HW8 - 1 4 mc c 1 L α 1 cp x 2 l c 2 4 mc c 2 L and Show...

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AAE 334, Fall 2011, Homework 8 Due Monday, September 12 at the beginning of class. 1. Show mathematically the effects of scaling airfoil camber on lift coefficient, quarter- chord moment coefficient, and center of pressure at the same angle of attack? That is, if one airfoil has camber of and another has camber of ( ) x z c ( ) x z a c where a is a positive constant, how do the lift coefficients, quarter-chord moment coefficients, and centers of pressure compare? Call the results for the first airfoil , , and . 1 , l c 1 , 4 / mc c 1 , cp x 2. Similarly, what if you add together two cambers, ( ) ( ) x z x z c c 2 1 + which individually have performance or characteristics , , 1 , l c 1
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Unformatted text preview: 1 , 4 / mc c 1 , L α , , , , 1 , cp x 2 , l c 2 , 4 / mc c 2 , L , and . Show what can you determine regarding the new values of , , 2 , cp x l c 4 / mc c L , and ? cp x Note: in recent years some students would assume a function for ( ) x z c and demonstrate the effects of one specific case. This falls far short of the goal here – proving the impact of changes for all camber lines. Thus you are to work with the unknown and very general , not one example of . You do, however, assume that all airfoils under consideration satisfy the assumptions for thin airfoil theory. ( ) x z c ( ) x z c...
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