16100lectre44_cj

16100lectre44_cj - Implications of Linearized Supersonic...

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Implications of Linearized Supersonic Flow on Airfoil Lift & Drag To begin, we will divide the airfoil geometry into camber and thickness distributions: ) ( 2 1 ) ( ) ( ) ( 2 1 ) ( ) ( sin cos x x y x y x x y x y j U i u U U c c u τ α = + = + = l v v v Note: The x -axis, which is the axis defined through the leading edge and trailing edge points, is used to define the freestream angle of attack. The chord line is the line connecting . . e i to . . e t and, the chord length is the distance between these points. To calculate the lift and drag, we need to integrate the pressure forces around the airfoil. = airfoil ds n p F v v when n v points out of the airfoil surface. Now, we begin specializing this formula for the assumptions of linearized flow, i.e. (small thickness) (small camber) (small ) The normal on the upper surface is y i x 1 ) ( x y c ) ( x y u ) ( x ) ( x y l 1 1 1 << << << c y c c
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Implications of Linearized Supersonic Flow on Airfoil Lift & Drag 16.100 2002 2 j ds dx i ds dy n j ds dy i ds dx t u u u u v v v v v v + = + = But, since we have thin airfoils dx ds , thus j i dx dy n u v v v l 1 + = Similarly, on the lower surface j i dx dy n v v v l l 1 = Thus, the force may be written: () ∫∫ + = + = = c u c u u cc u u u u dx p p j dx dx
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre44_cj - Implications of Linearized Supersonic...

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