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On the ‘inverse phugoid problem’ as an instance of non-linear stability in pitch

Published online by Cambridge University Press:  04 July 2016

L. M. B. C. Campos  and
A. J. N. M. Aguiar
L. M. B. C. Campos
Affiliation:
Instituto Superior Técnico, 1096 Lisboa Codex, Portugal
A. J. N. M. Aguiar
Affiliation:
Instituto Superior Técnico, 1096 Lisboa Codex, Portugal
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Summary

The motion of an aircraft along a straight flight path inclined to the vertical is considered from an arbitrary initial velocity which may be far from steady flight speeds. The velocity and incidence, as a function of distance or time, provide a solution to the ‘inverse phugoid problem’ of finding the control laws that keep an aircraft on a straight flight path by exactly cancelling the phugoid instability (the short period mode is omitted by neglecting the rotational inertia of the aircraft). This is a non-linear problem, namely finding the motion of an aircraft from an initial condition far removed from a stable steady state, or finding the large amplitude deviations from an unstable equilibrium. The stability and instability problems are solved analytically using the following assumptions:

  1. (i) the aircraft flies subsonically so that only form and induced drag need be considered;

  2. (ii) the thrust consists of a constant term, minus a term specifying a dependence on velocity similar to that of the total drag; and

  3. (iii) the aircraft incidence is away from stall so that lift is a linear function of incidence.

The response curves show that:

  1. (i) flight at velocities below the lower steady flight speed, which is unstable, is difficult to maintain due to fast divergence towards the stall; and

  2. (ii) for an initial velocity above the lower steady flight speed, there is convergence towards the higher steady flight speed.

The convergence, in the latter case (ii), may be slow along a straight flight path, although it can be hastened by suitable manoeuvres.

Type
Research Article
Information
The Aeronautical Journal , Volume 93 , Issue 927 , September 1989 , pp. 241 - 253
Copyright
Copyright © Royal Aeronautical Society 1989 

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