# Disc brake effectiveness varies on rotor size?

1. Oct 3, 2008

### 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!

2. Oct 3, 2008

### 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.

3. Oct 3, 2008

### 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

4. Oct 3, 2008

### 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.

5. Oct 3, 2008

### 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

6. Oct 3, 2008

### 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.

7. Oct 3, 2008

### 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.

8. Oct 3, 2008

### Staff: Mentor

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.

9. Oct 3, 2008

### 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!

10. Oct 3, 2008

### Bergamini

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

11. Oct 3, 2008

### 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. :)

12. Oct 3, 2008

### rcgldr

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.

13. Oct 6, 2008

### nottheone

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.

14. Oct 7, 2008

### rcgldr

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).

Last edited: Oct 7, 2008
15. Jan 24, 2012

### Aircraft Mech

The thing about bigger rotors is that you are moving the caliper further from the center of the wheel, this creates more Torque, or leverage to the turning wheel which results in less effort required to slow the same mass down at the same speed, or the ability to stop faster.

Torque = Force X Arm

or

(Braking Power) = (Caliper power) X (Distance from center of wheel.)

http://en.wikipedia.org/wiki/Torque

16. Jan 24, 2012

### Aircraft Mech

its really easy to break torque on a rusty bolt if you have a good grip on the fastener, and a sufficiently long breaker bar or wrench. You would find this difficult with a good grip and a short wrench.

17. Apr 5, 2012

### cjsunny

hi, i may asking for advise, if the rotor or caliper being upgraded and bigger. will they need extra power of torque on changing the brake booster to efficiece the brake?

if there brake booster didn't upgrade to be bigger, will the rotor /caliper (upgraded) doesn't hold the disc efficiency. or something will happening. please advise

Thank you,

18. Apr 5, 2012

### Aircraft Mech

The brake caliper will have the same amount of power, only, the amount of leverage will increase. it will remove strain from the brake caliper and lever because less braking force will be required to oppose the same amount of momentum of the wheel. The frame and fork mounting locations must be sufficient to take the increased braking capacity, and the manufacturers of these parts will have information regarding max rotor size. I was a little confused about the entire post but if you have more questions i will do my best!

19. Dec 16, 2013

### Skinny12345

The frictional force between the discs depends on the coefficient of friction( mu) and the Normal Force between the discs. Assume the disc has a radius of R
f= μN
Hence the frictional force per unit area between the discs= μN/(pi x R x R)
If we now consider a small ring on one of the discs of radius r and width dr then the
torque dT acting on this ring =( force per unit area of disc) x area of ring = μN/(pi x R x R) x 2 pi r dr
If you now integrate from 0 to R then the total torque acting on the disc = 2/3 x μN x R
Hence the total Torque is proportional to the radius of the discs.
If you double the radius you double the torque.

Last edited: Dec 16, 2013
20. Dec 16, 2013

### sophiecentaur

On domestic cars, the discs are cast iron, which becomes much weaker when you drill or groove it. But cast is Cheap. In high performance cars, the situation is different and the brakes are designed to deal with much greater power dissipation requirements. Expensive alloys are used which can be machined to suit. (Likewise with motor bikes)
I think it's safe to say that modern high performance vehicle design involves many more variables than just the simple Torque = Force times Radius.
The callipers need to be bigger, if you want to dissipate more power ( More Energy in a short time and very frequently) so the fluid doesn't become damaged by excess temperatures. That means they must fit on a larger diameter disc. I believe that inboard brakes are often used to reduce the unsprung mass. That will have repercussions in cooling.

21. Jul 5, 2014

### 90245

Reviving an old thread to clear away some brake dust :)

Most road cars have plain rotors (no holes or slots) primarily for 3 reasons. First they are less expensive to manufacturer without holes and / or slots. Second, there is little or no benefit on a road car to offset cost. Thirdly, slots or holes reduce the useful life of the pads and rotors.

You see them on high performance and more expensive road cars for the look and to justify the higher replacement cost. Also, if the car is used for track days there is some benefit and if it is used in a one make or restrictive racing series requiring OEM brake disc there is great benefit, as explained below.

Drilled rotors have been used in racing because they are lighter but they typically crack prematurely as a result of having the holes an especially so on a heavier car or one using drilled brake rotors with marginal mass for the braking requirements. Porsche is one manufacturer who has used rotors with holes on racing cars but the rotors are well designed for the job.

Slotted rotors are what you see on the majority of professional racing cars that use iron rotors. Here are the reasons why they are used. All vehicle brakes, racing and highway, require an even transfer of the pad friction material onto the iron disc to work at their best. Racing friction, for the last 25+ years, has had a high metallic content making the transfer layer more important and in extreme racing conditions harder to control. Slots in the iron rotor greatly improve the quality of the transfer layer and also help keep extra debris cleared away. Pad wear is higher with the slots than without so clearing debris away is an important function.

"Pad gassing" and the need for holes or slots to deal with it is a non issue and especially so with today's metallic and semi metallic friction material. All pads and disc used in pro racing are pre burnished before they go on the car to insure a good transfer layer is in place. The process was innovated by and first introduced by a company in North Carolina, Pro-System, Inc. that also manufactures racing brake parts and tests friction material, discs and other brake components. That company has special dynamometers to properly test high performance and racing brake components.

Slotted rotors or drilled rotors may be better in water but it would be marginally so.

An added benefit to slotted rotors and to a much lesser degree drilled rotors is that they give better bite to the brakes, if that is desirable to the user.