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In another answer on SE Aviation it is mentioned that the ability to perform Pugachev's Cobra in a non-thrust-vectored aircraft needs "docile pitch behavior of the airframe up to approx. 110° angle of attack"

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Can an F-16 perform Pugachev's Cobra?

What does "docile pitch behavior" mean in this context? Does it mean that when the control surfaces are returned to neutral the aircraft has a natural pitch down moment that returns it to its horizontal position?

If so, does the pilot actually have control over how long he can hold the vertical position in Pugachev's Cobra? What control surface enables him to exercise this authority in the post-stall regime when I'd have assumed the control surfaces lack such authority?

Or is the holding time of the vertical attitude in Pugachev's Cobra beyond the pilot's control and only related to some sort of "natural period" of this maneuver in that aircraft linked to how long it takes the restoring moment to return the aircraft to its nose down attitude?

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"Docile" means no big pitching moments over the angle of attack range. Since the control power with fully stalled control surfaces is rather small, the airframe must not create strong pitching moments, but keep a small pitch-down moment so the airplane returns eventually to normal angles of attack which allow regular flight.

The maneuver is dynamic, so the pilot needs to build up a specific pitch rate. Inertia will keep the aircraft pitching up, and the small pitch-down moment (and aerodynamic damping) will reduce the pitch rate so that the pitch-up stops when the nose is pointing straight up. What follows is the consequence of the small pitch-down moment: The aircraft slowly returns to controlled flight, and once control authority is re-established, the pilot stops the pitching motion.

By selecting the initial pitch rate, the pilot can control the maximum angle of attack, but once he leaves the flight regime of attached flow, he has to wait until inertia and aerodynamics do their part.

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    $\begingroup$ @curious_cat: Yes. There might be more with specific elevator angles post-stall, but in essence that is it. $\endgroup$
    – Peter Kämpf
    Jan 13, 2016 at 8:17
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    $\begingroup$ Also, how come there isn't a lot of altitude loss during the Cobra? Aren't we converting a streamlined, low drag attitude into essentially a large air brake + spoiler? $\endgroup$
    – curious_cat
    Jan 13, 2016 at 8:27
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    $\begingroup$ @curious_cat Your high drag results in a speed loss primarily. $\endgroup$
    – Wirewrap
    Jan 13, 2016 at 8:46
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    $\begingroup$ @curious_cat Don't forget the thrust vector. At the top of the maneuver you're getting esdentially no lift. The engines are maintaining altitude. And I think the loss of airspeed is the whole purpose of the maneuver (besides looking cool). Turns a pursuer into the pursuee $\endgroup$
    – TomMcW
    Jan 13, 2016 at 22:19
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    $\begingroup$ @curious_cat: Elevator post-stall authority is very small. It will produce a drag force that is proportional to its projected area in streamwise direction. Say it is flying at 80° AoA. Rotating the fully-flying tail by -20° to 60° will change the projected area by (sin80°-sin60°)/sin80° = 12%. 12% less drag at the tail will add a small pitch-up increment. $\endgroup$
    – Peter Kämpf
    Jan 13, 2016 at 22:32

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