GATE 2021 AE – Question 34
A twin-engine airplane at 100 m/s and density 1.225 kg/m³ has S=50 m², b=10 m, engine thrust 8000 N and lateral engine arm 5 m. Right engine fails. With $C_{n_{\delta_r}}=-0.002$ per degree, the rudder deflection needed to balance yaw is ___ degrees.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 6.50 to 6.56
Explanation
If the right engine fails, the left engine's thrust $T=8000$ N acts at a lateral distance $y=5$ m from the centreline and produces a **yawing moment**:
$$N_{engine}=T\,y=8000\times5=40\,000\text{ N m}.$$
The rudder must produce an equal and opposite moment, $N_{rudder}=q\,S\,b\,C_{n_{\delta_r}}\delta_r$.
**Dynamic pressure:**
$$q=\tfrac12\rho V^2=0.5\times1.225\times100^2=6125\text{ Pa}.$$
**Balance:**
$$\delta_r=\frac{40\,000}{q\,S\,b\,|C_{n_{\delta_r}}|}=\frac{40\,000}{6125\times50\times10\times0.002}=\frac{40\,000}{6125}=6.53^\circ .$$
The required rudder deflection is **6.53°** (the sign only shows the direction).