The Master Cylinder

Master CylinderThe next step in the brake system is to convert the amplified force from the brake pedal into hydraulic fluid pressure. The master cylinder, consisting of a piston in a sealed bore with the brake pedal output rod on the one side and brake fluid on the other, performs this task.

As the pedal assembly output rod pushes on the piston, the piston moves within the cylinder and pushes against the fluid, creating hydraulic pressure. It’s really that simple; however, in order to determine how much pressure is generated at the master cylinder, we will need to dig into a few fluid calculations. Don’t flip to the classified ads just yet!

The pressure generated at the master cylinder is equal to the amount of force from the brake pedal output rod divided by the area of the master cylinder piston. If we assume a master cylinder diameter of 0.90 inches (with an area of about 0.64 square inches), the calculated pressure will be 558 pounds per square inch from the 360 lbs. of pedal output force from above {360 lb. ¸ 0.64 in2}. Whew – no more math for a minute…just stare at figure 2 for a while.

So, does this pressurized hydraulic fluid stop the car? Again, the answer is no, but like the brake pedal, making changes to the master cylinder can impact other characteristics of the brake system:

  1. Increasing the master cylinder piston diameter will decrease the amount of pressure generated in the fluid for a given input force. In the example above, if a 1.0" master cylinder were to be substituted, the output pressure would fall to approximately 450 PSI – a pressure reduction of nearly 20% for a +0.1" change in diameter. Small changes here make a big difference.
  2. Decreasing the master cylinder piston diameter works the same principle in reverse. Swapping in a 0.80" master cylinder will increase pressure to over 700 PSI – this time a 25% increase for a -0.1" change in diameter.

Given the relationship between master cylinder piston diameter and hydraulic force, it may seem desirable to use the smallest master cylinder possible. However, since there will always be some compliance (see Sidebar 2 - Compliance) within the system, the braking system has to have enough additional hydraulic fluid on hand to fill all the extra volume caused by the flexing of components during the compliance phase. Unfortunately, this is accomplished by increasing the diameter of the master cylinder, which, we just learned, reduces the pressure generated! Therefore, one has to make sure that the master cylinder has a large enough diameter to meet the fluid volume requirements of the system, but small enough to generate the pressure required. (There’s never an easy answer, is there?)

Sidebar 2 – Compliance

The first conclusion people come to when seeing this is "I’ll get the smallest brake pedal I can find, put it in the car, and make up for the decrease in pedal force amplification with a very small master cylinder!" Close, but in the real world there is another factor at work that should affect your decision – compliance. As pressure begins to build in the braking system, the various components in the system will flex until all clearances have been taken up. During this time seals, clearance parts, and other flexible components will stretch and deform, effectively increasing the hydraulic volume in the brake system.

To picture this, imagine blowing up a balloon inside a pop can. The balloon will expand freely until it comes in contact with the sides of the can. This is the stage of compliance…and the bigger the can, the greater the compliance. Once the balloon has taken up the volume of the can completely (similar to the brake system components completing their flexing), it gets much, much harder to blow more air into the balloon. This is the stage of pressurization.

In the braking system, compliance is highly undesirable - because it requires extra hydraulic fluid to fill this increased volume before pressure can build. In the pop can analogy, one would want the smallest pop can possible in order to minimize the amount of time required to get past the compliance stage and directly into the pressurization stage.

You could say that in this case, non-compliance is best…

The Brake Tubes and Hoses
Brake HosesOn the surface, the brake tubes and hoses have one of the easiest jobs in the braking system – transporting the pressurized brake fluid away from the master cylinder to the four corners of the car. It would be ideal to use the most rigid material possible to minimize the compliance in the system.

However, since the braking components at the wheels (calipers, pads, and rotors) are usually free to move around with the wheels and tires, a flexible portion is required – and flex equals compliance. Traditionally, auto manufacturers have used rigid steel tubing to get the fluid ‘almost all the way there’ and a short length of rubber coated nylon tubing to make the connection to the ‘moving stuff’, but even this short section of flexible tubing can cause significant compliance in a racing application. For this reason, we racers prefer to replace the rubber hose with a nylon tube covered by stainless steel braiding (see figure 3). Most people notice the reduction in brake pedal travel due to the reduced compliance immediately, but it usually depends on how old and compliant the old rubber coated hoses were at the time of replacement.

Although those cool-looking stainless steel brake lines will not make your car stop any faster on their own, the decrease in compliance and improvement in pedal feel can make a driver much more confident. They will probably provide some increased level of resistance to damage from flying debris as well. Did I mention they look cool?

The Caliper

CaliperThe caliper is one of the most familiar components to the racer, yet sometimes the most misunderstood. Like the master cylinder, the caliper is just a piston within a bore with pressurized fluid on one side. While the master cylinder used mechanical force on the input side to create hydraulic force on the output side, the caliper does the opposite by using hydraulic force on the input side to create mechanical force on the output side. The top view shown in figure 4 illustrates how the pressurized brake fluid working against the back side of the piston is converted into a squeezing or ‘clamping’ force.

