A general-aviation airplane at stable low-angle cruise has phugoid eigenvalues −0.02 ± i0.25 s⁻¹. With g = 9.8 m/s², find equilibrium speed in m/s, to 2 decimals.
The undamped modal frequency is the magnitude of an eigenvalue: $\omega_n=\sqrt{0.02^2+0.25^2}=0.25080$ s⁻¹. The approximate phugoid relation is $\omega_n=\sqrt2g/V$. Hence $V=\sqrt2(9.8)/0.25080=55.26$ m/s. Using only the imaginary part would use damped frequency instead of natural frequency.
More Special topics: Equations of motion, Euler angles, longitudinal and lateral-directional modes, Hohmann orbital transfers questions
GATE 2019 AE Q19– Which response shown in the figure represents a dynamically unstable airplane?
GATE 2024 AE Q62– For a general aviation airplane, one of the complex conjugate pair of eigenvalues for…
GATE 2023 AE Q24– Which one of the following figures represents the qualitative variation of absolute…
GATE 2022 AE Q45– For a conventional airplane in straight, level, constant velocity flight condition, which…
GATE 2021 AE Q44– Which aircraft dynamic-stability statements are correct?