How Formula One Engineers Use Science to Make the Fastest Cars in the World

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Abstract

Formula one also known as F1 cars are employed for Formula-one championships. Their unique feature is that they are single seater- open wheel racing cars. The wheels are outside the main car body. There is an engine which is placed behind the driver’s seat. This paper presents two major aerodynamics aspects of the Formula One Car: drag and downforce. Further, the research focuses on how various Formula One teams make the best use of the aerodynamic aspects of the car to make the cars the fastest. Furthermore, we discuss what exactly happens to the performance of a car in non-optimal weather conditions like rain, wind, freezing temperatures etc.

Keywords: Engineering Mechanics; Mechanical Engineering; Physics; Mechanics; Aerodynamics

Introduction

Formula One Racing is one of the most prominent forms of open wheel single seater racing cars. Open wheel cars are the cars that have tyres bulging out of the car’s main body unlike the conventional cars that we use daily that have tyres within the car’s body. The governing body for Formula One car is the Fédération Internationale de L’Automobile (FIA). Formula One racing involves 10 constructors also referred to as teams who compete for the world championship. Each constructor has two main race drivers with a few drivers as reserve. An individual formula one team can have number of people varying from 200 to 1200 people. A ton of money is invested in making formula one cars. For instance, as per the report of Motorsport magazine in 2018, Mercedes Benz AMG Formula One had a budget of 326 million euros in the year 20181,2. The race time has a 2-hour limit. All the cars are fuelled completely at the start of the race and refuelling is not allowed in between the race3.

Motivation

Formula One cars are similar to puzzle pieces. The individual pieces come together to form the whole puzzle. Similarly, there are multitude of components like design of the car; aerodynamic aspects like downforce, drag; and traction between the tyres and the track that come together to produce a car capable of clocking speeds over 300 km per hour. The maximum amount, called the Budget cap, a team can invest in making this racing car is fixed in order to make the competition a fair and level playing field.

Defining Research Questions

To do a systematic study of the domain, a variety of Research Question (RQs) have been established. These RQs are as listed below.

  • RQ1: What are the Aerodynamics aspects involved in F-1 cars?
  • RQ2: What are the important design elements for F1 cars?
  • RQ3: Why do cars heat up and why is cooling them essential?
  • RQ4: What the various weather conditions that effect the performance of the formula-one car?

The remainder of the review article is structured in such a way that Section 2 describes the various aspects of aerodynamics of formula-one car. The design Elements of the F1 cars is presented in section 3. The reasons for heating of cars and the ways to cool them is discussed in section 4. Next section highlights the weather conditions that effect the performance of
formula-one cars. Lastly the paper is concluded in section 6.

Aspects of Aerodynamics’ in Formula One Car

Initially, the primary focus was to have a streamline body of the car which helped in minimizing the air resistance. Then the researchers found that aerodynamics played a major role in the performance of the racing cars.

Aerodynamics is a field of fluid mechanics that deals with the flow of air around any object4,5. Specifically in the case of a Formula one car, aerodynamics means how the air interacts with the design of the car. Even the smallest aspects of a car can affect its aerodynamic performance. In fact, the driver’s helmet also contributes to the aerodynamic aspect of the car. Aerodynamics of the formula one car depend majorly on two types of forces: downforce and drag. The optimal combination for the formula one car is to have maximum downforce and minimum drag.

Drag

Drag is the air resistance that the car feels while moving through air at high speeds. This force resists the forward movement of the car. The formula one cars have a streamlined body shape that allows the car to move forward with experiencing the least drag. Streamlined shape means a shape that experiences very less resistance to the flow of fluids (in this case, air). However, there is a Drag force that opposes the path of the F1 car and causes it to slow down. Drag is the horizontal part of the aerodynamic force generated by the car as it moves through the air6. Nonetheless, air serves a much greater purpose in the overall design of the car.

Figure 1 explains that drag is also produced as a by-product of generation of downforce. The air is acting towards the direction of the wing as shown in the figure which is diagonally downward. Then this net force that is acting diagonally downwards will have one force acting towards right (drag) and towards to the ground (downforce). The resultant ‘net force’ is experienced in the direction as shown in figure 2. This net force is obtained as a result of force vectors- drag and downforce.

