1- by a singular integral equation and the Kutta con- dition at the trailing edge (TE): To the pressure difference across the surface
LATTICE METHOD FREE
W Frequency of oscillation P Free stream density
Reduced frequency k =Wb/U Free stream Mach number Number of boxes on a chord Number of boxes on senispanĬomplex amplitude of lifting pressure Complex amplitude of normal velocity at surfaceĬoordinates on the surface Cartesian coordinates The technique constitutes an extension of a method developed by S. Results com- pare closely with those from methods which pre- scribe lift-mode series, and from pressure measure- ments. method obviates the prescription of singularities in lift distribution along lines where normal velocity is discontinuous, and is readily adapted for problems of complex geometries. It is seen 5 posteriori chat the lifting elements and collocation stations can be located such that the Kutta condition is satisfied approximately. The load on each element is determined by satisfying normal velocity boundary conditions at a set of points on the surface. normal velocity induced by an elanent of unit strength is given by an integral of the subsonic kernel function. Northrop Corporation, Norair Division Hawthorne, CaliforniaĪpproximate solutions from the lineariied for- mulation are obtained by simulating the surface by a set of lifting elements which are short line- segments of acceleration potential doublets. Ab5lmct1 moy be published without permiision i f credit is airen to author and lo AIAA. Meeting NEW YORK, NEW YORK/JANUARY 22-24, 1968į l i r t wblicalion rights reserved by American Inflitule of Aeron3uiic1 and Ailronoulics.
RODDEN Northrop/Noroir Hawthorne, California A DOUBLET LATTICE METHOD FOR CALCULATING LIFT DISTRIBUTIONS ON OSCILLATING SURFACES IN SUBSONIC FLOWSĮ.
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