Definition
The tendency of an airplane in a medium- to steep-banked turn to continue rolling into a steeper bank without further control input from the pilot. It occurs because the outside (raised) wing travels through the air on a larger arc and at a higher airspeed than the inside (lowered) wing, producing more lift on the outside wing and rolling the airplane further into the bank.
Plain English
When an airplane is already banked steeply in a turn, it wants to keep rolling deeper into the turn on its own. The pilot has to actively use opposite aileron to stop the bank from increasing.
Context Anchor
Encountered during cruise turns and steep-turn practice, when the pilot is trying to maintain a steady bank angle instead of letting the turn get steeper.
Derivation
“Over-” means beyond or too much. In aviation, “bank” means the sideways tilt of the airplane’s wings in a turn. So “over-banking” means banking beyond the intended wing tilt.
Why Pilots Care
If left uncorrected the bank can become steep enough to raise load factor and stall speed, increasing the chance of an unintentional stall or loss of control.
Intuition Check
Do not read “tendency” as something the airplane will always do by itself in every turn. It means a natural tendency that becomes more noticeable as the bank gets steeper and must be controlled by the pilot.
Example Sentence 1
As the bank passed 45 degrees, the instructor pointed out the over-banking tendency and had the student apply slight opposite aileron to hold the bank steady.
Example Sentence 2
During a standard-rate turn the student recognized the over-banking tendency and used coordinated aileron and rudder to maintain the desired bank angle.