Why does a bicycle rolling down a hill stay upright?

[SteveDC]

A bike rolling down a hill will on average stay upright for longer than a free standing bike? I can't think of a way to explain why this is?

 

[infinite.curve]

A bike rolling down a hill will on average stay upright for longer than a free standing bike? I can't think of a way to explain why this is?

What do you mean by free standing?

A bike that is on a slope will run down that slope as long as it has 'balance' aka centre mass aka centre of gravity? The downward slope is strong.

 

[SteveDC]

By free standing I mean a bike that isn't rolling and just released in an upright position. This would still have a centre of gravity and should have just as much chance of staying balanced as a bike which is rolling, so why is it that the rolling bike can stay upright for longer.

For example a bike pushed down a hill will roll for quite a while before falling over, whereas a non-moving bike will most likely fall over straight away

 

[rcgldr]

The steering geometry of a bike tends to keep the bike veritcal. Most of this is due to "trail", which means the point of contact between the tire and pavement is "behind" the point where the line corresponding to the steering pivot axis intercepts the pavement. If the bike starts to lean, since the point of contact is behind the pivot axis, the downwards force from gravity at the front wheel axis and the upwards force from the pavement generate a torque that causes the front wheel to steer in the direction of the lean, enough to correct the lean and return to vertical, within a range of speeds.

The minimum speed at which a bike remains vertically stable (self-correcting) depends on the amount of trail (the distance from where the steering axis line intercepts the pavement back to the contact point of the front tire). The more trail, the slower the minimum speed. If the hill is steep enough to keep the bike above this minimum speed, then the bike will remain upright all the way down the hill, provided random disturbances (like a cross wind) don't cause it to veer off the street.

There's also a maximum speed, above which the bike will tend to hold whatever lean angle it currently has or fall inwards at an extremely slow rate due to gyroscopic reactions which greatly dampen any change in lean angle at higher speeds.

 

[solar71]

Centrifugal forces in the two wheels want to keep the front wheel straight. And the bike upright.
The wheels of a bicycle when spinning act as a gyro.

 

[CWatters]

The wheels of a bicycle when spinning act as a gyro.

That effect has been shown to be minimal or non-existent compared to the effect of trail in the steering geometry.

http://www.sps.ch/en/articles/various_articles/physics_of_bicycle_riding/

Probably the most important contribution to the understanding of bicycle physics is due to David Jones (Physics Today 23, April 1970) [1]. His first attempt to design an unridable bicycle by eliminating gyroscopic torques failed. Bicycles with tiny ball bearings instead of wheels proved to be perfectly ridable. Also compensating or even overcompensating gyroscopic torques by an additional dummy wheel turning in the opposite direction had no effect on rideability. His second attempt was successful. Bicycles which had a negative trail, i.e. a contact point K in front of the projection of the steering axis (see Fig. 1) were unridable. This demonstrated the importance of the steering geometry for bicycle riding.

 

[Baluncore]

That effect has been shown to be minimal or non-existent compared to the effect of trail in the steering geometry.

The gyroscopic effect is not non-existent, it can be “insignificant” when swamped by the riders antics or the trail adjustment. At higher speeds the gyroscopic effect becomes more significant.

So long as the bike is moving and it's lean results in the steering keeping the centre of gravity above the line between where the wheels contact the ground, it will stay upright.

“Rideability” is one thing because the rider has a brain and a dynamic body.

A forward moving “riderless” bike stays upright so long as it has either trail or gyroscopic front wheel steering.