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Unformatted text preview: AA311  Atmospheric Flight Mechanics Autumn 2010 University of Washington Homework 6 Solutions Problem 1 Part a. We can first convert to consistent, metric units F14 S = 54.5 m 2 W = 52 000 lbf 4.44822162 N 1 lbf = 231 308 N F E i = 27 800 lbf 4.44822162 N 1 lbf = 123 661 N i = 1, 2(thrust from engines) Runway d = 300 ft 1 m 3.2808399 ft = 91.44 m AA311  Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students S = 54.5 W = 52 000 H 4.44822162 L FE1 = 27 800 H 4.44822162 L FE2 = FE1; d = 300 1 3.2808399 20 54.5 231 308. 123 661. 91.44 Part b. If we assume that there is no difference between infinite and finite wings, we can use Appendix D with the c l vs. a curve for flaps of standard roughness to see that at a = c l = C L = 1.4 CL = 1.4; We require the lift to equal the weight in order to not lose altitude at the end of the runway W = L = C L q S recall: q = 1 2 r V 2 = C L I 1 2 r V 2 M S V = J 2 W r S C L N 1 2 where r = 1.225 kg m 3 (standard sealevel conditions) 2 hw06_solutions.nb Printed by Mathematica for Students infty = 1.225; Vinfty = 2 W infty S CL 1 2 70.3525 So we see that we require V = 70.35 m s 157 mi hr Part c. We can draw a free body diagram of the aircraft So the forces on the aircraft are / F = F E 1 + F E 2 + F C where F E 1 = thrust from engine 1 (123661 N) F E 1 = thrust from engine 2 (123661 N) F C = thrust from catapult So the acceleration experienced is given by / F = m a a = F E 1 + F E 2 + F C m note: m = W g a = F E 1 + F E 2 + F C W g (Eq.1) We note that the acceleration is constant because all terms on the right hand side are assumed to be constant We can obtain the velocity as a function of time using V H t L = t a H t L t + V H L note: a H t L = a hw06_solutions.nb 3 AA311  Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students V H t L = a t + V H L (Eq.2) We can find the position as a function of time by integrating Eq.2 p H t L = t V H t L t + p H L = t a t + V H L t + p H L p H t L = 1 2 a t 2 + V H L t + p H L (Eq.3) We now would like to find the time T when the aircraft reaches the end of the runway. We assume that the aircraft starts at rest V H L = 0 and at the back of the runway p H L = p H T L = d 1 2 a T 2 + V H L T + p H L = d recall: V H L = p H L = 1 2 a T 2 = d T = I 2 d a M 1 2 (Eq.4) We know that at t = T , we require that V H T L = V V H T L = V a T + V H L = V recall: V H L = a T = V recall: T = I 2 d a M 1 2 from Eq.4 a I 2 d a M 1 2 = V H 2 a d L 1 2 = V recall: a = F E 1 + F E 2 + F C W g from Eq.1 J 2 J F E 1 + F E 2 + F C W g N d N 1 2 = V 2 J F E 1 + F E 2 + F C W g N d = V 2 F E 1 + F E 2 + F C = W g V 2 2 d F C = W g V 2 2 d F E 1 F E 2 4 hw06_solutions.nb Printed by Mathematica for Students where g = 9.81 m s 2 g = 9.81; FC = W g Vinfty 2 2 d FE1...
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