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Spin recovery is one of the first things you learn in flight training. And the acronym "PARE," for Power, Aileron, Rudder and Elevator, is one of the most commonly taught techniques. So how does it work?
Airflow from your propellor strikes your horizontal stabilizer, generating a tail down force and raising the nose. Plus, if your center of thrust happens to be lower than your center of gravity, it creates a torque force that pitches the nose up. Moving the throttle to idle stops the pitch-up forces and makes it easier to lower your nose.
In a spin, each wing is stalled. But the low wing is at a higher angle of attack (and it's more stalled) than the high wing. Bringing the ailerons to neutral helps your wings reach the same angle of attack - decreasing the pitching and rolling moments.
Next, add rudder opposite the direction of the spin. If you're spinning to the left, add right rudder and vice versa. This helps break the rolling and yawing moment, stopping the spin.
You're stalled, so moving the elevator quickly forward decreases your angle of attack, ending the stall.
Once you've completed these steps, the stall will break and you'll literally fly out of the stall. Move your rudder to neutral once the aircraft stops spinning, and then raise the nose slowly to regain level flight.