GATE 2023 AE – Question 59
An airplane with wing planform area of 20 m2 and weight 8 kN is flying straight and level with a speed of 100 m/s. The total drag coefficient is 0.026 and the air density is 0.7 kg/m3. The total thrust required to introduce a steady climb angle of 0.1 radians is ____ N. (round off to the nearest integer)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2619
Explanation
**Step 1: drag in level flight.** At $V=100$ m/s with $\rho=0.7$ kg/m³, $S=20$ m² and $C_D=0.026$:
$$D=\tfrac12\rho V^2SC_D=0.5\times0.7\times100^2\times20\times0.026=1820\text{ N}.$$
**Step 2: steady climb.** Along the flight path, the thrust must balance the drag plus the component of the weight along the path:
$$T=D+W\sin\gamma .$$
With $W=8000$ N and $\gamma=0.1$ rad (so $\sin\gamma=0.0998$):
$$T=1820+8000\times0.09983=1820+798.7=2618.7\approx\mathbf{2619\ N}.$$
(Using the same speed and drag coefficient for the climb is the approximation made in the problem.)