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hw07_solutions

# hw07_solutions - AA311 Atmospheric Flight Mechanics Autumn...

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AA311 - Atmospheric Flight Mechanics Autumn 2010 University of Washington Homework 7 Solutions Problem 1 We can plot the data. From this we see that the drag polar should be described by C D = C D ,0 + C L 2 p e AR Note that we can write this as y = a 1 x 2 + a 2 x + a 3 where y = C D x = C L We can fit a second order polynomial to the data using @ P D = polyfit H C L , C D , 2 L . We then see that the constant a 1 should have the relationship that a 1 = 1 p e AR e = 1 a 1 p AR Furthermore, the constant a 3 should be C D ,0 a 3 = C D ,0 AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students

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So we see that C D ,0 = 0.025 e = 0.8 2 hw07_solutions.nb Printed by Mathematica for Students
Problem 2 Part a. See CalculateLineIntersections.m Part b. The result for the first set of data is shown below As can be seen, this correctly finds the three intersection points with good accuracy. The result for the second set of data is shown below hw07_solutions.nb 3 AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students

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As can be seen, if the mesh is less fine, the accuracy of the function degrades. The result for the third set of data is shown below As can be seen, if the lines do not intersect, the function returns empty vectors. 4 hw07_solutions.nb Printed by Mathematica for Students
Problem 3 From the problem statement, we have W = 38 220 N S = 27.3 m 2 AR = 7.5 e = 0.9 C D ,0 = 0.03 V = 350 km hr 1000 m km ÿ hr 60 min ÿ min 60 sec = 97.2 Å m s W = 38 200; S = 27.3; AR = 7.5; e = 0.9; CD0 = 0.03; Vinfty = 350 1000 1 1 60 1 60 ; We can obtain the conditions at sea level from Appendix A r = 1.225 kg ë m 3 ρ infty = 1.225; We can calculate the dynamic pressure q = Å 1 2 r V 2 qinfty = 1 2 ρ infty Vinfty 2 5789.45 The lift must equal the weight at straight and level flight C L = W q S CL = W qinfty S 0.241693 So the total drag coefficient is given by C D = C D ,0 + C L 2 p e AR hw07_solutions.nb 5 AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students

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CD = CD0 + CL 2 π e AR 0.0327547 So the thrust required is given by Eq.6.16 T R = W C L ê C
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hw07_solutions - AA311 Atmospheric Flight Mechanics Autumn...

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