# How a bicycle balances itself?

1. May 21, 2014

### amind

This is not really a homework,
1. The problem
I just noticed this (weird we don't think about so many things and take 'em for granted) :
When the Bike is moving forward( with some significant velocity ) it can balance itself,
I couldn't come up with an answer how...

2. The attempt at a solution
I have been thinking it's because one or both of:
1. Angular Momentum of the wheel.
It should be conserved when $\tau_{ext}=0$.
2. Static friction.
??? no idea how it could be applied

2. May 21, 2014

### haruspex

Various studies have been done on this over the years.
In one I remember from 50 years ago, the researchers considered a number of hypotheses. For each, they built a bicycle which, if that hypothesis was correct, should be 'unrideable'. (Or, at least, noticeably more difficult to ride.)
They concluded the most important consideration was steering geometry. If you take a line down through the steering axis you will find it hits the road somewhere in front of where the front wheel contacts the road. Can you see how this helps?
Another study later found that this is not the whole story. (It's mentioned in a thread on this forum from a few years back. I'll see if I can find it.) The gyroscopic effect of the front wheel (not the back wheel) can also be important. This explanation also works for a rolling disc. If you roll a penny, it doesn't fall over instantly. Why not? See what happens.

3. May 21, 2014

### amind

I appreciate you helping,thank you.

Can you please elaborate on that ?

4. May 21, 2014

### haruspex

Try rolling a coin. As it starts to fall over, what else does it do? How does that tend to counteract the fall?

5. May 21, 2014

### amind

Thanks...

6. May 21, 2014

### CWatters

Try this video from 2011..

Their calculations showed that neither gyroscopic or trail effect were important so they built a bike with no gyroscopic or trail and it still balances.

Last edited by a moderator: Sep 25, 2014
7. May 21, 2014

### rcgldr

The key feature in vertical self stability is a geometry that causes the front tire to steer in the direction of the lean. The normal way of doing this is with trail in the steering geometry as mentioned above (the contact point at the front tire is behind the point where the steering axis intercepts the ground). One alternative method used at some universities is to locate a weight in front of the bike so that the weight generates a yaw torque based on the direction of lean, resulting in the front tire steering into the direction of lean without requiring any caster or camber (trail) effects (there is some caster like effect since the front tire will tend to steer and roll rather than skid sideways).

Gyroscopic induced steering torque is related to a rate of change in lean angle, as opposed to the amount of lean angle, and only dampens the rate of lean as opposed to correcting lean angle to vertical. At high speeds, the gyroscopic forces overcome geometry based self correction, with a theoretical "capsize" tendency to fall inwards at an extremely slow rate, with the actual tendency to simply hold the current lean angle (either the rate of inwards fall is so small that it's imperceptible, or the centripetal related forces at the contact patch on the side of the tires generates an opposing torque to the "capsize" torque, and the torques effectively cancel each other).

Last edited: May 21, 2014
8. May 22, 2014

### amind

Reading all that it seems this is still debatable and there is no one common viewpoint , you choose the theory you find the best in your opinion ;)(kind of like quantum mechanics , /sarcasm )