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Offtopic - bicycle + motorcycle dynamics


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There have been articles, posts, and videos about bicycles and motorcycles that mention gyroscopic forces help stabilize a bike, but two wheeled stability is due to steering geometry, specifically "trail". If you draw an imaginary line from the steering axis to the ground, it it will intercept the ground in front of the contact patch on the ground. If the bike is leaned over, then the upwards force from the ground at the contact patch (coexistent with the downwards force of the contact patch onto the ground), creates a torque that steers the front tire inwards. 

Above some minimal speed for self-stability, the steering reaction to lean angle is enough to correct for a lean. 

The gyroscopic reaction torques dampen (oppose) the steering reaction to lean, and at very high speed (around 100 mph or more) on a motorcycle, the bike transitions from a tendency to straighten up into a tendency to hold the current lean angle. The math for an infinitely thin tire predicts an extremely slow increase in lean angle, called capsize mode, but for real tires (not infinitely thin tires), there is no perceptible change in lean angle if you relax on the handlebars. There is a very perceptible change in the amount of counter-steering effort it takes to change lean angle as speeds increase (the gyroscopic reaction torques resist steering and changes in lean angle as speed increases, requiring more torque applied to the handlebars to compensate).

In order to lean a bike, the tires need to be steered outwards so that the bike leans inwards. This happens somewhat automatically by body leaning (rider leans inwards, bike leans outwards), but doesn't work well on race type motorcycles with reduced self-stability (reduced trail), or if already leaned over somewhat. Motorcyle Safety Foundation now teaches conscious counter-steering, to initiate or adjust a lean angle.

Non-powered unicycles don't have any self-stability and advanced riders counter-steer to initiate or change lean angle.



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The "How Bikes Work" video near the start of the "How to ride an electric unicycle - understanding the dynamics" pretty much explains the steering geometry reaction to lean angle, but gyroscopic precession is a reaction to change in lean angle (specifically a reaction to the torque related to change in lean angle). If the lean angle is not changing, there is no gyroscopic precession, and even when the lean angle is changing, at all but the slowest speeds, the rate of precession is very slow due to the higher angular momentum of the front tire. The net effect of angular momentum of the front tire is to resist a change in steering direction as speed increases, so gyroscopic reactions act as a damper (oppose) to steering reaction, which can prevent over-correction, and that dampening to prevent over-correction does help with stability. 


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