GATE 2021 AE – Question 33
A jet aircraft has wing loading 1800 N/m², wing area 30 m², drag polar $C_D=0.02+0.04C_L^2$ and $C_{L,max}=1.6$. For air density 1.225 kg/m³, the speed for maximum endurance in steady level flight at sea level is ___ m/s (two decimals).
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Correct answer: 64.15 to 64.79
Explanation
**Maximum endurance of a jet** occurs at the minimum **thrust required** (minimum fuel flow, which is proportional to the thrust), so the airplane must fly at the maximum value of $C_L/C_D$.
**Maximise $L/D$** with $C_D=C_{D0}+KC_L^2$, $C_{D0}=0.02$ and $K=0.04$:
$$C_L=\sqrt{\frac{C_{D0}}{K}}=\sqrt{\frac{0.02}{0.04}}=0.7071 .$$
**Speed** from $L=W$ in level flight, $\tfrac12\rho V^2C_L=\dfrac WS$:
$$V=\sqrt{\frac{2\,(W/S)}{\rho\,C_L}}=\sqrt{\frac{2\times1800}{1.225\times0.7071}}=\sqrt{4156}=\mathbf{64.47\ m/s}.$$
(Check: $C_L=0.707<C_{L,max}=1.6$, so the airplane can fly at this point.)