If you skipped over the first two chapters, you missed the big news: brakes don’t stop your car. If you didn’t skip them, well, now you have heard it again. In case you have not caught on by now, this is a point that needs to be driven home.
Yet you know that when you press on the brake pedal the vehicle will, in most cases, slow down. Usually, the more you push on the pedal, the more deceleration you feel. Heck, the vehicle might even stop. Eventually, anyway.
Although the tire ultimately stops the car, it’s the combined contributions of the brake system components that multiply the driver’s leg force to stop the car. For this reason, methodical brake system design is required to ensure that all performance expectations are met. (StopTech)
Chapter 1 taught you that between the effects of tire rolling resistance, driveline frictional losses, and aerodynamic drag, the kinetic energy of the vehicle in motion can be absorbed without the need for a separate vehicle brake system. However, there are often times when the rate of energy conversion is not sufficient enough to produce an acceptable rate of deceleration (such as driving around town, let alone on a race track). This is where the brake system steps in, and certain modifications may prove useful to the casual driver, high-performance enthusiast, and pro racer alike.
Now, before analyzing the benefits (and tradeoffs!) of adjustable proportioning valves, 6-piston calipers, floating rotors, DOT 5.1 brake fluid, and stainless steel braided brake lines, it’s necessary to take a high-level look at a typical brake system. Knowing the roles of the individual components will better prepare you for the detailed discussions to come.
Driver Applied Force
Brake systems are fitted to vehicles in order to increase their deceleration capability. They accomplish this task by converting energy at a higher rate than the aforementioned passive mechanisms. In fact, the rate of energy conversion is limited only by the tractive capability of the tires and the thermal capacity of the brake system components.
None of this matters one bit, however, if the driver does not press on the pedal in the first place. If you neglect the effects of tire rolling resistance, driveline frictional losses, and aerodynamic drag for the rest of this chapter, it’s only the force exerted by the driver on the brake pedal that creates slip (and hopefully force) at the contact patch. It’s not quite like Fred Flintstone, but all of the force the brake system generates ultimately comes from the driver’s leg.
With that said, most people are not strong enough to decelerate a 3,000-lb vehicle at a reasonable rate from even 20 mph using only their leg muscles. The brake system is therefore designed to amplify the leg force generated by the driver (while of course still converting kinetic energy into heat). This brings forward the concept of brake system gain.
Gain
Gain is really nothing more than a fancy way of saying multiplication. The brake system gain relates the amount of brake system force input to brake system force output. In equation form:
Brake system gain (unitless) = total brake force (lb) ÷ driver’s leg force (lb)
For example, if a leg force of 50 pounds on the brake pedal nets a total brake force of 2,000 pounds at the four contact patches, the brake system gain is 40. You could also say that the system increased force at a 40-to-1 ratio, or that the gain was 40:1.
So where does the brake system gain come from? In brief, each of the brake system components is designed to provide its own gain through some type of mechanical advantage. The overall brake system gain is therefore equal to the individual brake system component gains all multiplied together.
The gain of a brake system component is simply the relationship between the force coming in and the force going out. In the case of a brake booster, the ratio of these two forces is called the boost gain. (Randall Shafer)
If a brake system is designed properly, even the very weakest driver should be capable of generating enough leg force to decelerate the vehicle at the limit defined by the tire-to-road interface. This dictates that every vehicle has a unique gain requirement. As a result, much of the art of brake system design revolves simply around developing the appropriate amount of gain.
Force Distribution
In addition to amplifying the driver’s leg force, the brake system must also distribute all of this amplified force to the four corners of the car, ultimately directing it to the four tire contact patches. It may also need to modify the brake force distribution as a function of deceleration, speed, or vehicle loading.
While brake force distribution is a critical responsibility of the brake system, you‘ll need to wait until Chapter 4 to learn more. For the remainder of this chapter, the focus is on brake system gain.
Brake System Overview
It’s now time to analyze the mechanical attributes, the functional responsibilities, and gain characteristics of each individual brake system component. Note that this is required reading before jumping to Chapters 5 through 10 which go into much deeper detail!
The Brake Pedal
Most people are already familiar with the brake pedal pad—it’s where you press to make the your vehicle stop! But while most of you are aware of the part of the pedal that makes contact with your foot, two equally important components of the pedal assembly, the output rod and fulcrum, are generally out of sight. Together, these three separate parts define the brake pedal assembly.
The brake pedal is really just a big lever under the dash. As driver applies leg force to the brake pedal, the output force is amplified based on the pedal’s geometry. (Randall Shafer)
The primary function of the brake pedal assembly is to harness and multiply the force exerted by the driver’s leg. The amount of amplification, or gain, is a function of the brake pedal leverage.
You probably learned the concept of leverage on a teeter-totter—the farther you sit from the middle (the pivot point, or fulcrum), the more weight you can lift on the other end. In the case of the brake pedal assembly, the fulcrum is at the top of the brake pedal arm, the brake pedal pad is on the opposite end, and the output rod is somewhere in between. Based on the distance between these features, the pedal ratio can be defined as:
Pedal ratio (unitless) = distance, pad to fulcrum (in) ÷ distance, output rod to fulcrum (in)
Because the distance from the pad to the fulcrum is longer than the distance from the output rod to the fulcrum, the pedal ratio is a value greater than one. For example, if the distance from the pad to fulcrum was 12.00 inches and the distance from the output rod to the fulcrum was 3.75 inches, the pedal ratio would be 3.2:1.
In order to calculate the brake pedal output force, one simply needs to multiply the driver leg force and the pedal ratio as follows:
Brake pedal output force (lb) = driver leg force (lb) x pedal ratio (unitless)
To put some real-world numbers into the equation, if a driver leg force of 41 pounds were multiplied by the previously defined 3.2:1 pedal ratio, the output rod force would equal approximately 131 pounds. At first glance this would appear to be a good thing, and in one regard, it is.
Because the driver can apply a significant amount of leg force to the brake pedal arm, it must be made strong enough to avoid excessive bending or deflection. The photo above compares an I-beam-shaped brake pedal arm on the right to a thinner clutch pedal arm on the left. (Randall Shafer)
Unfortunately, gain isn’t a free lunch. More gain brings more force multiplication, but at the cost of increased pedal stroke, or travel, which is generally viewed as undesirable. For example, doubling the pedal ratio to 6.4:1 would double the output (approximately 262 pounds of output rod force), but would require the pedal to travel twice as long of a distance to achieve this result.
The primary design compromise for the brake pedal therefore becomes juggling pedal ratio and pedal travel. You can’t have your cake and eat it too.
The Brake Booster
The brake pedal output rod force is fed through the firewall and into the back of the brake booster. Brake boosters, or simply boosters, come in many colors, shapes, and sizes, yet they are all designed to do the same thing—they amplify brake pedal output rod force. The booster’s inner workings can be quite complex, but fundamentally they rely on a pressure differential working across an internal diaphragm or piston to create a booster output force that is proportional to the brake pedal output rod force. In equation form:
Booster output force (lb) = brake pedal output force (lb) x boost gain (unitless)
Continuing the example, given a boost gain of 5.9:1 (typical for a conventional passenger vehicle brake booster), you can calculate that a 131-lb brake pedal output rod force would be translated into 774 pounds of booster output force.
