But will the gyroscopic force affect the lean angle? The force tries to keep the wheels in the same orientation as they are and so will act against the turning, so I can imagine them working against the steering, but not for or against the leaning.

It’s been about a decade since I took Satellite Dynamics, but here’s what I’ve got….

The analysis presented was probably fine, but only if you assume that the bike is constantly at the lean angle and didn’t actually go around in a circle… but rather just applied the centrifugal force without accounting for the rotating coordinate system that is the bike.

We know that the motorcyclist needs to approach a lean from a vertical position (often quickly), so you need to analyze what forces are applied to the bike as it’s approaching an angle. IIRC, you’d experience a moment about the wheel axes in the opposite direction of the lean, which I presume is below the CG of the bike. I’d venture to say that the dynamics (as opposed to the statics) of going into the lean are favorable in terms of adding downforce at the tire contact patch. Rising from the lean would produce the opposite effect.

And then we should probably talk about the gyroscopic effects of the whole bike going in a circle, which I’d assume are less than the gyroscopic effects of the wheels… but still appropriate to include in the analysis.

Much has been written on this topic. I experience these effects every day, but often like to re-read analytic descriptions like on Wikipedia.

I’ll simply add for now that the motor’s rotating mass is also a sizable contribution to gyroscopic effects. One day-to-day result is that my electric motorcycle turns far more smoothly and nimbly than my petrol-powered motorcycle. But that also has other factors like tire camber / width. Nothing is simple in motorcycle dynamics.

FWIW, the article doesn’t take into account the gyroscopic forces of the wheels, which are probably quite significant.

But will the gyroscopic force affect the lean angle? The force tries to keep the wheels in the same orientation as they are and so will act against the turning, so I can imagine them working against the steering, but not for or against the leaning.

It’s been about a decade since I took Satellite Dynamics, but here’s what I’ve got….

The analysis presented was probably fine, but only if you assume that the bike is constantly at the lean angle and didn’t actually go around in a circle… but rather just applied the centrifugal force without accounting for the rotating coordinate system that is the bike.

We know that the motorcyclist needs to approach a lean from a vertical position (often quickly), so you need to analyze what forces are applied to the bike as it’s approaching an angle. IIRC, you’d experience a moment about the wheel axes in the opposite direction of the lean, which I presume is below the CG of the bike. I’d venture to say that the dynamics (as opposed to the statics) of going into the lean are favorable in terms of adding downforce at the tire contact patch. Rising from the lean would produce the opposite effect.

And then we should probably talk about the gyroscopic effects of the whole bike going in a circle, which I’d assume are less than the gyroscopic effects of the wheels… but still appropriate to include in the analysis.

Much has been written on this topic. I experience these effects every day, but often like to re-read analytic descriptions like on Wikipedia.

I’ll simply add for now that the motor’s rotating mass is also a sizable contribution to gyroscopic effects. One day-to-day result is that my electric motorcycle turns far more smoothly and nimbly than my petrol-powered motorcycle. But that also has other factors like tire camber / width. Nothing is simple in motorcycle dynamics.

Far enough that the limiting factor is the width of the engine, and the requirement to keep the weight down low.

It’s pretty much a balance between the friction of the tires, and G forces/centripetal force induced by the turn.

Reminds me of motorcycles doing those cage sphere stunts:

https://www.youtube.com/watch?v=6QAspo38GI0