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Ae311_fall_2011_hw_6

# Ae311_fall_2011_hw_6 - Prof Daniel J Bodony AE311 Fall 2011...

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Prof. Daniel J. Bodony AE311, Fall 2011 HW #6 Due 5 pm Wednesday, November 30, in the AE311 dropbox Problem 1 In thin airfoil theory we showed in class that the circulation distribution γ ( θ ) could be written as γ ( θ ) = - 2 U A 0 1 + cos θ sin θ + summationdisplay n = 1 A n sin( n θ ) where the airfoil has chord c , lies between x = 0 and x = c and the coordinate θ was related to x by x = c 2 (1 - cos θ ) . If the airfoil camber line is y = η ( x ) then the coe ffi cients A i are given by A 0 = α - 1 π π integraldisplay 0 d η d x ( θ ) d θ, A n = 2 π π integraldisplay 0 d η d x ( θ ) cos( n θ ) d θ n = 1 , 2 , . . . From these definitions, show that (a) The net circulation Γ = c integraltext 0 γ ( x ) d x is Γ = - U c π parenleftbigg A 0 + A 1 2 parenrightbigg (b) The lift is L = ρ U 2 c π ( A 0 + A 1 / 2). (c) The sectional lift coe ffi cient is c = 2 π ( A 0 + A 1 / 2). (d) The sectional lift coe ffi cient can be written c = 2 π ( α - α ZL ). What is α ZL in terms of η ( x )?
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