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Midterm 2

Midterm 2 - AOE 3104 Aircraft Performance Exam#2 Solutions...

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AOE 3104 Aircraft Performance Exam #2 Solutions Problem 1. (35 points) The installed sea-level power for a single-engine, propeller-driven aircraft is P A = 80 hp. The nominal weight of the aircraft is W = 2500 lb and the planform area is S = 150 ft 2 . The stall lift coefficient is C L max = 2 . 0. Flight testing has established the power required curve illustrated below. Determine the following: The minimum and maximum speed at sea level. The parameters C D 0 and K (assuming a parabolic drag polar). The maximum climb rate at sea level. The absolute ceiling altitude. 40 60 80 100 120 140 160 180 200 220 240 30 35 40 45 50 55 60 65 70 75 80 Equivalent Airspeed, V eq (ft/s) (Power Required)* σ 1/2 (hp) h G (kft) σ 0 1.0000 5 0.8617 10 0.7386 15 0.6295 20 0.5332 25 0.4486 30 0.3747 35 0.3106 40 0.2471 45 0.1945 50 0.1531 Solution. Part 1 (10 points) The minimum and maximum speed are obtained by find the intersection of power available and power required. Note, however, that the minimum speed, as determined in this way, may be unattainable because the aircraft would stall. In that case, the stall speed is the minimum speed. From the plot, we see that V min 50 ft / s (?) and V max 230 ft / s To check V min , we compute V stall = radicalBigg 2 W ρSC L max 84 ft / s > 50 ft / s so V min = V stall and V max 230 ft / s

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Part 2 (10 points) We can find the minimum power, and the corresponding equivalent airspeed, directly from the plot: P min = (40 hp)(550 (lb ft / s) / (hp)) = 2200 lb ft / s and V mp 125 ft / s We also know that P R = D * V , so P min = D mp V mp = C D mp parenleftbigg 1 2 ρV 2 mp S parenrightbigg V mp = 4 C D 0 parenleftbigg 1 2 ρV 2 mp S parenrightbigg V mp so C D 0 = P min ( 2 ρSV 3 mp ) 1 = 0 . 0158 We also know that W = C L mp parenleftbigg 1 2 ρV 2 mp S parenrightbigg = radicalbigg 3 C D 0 K parenleftbigg 1 2 ρV 2 mp S parenrightbigg so K = 3 C D 0 parenleftBig 2 W ρV 2 mp S parenrightBig 2
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Midterm 2 - AOE 3104 Aircraft Performance Exam#2 Solutions...

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