16100lectre15_cg

16100lectre15_cg - z Thin Airfoil Theory Summary(x = thickness z(x = camber line x c Replace airfoil with camber line(assume small c z z(x = camber

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Thin Airfoil Theory Summary Replace airfoil with camber line (assume small c τ ) Distribute vortices of strength ) ( x γ along chord line for 0 x c . Determine ) ( x by satisfying flow tangency on camber line. 0 () 0 2( ) c dZ d V dx x γξ ξ α πξ  −− =   The pressure coefficient can be simplified using Bernoulli & assuming small perturbation: x z c τ (x) = thickness z(x) = camber line x z c z(x) = camber line x z c γ (x)dx
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Thin Airfoil Theory Summary 16.100 2002 2 {} 2 22 2 2 2 2 2 2 higher order 1 2 11 () 1 1 2 2 1 2 p pp c V p Vu V p V V u V V V VV u u V V uuV ρ ∞∞ = ++ + = + −+ + ⇒= + =− + ± ± ± ± ± ±± ± ²³´³µ 2 p u C V ± It can also be shown that 2 lower upper upper lower p p p upper lower xu x CC C u u V γ ⇒∆ = = () 2 p x Cx V Symmetric Airfoil Solution For a symmetric airfoil (i.e. 0 dz dx = ), the vortex strength is: θ α sin cos 1 2 ) ( + = V But, recall: (1 cos ) 2 c x
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Thin Airfoil Theory Summary 16.100 2002 3 2 2 cos 1 2 sin
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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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16100lectre15_cg - z Thin Airfoil Theory Summary(x = thickness z(x = camber line x c Replace airfoil with camber line(assume small c z z(x = camber

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