Resolution of two vectors: Drag and Downforce)7,8

Downforce

It was in the year 1960’s that engineers got to know about downforce. In a layman’s language, downforce is the downward force being applied on the car that makes the car better with the track providing it with much more traction allowing it to steer through corners. To add further, reducing the drag, helps the car to move at high speeds on the Straight. Straight is the part of the track where there are no corners. On contrary, it is the downforce that allows the car manoeuvre through the corners at high speeds. The formula one cars are designed in such way that they stick very close to the ground9.

Downforce is defined as the downward force that allows the car to keep a good hold with the track and have high cornering speeds. The wings and the overall design of the car contribute in producing downforce. Downforce is primarily impacted by three theories, namely, the Venturi effect, Bernoulli’s theorem and the Continuity Equation.

Venturi effect

Venturi effect states that whenever a fluid is allowed to pass through a constricted area, the pressure of the fluid decreases. Also, when the fluid passes through a larger area, the pressure increases10.

Bernoulli’s theorem

Bernoulli’s theorem gives us a mathematical expression between fluid pressure and velocity of the fluid.

There is an inverse relationship between fluid pressure and velocity of the fluid. Meaning, if the velocity of a fluid decreases, the pressure of the fluid increases and vice versa. The Bernoulli’s Theorem is represented numerically as in equation 1 and 211.

    \[P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2\]

    \[P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = \text{Constant}\]

Continuity Equation

The air flows faster under the car as compared to air’s speed in the atmosphere. This can be explained with the help of continuity equation which describes a relationship between area and velocity. As the product of area and velocity is constant, a decrease in the area causes the velocity to increase. Since the car is extremely close to the ground, so the area is significantly reduced. This causes the speed of the air flowing under the car to increase12. This eventually creates a vacuum effect. Thus a downforce is created giving the tyres more traction (grip) with the track. Below Equation shows the expression for the Continuity Equation13.

    \[A_1V_1 = A_2V_2\]

Where,
(A_1) = Area of cross-section of region 1
(V_1) = Flow velocity in region 1
(A_2) = Area of cross-section of region 2
(V_2) = Flow velocity in region 2

Combined Effect of Venturi effect, Bernoulli’s theorem, and continuity equation

The designers, engineers and the aerodynamicists exploited these principles to design the fastest cars on the planet. The formula one cars are designed in such a manner that they are extremely close to the ground which allows them to move faster due to increased downforce. Venturi effect, Bernoulli’s theorem, and continuity equation help us explain this phenomenon.

In the case of the formula one car, low ground clearance decreases the areas which increases the velocity of air passing under the body. Bernoulli’s theorem states that whenever a fluid is moving at a high speed, the fluid will create an area of low pressure. The same thing happens when the air under the body of Formula one car moves with high speed creating a low pressure under the car. The fluid always moves from an area of high pressure to an area of low pressure. The

pressure of air is high around the car comparatively to the pressure of the air under the car. Thus, pushing the car to the ground and increasing the traction between the tyre and the track. The traction between the tyre and the track determine the grip and speed of the car. The more grip a tyre has, the driver will feel more confident about the car and will be able to manoeuvre the car more efficiently which will indirectly affect the performance in the race. More traction with the track also enables the formula one car to have high cornering speed. Since all the race tracks are not straights and have curves, it becomes essential for cars to maintain a good high speed even while it is turning on the corner14,15.

To summarize, the three significant factors that play a major role in helping a Formula One car to reach lightning speeds are increasing downforce, reducing the drag and reducing the friction between the tyres and the track. Since a long time, the designers, the engineers and the aerodynamicists have been experimenting with the design of the car so the car experiences the least drag and produces the maximum downforce. For the car to run at great speeds with the help of downforce and drag, the car must maintain its optimal temperature. There are numerous design elements incorporated in a formula one car to maintain its optimal temperature while it is racing16.

Not only aspects like downforce, drag and design affect the performance of the car, even the design of the tracks influence the performance of the car. Some tracks require cars to produce the maximum downforce whereas the other tracks require car to experience the least drag17.

Types of Tracks

There are two types of tracks that a team can experience during a race: High downforce tracks and power tracks. In a high downforce track, it is the downforce of the car that provides the essential power for the car to move around the circuit. The power of engine does not contribute that much to the performance of the car as compared to the downforce. In a high downforce track, we experience a lot of corners rather than straight ways. For instance, the Monaco grand prix has a lot of corners and cars here are set up to high downforce setup to allow the drivers manoeuvre the car around the corners without any difficulty.

