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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
Thin Airfoil Theory Summary 16.100 2002 3 2 2 cos 1 2 sin

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online