## Aerodynamics

Aerodynamics

Aerodynamics is a large subject to generalize as it encompasses a wide range of techniques and applications. As this site is about Formula 1, this article is mostly about wings, rather than other forms of generating downforce such as tunnels in the case of indycars and airdams and splitters in saloon car racing. Some of these effects are used in one form or another in F1 so they will be covered briefly.

With 2006 cars running the less powerful V8 engines instead of V10 engines, aerodynamics are even more of a factor than ever. The V8 engines require less cooling than the V10s so teams invested a lot of time in reducing elements such as the sidepods and engine air takes to impove the aerodynamics of the cars.

The Bernoulli Principle

The Bernoulli principle has a big role in the operation of the aerodynamic surfaces of an F1 car. The Bernoulli principle is expressed by an equation (known as Bernoulli’s equation) which states that for a given volume of fluid, the total energy remains constant due to the principle of the conservation of energy. This means that When a fluid is in relative motion, the energy is split into the ‘parts’. The sum of these parts will not exceed a certain value which will remain constant as long as the external conditions do not change.

The three parts of the total energy are:

1)  The pressure energy within the fluid.
2)  The movement of the air (kinetic energy)
3)  The potential energy of the air (in this case, elevation)

This can be written as:

p + 1/2 r v2+ rgh = some constant

p = Pressure
r = Density of fluid
v = Velocity of fluid
g = Acceleration due to Gravity
h = Height of fluid above some reference point

Your average track is fairly level, so a race car will not have enough change in elevation to make the potential energy a variable, so we take this potential energy as a ‘constant’and therefore are able to remove it from the equation. This leaves us with:

p + 1/2 r v2 = some (other) constant

We can rewrite this as:

p + q = H

p = static Pressure
q = 1/2 rv2 = dynamic pressure
H = some (other) constant

This basically means that if the dynamic pressure increases, the static pressure has to decrease and if the dynamic pressure decreases, the static pressure will increase. This means that if we speed up a fluid, the pressure will fall.

Wings

We shall start by looking at a wing cross-section designed as it was meant to be used – to produce lift on an aeroplane. As the wing moves through the air it splits the air into two streams. One stream travels over the wing and one travels under the wing. Because of the way the wing is shaped, the distance across the top of the wind is greater than the distance across the bottom of the wing. This causes the air flowing over the wing to move faster than the air flowing under it.

As we have seen above, Bernoulli’s equation states that a faster moving fluid has a lower pressure than a slower moving one. This means that the faster moving air above the wing has a lower pressure than the air flowing under it. This pressure difference causes the wing to move towards the area of low pressure i.e. in an upwards direction. This phenomenon is known as lift and this is what keeps planes from falling from the sky. The lift on a wing is proportional to its’ area – the larger the area, the more lift is produced.

An inverted wing is used on racing cars. An inverted wing is basically a standard wing fitted upside-down. This means that the lift that is produced is in the opposite direction to a standard wing – this type of lift is known as ‘negative lift’, otherwise known as downforce. This downforce forces the car onto the road which in turn forces the tyres down onto the road with a lot more force than the weight of the car alone. The grip that tyres can produce increases roughly in a linear manner with increasing load (downforce in this case). Therefore with the increase in downforce, the load on the tyres increases meaning that the grip the tyres have is increased proportionately. This allows the drivers to go faster around corners than in a car without the downforce and produces significant time savings.

Usually, two wings are used – one at the rear and one at the front. This is done to balance the forces so that the grip is roughly equal at both ends of the car otherwise the handling of the car would be terrible, especially at higher speeds when maximum downforce is achieved.

Lift and Drag

A very important aspect of aerodynamics and wings to remember is, as mentioned, the dependence on speed. Speed has an effect on both the lift developed by the wing and also its drag. Drag is the resistive component of the lift force.

If you’re a fan of F1, or just a budding aerodynamicist, why not join our forum?

## 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

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.

## Tyres

Tyres

At top speed, an F1 tyre will be making 50 rotations a second. An F1 tyre will rotate approximately 150,000 turns over a full racing distance

Modern high performance tyre construction is a closely guarded secret maintained by a privileged few. However, there are similariteis in construction and performance between all the tyres that are a useful model for car performance optmisation.

