Investigation of effect of altitude on longitudinal modes of aircraft

In this work, aircraft oscillating motion in longitudinal axis has been analyzed. Aircraft like other dynamic systems have some damping properties to kill the disturbance from its equilibrium position. If aircraft is underdamped, it will have some oscillations (to and fro motion) about its equilibrium position. In longitudinal motion of an aircraft these oscillations are of two mode types, one with very long time periods (order of 30 sec or more) called long period or phugoid mode and the second with short time period called short-period mode. Previously on this topic work has been done in finding the longitudinal modes response with constant altitude assumption. In this study, effect of varying the altitude has been analyzed on longitudinal modes of aircraft. As, this study will be necessary to design autopilot for aircraft flying in a range of altitude. Aircraft has been considered as rigid body, equations of motion have been developed by Newton's second law. These non-linear differential equations have been linearized by Small Disturbance Theory. Different assumptions have been used for solving the equation of motion. Computer code has been utilized to find eigen values for exact solution and effect of variation of altitude has been plotted for three different aircrafts. Moreover, different longitudinal approximations have been utilized to find damping ratio and frequency of oscillation for a fighter jet and a transport jet aircraft. Increasing altitude has very significant effect at high speeds (higher Mach no), and has less effect at low speed. Moreover, phugoid mode is more sensitive to altitude variation then short period mode. This work will be helpful for predicting the stability of aircraft and designing aircraft autopilot. In future more work should be done on the compressibility effects and engine thrust variation.