HW7solution

# HW7solution - September 12 version – final corrected...

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Unformatted text preview: September 12 version – final corrected version. AAE 334, Fall 2011, Homework 7 SOLUTION Due Friday, September 9 at the beginning of class. The camber line, , of a thin airfoil of chord length c is given by the piecewise continuous function: ( ) x z c ( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ≤ ≤ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = c x c for c x c x c x for c x c x c x z c 3 . 6 . 4 . 245 9 3 . 6 . 2 . Use the results of thin airfoil theory to solve (to two significant figures) for the: 1. section lift coefficient for flight at 4 degrees angle of attack. 2. pitching moment coefficient about the quarter-chord point for flight at 4 degrees angle of attack. 3. The zero-lift angle of attack in degrees. Show your work neatly with sufficient explanations of your method. Results of thin airfoil theory to use are: ( ) ( 1 2 2 L l A A c ) α α π π − = − = ( ) 1 2 4 / , 4 A A c c m − = π So to compute , , and , you need the slope of the camber line, A 1 A 2 A dx dz c : ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ≤ ≤ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = c x c for c x c x for c x dx dz c 3 . 2 6 . 245 9 3 . 2 6 . 2 . Transform to o θ and combine terms: ( ) ( ) [ ] ( ) ( ) [ ] ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ≤ ≤ − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = c for for dx dz o o o o o o c θ θ θ θ θ θ θ θ 1 1 cos 1 6 . 245 9 cos 1 2 1 2 6 . 245 9 cos 1 2 . 12 . cos 1 2 1 2 6 . 2 ....
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## This note was uploaded on 02/21/2012 for the course AAE 334 taught by Professor Collicott during the Fall '09 term at Purdue.

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HW7solution - September 12 version – final corrected...

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