GATE 2022 AE – Question 32
An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio is (round off to two decimal places).
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Correct answer: 5.64 to 5.70
Explanation
For an unpowered glider in steady gliding flight at a glide angle $\gamma$ below the horizontal, the forces along and perpendicular to the flight path give
$$W\sin\gamma=D,\qquad W\cos\gamma=L .$$
Dividing,
$$\frac DL=\tan\gamma\;\Rightarrow\;\frac LD=\frac{1}{\tan\gamma}=\cot\gamma .$$
For $\gamma=10^\circ$:
$$\frac LD=\cot10^\circ=\frac{1}{0.17633}=\mathbf{5.67}.$$