The tyres is constructed around something call the ‘bead’. This is a steel ring which runs around the inside of the wheel rim. There are two beads per wheel – one fits the inside rim and the other, on the outside rim. These two beads are connected together by incredibly strong man made fibres – typically a material such as kevlar, nylon or rayon. These fibres are not set at 90 degrees to the rim – they are usually set at angles of about 2-9 percent from the true radial.

Grooving

If you have a smooth surface, the more rubber you have against the surface, the more traction you will have. By cutting grooves in the tyres, you lose some surface area meaning you lose some traction. An interview with Bridgestone’s Hisao Suganuma a while back quoted him as saying that a slick tyre may well be 2 seconds a lap quicker than a grooved tyre under the same set of conditions. The tarmac has to be smooth – not like our roads – so as to get the most traction. If you have conditions such as mud, obviously tread will give you an advantage as it will ‘bite’ into the road giving you better traction.

However, that isn’t the full story. The longer answer is, it depends on the track and the car.

Anytime you put a groove or a sipe into a tyre, the wear on the tyre will accelerate. The trick is to find a balance between grip and wear. You can sipe a tyre to prevent the tread surface from glazing over and becoming a slick tyre.

Soft and hard tyres will obviously also make a difference. Grooved soft tyres are normally best for qualifying or in short stints in the wet. They are best used when the track is moist and there isn’t a lot of friction. This is because they wear at a much faster rate than hard tyres, so you want to minimise the wear on them. Grooves in soft tyres help to clear away dirt and rain (hence also why wet tyres have deeper grooves in them than dry tyres). The softness of a tyre is determined by the amount of carbon, sulphur and oil in it. The more oil there is, the softer the tyre.

Hard tyres withstand grooving much better than soft tyres. On asphalt and similar surfaces, it is easy to run with no grooves at all. However, you can groove the shoulders of a tyre to help clean away loose dirt and moisture. You can also sipe the shoulders on hard tyres to help cars running lower tyre pressures on slick tracks. The sipes help to stop glazing and help reduce traction loss.

There are three main groove shapes which are used – square, V-shaped and sipe. Square grooves are the same width and depth all the way around. V-shaped grooves start out wide at the top and taper down to nothing. Sipes are thin slips cut by installing the blade upside down and using ends of the blade to cut slices in the tyre.

V-shaped grooves are often used where the track is expected to need more tread contact later in the race because as the tyre wears down, the grooves begin to shrink and then to disappear. Square tyres are almost the same, except that they are better on a more abrasive track. Sipes are used to make the tread more pliable. They also help to maintain a more consistent wear that helps keep the tyre uniform.

If a track gets hot, tyres may start to blister, or even melt. Grooving can help to control this by moving air across the tyres to keep the tread temps down. Grooving also increases the surface area by which heat can transfer away from the tyre. However, there is a fine balance between heat dissipation, and wear and tear on the tyre. The best balance is to groove in the centre of the tyre instead of cutting all the way across it to limit the weakening effect of the grooves. This is best because it means you have as few grooves as possible (for speed purposes) but gives a good cooling effect.

Slip Angles

Tyres do not go exactly where the driver points them unless they are going in a straight line. Slip angles are the degree of angular distortion which occurs from the twisting of the bead relative to the footprint ie the angle between the wheel’s actual direction of travel and the direction in which it is pointing. The slip angle results in a force which is perpendicular to the direction of the wheel’s travel. This is known as the cornering force. The cornering force increases approxmiately in a linear fashion for the first couple of slip angle degrees. As the slip angle increases more, the force increases in a non-linear fashion before starting to decrease again.

A tyre which has a non-zero slip angle will become deformed. As the tire rotates, the friction between the contact patch and the road result in individual tread ‘elements’ (infinitely small sections of tread) remaining stationary with respect to the road. If a side-slip velocity u is introduced, the contact patch will be deformed. As a tread element enters the contact patch the friction between road and tire means that the tread element remains stationary, yet the tire continues to move laterally. This means that the tread element will be deflected sideways. In reality it is the tyre/wheel that is being deflected away from the stationary tread element, but convention is for the co-ordinate system to be fixed around the wheel mid-plane. As the tread element moves through the contact patch it will be deflected further from the wheel mid-plane. This deflection creates the slip angle, and hence the cornering force.

