Why is it easier to balance on a moving bike than a stationary one?

[rcgldr]

The situation when the bike is recovering from a lean, is that the handlebar is turned inwards. And the handlebar needs to be straightened before the bike is straightened, otherwise it will overshoot and lean to the other side.

My issue is with the demonstration that shows the wheel turning inwards as the lean increases, but not showing that gyroscopic reaction alone would steer the wheel outwards while the lean decreases, but still leaning, which would prevent recovery (and is what happens at high speeds in capsize mode). The demonstrations imply that gyroscopic reaction adds to the corrective steering response related to steering geometry, when instead it acts as a damper, opposing the corrective steering response.

explain the stability of a single rolling wheel, where there is no steering geometry, just the gyroscopic steering, which in your opinion just opposes recovery from lean.

A single rolling wheel experiences a yaw torque when turning that translates into a corrective roll reaction. If a single rolling wheel is released at a leaned angle, it's rate of recovery (if recovery even occurs) is slow compared to that of a bicycle released at the same speed and lean angle, and if the initial lean angle is large enough and/or the speed low enough, the single rolling wheel travels in a circle (a spiral as it slows down) and doesn't recover to a vertical orientation. There's also the small effect of the contact patch being on the side of the tire when leaned, which creates a small outwards roll torque, but the gyroscopic reaction would be to steer outwards opposing the correction.

 

[A.T.]

opposing the corrective steering response.

The gyroscopic reaction doesn't oppose what the steering geometry would do on it's own. Without the gyroscopic effect the steering geometry would also straighten the handlebar during recovery from lean.

 

[rcgldr]

The gyroscopic reaction doesn't oppose what the steering geometry would do on it's own. Without the gyroscopic effect the steering geometry would also straighten the handlebar during recovery from lean.

During lean recovery, as the lean decreases, the inwards steering also decreases, but it's still inwards, while the gyroscopic reaction would tend to steer outwards (opposing / dampening steering geometry reaction), but the steering geometry dominates so the steering remains inwards (unless in high speed capsize mode). Absent the steering geometry, there would be no lean recovery, as gyroscopic reaction is zero when the roll torque is zero, which occurs once the steering results in a coordinated and leaned turn. If while leaned, a disturbance causes the lean to decrease, an outwards roll torque and an outwards gyroscopic steering reaction would occur, until the roll torque returns to zero, and the bike would remain leaned.

 

[A.T.]

During lean recovery, as the lean decreases, the inwards steering also decreases,

Due to both: steering geometry and gyrosopic reaction.

but it's still inwards, while the gyroscopic reaction would tend to steer outwards

If by "steer outwards" you mean "straighten the inwards steer", then the steering geometry is doing that too.

(opposing / dampening steering geometry reaction),

I see no opposition, as both are straightening the inwards steer.

 

[rcgldr]

I see no opposition, as both are straightening the inwards steer.

During lean recovery, geometry steering reaction generates an outwards roll torque, while gyroscopic steering reaction tries to oppose outwards roll torque (absent other steering inputs, gyroscopic steering steers to eliminate any roll torque). At moderate speeds, geometry dominates and a bike is self stable. At high speed, gyroscopic reaction dominates and a bike is unstable, falling inwards at a very slow rate, called capsize mode. On a racing motorcycle at high speed, a bike tends to hold a lean angle, so if the bike is falling inwards, the rate is so slow that it's imperceptible.

 

[A.T.]

During lean recovery, geometry steering reaction generates an outwards roll torque, while gyroscopic steering reaction tries to oppose outwards roll torque

Not really. The lean reducing roll torque depends on the state of the steering, which was originally turned inwards by both: geometry and gyro. During lean recovery, both effects reduce the amount of steering.