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phugoid - Notes on the Control of an Aircraft with Throttle...

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Notes on the Control of an Aircraft with Throttle Only There are a few (rare) examples of flight control system failures that left aircraft with no elevator control. In these cases, pilots have attempted to control the vertical position of the aircraft using thrust changes only. This turns out to be very hard to do, because the resulting dynamics are hard for a pilot to control. Below, we derive the dynamics of an aircraft under those conditions. To simplify the problem, we use the phugoid approxima- tion . In the phugoid approximation, the aircraft is treated as a point mass, and the pitching dynamics of the aircraft are ignored. Furthermore, only the motion of the aircraft in the vertical plane (the longitudinal motions) are considered. The states of the aircraft are then h = altitude of aircraft v = velocity of aircraft (1) γ = flight path angle of aircraft The flight path angle of the aircraft is the angle of the velocity vector with respect to horizontal, with a positive γ indicating that the velocity vector is above the horizon. The dynamics of the aircraft can be fairly easily derived, using only Newton’s laws, and a little aerodynamics. First, find h ˙ , the rate of change of the altitude. h ˙ is determined completely by kinematics, so that h ˙ = v sin γ (2) Next, v ˙ is the rate of change of the velocity vector, which is the acceleration of the aircraft in the direction of the velocity vector, so that T
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