How much the pitch (horizontal orientation) can differ from the angle of attack? I am trying to understand the claim that "angle of attack indicator was unfortunately not available", contributing to problems during Air France Flight 447. Attitude indicator most likely was available?
The angle of attack is the angle between the wing (wing chord to be precise) and the direction of travel (undisturbed airflow). The angle of pitch is the angle between the main body axis and the horizon. The difference can theoretically be any angle, but during normal flight it will be limited to about 15 degrees.
The reason that the angle of attack sensor was inoperative was due to low airspeed. Below 60 knot IAS the indication is unreliable and therefore the indicator is inhibited. This also inhibits the stall warning. This lead to the confusing situation that lowering the nose to correct the stall increased the airspeed beyond 60 knots, thereby reactivating the stall warning.
It can be. Remember that the angle of attack is the angle between the chord line of the airfoil and the relative wind. Imagine if the plane is level with the horizon with zero airpseed. It will fall straight down, putting the angle of attack close to 90 degrees with the pitch close to zero.
That said, during normal flight it's not likely that pitch and angle of attack will be excessively different. But honestly the two aren't closely related: You can exceed the critical angle of attack and stall at any pitch, bank, or yaw angle.
Just want to add the image.
Angle of attack is relative to the direction of relative wind (which is equivalently relative to the direction the plane is going, if in still air and the angle of incidence = 0, i.e. the wing is mounted parallel to the longitudinal axis of the plane), while pitch is relative to the horizontal axis. Angle of attack depends on the pitch, current velocity of the aircraft and the wind. They can be different.
Angle of attack is important to the aerodynamics (amount of lift, drag, etc.), while pitch tells you the aircraft's orientation relative to the ground.
Assumptions for the image: still air and angle of incidence is 0.
Just watch this video of a looping gone bad during a flight display. At 1:40 into the video it becomes painfully obvious by how much both can diverge in extreme situations.
The flight path angle is the difference between pitch attitude and angle of attack. If pitch attitude and angle of attack would be equal, the airplane could only fly straight ahead at the same altitude. Once it climbs, it has to increase pitch attitude at constant angle of attack. With enough thrust or speed, both can be 90° apart.
Now consider flying inverted: Both are almost 180° apart.
In a dive, again the difference will become large because the flight path angle takes on negative values.
The more fun it makes to fly an aircraft, the more both angles diverge. Only boring aircraft will keep both of them at similar, low values.
How much the pitch (horizontal orientation) can differ from the angle of attack?
270 degrees appears to be the maximum angle that the pitch attitude can differ from the angle-of-attack.
Some examples of extreme differences between pitch attitude and angle-of-attack:
Jet fighter or aerobatic airplane or aerobatic glider in a prolonged vertical climb. (May be a steady-state situation or the aircraft may even be gaining airspeed or it may just be a "zoom" climb where airspeed is exchanged for altitude; obviously only the latter is possible with the glider.) For simplicity assume a symmetrical airfoil. Pitch attitude is 90 degrees, angle-of-attack is zero degrees, for a difference of 90 degrees.
Now the throttle (if present) is pulled back to drop the engine power to zero, but the nose is kept pointing straight up until the aircraft starts to tailslide backwards. Pitch attitude is still 90 degrees, but angle-of-attack is now 180 degrees, for a difference of 90 degrees.
Now imagine the tailsliding aircraft experiences a slight variation in angle-of-attack-- perhaps due to a horizontal wind gust striking the aircraft-- that changes the direction of the relative airflow by one degree, so that the relative airflow is aimed slightly toward the top surface of the wing, rather than aimed directly at the trailing edge. Now the angle-of-attack has changed from 180 degrees (which also could be called minus 180 degrees) to minus 179 degrees. Now the difference between angle-of-attack and pitch attitude is 269 degrees.
Flat spin with flight path approximating a vertical descent. Angle-of-attack may be close to 90 degrees, but pitch attitude may be close to zero degrees. Actually on the retreating wing it would seem the angle-of-attack may go beyond 90 degrees (wing actually moving backwards relative to the airmass, so the local airflow comes partly from behind), in which case the difference between angle-of-attack of that wing, and pitch attitude of the aircraft, would also go beyond 90 degrees.