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MAE305_pset06s

# MAE305_pset06s - M&AE 3050 Problem Set 6 Solution Fall 2009...

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M&AE 3050 Problem Set 6 Fall 2009 Solution 1. An airplane has a wing planform area of S = 60 m 2 , a wing span of b = 24 m, and a gross mass of M = 25 , 000 kg. It is in level, unaccelerated ﬂight, which implies L = Mg at a true airspeed of V = 225 m/s, a density altitude h d = 12 , 500 m, at an air temperature T = 227 K. (a) What is the value of the lift coeﬃcient under these conditions? (b) Assuming the spanwise eﬃciency factor is e = 0 . 95, what is the induced drag? What is the ratio of lift to induced drag? Solution (a) The wing has a planform area S = 60 m 2 , a span b = 24 m and a gross mass of M = 25 , 000 kg. At a density altitude h d = 12 , 500 m, from Appendix B in Anderson, density ρ = 0 . 28837 kg/m 3 . The true airspeed V = 225 m/s and the lift L = Mg . L = C L q S = Mg q = 1 2 ρ V 2 q = 1 2 (0 . 28837)(225) 2 = 7 . 2994 × 10 3 N/m 2 C L = Mg q S C L = (25 , 000)(9 . 81) (7 . 2994 × 10 3 )(60) = 0 . 56 (b) In order to calculate the induced drag D i , we first calculate the induced drag coeﬃcient C D,i , assuming a spanwise eﬃciency factor e = 0 . 95 C D,i = C 2 L πeAR AR = b 2 S = (24) 2 (60) = 9 . 6 C D,i = (0 . 56) 2 ( π )(0 . 95)(9 . 6) = 0 . 0109 The induced drag D i is then D i = C D,i q S D

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