How Brakes Work
We
all know that pushing down on the brake pedal slows a car to a stop. But how
does this happen? How does your car transmit the force from your leg to its
wheels? How does it multiply the force so that it is enough to stop something
as big as a car?
When you depress your brake pedal, your car transmits the
force from your foot to its brakes through a fluid. Since the actual brakes
require a much greater force than you could apply with your leg, your car must
also multiply the force of your foot. It does this in two ways:
- Mechanical advantage (leverage)
- Hydraulic force multiplication
The
brakes transmit the force to the tires using friction, and the tires
transmit that force to the road using friction also. Before we begin our
discussion on the components of the brake system, we'll cover these three
principles:
- Leverage
- Hydraulics
- Friction
Leverage and Hydraulics
In the figure below, a force F is being applied
to the left end of the lever. The left end of the lever is twice as long (2X)
as the right end (X). Therefore, on the right end of the lever a force of 2F is
available, but it acts through half of the distance (Y) that the left end moves
(2Y). Changing the relative lengths of the left and right ends of the lever
changes the multipliers.

The basic idea behind any hydraulic system is
very simple: Force applied at one point is transmitted to another point using
an incompressible fluid, almost always an oil of
some sort. Most brake systems also multiply the force in the process. Here you
can see the simplest possible
hydraulic system:

Simple hydraulic system
In the figure above, two pistons (shown in red)
are fit into two glass cylinders filled with oil (shown in light blue) and
connected to one another with an oil-filled pipe. If you apply a downward force
to one piston (the left one, in this drawing), then the
force is transmitted to the second piston through the oil in the pipe. Since
oil is incompressible, the efficiency is very good -- almost all of the applied
force appears at the second piston. The great thing about hydraulic systems is
that the pipe connecting the two cylinders can be any length and shape,
allowing it to snake through all sorts of things separating the two pistons.
The pipe can also fork, so that one master cylinder can drive more than one
slave cylinder if desired, as shown in here:
Master cylinder with two slaves


Hydraulic multiplication
To determine the multiplication factor in the
figure above, start by looking at the size of the pistons. Assume that the
piston on the left is 2 inches (5.08 cm) in diameter (1-inch / 2.54 cm radius),
while the piston on the right is 6 inches (15.24 cm) in diameter (3-inch / 7.62
cm radius). The area of the two pistons is Pi * r2. The area of the
left piston is therefore 3.14, while the area of the piston on the right is
28.26. The piston on the right is nine times larger than the piston on the
left. This means that any force applied to the left-hand piston will come out
nine times greater on the right-hand piston. So, if you apply a 100-pound
downward force to the left piston, a 900-pound upward force will appear on the
right. The only catch is that you will have to depress the left piston 9 inches
(22.86 cm) to raise the right piston 1 inch (2.54 cm).
Friction
Friction is a measure of how hard it is to slide
one object over another. Take a look at the figure below. Both of the blocks
are made from the same material, but one is heavier. I think we all know which
one will be harder for the bulldozer to push.
To understand why this is, let's take a close
look at one of the blocks and the table:

Because friction exists
at the microscopic level, the amount of force it takes to move a given block is
proportional to that block's weight.
Even though the blocks look smooth to the naked
eye, they are actually quite rough at the microscopic level. When you set the
block down on the table, the little peaks and valleys get squished together,
and some of them may actually weld together. The weight of the heavier block
causes it to squish together more, so it is even harder to slide.
Different materials have different microscopic
structures; for instance, it is harder to slide rubber against rubber than it
is to slide steel against steel. The type of material determines the coefficient
of friction, the ratio of the force required to slide the block
to the block's weight. If the coefficient were 1.0 in our example, then it
would take 100 pounds of force to slide the 100-pound (45 kg) block, or 400
pounds (180 kg) of force to slide the 400-pound block. If the coefficient were
0.1, then it would take 10 pounds of force to slide to the 100-pound block or
40 pounds of force to slide the 400-pound block.
So the amount of force it takes to move a given
block is proportional to that block's weight. The more weight, the more force
required. This concept applies for devices like brakes and clutches, where a
pad is pressed against a spinning disc. The more force that presses on the pad,
the greater the stopping force.
Coefficients
An interesting thing about friction is that it
usually takes more force to break an object loose than to keep it sliding.
There is a coefficient of static friction,
where the two surfaces in contact are not sliding relative to each other. If
the two surfaces are sliding relative to each other, the amount of force is
determined by the coefficient of dynamic friction,
which is usually less than the coefficient of static friction.
For a car tire, the coefficient of dynamic
friction is much less than the coefficient of static friction. The car tire
provides the greatest traction when the contact patch is not sliding relative
to the road. When it is sliding (like during a skid or a burnout), traction is
greatly reduced.

Before
we get into all the parts of an actual car brake system, let's look at a
simplified system:
You
can see that the distance from the pedal to the pivot is four times the
distance from the cylinder to the pivot, so the force at the pedal will be
increased by a factor of four before it is transmitted to the cylinder.
You
can also see that the diameter of the brake cylinder is three times the
diameter of the pedal cylinder. This further multiplies the force by nine. Altogether,
this system increases the force of your foot by a factor of 36. If you put 10
pounds of force on the pedal, 360 pounds (162 kg) will be generated at the
wheel squeezing the brake pads.
There
are a couple of problems with this simple system. What if we have a leak?
If it is a slow leak, eventually there will not be enough fluid left to fill
the brake cylinder, and the brakes will not function. If it is a major leak,
then the first time you apply the brakes all of the fluid will squirt out the
leak and you will have complete brake failure.
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