F1 Specifics

F1 typres must have four longitudinal grooves on them. Each groove must be 2.5mm deep and spaced 50mm apart. The are constructed with very soft rubber compounds to give optimum grip. Because of this, they wear very quickly so tyre choice is a critical part of an F1 teams’ decision making process.

A car with a heavy fuel load will wear the tyres a lot faster. There will always be a compromise between achieving the best grip/wear rate from the tyres and the speed, fuel consumption and handling of the car. F1 cars shed a lot of rubber when cornering. These collect in little ‘balls’ at the side of the track and are commonly referred to as ‘marbles’. When a car goes over these marbles, the tyres lose contact with the track surface which can cause the car to slide due to the lack of grip.

Optimum tyre temperatures are generally between 90 and 110 degrees centigrade. Tyre warmers are used to heat the tyres up in the pit lane or on the grid to get them up to a about 90 degrees centigrade to provide the car with a reasonable level of grip. Within a few corners at racing speed, the tyres will be up to full racing temperature. Tyres at this temperature will in fact be hot enough to fry an egg on!

Pace cars can cause a number of problems for F1 cars – the tyre temperatures can fall below their optimum causing a lack of grip, and the suspension can bottom out.  Tyre pressure is a fundamental element of the suspension system – it affects both the spring rate and the ride height of the car. Gas increases in volume when it heats up. As the temperature in the tyres decreases, the volume of gas in the tyre will also decrease which causes a lower ride height. This can cause the car to bottom out and go off the road. Drivers will often weave from side to side when behind the pace car to keep the tyres warm and decrease their chances of damaging their cars.

## Suspension

Suspension

The suspension’s main job is to hold the tyres where the car’s designer of the car intended them to be. This usually means perpendicular (at ninety degrees) to the track. This permits the tyre to generate maximum grip as it’s footprint – the area in contact with the group – is as large as it can be. However, when the car is not in motion, the tyres are often not perpendicular. We shall see more about this below.

Another important job that the suspension of a racing car is to absorb the inevitable bumps in the track surface. This also plays a large role in keeping the tyres in their ideal position i.e. in contact with the road. It also makes the ride more comfortable for the driver, though in modern racing suspension settings are so hard that the travel is limited to just a few millimetres. This is mainly to optimise the aerodynamics of the vehicle than for any other reason.

The basics

There are a number of terms used to describe the motion of the car’s chassis. These are based on nautical descriptions of ships’ movement when at sea.

Heave: This is the motion of the chassis when all four wheels go up or down in unison – when the chassis goes up and down but there is no backward/forward or side to side movement

Pitch: This is when the front and rear of the chassis go in opposite directions – either up or down. However, there is no side to side movement. This oftern occurs when the car is under acceleration (the front of the car raises and the rear of the car is pushed down) and braking (the rear of the car raises and the nose dips).

Roll: This is the side to side movement of the car. This occurs when the suspension on the outer side of the car compresses as the innter suspension extends. This tends to occur whilst the car is cornering.

Warp: This is the movenemt of the diagonally opposed wheels in opposite directions eg the front right suspension compresses as the rear left extends out.

Yaw: This is the rotation of the car in the horizontal plane around a vertical axis. This usuallly occurs when the car is cornering.

Normally, these things will not happen in isolation. In reality, the movement of the suspension combines several of these things at any one time. The terms are used to combine chassis and suspension movement into their constituent parts to make it easier to understand.

There are also a number of terms to describe the location and alignment of the wheels and the hubs.

Track: This is the distance between the centrelines of the wheels. It can vary from front to back, and happens quite often.

Wheelbase: This is the distance between the front and rear axlelines. It is not supposed to be different side-to-side but can be with asymmetric cars or cars that have been damaged in accidents.

Toe-in and Toe-out: Toe-in and toe-out describes the angle of the front and rear wheels when viewed from above. When the fronts of the wheels are closer together than the rears, the pair of wheels are said to be toed-in. When the fronts of the wheels are further apart than the rears then they are toed-out. Sometimes the rear wheels are deliberately toed-in to make the car more stable under acceleration.

