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I've found pictures and videos of jets rotating 90 degrees so that one wing points straight down to the ground and the other is straight up, then they suddenly turn away from their course while remaining in that position.

Here's a video of that maneuver (link goes to 2:10).

What are the aerodynamics that can make this kind of turn possible? In a lot of YouTube videos this type of turn happens after aerial refueling. Is this type of turn possible on a large airliner, and if it is, when do pilots of this airliner ever use this method in flight?

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The maneuver is called a "breakaway maneuver" or simply a "break", it's also sometimes colloquially referred to as "peeling off" in the context of aircraft leaving formation. You can see it more clearly in this video:

This is a standard maneuver used when disengaging from a intercepted target, or as a way to safely exit formation flight ensuring that the departing aircraft is clear of the rest of the formation group.
It also has tactical advantages as seen in the photo you posted (when being tracked by an infra-red/heat-seaking missile, dropping flares and a hard breakaway is one technique used to convince the missile that the flare is actually your engine, by getting your real heat source out of its "line of sight" quickly).


Aerodynamically the breakaway maneuver is nothing more than a steep turn: Roll the aircraft into the desired bank, setting power and pitch up to maintain your altitude and airspeed in the turn as desired.
A Cessna 152 flying in formation could break away using the same maneuver, though the bank angle and airframe loading (G forces) would need to be maintained within the aircraft's limitations.

The primary difference with fighters and attack aircraft is that the bank angle is dramatically steeper (in the extreme, a 90-degree "knife-edge" bank) and the turn much tighter because these aircraft have the excess power (thrust) required to sustain flight in that configuration and are sturdy enough to withstand the G loading induced by a "hard pull" in the breakaway maneuver. The abrupt wings-up turn along with the nice roar you get advancing the throttles makes the maneuver an impressive one for airshow crowds to watch.

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    $\begingroup$ Could you develop a bit how the altitude is maintained while the wings are rolled 90°, and the vertical component of the lift seems null? Is that possible with the lift of the fuselage, or some rudder deflection? $\endgroup$ – mins Sep 17 '15 at 18:14
  • $\begingroup$ @mins Much like in a straight vertical climb thrust is what's keeping you in the air in a knife-edge turn, along with excess energy (airspeed) you may have from whatever maneuver lead you into the turn. How long you can maintain altitude in that configuration depends on how much excess energy you have to make up for the fact that your regular lift vector is no longer pointing "up" - a Cessna 152 couldn't do it for more than a few seconds (if at all), while an F-16 could sustain knife-edge flight much longer. $\endgroup$ – voretaq7 Sep 17 '15 at 18:20
  • $\begingroup$ Thanks. I understand that can work only if the longitudinal axis is not horizontal and the thrust is directed a bit up upwards like this (Youtube). $\endgroup$ – mins Sep 17 '15 at 18:37
  • $\begingroup$ The angle of bank in a level turn is less than 90 degrees. It can get real steep, but if t was 90, the nose would slice down. $\endgroup$ – MikeY Apr 28 at 0:39

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