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I feel sure that you fully understand all of the principles, but the final statement regarding reduction of angle of attack rather than increasing airspeed (with power) is the basic fundamental for teaching new pilots the art of stall recovery; in fact, they are taught to do both... reduce angle of attack (to unstall the wing) and simultaneously applying power.
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Unfortunately however, very few seem to understand the two totally separate and unrelated things acheived by such actions even when done in parallel.
Application of power has absolutely nothing to do with stall recovery. Stall recovery involves unstalling the wings by reducing the angle of attack. No more and no less.
A PA28, A Glider and a Tornado all recover from a stall in exactly the same way - the angle of attack is reduced below the stalling angle of attack.
Power is simply used to reduce the amount that the subsequent flight path has to point towards earth in order to regain suficient airspeed to a) avoid re-entry to the stall and b) climb away with less drag than one has 1kt above the stall.
With no power, gravity is all one has to accelerate the aircraft.
With full power less use is made of gravity because the thrust accelerates the aircraft and only a very temporary shallow descending flight path is required to regain suficient speed.
People may think that they are recovering from a stall with power alone but they are not - they are simply maintaining a constant (balistic) flight path and ensuring that thrust exceeds drag. As the aircraft accelerates, the angle of attack required to maintain that flight path reduces.
Examiners are quite right to fail anyone that uses any method to recover from a stall other than reducing the angle of attack.
As I said, any pilot flying an approach will be using all the controls incvluding power to maintain the desired flightpath and airspeed. One will say that they are using point and power. Another will say that they are using something else. However, when you sit back and watch they fly a correct approach with whatever adjustments are necessary they both do exactly the same thing with the controls - if they did not then either the flight path would end up being wrong or the airspeed would wander all over the place.
So what we have is simply two camps that do exactly the same thing but think of their actions in different ways.
Regards,
DFC