In order to calculate the amount of clamping force generated in the caliper, the incoming pressure is multiplied by the area of the caliper piston. In our example, the 558 PSI that had been generated at the master cylinder has traveled through the brake pipes and lines and is pushing against two 1.5" pistons per caliper. Therefore, the ‘effective area’ of the caliper will be equal to two times the area of a single 1.5" piston. Working the numbers reveals that 558 PSI will generate 2,068 pounds of clamp load {558 PSI x 1.84 in2 x 2}.

As you have probably already guessed, increasing the caliper piston diameter increases the clamp load for a given input pressure – but again, this does not stop the car. Putting on bigger calipers might seem like a good idea at first, but the tradeoffs might make you think twice:

  1. Increasing the diameter will increase the compliance in the system (bad news for pedal feel!)
  2. Increasing the diameter will increase the size and weight of the caliper (bad news for unsprung weight!)
  3. Increasing the diameter will increase the fluid volume requirement of the system (bad news for master cylinder sizing!)

So, when thinking about that big 6-piston caliper conversion, keep in mind that the size and number of caliper pistons on your car were originally matched to the brake pedal and master cylinder to generate an appropriate clamp load for a given brake pedal input force. Changing any one of the components will shift the balance one way (increased pressure required) or the other (higher pedal forces required) to generate the same clamp load. Remember – bigger calipers don’t create any more ‘stopping power’ and they do not ‘decrease stopping distance’ – they just generate higher clamp loads for a given pressure input.

One final caliper note of interest: you may have heard the terms ‘fixed caliper’ (indicating that the caliper body is bolted directly to the suspension upright) and ‘floating caliper’ (indicating that the caliper body is free to ‘float’ on sliding guide pins) in the paddock. Although there are pros and cons associated with each type, there is not enough room in this article to dig into the details of their design differences. For now, let it suffice to say that the above math works out the same for either design.

So, to this point, our example brake pedal, master cylinder, and caliper have amplified the original 90 pounds of driver input to over 2,000 pounds – an increase of more than 22 times, but we still haven’t stopped the car.

The Brake Pads

Brake Pad and RotorThis part might surprise some and offend others, but it is a big misconception that changing brake pad material will magically decrease your stopping distances. In fact, you may have even seen published ‘data’ which attempts to correlate stopping distance to friction coefficient. Although it may appear that there is a relationship between the two, there really isn’t…and here’s why.

The brake pads have the responsibility of squeezing on the rotor (a big steel disc which is mechanically attached to the road wheel) with the clamping force generated by the caliper. There is a lot of black magic surrounding the material composition and formulation of the friction puck, but what really matters is the effective coefficient of friction between the brake pad and the rotor face.

By knowing the clamp load generated by the caliper and the coefficient of friction between the pad and rotor, one can calculate the force acting upon the rotor. In this particular example, let’s assume the brake pads have a coefficient of friction of 0.45 when pressed against the rotor face. The rotor output force is equal to the clamp force multiplied by the coefficient of friction (which is then doubled because of the ‘floating’ design of the caliper) – or in this case {2,068 pounds x 0.45 x 2} = 1,861 pounds (see figure 5). Nothing magical about it.

By increasing the coefficient of friction of the brake pads, the results are the same as increasing the caliper piston diameter – higher forces will be generated for the same input. But as before, this force is not what stops the car. So why change brake pad materials in the first place? Because increasing the coefficient of friction can allow for the use of smaller/fewer caliper pistons and/or will reduce the amount of pedal force that the driver needs to apply in order to generate a given rotor output force.

That’s about it from a design standpoint, but the racer has another point to consider – heat! In the example above, the rotor output force was calculated assuming that the coefficient of friction between the brake pad and the rotor was constant, but in the real world, this is not the case. As the temperature of the components change, the physical properties of those components change, and in the case of the brake pads, the coefficient of friction can change dramatically! While street pads might have a coefficient of 0.30 around town, after a few laps on the track, the coefficient can drop to below 0.10, a condition commonly known as ‘brake fade.’ (note: this should not be confused with brake fluid fade which results from water in the brake fluid turning to vapor at high temperatures) On the racetrack, this means that the brake pedal force required to stop changes from lap to lap. And as racers, we know this can be kind of, well, ‘unsettling’ - to say the least.

So, back to the black art of friction materials. While a ‘coefficient of friction’ number is a nice data point to consider when modifying a braking system, what is even more important is the ability of the material to maintain that coefficient under a variety of driving conditions. Brake pads with radical changes in coefficient over their operating range are not a racer’s best friend. Be sure to select one that remains relatively stable under the operating conditions you are expecting, but don’t expect any shorter stopping distances, because, the brake pads don’t stop the car!