I understand that most GA airplanes and gliders exhibit an *underbanking tendency* at low bank angles and an *overbanking tendency* at high bank angles.

According to the [Airplane Flying Handbook](https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/airplane_handbook/media/05_afh_ch3.pdf), chapter 3, page 3-11, if the aircraft is in steady, coordinated flight at a bank angle less than about 20 degrees, then

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> This shallow bank is such that the inherent lateral stability of the airplane slowly levels the wings unless aileron pressure in the desired direction of bank is held by the pilot to maintain the bank angle.
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On the other hand, if the aircraft is in steady, coordinated flight at a bank angle greater than about 45 degrees, then

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> The airplane continues in the direction of the bank even with neutral flight controls unless the pilot provides opposite flight control aileron pressure to prevent the airplane from overbanking.
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What causes these underbanking and overbanking tendencies, exactly? How do they work?

I know that when an aircraft is in a coordinated turn, the situation as experienced by the aircraft is almost identical to straight flight. As far as I know, the only significant differences are the following:

1. The outside wing will see a greater airspeed than the inside wing, which will mean:
	1. The outside wing will produce more lift than the inside wing, producing a rolling moment to the inside.
	2. The outside wing will also produce more *drag* than the inside wing, producing a yawing moment to the outside.
	3. On the other hand, the outside wing will also see a shallower angle of attack than the inside wing, which will partially negate both of the above effects. I'm guessing that the lift effect will be negated more strongly than the drag effect.
2. The nose will see relative wind from the inside of the turn (which will have no significant effect); and the tail will see relative wind from the outside of the turn, which will produce a yawing moment to the outside.
3. Since the rudder is deflected towards the inside of the turn, the vertical stabilizer will produce a rolling moment to the outside.

So my questions are:

Is my understanding of the rolling and yawing forces in turning flight correct? Are there any significant effects I've missed? And how large is each of these effects—which ones are the big ones, and which ones are insignificant? And most of all, how come there's an underbanking tendency in shallow turns, but an overbanking tendency in steep turns?