In comparison to the high downforce tracks, we have power tracks where there are more straight ways rather than corners. Here the cars must have the ability to overcome the drag experienced by the cars. This drag resistance of the car is overcome by the power of the engine. Downforce does not contribute that much to the overall performance of the car18.

Other Factors

Thrust Angle

It is an imaginary line which is 90 degrees from the centre line of the rear axle. The driver can increase/decrease the thrust by either changing the gears or by revving the engine or by both. However the weight remains constant. For cars running on the straight track, the thrust angle coincides with the vehicle centre line. But, in case of circular racing tracks, the thrust angle can affect the rear steer. So, this thrust angle can be altered based on conditions of the track19.

Lift and Coast

It means that the driver lifts his foot off the throttle before encountering the turn and then coasts into it. This saves fuel, but on the cost of slowing down the vehicle. The slowing down of the car helps it to push even more and thus helps it to come out of the corner. Coasting means that the racing car is going down an incline by gravity and by the vehicle’s momentum20.

Weight

The weight of cars has increased by 5\% approx. Now the weight is nearly 800 kilos. This is because the wheels are heavier now. These new tyres are designed in such a way that they are less prone to overheating. Also, the safety requirement to protect the drivers has increased21.

Design Elements of a formula one car: A Formula

Formula One car is a complex piece of machinery that requires tremendous efforts from the designers, aerodynamicists and the engineers to develop a car that is better than all the other cars on the track. The various parts of a formula one car are: wings, sidepods, tyres and the diffuser. The wings are further classified into a frontinto front wing (present at the front of the car) and a rear wing (present at the end of the car). All these parts of the car play a significant role in the overall flow of air through and around the car.

Front Wing

The front wing plays a prominent role in the overall flow of the air through the car since it is the first and foremost part of the car that comes in contact with the air. Therefore, the front wings have to be designed closely. The front wing also have different parts to it: Nosecone, end plates. Nosecone is an inlet in the centre of the wing that directs the clean air under the body of air which allows to create downforce. The mechanism how downforce is created due to this clean air is described under the section of aerodynamics22.

The end plates of the front wing produce vortices (Tornadoes of clean air) to pass them through the side of the tyre without going over the tyre as that air will become turbulent (air that interacts with the tyre becomes turbulent since it does not flow in a linear flow) and will affect the overall aerodynamics of the car. This air is used by the side pods. Upper wing of the front wing helps in making the clean air pass over the front tyres without making the air turbulent and eventually goes into side pods which eventually cools the engine and other components which is further explained under the heat section. The front wing is the exact opposite of an airplane wing. The air above the wing experiences resistance while moving due to the shape of the wing reducing the velocity creating high pressure due to Bernoulli’s theorem. Low pressure under the wing because the air experiences no resistance due to the unrestricted flow under the wing. This increases the velocity of air under the wing which eventually creates a low pressure due to Bernoulli’s theorem. Therefore, air moves from high pressure to low pressure and pushes the car towards the car. Hence downforce. The angle of attack can be adjusted. The wing can be moved up creating more downforce and lowering the wing will create less downforce since less high pressure will be created23.

The side angle of the rear wing of Formula One Car24.

Rear Wing

The rear wing of Formula One Car contributes in generating downforce. For simplicity, we will be understanding the functioning of the wing in an airplane which produces lift and exactly the reverse of this helps in producing downforce. As seen in figure 2, the air flows above the wing and below the wing and eventually meets at the end of the wing25.

The area covered by the air above the wing is much more than the area covered by the air below the wing. Therefore, to meet at the same time the air above wing have to move with much greater speed than the air moving below the wing. As per Bernoulli’s theorem, an area of low pressure is created above the wing due to high velocity of air and an area of high pressure is created below the wing due to low velocity of air. Air, for that matter fluids, always move from area of high pressure to low pressure. As a result, the air pushes the wing in the upward direction producing lift and allowing the plane to fly in air. This is the exact opposite in the car of a formula one car. Area of high pressure is generated above the wing and an area of low pressure is generated below the wing. As a result, the air pushes the car to the ground providing it with more downforce26.

Diffuser

Diffuser plays an important role in the overall aerodynamics of the car. It works on the Venturi effect and Bernoulli’s theorem. Therefore, pressure at the back of car increases. There is low pressure already under the car. There is higher pressure difference. Therefore, it creates a vacuum effect so more is the downforce27. The diffuser at the back of the car have divider in it which reduces the amount of turbulent flow making the air flow in a more linear manner. Resulting in an overall increase in performance of the car28.

