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Homework #7

Homework #7 - AOE 3104 Homework#7 Solutions Problem 1 Wind...

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AOE 3104 Homework #7 Solutions Problem 1. Wind tunnel tests yield the following data for lift coefficient and pitch moment coefficient about the half chord line of a given wing: ¯ α (deg) C L C m 1 / 2 -4.0 -0.257 0.149 -2.0 0.030 0.084 0.0 0.194 0.062 2.0 0.210 0.020 4.0 0.540 -0.033 6.0 0.752 -0.066 Using the software of your choice (e.g., Matlab or Excel), determine C L α ) and C m 1 / 2 α ) using a linear least squares fit. Plot the data and the curve fits. Determine h ac and C m ac . -4 -2 0 2 4 6 8 10 -0.5 0 0.5 1 1.5 C L -4 -2 0 2 4 6 8 10 -0.2 -0.1 0 0.1 0.2 α (deg) C m Figure 1: Least squares fits for C L α ) and C m α ) versus ¯ α . Solution. Using Matlab’s polyfit and polyval functions, one may obtain the plots shown in Figure 1. The data fits suggest that C L α ) = 0 . 136 + 0 . 093 ¯ α (1) C m 1 / 2 α ) = 0 . 0582 - 0 . 0197 ¯ α. (2) The neutral point can be found by differentiating the identity C m 1 / 2 = C m ac + C L ( h 1 / 2 - h ac )

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with respect to ¯ α and solving for h ac : h ac = h 1 / 2 - 1 C L α parenleftbigg ∂C m 1 / 2 ¯ α parenrightbigg = 1 2 - - 0 . 0197 0 . 093 0 . 711 The easiest way to find C m ac is to solve (1) for ¯ α 0 L and substitute into (2). Doing so gives
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Homework #7 - AOE 3104 Homework#7 Solutions Problem 1 Wind...

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