Camber: This is the angle of the wheel when viewed from the front or rear. Positive camber is when the tops of the wheels are further apart than the bottoms. Negative camber is the opposite and is most often used all round on a car, although it may not be the same on both the front and the rear wheels. Camber is generally the same from side-to-side on cars that have to turn in both directions. On cars that do not have to turn in both directions a great deal e.g. Indycars on the speedways, the camber can vary from side to side and this is often of benefit. Positive camber is rarely used except in the case of Indycars and sometimes one side of the car will have positive camber whilst the other has negative.

F1 Suspension

Suspension design in F1 has changed little in recent years. All teams now adopt inboard suspension operated via rockers by push or pull rods which are attached at one end to the rockers and at the other to the outboard end of the wishbone. Cars now use what is known as ‘active suspension’ which was first debuted by Lotus in 1987. This system means that the suspension arms in the car automatically move up and down ‘lifting’ the wheels over kerbs (as opposed to being devices which only move when the car hits potholes and bumps) meaning the car can maintain a more consistent ride height, which in turn means better downforce.

Front Suspension

Shock Absorbers on the top of the car’s nose absorb the bumps. These are not directly joined to the suspension arms, but are connected via push rods. The Anti-roll bar is located next to the shock absorbers. It prevents the car from tipping (‘rolling’) when the car is cornering. The Suspension Arms move up and down as the track surface undulates to try and keep the car’s height as consistent as possible.

Rear Suspension

The rear suspension must be able to handle all the traction and acceleration loads. The rear shock absorbers are mounted in a similar fashion to the front, but are placed next to the transmission.

## Composites and Chassis

The temperature in an F1 cockpit can routinely reach 50 degrees centigrade, despite the car moving at 200mph.

Composites

Modern F1 chassis are lighter and stronger than ever thanks to composite materials. One of the first major uses of a composite material in F1 was in 1966 when Bruce McLaren’s McLaren featured a chassis made of ‘Mallite’. This consisted of a layer of balsa wood sandwiched by two layers of aluminium and made for an incredibly light and stiff material. This concept is still used today except that the balsa wood has been substituted for aluminium honeycomb and the aluminium skin is today made of carbon fibre.

Carbon Fibre

Firstly, carbon fibre. In the composites industry things are done generally in layers. Each layer lies upon it’s neighbour and together they form a strong structure. In F1, a lot of these layers are made from carbon fibre and this is produced in the form of a cloth, made as the name suggests, from fibres of carbon. How the cloth is woven determines, to some degree, the component’s final physical properties. To ensure the resulting carbon fibre has optimal strength, each layer is laid a 45 degree offset to the layer beneath it. Typically a carbon fibre shell will have eight or more layers.

With a composite such as carbon fibre, it is important to remember that their great strength is available only when loaded in tension i.e. the ends of the component are being pulled apart. This is due to the fact that the fibres that are held in the resin, themselves have only strength under tensile loading. If any other loads i.e. compressive or bending loads are fed into a carbon component, it will usually fail under a much lower load than if loaded in tension.

The Chassis

The most important factor in a racecar chassis is that it must have as much torsional rigidity as possible. this means that it much be able to resist both twist and flex. The chassis must be able to twist and flex to an extent, however it should be minimised to reduce the risk of the chassis weakening (which produces poor handling) or even breaking. The more the chassis twists and flexes, the weaker the chassis becomes and the more prone it becomes to breaking. This is why chassis’s will be ‘retired’ after several races – the chassis will have lost some torsional regidity and hence need to be phased out.

The modern day race car chassis is a monocoque – this means it is a single shell that combines both the frame of the car and the bodywork. The FIA likens these monocoques to ‘survival cells’ as this is part of the car which is designed to protect the driver in the case of a crash. Extra materials are used around the monocoque – things such as crushable areas around the cockpit sides – to offer the driver a greater deal of protection. The cell itself is made from up to 12 layers of carbon fibre – this is twice as strong as steel and five times lighter.

No two teams have identical chassis, although they all follow the same basic principles. Things that may affect the chassis include the size of the fuel tank, the weight of the chassis and the downforce that can be produced. These things are likely to be tweaked from season to season and from team to team so the chassis are in a constant state of change.