Sidepods

Sidepods are inlets that are just beside the cockpit which allows fresh and clean air to enter through this. Sidepods also have the radiators which help in cooling the internal parts of the car. This is further explained under the cooling section of this paper. Side pods eventually open at the end of the car to allow hot air to rush out of the car. The teams often increase the size of the rear openings of the sidepods during a hot race such as Bahrain Grand Prix because the more and more air is required to cool the components of the car. Therefore, a bigger outlet of the sidepod is required at the end of the car to allow this hot air to exit29.

Tyres

Another significant part of the Formula One car which is the tyres of the car. The optimal temperature at which these tyres perform to their maximum is at 1000C. The reason for this is that the tyre has a lot of traction with the road allowing the driver to manoeuvre the car at high speeds at the corner. To keep the tyres at their optimal temperature, the Formula One teams use various techniques. The new tyres which are not under use are kept under tyre warmers which is connected to a heater which keeps the tyre at the optimal tyre temperature that provides the maximum traction. Once the tyre is put on the car, the engineers in the pit always keep them wrapped in tyre blankets so that the tyre temperature does not degrade or fall below the optimal temperature. Naturally the tyre is at optimal temperature during the race because of the friction that is produced between the tyre and track. Heat is always a by-product of friction. As a result, the cars are faster on hotter tracks such as Bahrain Grand Prix or Saudi Arabia Prix because of the atmospheric heat which contributes to keep the optimal temperature of the tyre30.

Types of Tyres

There are five different types of tyres available in Formula One Cars which are soft, medium, hard, intermediates and wet. The name is derived from how hard the rubber is on the tyres. For instance, soft provides the maximum grip and the maximum speed but at the same time wears at the fastest rate. On contrary hard do not provide that much grip as compared to soft but it runs for the longest time. The choosing of tyre boils down to strategy and conditions of the track. The soft tyres are ideally suggested for short time period where a driver needs maximum pace. For instance, the qualifying where each driver tries to completes one lap of the track in the shortest time which will decide the starting positions for the race on Sunday. On contrary, hard tyres are suggested for long run because they don’t degrade as fast as the mediums and the softs31.

Impact of heating and Cooling

Formula one cars operate at very high speeds. At these high speeds, the cars heat up to very high temperature. So, cooling of engine, gearbox, brakes etc is essential. This section describes the heating and cooling effect on the performance of the formula-one car.

Heating Effect

Formula one cars can become a scorching ball of heat due to the various components of the car that produce heat including the combustion engine and the hybrid system of the car. For the car to perform to its optimal efficiency and performance, it is integral to cool the various heating parts of the formula-one car as we move through the race. The basic principle behind cooling of any substance is that a colder substance is used to cool a hotter substance. The cooler substance encounters the hotter substance, takes the heat away from the hotter substance till the point both the substances are at the same temperature. To cool components in a formula-one car, we must keep doing it continuously and it should not be a static process. The most significant coolant is the air flowing through the car. The aerodynamicists must design the car in such a manner that the air aids in cooling the components of the car but at the same time do not affect the streamline flow of the air around the car which allows to reach glass shattering speeds during the race32.

It is important for the Formula One car to maintain the optimal temperature both while it is moving at glass shattering speed during the race and while it is standing still at the start of the race at the grid.

Cooling Effect

Cooling of cars and the drivers driving these exquisite pieces are important. Cooling while moving as well as when stationery is to be kept under consideration.

Cooling while Moving: The air not only helps in the overall aerodynamics of the car but also plays a pivotal role in the cooling of the different components of the car which the ICE M(internal combustion engine), MGU-H (Motor generator unit-hybrid), MGU-K (Motor generator unit-kinetic) and the electronics of the car. Here we specifically talk about cooling the combustion engine while the car is moving through air while racing. Talking about the engine of the Formula One car, the aerodynamicists use a mixture of water and glycol to cool the engine. This mixture is allowed to pass through the various parts of the engine through a pipe. By convention the heat flows from a higher temperature to a lower temperature and this mixture being cooler than the engine takes the heat away from the engine, reducing the engine temperature. Formula One cars specifically use a mixture of water and glycol because the mixture have a high boiling point of 2280 Fahrenheit allowing it to withstand the excruciating heat evolved by the engine. This mixture is pumped through the engine and the colder air from outside through the radiator is allowed to interact with the mixture of water and glycol that has absorbed heat from the engine. The cooler air is allowed to enter the radiator through airbox which is an inlet just situated above the cockpit. Colder air is allowed to take the heat away from this hot mixture which is allowed to escape the car through the exhaust situated behind the car to prevent it from doing any damage to the car. The same principle is used to cool the gearbox of the formula one car but instead of using a mixture of water and glycol, the Formula One cars use oil to cool down the gearbox. The brakes are cooled with the help of fast-moving air which absorbs the heat from the hot brakes and exits the car after it has absorbed the heat33.

