newtonian mechanics - 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:

1. 
   

   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.

   
   


2. 
   

   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.

Answer

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:

1. 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


2. 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


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


4. 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.