Disc brake effectiveness varies on rotor size?

[Bergamini]

Hey -

I am a bike mechanic with a large interrest in physics. I know that a larger disc brake rotor provides a greater braking effectiveness, but how can you mathmatically prove it by using physics formulas? And what formulas would be useD?

Any ideas would be highly appriciated!

[gmax137]

Seems like for a given force at the lever, bigger pads would just "spread out" the force between the pad & the rotor such that the total normal force remains the same but the porce per square inch of rotor decreases. But, I've been told that larger brake pads allow for better cooling and don't get as hot (for the same braking effect). And keeping the pad & rotor temperatures down keeps the friction coeff high, improving the braking.

As far as the rotor itself, it seems like the further it (or really, the pad/rotor contact) is from the axle the more leverage or torque the braking force would have. Have you seen the rotors way out near the wheel rim - intended to maximize this torque.

These considerations are combined in a compromise that also considers unsprung weight and the "gyro" effect on the rotating wheel assembly.

[Bergamini]

thanks, I am aware of all of the aspects above.
Note: This is about Mountain Bike disc brake systems (though it is in principle the same as every other type of Disc Brake system).

I am looking for the formula that will prove that a 203mm rotor will have greater torque force than a 160mm.
Does anyone know what I could look for, or does anyone have any suggestions?
Thanks

[brewnog]

The formula you need is Torque = Force x distance
In your case, braking torque is equal to the retarding force provided by friction between the pads and rotor, multiplied by the radius of the contact point between the pad and rotor.

This also explains why door handles are found on the side of the door opposite the hinge, why longer spanners are needed to tighten bigger bolts, and why large disc brakes can stop a bike more quickly than small brakes.

[Bergamini]

The numbers needed for these calculations are extremely hard to find.
I am hoping that someone would know a formula that could easily describe the connection between leverage differences.

It is a 1" difference in radius, that would show, would it not?
The plan is to keep it as simple as possible stickin to rules of physics and showing a very clear indication of leverage/torque and how that would affect the braking effectiveness.

thanks

[brewnog]

I've provided the formula. For a given frictional force between the pads and disc, a 15% increase in rotor diameter will give a 15% increase in torque.

[mgb_phys]

For a bicycle disc brake you are limited by how much force you can apply with the pads, so you need to translate that into as much torque as possible.
The torque is force*distance from the hub as brewnog said - it's like trying to stop a spinning wheel with your finger on the tire as opposed to putting your finger on the hub.

On cars you can put much more force on the pads (better hydraulics) so the limiting factor is cooling the dics.

[Borek]

I would say that limiting factor is a friction between tyre and ground; it is not that hard to make a brake that is able to lock the wheels.

[mgb_phys]

Yes, I meant ln the sense of what drives the rotor size.

On motorbikes I think it's bigger=cooler looking, it's fairly easy to lockup the tires on them as well!

[Bergamini]

thanks guys, u've strenghtened my previous idea and helped me prove it! Thanks ppl!

[Type_R]

Not only do I do electronics engineering, but I love racing cars.
So I had study about braking systems. My research led me to conclude that bigger the rotor....The better coolling. Why is this? Because of larger surface area which allows easier heat transfer. The brake rotor gets cooled by its surrounding environment....if you have a smaller rotor being cooled by its environment due to thermodynamics versus the rate of the increase of heat due to friction, you'll see its much easier for smaller rotor to get overheated. Rather than having a larger surface area for heat to expand out more and be cooled much easier. Rather than having an extreme focus of heat on the smaller rotor. People think because you can lock your tires up with stock rotors...That larger ones are worthless. Well I'd have to argue that you're wrong. As you brake hard you have an amount time and distance before you completely come to a stop. The more time and distance covered the more heat you occur. So as this heat is increased the time it takes for you to come to a stop without "totally locking them up" since the brakes are hotter, rather than if you had a larger rotor. So sure with stock rotors you can lock them up instantly because the brake rotors are cool at that point. But try to having your full braking strength when your rotors get hott...You'll be outbraked easily. Not only that...If you race cars, you're constantly braking, throttle, and more braking. Therefore your rotors have no time to cool off....So you're using hot rotors to brake with....Now here where "drilled" and "slotted" rotors come in. When your rotors get extremely hot a gas gets generated inbetween the pad and rotor contact which decreases the friction. I prefer slotted to remove the gasses over drilled because
1)Drilled rotors crack
2)Drilled rotors remove more Surface Area than slots do thus hindering braking performance

Anyways this is all my own theory from my researching.......I may be wrong. :)

[Jeff Reid]

Rotors are usually drilled or slotted to give debris or water a place to go so it doesn't get stuck beteen rotor and pad. Rotors can also be drilled to make them lighter, or for light applications, like a bicycle, the rotors can use spokes, but generally just making the rotor thinner or sandwiching 2 thin rotors seperated by a spoke structure will also make them light and strong.

[nottheone]

Rotors are usually drilled or slotted to give debris or water a place to go so it doesn't get stuck beteen rotor and pad. ...

I have to disagree with this. You will find that most cars have neither holes or slots in the rotors. You will see holes in rotors of high performance cars generally and they will be bigger rotors. They are there for cooling, gas dispersion and lightening, not for debris or water. If they were there for that all vehicles would have them. The higher performance the vehicle, the more likely it will be to undergo higher speed stops more often. One way performance cars are tested is with the 0 to 100 to 0 run. This tests both acceleration and braking.

[Jeff Reid]

Rotors are usually drilled or slotted to give debris or water a place to go so it doesn't get stuck beteen rotor and pad.

You will find that most cars have neither holes or slots in the rotors.True, but virtually all motorcyles rotors have holes or slots because the rotors are exposed. I was thinking motorcyles because there are more motorcycles than racing cars. For racing cars, it's usually holes for cooling, brake pad release, and being lighter.

It's my understanding that high end racing brakes, like carbon fiber and ceramic brakes, use vented rotors without holes or slots. These are essentially two thin disks, that sandwich a vane type structure (as mentioned above).