GATE 2023 AE – Question 60
The maximum permissible load factor and the maximum lift force coefficient for an airplane is 7 and 2, respectively. For a wing loading of 6500 N/m2 and air density 1.23 kg/m3, the speed yielding the highest possible turn rate in the vertical plane is ___________ m/s. (round off to the nearest integer)
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Correct answer: 192
Explanation
**Highest possible turn rate** in a vertical-plane (pull-up) manoeuvre occurs at the **corner speed**, where the maximum lift coefficient and the maximum load factor are reached at the same time.
**Load factor at the corner:** $n_{max}=\dfrac{L}{W}=\dfrac{\tfrac12\rho V^2SC_{L,max}}{W}$, so
$$V=\sqrt{\frac{2\,n_{max}\,(W/S)}{\rho\,C_{L,max}}}.$$
**Numbers.** $n_{max}=7$, $W/S=6500$ N/m², $\rho=1.23$ kg/m³, $C_{L,max}=2$:
$$V=\sqrt{\frac{2\times7\times6500}{1.23\times2}}=\sqrt{\frac{91\,000}{2.46}}=\sqrt{36\,992}=192.3\approx\mathbf{192\ m/s}.$$