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16100lectre15_cg

16100lectre15_cg - z Thin Airfoil Theory Summary(x =...

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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 γ by satisfying flow tangency on camber line. 0 ( ) 0 2 ( ) c dZ d V dx x γ ξ ξ α π ξ = 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 higher order 1 2 1 1 ( ) 2 2 ( ) 1 1 2 2 1 2 p p p c V p V u V p V p p V u V V V V V u u V V u u V V V ρ ρ ρ ρ = + + + = + + + = + + + = + = − ± ± ± ± ± ± ± ± ± ± ²³´³µ 2 p u C V = − ± It can also be shown that ( ) ( ) ( ) 2 ( ) lower upper upper lower p p p upper lower x u x u x C C C u u V γ = ⇒ ∆ = = ± ± ± ± ( ) ( ) 2 p x C x V γ = Symmetric Airfoil Solution For a symmetric airfoil (i.e. 0
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