Question

Long-Period Approximation of Longitudinal Motion (Phugoid)Consider an example aircraft flying at low-speed: ft/s2000=u, assuming unpowered (gliding)flight, and neglecting compressibility effects, with 0.0061 / suX= − and 0.322 / suZ= −. The long-period approximation of aircraft motion yields the following equation:

Find the natural frequency and damping ratio of the system. (note: for unit-consistency, you must expressg in ft/s2).

Long-Period Approximation of Longitudinal Motion (Phugoid) Consider an example aircraft flying at low-speed: 4 = 200 ft/s, assuming unpowered (gliding) flight, and neglecting compressibility effects, with X. =-0.0061 /s and Z. =-0.322 /s. The long-period approximation of aircraft motion yields the following equation: [40] [-2. /u 0140 Find the natural frequency and damping ratio of the system (note: for unit-consistency, you must express g in ft/s).

Answer 1

Co ů - Xudurg AO 3 - (1) DO – Zu Au J - (2) dibeberentiate ea. sü xu. Al-GAO substitute eq. (2) an above süxu. Aů - g (- Zu au sü - Xu su +(9 Zu) AU bürxu Aů - gzy Au=0 0 Zu=-0.322. 10=200 g= 32.2 Xu = -0.0061, Aut0.0061 Au +0.05184 All =0 WA = Jo.05184 = 0.2247 sadls wn = 0.2277 ods 0.0061 = 0.0134 6 = 16 = 0.0134 2 (0.2274)