Question

For the jet aircraft data provided, the speed for maximum endurance in steady level flight is \(\underline{\hspace{1cm}}\) m/s (round off to two decimal places).

Hint:

Maximum endurance for jet aircraft occurs at the condition of minimum drag, which corresponds to \( C_L = \sqrt{C_{D_0}/k} \).

Answer 1

Correct Answer: 64.3

Maximum endurance occurs at minimum power required, which for a jet aircraft occurs at minimum drag:
\[ C_D = C_{D_0} + k C_L^2 \] Given:
\(C_{D_0} = 0.02\), \(k = 0.04\), \(C_{L,\max}=1.6\)
Wing loading: \(W/S = 1800\), density \(\rho = 1.225\), wing area \(S=30\).
Lift in level flight:
\[ L = W \] So,
\[ C_L = \frac{2W}{\rho V^2 S} \] For minimum drag:
\[ C_L = \sqrt{\frac{C_{D_0}}{k}} = \sqrt{\frac{0.02}{0.04}} = \sqrt{0.5} = 0.707 \] Now compute velocity:
\[ V = \sqrt{ \frac{2W}{\rho S C_L} } \] Aircraft weight:
\[ W = (W/S)\, S = 1800 \times 30 = 54000\,\text{N} \] \[ V = \sqrt{\frac{2\times 54000}{1.225 \times 30 \times 0.707}} \] \[ V = \sqrt{\frac{108000}{25.957}} = \sqrt{4161.1} = 64.5\text{ m/s} \] Rounded to two decimals:
\[ V = 64.50 \text{ m/s} \]