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GATE 2020 AE – Question 56

Flight Mechanics & Space Dynamics · Airplane performance: drag polar, take-off and landing, climb and descent, ceilings, range and endurance, load factor, turning flight, V-n diagram, winds · 2 marks · Numerical answer

A propeller-driven general-aviation airplane cruises at sea level (density 1.225 kg/m³) for maximum range. Its drag polar is CD = 0.025 + 0.049CL² and wing loading is 9844 N/m². Find speed in m/s, to 1 decimal place.

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Correct answer: 149.0 to 151.0

Explanation

For a propeller airplane with the usual constant-efficiency/fuel-consumption model, maximum range occurs at maximum L/D. Thus $C_L=\sqrt{C_{D0}/k}=\sqrt{0.025/0.049}=0.714286$. Lift equilibrium gives $V=\sqrt{2(W/S)/(\rho C_L)}=150.0$ m/s. The maximum-endurance condition would use a different lift coefficient.

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