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If you have ever considered upgrading your brakes to larger ones and did a bit of research online you have probably found out that, contrary to intuition, bigger brakes won't reduce your braking distance. On the other hand we all know that upgrading to wider tires can improve both your cornering and braking. So the underlying question we're answering today is why does surface area matter with tires but not with brakes.

If this is your first time hearing it than you might be surprised to learn that upgrading from stock brakes and calipers to larger brakes and calipers will not reduce your braking distance. This is surprising because intuition tells us that if we increase the surface area of both the brake and caliper than we increase the amount of friction which should improve braking and stop the car faster.

But, physics disagrees with intuition and physics says this: F = μN
Yes, it's a formula but don't get scared it's the simplest formula there is. And it tells us that F, which is frictional force equals the coefficient of friction which mu or mew different people pronounce it differently, it's a Greek letter times the normal force.

So let's explain this a bit. Frictional force is obviously the amount of friction. The higher the frictional force the more friction we need to overcome and the harder it will be to move a certain object. The coefficient of friction is a constant and it depends on the nature of the material and surface roughness. For example sandpaper has a much higher coefficient of friction than glass. Basically the coefficient of friction tells us how friction-y a particular material is. Our normal force is the force acting on the object and pressing it down. In case of a stationary object that force will be the weight of the object pressing it against the surface.
As you can see there's no surface area in the formula. Physics doesn't care if the object is on it's side or on it's face. Even if the difference in surface area is extreme the frictional force is the same because the weight of the object is the same and the material is the same no matter how we place the object.

Although we increase the number of hills facing each other when we increase the surface area we are also distributing the same force over a larger surface area which means that the hills interlock less, they touch each other less. This is why stabbing yourself with a needle is far more painful than doing the same thing with let's say a bottle. You may apply the exact same force in both scenarios but in the case of the needle all the force is concentrated on an extremely small surface area leading to a much higher pressure. In case of the bottle the force gets distributed over a larger area leading to reduced pressure. The same thing happens with our plank. Friction stays the same because we're offsetting the increased number of peaks with reduced pressure on the peaks since we're distributing the same force over a greater surface area.

Ok but then but why do all the fancy sports cars have giant brakes which are obviously so much larger than the brakes on most other cars? The answer is heat or more accurately the prevention of brake overheating.
If you observe brakes more closely you will see that almost everything has to do with heat management. For example brakes on cars are tucked in inside the wheels and the body of the car which means that they receive far less airflow than brakes on motorcycles which are sitting directly in the air stream. This is why car brakes are ventilated and motorcycle brakes are not. Ventilation works to try and flush out as much heat out of the brake system as possible. Why is heat such a problem with brakes? Because it leads to brake fade. When brakes overheat a thin layer of gas forms on the surface and this leads to reduced friction and braking performance otherwise known as brake fade.

So this formula applies to brakes but it does not apply to tires. Many tests have been done over the years and have proven that wider and larger tires improve braking and cornering performance. The answer is surprisingly obvious. Brakes are solid and rigid.....tires are elastic. They're made from rubber after all. Brakes are not designed to deform or change shape under normal operation. Tires deform and change shape all the time. The loads applied on brake pads and rotors are simple – the brake pad only moves in one direction. The loads applied on tires are very complex and ever-changing

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