GATE 2022 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 conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at a constant speed of 100 m/s at sea level. Taking the acceleration due to gravity as 10 m/s2, the bank angle of the airplane is degrees.

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Correct answer: 45

Explanation

**Level turn.** In a coordinated level turn at bank angle $\phi$, the lift has a vertical component that balances the weight and a horizontal component that supplies the centripetal force:
$$L\cos\phi=W,\qquad L\sin\phi=\frac{WV^2}{gR} .$$

Dividing,
$$\tan\phi=\frac{V^2}{gR} .$$

**Numbers.** $V=100$ m/s, $R=1000$ m, $g=10$ m/s²:
$$\tan\phi=\frac{100^2}{10\times1000}=\frac{10\,000}{10\,000}=1\;\Rightarrow\;\phi=\mathbf{45^\circ}.$$

(The mass of 5000 kg cancels out.)