Question

An aircraft with twin jet engines has: 
Thrust per engine = 8000 N 
Spanwise distance between engines = 10 m 
Wing area = 50 m\(^2\), Wing span = 10 m 
Rudder effectiveness: \( C_{n_{\delta r}} = -0.002/\text{deg} \) 
Air density at sea level: \( \rho = 1.225 \, \text{kg/m}^3 \) 
The rudder deflection, in degrees, required to maintain zero sideslip at 100 m/s in steady and level flight at sea level with a non-functional right engine is ________ (round off to two decimal places).

Hint:

Engine-out control requires balancing asymmetric thrust moment using rudder aerodynamic moment.

Answer 1

Correct Answer: 6.5

Asymmetric thrust moment:
\[ N_\text{eng} = T \cdot \frac{d}{2} = 8000 \times 5 = 40000 \, \text{N·m} \] Yawing moment from rudder:
\[ N_r = q S b \, C_{n_{\delta r}} \, \delta_r \] Dynamic pressure:
\[ q = \frac{1}{2}\rho V^2 = 0.5 \times 1.225 \times 100^2 = 6125 \, \text{Pa} \] Substitute values:
\[ N_r = 6125 \times 50 \times 10 \times (-0.002)\delta_r \] \[ N_r = -6125 \, \delta_r \] Equilibrium:
\[ N_r + N_\text{eng} = 0 \] \[ -6125 \delta_r + 40000 = 0 \] \[ \delta_r = \frac{40000}{6125} = 6.53^\circ \]