Back in
February, an article describing brake upgrades made to the GRM project Ro-Spit introduced
a number of basic braking concepts and reviewed several brake component upgrade
possibilities that are available to racers and enthusiasts. However, before any of us go
running off to the aftermarket for our own NASCAR 6-piston calipers, F1 carbon-fiber
rotors, and 50 feet of stainless steel braided brake lines, it would be wise to take a
deeper look into braking systems. We just might find that once we gain a fundamental
understanding of what each of these components really does (and more importantly,
what each does not do), we will be better prepared to make the right decisions when
modifying (or choosing not to modify) our own rides.
What Do Braking Systems Really Do?
Although Tim touched on this critical fact briefly in his
story, this is one of those statements that every racer should be forced to write on the
blackboard 1,000 times:
Your brakes do not stop your car. (999 to go - start writing…)
Of course, the next question is: "What DO your brakes do?" In
plain English, your brakes convert ‘the energy of motion’ into ‘heat’
An engineer would say the brakes are responsible for turning the kinetic energy of your
speeding car into thermal energy (see Sidebar 1 – Speed vs. Heat for more
details). But in either case, your brakes are not stopping your car. Surprised?
Sidebar 1 – Speed vs. Heat
Just for fun, let’s have a closer look at the equations for the
conversion of kinetic energy (KE) into heat (Q):
KE = ( ½ ) x (vehicle weight) x (speed of the vehicle)2
Q = (rotor weight) x (rotor material constant) x (temperature rise)
Since Mr. Isaac Newton stated that energy can be neither created nor
destroyed, all of the KE from the car must be completely turned into Q. What does this
tell us? KEbefore = Qafter!
Now, if we assume that…
the weight of the car stays constant with us
the weight of the rotor remains constant with use
Newton was right
…then the ‘speed of the vehicle squared’ is proportional
(directly related) to the ‘temperature rise in the brakes’. If you pull out your
calculator, you can prove that if the speed at which the brakes are used increases by 40%
(60 mph vs. 95 mph, for example), the temperature rise in the brakes resulting from that
stop would increase by nearly 100% {1.4 x 1.4}!
This factor is often overlooked by racers who add horsepower to their cars
and can’t figure out why their brakes don’t seem to work as well when they
‘only gained 10 mph’ on the straights. Lesson learned: small changes in speed
can have a huge impact on brake temperatures! |
So what DOES stop the car? Good question.
There are many "things" that can stop your car– and several of them have
nothing at all to do with your braking system. We all have experienced this first hand as
we let off the accelerator pedal and feel the vehicle begin to slow - even without
stepping on the ‘pedal in the middle’.
In theory, any "thing" that can generate a force
which opposes the motion of the car (like the wind pushing on the front of the car or
gravity as the car climbs the hill) will eventually stop the car; however, there are often
times that we need to slow at a greater rate than what headwinds and gravity can deliver.
In these cases, we depend upon the brakes to ‘assist’ in the stopping process.
The next logical question then would be, "how do the
brakes ‘assist’ in stopping the car?" To answer, we need to look at each of
the pieces of the braking system puzzle.
The Brake Pedal
Most GRM readers are probably somewhat familiar with the
brake pedal. But while most of us probably think of the brake pedal only as the flat part
that makes contact with the foot, remember that an equally important part of the brake
pedal assembly, the output rod, continues out of sight. Together, these parts
compose the brake pedal assembly.
The sole function of the brake pedal assembly is to harness
and multiply the force exerted by the driver’s foot. It does this thanks to a concept
known as "leverage." We all learned the concept of leverage on a teeter-totter
– the farther you sit from the middle (the pivot), the more weight you can lift on
the other end. In the case of the brake pedal assembly, the pivot is at the top of the
brake pedal arm, the pad (where we step) is on the opposite end, and the output rod is
somewhere in between. In the example illustration (figure 1), a driver input force
of 90 pounds is multiplied by the 4:1 ratio into 360 pounds {90 lb. x 4} of output force.
Does the output rod directly stop the car? No. So a) would we want to make
any changes to the brake pedal, and if we did b) how would this impact the brake system
performance?
There are several answers, each with their own set of pros and cons:
Increasing the ratio (8:1, for example) would further amplify driver
input force, but would make the pedal travel through a longer distance to achieve the same
output. In the given example, the 90 pound input would generate 720 pounds output, but
with twice the pedal travel.
Decreasing the ratio (3:1, for example) would reduce the overall size
and weight of the brake pedal assembly, but would decrease the amount of amplification
– the 360 pounds in the example would fall to just 270 pounds. To generate the same
360 pound output, the driver would need to press the pedal with 120 pounds of effort!
So, will changing the brake pedal make the car stop any faster? Not by
itself. But one can tune the pedal output force and pedal travel characteristics by making
changes to the pedal ratio.
The Master Cylinder
The 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:
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.
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
On 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
The 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:
Increasing the diameter will increase the compliance in the system (bad
news for pedal feel!)
Increasing the diameter will increase the size and weight of the caliper
(bad news for unsprung weight!)
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
This 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!
The Rotor
The 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:
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}.
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
Time 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:
Change the brake system to increase the force between the tire and the
road for a given pedal input force
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:
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.
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!
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.
- 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. |
