At what angles of attack do aircraft typically fly at? How much of a margin is there before aircraft stall due to an increase of an angle attack due to factors such as gusts or rotation of the wing section due to deformation?
It depends basically on the wing section. Some of them stall at a higher angle of attack than others...
To quote typical values (for wing + body, since not only the wing gives lift...) a given plane may achieve the flattest glide (best range, L/D = 12, at 155 knots) with an angle of attack of 4º. If you wish to fly slower, you can do it at 115 knots, with L/D = 8, and a steeper AoA (13º) or you can choose to fly faster, at 210 knots, always with L/D = 8, but with an AoA of 1.5º.
Thus, and except for the best L/D, there are always two angles of attack for the same L/D, one of them steep (slower flight) or flat (fast flight)...
The stall, for the example I'm quoting (book 'Mechanics of Flight, by A.C. Kermode)' takes place at 15º...
It depends. These factors influence the flight angle of attack:
- Altitude. Higher up the air is thinner, so the flight angle of attack tends to be higher.
- Aircraft speed. Fast airplanes sometimes need to limit lift by flying at a slightly negative angle of attack.
- Wing camber and incidence. High camber means high lift already at zero angle of attack. Extreme cases like the B-52 need to fly with a visible nose-down attitude when flying low and fast or when the high lift devices are deployed.
- Aircraft weight. This is both influenced by aircraft mass and the load factor flown.
- Wing sweep. Higher sweep means lower lift curve slope, so a higher angle of attack is needed. Thankfully, stalling is also delayed, in extreme cases (delta wing) above 30°.
- Aspect ratio. A lower aspect ratio works in similar ways to sweep: Stall is delayed to higher angles. Gliders, on the other hand, stall already at 10° - 15° angle of attack (depending on flap settings).
- Mach number: At transsonic speeds the developing shocks on the wing can stall the aircraft at much lower angles than those usual at low speed.
- Rate of angle of attack change. In dynamic manoeuvers the stall lift coefficient could be pushed up by 50%.
- Directional stability: The F-4 Phantom II is limited to 23° angle of attack simply because the vertical tail will be insufficient at higher angles. Here the aircraft does not stall but is artificially limited.
Normally, the designer tries to set the wing incidence such that the fuselage is level at the design speed and altitude. The wing angle of attack is then also near zero or at low, single-digit degrees. The stall angle of attack, however, is all over the place, from high single-digit values (high-speed stall) up to more than 30° (highly swept, low aspect ratio configuration with vortex lift).
An aircraft typically flies at angles of attack range about 2-5 degrees, depending of the flight altitude, speed and g-load of maneuver. It's much more (about 10-12 degrees) when flight speed is near to take-off and landing speed. The critical angle of attack when an aircraft goes to stall usually is about 15 degrees, mainly depending of the wing plane form, flight Mach number, the wing section profile and flaps position. So the safety margin is about 10 degrees, but the margin drastically decreases in take-off and landing. Therefore it's dangerous when an aircraft, say, is in approach to landing while undergoes a vertical gust that may lead the aircraft into stall.