Braking

A family hatchback car needs 45 metres to stop from 60 MPH. An F1 car needs just 18 metres.

Braking Systems

In order for a race car to cover a section of track as fast as possible, it must do so in the shortest possible time. This means it must have a high speed. This can be shown as:
v = s/t

v: Velocity
s: Speed
t: Time

This is a basic equation most people will be familar with. So, in order for our speed to be as fast as possible and our time as small as possible, there are a few things we must make sure our car is good at:
– The top speed must be high
– It must have good straight-line acceleration (linear acceleration)
– It must have good cornering power (lateral acceleration)
– It must have good brakes (linear deceleration)

A car with good brakes has ‘feel’ in them. This gives confidence to the driver and this alone can reduce lap times.

Deceleration of a Car

To start with, we must start with the (slightly obvious) basics.

First, what is making our car decelerate? There are a combination of factors. Some factors will have more effect than others.

The factors are:

– Aerodynamic drag
– Engine braking
– The tyres’ rolling resistance
– Internal friction of the braking system
– Internal friction of the parts eg the bearings.

The only ones where there can be direct control are engine braking and the fricton of the braking system. Engine braking is not often employed in racing cars because modern brakes are so good. So, the main factor used is the friction of the braking system itself.

In order for any object to decelerate, it has to lose energy. This energy has been given to the object (the car) by the fuel via the engine. This energy gives the car it’s speed. The energy that needs to be lost is movement energy, otherwise known as kinetic energy. The law of the conservation of energy states that energy cannot be created or destroyed, however it can be changed from one form to another. The mathematical formula to state this is:

E = 1/2 mv 2 – 1/2 mu 2

Where
E = Energy dissipated by brakes in Joules (J)
m = Mass of car in kilograms (kg)
v = initial speed of car in metres per second (ms-1)
u = final speed of car in metres per second (ms-1 )

We can simplify this to:

E = 1/2 m(v 2 – u 2)

With braking systems, friction is used to convert the kinetic energy in the car into heat (and also a tiny amount of sound). This dissipates into the environment around the car – the air passing over the brakes carries away the heat and therefore the energy.

To give a sense of perspective, we can look at an example:

If our race car is running at 205mph and it has to slow to 75mph for the corner, and we know that it weights 600kg, we can work out the amount of energy the car needs to lose in order to achieve this braking. To make matters simpler, we will ignore aerodynamic drag although this would also dissipate some of the kinetic energy because the air flow over the surface of the car produces friction. This means our answer will only be an approximation,

First, let’s convert our mph figures into metres per second.

205 mph = 205 x 0.44704 = 91.6432 metres/second
70 mph = 70 x 0.44704 = 31.2928 metres/second

Put our figures into the aboe equation for energy:

E  = 1/2 x 600 x (91.64322 – 31.29282)

= 300 x 7419.236774 Joules
= 2225771.032 Joules

This is enough energy to light a 100W light bulb for six hours. If we factor in the aerodynamic drag, we will find that the overall figure is in fact slightly smaller as the drag has dissipated some of the energy away, hence slows the car slightly.

Performance

An F1 car can get from 200mph to a standstill in just 4 seconds and the driver will be subjected to about 5.2Gs. To achieve this immense deceleration, F1 car use carbon fibre brake discs. When braking into a corner, the discs will heat up from 400 degrees centigrade to 1000 degrees centigrade. This will happen up to 800 times per race.

F1 brakes are 28mm thick and have a diameter of 278mm. Each disc weighs less than 1kg. The discs themselves rotate at the same speed as the car wheel. The brake pad is located beside and around it. When the brake pedal is pressed, a caliper grasps the disc. Brake fluid is then pushed into pistons in the caliper. Often, the discs are drilled. This is to give them more air flow and help keep their temperature down.

Brake fluid is kept in two master cylinders which are housed in the car’s nose. The front and rear systems are connected separately so that if one fails, the driver will still be able to slow down because the second one will still be in operation.