The Rotor

RotorsThe rotor actually stops the car – just kidding! Like the other parts of the system mentioned so far, the rotor (see figure 6) does not stop the car; however, unlike the other braking system components, the rotor serves two purposes. In order of appearance, they are:

  1. The rotor acts as the frictional interface for the brake pads. But because it is a spinning object, it reacts to the output force by absorbing the torque created (any time a force is applied to a spinning object, a torque is generated.) In this case, if we assume the force to act at a point midway across the rotor face (6.2" from the center of rotation in our example) then the torque is equal to about 964 ft-lb. {1,861 pounds x 6.2" ¸ 12 inches per foot}.
  2. The rotor must also absorb the heat generated by the rubbing of the brake pads against the rotor face.

In the case of item (2) above, the rotor dissipates the heat generated by warming the air surrounding the rotor (this is why brake cooling ducts are so useful), but where does the torque go? 964 ft-lb. sure is a lot of torque, and it has to go somewhere... (But, before YOU go any further, you might want to check our Tech Article dedicated to rotor modification - Those Poor Rotors).

The Wheels and Tires
wheels and tiresTime to get down to business – and time to stop the car. Because the wheel and tire are mechanically bolted to the rotor, the torque is transferred through the whole assembly – rotor, hub, tire, and wheel. And now, the moment we have all been waiting for…

It is the interface between the tire and the road that reacts to this torque, generating a force between the tire and the road that will oppose the motion of the vehicle. The math looks just like the equation to calculate the torque in the rotor, but in reverse (see figure 7 too). Crunching the numbers based on a 275/35R17 tire with a rolling radius of 12.2 inches shows that a force of 942 pounds is generated between the tire and road, opposing the motion of the vehicle. Ladies and gentlemen, this is what stops the car…not the brake pads, not the rotors, not the cool stainless steel brake lines – it’s road reacting against the tire!

Now, in order to finish the job, all that is necessary is to add up all the forces (remember, there is a force acting on every wheel with a brake) and run through a little more math. In case you haven’t noticed, we engineers just love this math stuff!

Adding the Forces

As that famous guy Newton said, force = mass x acceleration {F=MA}. Or stated another way, the acceleration (or deceleration as the case may be) of an object will be equal to the sum of all of the forces acting on the object divided by the weight of the object.

Before we can sum up all the forces, there is one last little important fact to consider – the tire forces are not the same for the 4 corners of the car. Due to the static weight distribution of the car, the location of the center of gravity of the car, and the effects of dynamic weight transfer under braking (just to name a few), the rear brakes are designed to generate much smaller forces than the forces generated by the front brakes. For the sake of argument, and for this exercise, we’ll say the split is 80% front and 20% rear, but the actual distribution is dependent on the specific vehicle configuration.

So, if each front tire generates 942 pounds of force then we can calculate that each rear tire generates 20% of that, or 188 pounds. Adding up the four corners now gives us a total of 2260 pounds of force acting on the vehicle between the four tires and the road.

Rearranging Newton’s homerun mentioned above, {decel = force ¸ weight}, we can calculate that the total deceleration of the vehicle is 0.84g’s, or {2260 pounds force ¸ 2640 pounds weight}. Easy, right?

Calculating the Distance

Ok – last equation of the day. Given a vehicle speed of, say, 100 miles per hour, and the deceleration level from above, we can now calculate the distance required to bring the car to a stop. But, in order to make sure the answer comes out in "feet" we first need to juggle the numbers around a little bit:

100 miles per hour = 147 feet per second
0.84g’s = 27.0 feet per second per second

Apply the equation for stopping distance {distance = (initial speed)2 ¸ (deceleration x 2)} and low and behold, exactly 400 feet are required to bring this car down to a stop from 100 miles per hour (given our original pedal input force of 90 pounds). Tah dah! The car is now stopped.

Limiting Factors

From this example, it would appear that in order to make the car stop in a shorter distance, there are two options:

  1. Change the brake system to increase the force between the tire and the road for a given pedal input force
  2. Press on the brake pedal harder

This theory holds true, but only up to a point. Anyone who has even driven on a icy road will get this right away. As the brake pedal force is gradually increased, the deceleration rate will also increase until the point at which the tires lock. Beyond this point, additional force applied to the brake pedal does nothing more than make the driver’s leg sore. The vehicle will continue to decelerate at the rate governed by the coefficient of friction between the tires and the road. As you can imagine, the coefficient of a given tire on ice is much lower than the coefficient of that same tire on dry pavement…hence the increased deceleration possible on the dry paved surface.

You can take this one to the bank. Regardless of your huge rotor diameter, brake pedal ratio, magic brake pad material, or number of pistons in your calipers, your maximum deceleration is limited every time by the tire to road interface. That is the point of this whole article. Your brakes do not stop your car. Your tires do stop the car. So while changes to different parts of the brake system may affect certain characteristics or traits of the system behavior, using stickier tires is ultimately the only sure-fire method of decreasing stopping distances.

So Why Would Anyone Want to Modify Their Brakes?

So, if changing braking system components does not provide "increased stopping power" or "shorter stopping distances", why even consider changes in the first place? Why not just leave the brakes alone and buy new tires? Quite simply, making changes to your braking system can have a very real, very significant impact on four other areas of brake system performance other than stopping distance:

  1. Driver tuning. Modifying your brake system component sizing (brake pedal ratio, master cylinder piston diameter, caliper piston diameter, rotor diameter) can be performed to adjust the feel of the car to suit the driver’s tastes. Some drivers prefer a high, hard pedal while others prefer a longer stroke. In this regard, tuning your brakes is a lot like tuning your shocks – every driver likes something different, and there is no right answer within certain functional limits. These components can be adjusted in small steps to achieve a feel that the driver prefers.
  2. Thermal control. Modifying your brake system mass (rotor weight) can be utilized if there is a thermal concern in the braking system. If your brakes work consistently under your driving conditions, then adding ‘size’ to the braking system will accomplish nothing more than increasing the weight of your vehicle. But if high temperatures are having an adverse effect on braking system performance, or other components in general (wheel bearings for example), then you should consider "super-sizing". Of course, brake cooling ducts can really help out here as well!
  3. Temperature sensitivity. Modifying your brakes to address the presence of high temperatures (brake pad material and brake fluid composition) should only be considered if your thermal concerns cannot be resolved by "super-sizing". This is really just a Band-Aid for undersized systems…like those found on Showroom Stock racecars that are not permitted by their rules to upsize or cool their brakes. One might argue that it is more cost-effective to install ‘better’ brake pads and brake fluid than it would be to upsize the rotors, but all that heat still needs to go somewhere – and more often than not it will find the next weak link in the system.
  4. Compliance. Any changes that you can make to your braking system to reduce compliance will increase the overall efficiency of the system – improving pedal feel, wear, and stop-to-stop consistency. Think of it as ‘balancing and blueprinting’ your braking system.

In summary, brake system modifications have their place to help make your ride more consistent, predictable, and user-friendly; however, if your ultimate goal is to decrease your stopping distance, look no further than the four palm-sized patches of rubber connecting your ride to the ground.