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Homework 3

# Homework 3 - AOE 3104 Homework#3 Solutions Problem 1 An...

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AOE 3104 Homework #3 Solutions Problem 1. An aircraft weighs 12 , 500 N and has a 20 m 2 wing area, an aspect ratio of 6 and efficiency factor e = 0 . 9. If C D 0 = 0 . 02, (a) Calculate the values of the minimum drag force D min and the airspeed for minimum drag V md at standard sea level conditions. (b) Assuming a constant sea level thrust T SL = 5000 N, find the maximum speed V max and minimum speed V min at sea level. (c) Calculate the airspeed for minimum power V mp at standard sea level conditions and the value of minimum power required P req , min . Solution. First, compute the induced drag parameter K = 1 πeAR = 1 π (0 . 9)(6) = 0 . 0589 Because D = W D L = W C D C L in equilibrium, constant-altitude flight, the minimum drag force (at any altitude) is D min = W C D md C L md = W 2 C D 0 radicalbig C D 0 /K = 2 W radicalbig KC D 0 = 858 N and the speed for minimum drag at sea level is V md = radicalBigg 2 W ρSC L md = radicalBigg 2 W ρS 4 radicalbigg C D 0 K = 41 . 9 m / s Next, because this is a constant thrust aircraft, we may compute the minimum and maximum speed from the quadratic equation V 2 = T 0 C D 0 ρS ± radicalBigg parenleftbigg T 0 C D 0 ρS parenrightbigg 2 - 4 KW 2 C D 0 ρ 2 S 2 Given T 0 = 5000 N, we compute V max = 142 m / s and V min = 12 . 3 m / s Of course, the value of V min given above is only a candidate value for the minimum speed, It may be lower than the stall speed of the aircraft, in which case, the given value of minimum speed may not be sustained in equilibrium flight. However, the stall speed can not be computed from the information given; you were not given C L max for this problem.

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