Why do you have less control over a bicycle with a broader steer? I recently had an argument with someone on why a bicycle with a broader steer gives you more control. We both had different answers to this question and neither could convince the other.
First a schematic drawing of the situation:

Both claims assume that the only force on Body is gravity, denoted $F_g(Body)$. This force is carried on through the bicycle to where the wheel touches the floor. The bicycle is assumed to have no mass.
Now the two claims:

*

*Your body and both hands form a triangle. This means that the force $F_g(Body)$ is split up in  horizontal component vectors and  vertical component vectors. The claim is that this by this, not all of $F_g(Body)$ is directed downwards anymore. So the force acting on the floor through the wheel would be less than $F_g(Body)$. If the steer is broader, the horizontal components will increase in size and thus the vertical components will decrease in size. Meaning that you wouldn't press down on the floor as hard with a broader steer resulting in less friction=less control.
The steer would provide a counter force for the horizontal components.


*When you're steering, the bicycle is leaning. So the point where the wheel is touching the floor could then be considered a fulcrum.  A broader steer would mean a greater distance to the fulcrum, thus a bigger moment. This would be harder to compensate=less control.

My question now is: "Why do you have less  control over you bicycle when the steer is broader. I would like to know the correct physical explanation and what is wrong with the claims (or perhaps somethings wrong with our assumptions)."

N.B. I am not a physicist  myself (I'm a mathematician), so forgive if I made some obvious mistakes.
 A: The mechanics of steering a bicycle are more complicated than you think - as evidenced by the fact that it's quite easy to ride a bike without touching the handlebars, for example.
The key to the stability of a bicycle is the angle of the fork - both the angle of the main pivot, and the offset of the wheel with respect to that pivot - and the point where that line meets the road (green dashed line in the below):

When the bike starts to "fall over", the wheel will start to turn because the green line intersects the road in front of the point of support of the wheel. And when the dashed line is in front of the wheel, it will turn the wheel in the right direction to "counter the lean" - in other words, it is a stable situation.  If the fork is bent so the green line ends up behind the support, the bike becomes impossible to control.
Now assuming that the fork is correctly sized and aligned for the bike, the question becomes "what is the role of the handlebars?". These allow you to either amplify, or counter, the force that the wheel is exerting by itself. Wider handlebars do three things:


*

*because they provide a longer lever, you will feel less force when the wheel is trying to turn: you therefore "feel" the natural movement of the bike less well

*The longer lever means that you need to move your hands more to make a small adjustment - this makes it feel like your actions are not doing anything

*At the same time, once you get used to the longer handlebars, you would in principle be able to make more precise adjustments

*Really long (and heavy) handlebars could in principle change the inertia of the system (you notice this when you hang heavy shopping bags on your handlebars), but it's not likely to be a problem with normally-sized bars


I think that points (1) and (2) in particular will give you the sense that you have less control over the bike, although (3) could, in experienced hands, provide the opposite sensation. But by FAR the most important factor in the control of your bike is the correct alignment of the fork.
A: Its easy...when you get used to riding a bike with one steer, you get used to the fact that same movement of your arms turn the steer in the same angle. But, if you make the steer shorter, that same movement will turn the wheel more, and you will be somewhat out of control, because your instincts are now a bit off...its all about the difference between angle and displacement, if you are close to the point, origin of the angle, you need less displacement, and if you are far from this point, you need more displacement. FOR THE SAME ANGLE, of course.
A: I think that wider steer actually increases your control over the bike.
From bicycle design point: the steer widths are different on different types of bikes. Bikes designed for paved roads only have the narrowest steers. Logic suggests that riders want better control on more rough terrain. There are even bike bar ends that can further increase the distance between your hands.
Wider steer provides more leverage, so:


*

*Wheel turns cause larger displacement of your hands. You can't detect force, but you can detect movement of your arms. This means that you can detect smaller turns of the steering wheel.

*Wheel turns apply less force to your hands. That means that the mass of your arms resists that movement better. You don't even need a conscious effort to counter sudden turns!

*Force applied by your hands is amplified, so you need to apply less force to steer your wheel.

*But, of course, you need to move your hands more to turn your wheel by the same amount, but that also means more precise control of steering wheel direction.
(1) and (2) mean that it's you who control the steering wheel and not the other way around, but that's not needed on a paved road. (4) is more of a personal experience: changing to a wider steer will make you feel as moving hands too much, but changing to a narrower steer will make you feel as applying to much force to steer.
You can make an experiment: have one person grip at handlebars and another person grip somewhere in between, then have them try to turn the wheel in the opposite direction. Given the same physique the wider grip should win. Isn't that better control?
A: Another factor that can also contribute to the self-stability of traditional bike models is the distribution of the mass in the steering mechanism, which includes the front wheel, the fork and the handlebars. If the center of mass of the steering mechanism is in front of the steering axis, then the force of gravity will also cause the front wheel to move in the direction of inclination. This can be seen by leaning a stationary bike to one side. The front wheel generally moves on that side regardless of any interaction with the ground. Additional parameters such as the center-of-mass front-to-back position and the center of mass elevation also contribute to the dynamic behavior of a bike.
Source: Wikipedia
