I'm sorry, I guess I didn't follow my own advice. I was not trying to say that AOA IS Pitch, but that the actual physical AOA (# of deg) is the same as the actual physical pitch angle (again, # of deg) when on a takeoff roll, prior to lifting off.
Exactly... But as soon as you lift off, if you keep the same pitch attitude, your AoA is lowered.
In fact, this brings to mind a simple formula that could be taught: When upright and not banking, Angle of Attack plus Angle of Travel = Angle of Pitch plus angle of incidence. Since angle of incidence does not change, for the rest of this post we'll just assume it's zero for simplicity.
If we were to be able to make a flight from takeoff to landing without making any turns, and using level runways, here's what would be happening:
1) During the takeoff roll, if the runway is level, AoT=0, so AoA=pitch.
2) Upon rotation to climb pitch, AoA increases. AoT=0 until liftoff so AoA=pitch until liftoff. Increased AoA means increased lift, and lift>weight momentarily, which accelerates the airplane upward.
3) Holding climb pitch just after liftoff, as the airplane accelerates upward at climb attitude, AoT increases due to lift being greater than weight but pitch attitude remains the same, resulting in a lowering angle of attack. When the angle of travel (still at the same pitch attitude) has increased enough to result in the angle of attack lowering to the point where lift = weight once again, we will be in a steady-state climb.
4) During steady-state climb, AoT+AoA=Pitch, and all three will be positive. Lift will also equal weight.
5) At the top of the climb, we lower pitch, which lowers the angle of attack, which results in lowering lift, so lift < weight which results in negative vertical acceleration, which lowers climb rate, which results in the positive angle of travel being reduced.
6) When climb rate and angle of travel are down to zero, we hold our pitch steady, the angle of travel will once again be zero, and angle of attack (this is important!) will be the SAME as it was during the steady-state climb at the same indicated airspeed (actually, it will be negligibly lower due to the slightly lower weight of the aircraft due to fuel burned, but not enough for us to notice!)
7) As we accelerate from climb speed to cruise speed, the increasing indicated airspeed means that we don't need such a high angle of attack to maintain the same lift. We slowly lower pitch attitude (and trim nose-down for the higher speed) as we accelerate. AoT=0, so AoA equals pitch again, and lift = weight while we're in a steady state vertically.
8) Transition to descent: Let's say we're going to descend at cruise speed, leaving trim unchanged and lowering power. Lowering power means that there will be more drag than thrust. That will slow the airplane down, and since we're trimmed for cruise airspeed, the nose will lower to compensate. When the nose lowers, AoA will be reduced, again resulting in weight being greater than lift, resulting in downward acceleration. Since we started with our vertical speed and AoT at zero, the downward acceleration will result in a descent. If we hold descent attitude, the AoT will lower until once again the AoA is back to the same value it was at in cruise. So, since we have the same indicated airspeed as we had at the end of cruise, once the AoT is lowered to where the AoA is the same as it was in cruise, we'll have a steady-state descent.
9) In the steady-state descent, lift=weight. AoT will be negative, pitch will be somewhere around zero, AoA will still have the same positive value as it did in cruise if we are still at cruise airspeed.
10) Let's just say we transition to our landing speed in the descent. As we slow down, we'll need a higher AoA to develop the same amount of lift. To keep the descent rate the same, we'll need the same amount of lift and we'll need to increase both pitch attitude and AoA as we slow down. Then, we'll maintain that pitch attitude and AoA to keep the same rate of descent.
11) We're on final, getting ready to flare. We pull back to increase pitch and AoA, which increases lift, so lift>weight again which results in an upward acceleration, reducing our descent rate. We also pull power. We'll then be in a very slight steady-state descent, slowing down and needing to increase pitch and AoA to maintain the steady state. If we do it right, our mains will touch the ground at or before we reach the stalling AoA. At that point, AoT=0 again (level runway), AoA=pitch (again, assuming 0 angle of incidence) and if we hold the same AoA we had just after touchdown, the weight will slowly transfer to the landing gear as we lose lift due to the slower airspeed as we roll out.
(That was fun. Am I a geek? 
)
Chuck, I understand what you're trying to get at with your example, but I have to beg to differ with it. If you're on a downslope takeoff roll into a headwind, all the wind in front of you is going to deflect upslope and run parallel to the ground, thus not allowing you to have a negative AOA. Now, if you're at altitude and you start a descent, then you can have a negative AOA, but it doesn't seem logically possible if you're on the ground.
Right again, PJ.
Then again, I'm just a 75-hr pilot, I could be wrong (it's happened once before and I'll never forget it!).
We wouldn't LET you forget it!
I wonder how many OWT's started this way... With a simple misunderstanding of a person of authority.