You want physics, you get physics.
You push on the left handlebar.
The steering momentarily veers to the right taking the tire track out to the right (from under the center of gravity).
The bike pivots around its center of gravity, thus leaning left.
The combination of gyroscopic effects and torque reactions between the tire contact patch and the steering axis lead to a situation in which the steering PUSHES BACK AGAINST YOU i.e. the steering moves back to the left. At a certain balance point, the steering will have PUSHED BACK against the force that you imposed, just enough so that the forces carrying the bike to the outside of the curve are balanced by gravity wanting to make the bike fall in. At this balance point, the steering will have turned itself back to the left by enough to carry the correct tire track around the curve, which requires that the steering be slightly left of center at this point. Don't confuse that eventual steady-state condition, with the forces that the rider had to impose in order to create that condition and with the momentary transient conditions that the bike had to go through in order to reach that balance. The rider had to push left ... the steering momentarily turned right which caused the lean angle to go left ... various forces resulting from this reaction turned the steering left pushing back against the rider's imposed force, until the situation reaches the rider's desired lean angle, at which the rider's removal of left-pushing forces causes the bike to stop increasing its leftward lean angle.
By the way, if the steering and tire geometries are correct, it should require nearly zero input from the rider to maintain a steady lean angle once it has been achieved. If your tires are worn out, or the tire pressures are wrong, or if the suspension and steering geometry of your bike are wrong, or if inappropriate tire sizes or profiles have been installed ... that might not be the case. I am very insistent on setting up my race bike so that it has neutral steering (it requires no input from the handlebars to maintain steady lean angle) and because I know how correct steering feels, I am fussy about it with my street bikes as well. It's also why I cringe whenever I read about riders who want to make drastic ride height changes (generally, lowering) or install fashionably fat wheels or tires on a bike that didn't originally come that way. You can do stuff to make your bike work better ... or you can do stuff to make your bike look a certain way but otherwise completely bugger it up and turn it into an ill-handling beast that won't turn and wants to do nothing but put you straight into the guard rail or ditch at the outside of every corner.
You push on the left handlebar.
The steering momentarily veers to the right taking the tire track out to the right (from under the center of gravity).
The bike pivots around its center of gravity, thus leaning left.
The combination of gyroscopic effects and torque reactions between the tire contact patch and the steering axis lead to a situation in which the steering PUSHES BACK AGAINST YOU i.e. the steering moves back to the left. At a certain balance point, the steering will have PUSHED BACK against the force that you imposed, just enough so that the forces carrying the bike to the outside of the curve are balanced by gravity wanting to make the bike fall in. At this balance point, the steering will have turned itself back to the left by enough to carry the correct tire track around the curve, which requires that the steering be slightly left of center at this point. Don't confuse that eventual steady-state condition, with the forces that the rider had to impose in order to create that condition and with the momentary transient conditions that the bike had to go through in order to reach that balance. The rider had to push left ... the steering momentarily turned right which caused the lean angle to go left ... various forces resulting from this reaction turned the steering left pushing back against the rider's imposed force, until the situation reaches the rider's desired lean angle, at which the rider's removal of left-pushing forces causes the bike to stop increasing its leftward lean angle.
By the way, if the steering and tire geometries are correct, it should require nearly zero input from the rider to maintain a steady lean angle once it has been achieved. If your tires are worn out, or the tire pressures are wrong, or if the suspension and steering geometry of your bike are wrong, or if inappropriate tire sizes or profiles have been installed ... that might not be the case. I am very insistent on setting up my race bike so that it has neutral steering (it requires no input from the handlebars to maintain steady lean angle) and because I know how correct steering feels, I am fussy about it with my street bikes as well. It's also why I cringe whenever I read about riders who want to make drastic ride height changes (generally, lowering) or install fashionably fat wheels or tires on a bike that didn't originally come that way. You can do stuff to make your bike work better ... or you can do stuff to make your bike look a certain way but otherwise completely bugger it up and turn it into an ill-handling beast that won't turn and wants to do nothing but put you straight into the guard rail or ditch at the outside of every corner.
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