hw08_solutions

# Hw08_solutions - V Â The resulting plot is shown below AA311 Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students Part

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AA311 - Atmospheric Flight Mechanics Autumn 2010 University of Washington Homework 8 Solutions Problem 1 Part a. Finding the Rate of Climb First, we seek the maximum climb angle possible, q max . Finding this requires finding where the power available equals the power required for climb. P R , c H V , q L = P A H V L where P R , c H V , q L = V K Å 1 2 S V 2 r K C D ,0 + 4 W 2 cos H q L 2 AR e p S 2 V 4 r 2 O + W sin H q LO (Eq.B.2) P A H V L = h P However solving this for q is difficult analytically, so we propose a numerical solution. 1. Determine P A H V L (how power available is a function of V ) 2. Pick a value of V = V ,curr 3. Plot the function P R , c I V ,curr , q M vs. q 4. Plot P A I V ,curr M vs. q (should be a straight line since this is simply the power available at V ,curr and is not a function of q ) 5. Determine where the two plots intersect, this is q max 6. Obtain RoC = V ,curr sin H q max L This can be repeated for various

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Unformatted text preview: V Â¶ The resulting plot is shown below. AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students Part b. With knowledge of the maximum climb angle, the rate of climb is given by RoC = V Â¶ sin H q max L We can compare this with Eq.6.50 which is an approximation of rate of climb. The results are shown below 2 hw08_solutions.nb Printed by Mathematica for Students As can be seen, Eq.6.50 is a good approximation at low climb angles. hw08_solutions.nb 3 AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students Problem 2 Not applicable. 4 hw08_solutions.nb Printed by Mathematica for Students...
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Hw08_solutions - V Â The resulting plot is shown below AA311 Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students Part

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