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# hw5 - 16.100 Homework Assignment 5 Due Wednesday October 12...

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16.100 Homework Assignment # 5 Due: Wednesday, October 12, 9am Reading Assignment Anderson, 3 rd edition: Chapter 5 Section 5.1 – 5.3 All of the reading will be directly useful in the problems. In this homework, we will apply Prandtl’s lifting line to predicting the lift and induced drag of a tapered wing. The wing is symmetric about the root and the planform is shown below: c t y c r b / 2 The airfoil of the wing is symmetric (uncambered). In this homework, we will specifically be looking at the cruise performance of the wing and considering how different taper ratios, r t c c / = σ (in Problem #1), and geometric twist distributions, ) ( y g α (in Problem #2) affect the induced drag. Problem #1: Effect of Taper Ratio and Aspect Ratio (50%) In this problem, we will analyze the impact of taper ratio and aspect ratio on an untwisted, 0 ) ( = y g α . We will assume that the circulation distribution can be well approximated by the first two odd terms (i.e. n=1 and n=3) in the Fourier series expansion: ( ) = = Γ N n n n A bV 1 sin 2 θ θ where θ cos 2 b y = Note: we will only use odd terms as the even terms are asymmetric about .

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