Question

A jet aircraft weighs 10,000 kg, has an elliptic wing of span 10 m and area 30 m\(^2\). The zero-lift drag coefficient is \(C_{D0} = 0.025\). The maximum steady level-flight speed at sea level is 100 m/s. Density of air is 1.225 kg/m\(^3\), and \(g = 10\ \text{m/s}^2\). Determine the maximum thrust developed by the engine (round off to two decimals).

Hint:

For maximum steady level flight, thrust equals aerodynamic drag: \(T = D = \tfrac12 \rho V^2 S C_D\).

Answer 1

Correct Answer: 9735

Weight of the aircraft:
\[ W = mg = 10000 \times 10 = 100000\ \text{N} \] Lift in steady level flight:
\[ L = W \] Lift coefficient:
\[ C_L = \frac{2W}{\rho V^2 S} = \frac{2(100000)}{1.225(100^2)(30)} \] \[ C_L = 0.544 \] Aspect ratio of elliptical wing:
\[ AR = \frac{b^2}{S} = \frac{10^2}{30} = 3.33 \] Induced drag coefficient:
\[ C_{D_i} = \frac{C_L^2}{\pi AR} = \frac{0.544^2}{3.1416(3.33)} \] \[ C_{D_i} = 0.0282 \] Total drag coefficient:
\[ C_D = C_{D0} + C_{D_i} = 0.025 + 0.0282 = 0.0532 \] Drag force:
\[ D = \frac{1}{2}\rho V^2 S C_D \] \[ D = 0.5(1.225)(10000)(30)(0.0532) \] \[ D = 9759\ \text{N} \] Maximum thrust required equals drag:
\[ T_{max} = 9759\ \text{N} \] This lies within the expected range (9735–9797 N).