GATE 2025 AE – Question 52
A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m$^3$, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane's thrust to weight ratio is ______ (rounded off to one decimal place).
| Airplane speed | 80 m/s |
|---|---|
| Lift coefficient, $C_L$ | 0.8 |
| Aspect ratio | 6 |
| Oswald efficiency factor | 0.8 |
| Zero-lift drag coefficient | 0.02 |
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Correct answer: 0.19 to 0.21
Explanation
In a steady climb, $T = D + W\sin\gamma$ with $\sin\gamma = \frac{10}{80} = 0.125$ and $L = W\cos\gamma$. The drag coefficient is $C_D = 0.02 + \frac{0.8^2}{\pi \times 0.8 \times 6} = 0.0624$, so $\frac{D}{L} = \frac{0.0624}{0.8} = 0.078$ and $\frac{D}{W} = 0.078 \times 0.992 = 0.077$. Then $\frac{T}{W} = 0.077 + 0.125 = 0.20$.