# Why bicycle deviates from equilibrium if I leave the handle?

If I cycle at high speed and my hands are holding the handle, in this case, the system: bicycle+me is effectively a rigid body and by conservation of angular momentum (of wheels), I don't fall aside. However, once I leave the handle, the system is no longer a rigid body, since the handle and the front wheel can now have motion w.r.t. to me and the rest of the cycle body. Still, conservation of angular momentum applied on individual wheels should guarantee that I still don't fall but this time the front wheel wobbles uncontrollably and causes disbalance. Why is it so? (is this helpful: Most of the linear momentum is still with me and front wheel has negligible linear momentum)

• Related: physics.stackexchange.com/q/506/2451 and links therein. Commented Feb 9, 2020 at 8:43
• Your premise is wrong: you are not a rigid body. As one can see on snow, a cyclist is constantly weaving left and right, falling over alternatingly to the left and to the right, all the time steering to get the contact point below the center of gravity.
– user137289
Commented Feb 9, 2020 at 9:59

This is a complicated problem, but it has been solved. Here are the essentials:

First, humans can learn how to make an unstable device like a bicycle stable enough to ride. The ability to keep a bike upright becomes "muscle memory" in that the process becomes automatic, not requiring conscious thought to perform. This makes it possible for people to ride bikes which have been mechanically altered to make them deliberately more unstable than they are to begin with- and this makes it difficult to determine how intrinsically stable or unstable a bicycle is if it is being ridden by a person who knows how to ride.

Second, note that the front wheel of the cycle possesses angular momentum while it is rotating fast. This is represented by a vector, sticking out of the end of the wheel's axle, which wants to maintain the direction in which it is pointed- but only when the wheel is rotating fast. It is that resistance to change of direction which lends stability to the cycle at high speeds, letting you remove your hands from the bars for short periods without immediately crashing. This source of stability goes away at low speeds, making the cycle wobble sideways if you let go.

But this is not the whole story. The angle with which the fork tubes approach the ground places the intersection of a line through the fork tubes and the ground ahead of the point at which the tire contacts the ground. That offset is called trail and provides additional stability by causing the forks to naturally turn into a lean and thereby help keep the bike upright even if it has no rider.

Note that with a human rider, it is possible to keep a bike upright even with zero trail and no angular momentum effects, but human effects on stability with respect to steering and balance can and have been removed from the analysis by running bicycle simulations on computers, and a lot has been written about this. You will find it in the mechanical engineering literature under the title of tracking vehicle dynamics.

• @pieter, were those experiments performed with a human rider or an automated system? Commented Feb 9, 2020 at 20:11
• will edit to include trail and rake. -NN Commented Feb 9, 2020 at 20:21
• @pieter, see my edits and comment please. -NN Commented Feb 9, 2020 at 20:36
• Here's a paper from 2011 where they experiments showing that neither the angular momentum of the wheel nor the trail effect are necessary for stability. There's also some good theoretical work. bicycle.tudelft.nl/stablebicycle/StableBicyclev34Revised.pdf Commented Feb 9, 2020 at 20:58
• @LukePritchett But I see that angular momentum of the front wheel plays a larger role than what I remembered. Thanks!
– user137289
Commented Feb 9, 2020 at 21:14