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5 Answers

Phugoid and Angle of Attack

Asked by: 3788 views ,
Aerodynamics

Why does the angle of attack remain nearly constant as a phugoid mode oscillation progresses?  I've seen the plots showing this to be true, but don't have a good way of explaining analytically or physically why this is the case, other than that "it's what the equations say will happen."  I understand that, in steady state/equilibrium, a fixed elevator position corresponds to a given angle of attack.  But why should the AoA also stay constant during the oscillatory part of the phugoid before steady state is reached?  

P.S. The only progress I've made so far is to try to identify the ways that AoA can be changed (which I understand to be via pitch and flight path angle) and to understand how these change during the phugoid.  The pitch certainly oscillates during a phugoid, and so does the flight path angle due to the oscillating vertical speed.  But why should these effects necessarily cancel each other out, as would seem to be required for us to observe the constant AoA behavior in the phugoid?

(I ask about this in order to more generally understand why AoA and power control airspeed and vertical velocity, respectively, in the way they do.)

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5 Answers



  1. Nathan Parker on Jul 14, 2012

    The AoA remains constant during a phugoid because the elevator/horizontal stabilizer causes the airplane to weathervane into the relative wind.  Sure, if you were to look at things millisecond by millisecond, you’d see brief changes in AoA until the static longitudinal stability asserts itself, but a pure phugoid is devoid of such things, by definition.  All real airplane oscillations will be a combination of phugoid and short period pitching oscillation, although the latter is well damped in our little airplanes.
     
    And you’re right, this is related to how AoA controls airspeed, since the airplane goes through a phugoid when the AoA is changed at a particular airspeed.

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  2. Dan Bernard on Jul 14, 2012

    Thanks, Nathan.  I understand how the weathervaning occurs by virtue of the aircraft’s positive static stability (an increase in AoA leads to a pitch down moment).  Why does this explain how the AoA remains nearly the same, though?  Is any AoA change during the phugoid is so small and gradual that it is simultaneously/immediately accompanied by a pitch change of the same magnitude in the opposite direction, canceling out the AoA change?  It seems like “things” would need to work out just right for this to be the case (or maybe not, since the period of a phugoid is relatively long and changes occur slowly?).
    The particular example I had in mind is an aircraft trimmed for straight and level, steady flight being given a sudden addition of thrust.  Ignoring any pitching moments from thrustline or propwash effects, the aircraft accelerates forward, speed increases, lift goes up, and the aircraft accelerates upward.  The new upward aircraft velocity causes the AoA to change.  So the idea is that this (small) AoA change is immediately cancelled by a change in the pitch due to static stability?

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  3. Nathan Parker on Jul 14, 2012

    “So the idea is that this (small) AoA change is immediately cancelled by a change in the pitch due to static stability?”
     
    Yes.  The nose up moment produced by small AoA changes on the main wing and horizontal stabilzer is presumed to be instantaneous.  If it isn’t, the aircract has a short period mode intermingled with the long-period mode (phugoid), as would be the case in real life.  A pure phugoid is an idealization.
     
    (I’d be careful about using pitch in this way…pitch is typically used to define the angle of the longitudinal axis with the horizon, whereas here we mean a positive pitching moment or nose up moment.)
     

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  4. Brian on Jul 17, 2012

    ” I understand how the weathervaning occurs by virtue of the aircraft’s positive static stability (an increase in AoA leads to a pitch down moment). Why does this explain how the AoA remains nearly the same, though?”
     
    The underlined answer’s to your question. The nose down pitching moment, in scientifically perfect world, will exactly match the disturbance and leave no resultant change in AOA. Keep in mind, this discussion is predicated on an ideal. An ideal that will never be reached in a real world scenario, but instead is defined merely to simplify analysis for those engineering the aircraft.
     
    Nathan, does stick fixed vs stick free stability make any difference. Or does the definition of phugoid remain unchanged. I was just reading in “Mechanics of Fligt” how the aerodynamic center takes on a less restrictive definition to account for aerodynamic nonlinearities. (Page 458) Instances like this make me wonder if, a the calculation process evolves, definitions like the traditional long period oscillations talked of here take on less restrictive form to adapt. Any insights?

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  5. Brian on Jul 17, 2012

    ” positive static stability (an increase in AoA leads to a pitch down moment)”
     
    Sorry, apparently underlining doesn’t work. This is the sectin of our quote that was supposed to be underlined, and is the answer to your question that follows.

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