Cooling while stationary: Cooling mechanism is also required when the car is stationary i.e. either standing at the grid for the start of the race or in the pit lane. The engineers make use of an external leaf blower to mimic the flow of air around the car when it is moving. However, they use dry ice (which is solidified carbon dioxide) at the inlet of the leaf blower so that the air pumped out of the blower is cool enough to cool the components of the car and to fulfils its function. Dry ice is used due to its property of sublimation. It converts directly from solid to gaseous form without converting into liquid state. This helps the engineers without causing any water leakage on the track34.

Cooling the Drivers: Another aspect of cooling is that the drivers who drive these magnificent cars also needs to be cooled down during the race as the cockpit temperature can reach a searing 1220 Fahrenheit. Such high temperatures are beyond the the limit that a normal person can bear. Over a 2-hour race period a driver loses about 3 kg of bodily fluid due to dehydration during the race.

There are few things that help in cooling the drivers. Drivers usually have cooling collars that have dry ice filled in them to cool down the blood. In addition, they have cooling vests filled with dry ice that help in cooling various parts of the body which include the chest, the back etc. Above all of this, it is the driver’s training and resilience as well as the passion for the sport that allows him to endure such extreme weather conditions. Many of the drivers train with their racing suits on or train in sauna to make their bodies accustomed to the excruciating high temperatures of the cockpit35,36.

Impact of Weather Conditions

The formula one cars are designed in a such a manner that they are able to endure all the extreme weather conditions around the world as they drive in varied weather conditions around the world. The impact of various weather conditions like rain, wind, freezing temperature etc on the performance of F1 car are discussed in this section.

Rain: Rain can prove to be a challenge for formula one drivers because rain drastically reduces the friction between the tyre and the track giving it the least grip possible. For a formula one car to perform to its optimal level, the grip between the tyres and the track should be high. To combat this problem of grip or traction, Pirelli (the official tyre manufacturers that provide all teams of formula one with tyres) introduced two different compound tyres which are the Wet tyres and the Intermediate tyres.

Wet tyres are suggested to be used when there is standing water on the track and intermediates are to be used when the track is wet and there isn’t much standing water on the track. These tyres have treads in them that increase the traction between the tyre and the track.

In addition to the problem of grip, drivers also experience visibility problems because of the mist that flows from the car in front. It is the skill of the driver that helps him to tackle this problem. In some scenarios, the teams might want to raise the front part of the car a little higher than usual if there is standing water on the track to help improve the visibility of the driver. However this reduces the aerodynamic flow of air under the car making the car go slower than usual. As discussed in above sections, the closer the car is to the ground, the quicker it will go because of the continuity equation, Venturi effect and Bernoulli’s theorem37.

Wind: The wind does not affect the overall aerodynamics of the car as much but strong gusty winds can definitely affect the flow of air around the car. Thus, the teams have to prepare for such scenarios well before the race begins. A wind that is flowing in the direction of motion or the direction in which the car is moving will help the car move even faster because it cancels out or reduces the drag experienced by the car. On contrary, a wind that is flowing against the direction of motion or against the direction in which the car is moving will make the car move slower as the drag increases, resisting the motion of the car. It is similar to the effect when we are moving against the wind, we feel resistance from the air and difficulty in moving forward.

Freezing temperatures: Very low or freezing temperatures is another challenge that needs to be taken into consideration. During such weather conditions, it is difficult to heat the tyres. The tyres have low grip as the friction is less. Before the commencement of race, blankets were used for the tyre to increase their temperatures. But these have been banned. The best performance of tyres is expected at around 1000 F38.

Strategy: The bridge between winning and losing a Formula One race is strategy. The aim is to make the car perform to its maximum potential so that it is performing better than other cars on the track and finish the race at the highest possible position. Though the weather conditions are not under one’s control, however decision on type of tyre is a key factor of strategy. Therefore, a strategy has to be devised to chose the type of tyre amongst Soft, Medium, and Hard tyres. Soft tyres provide the maximum grip and allow the car to have a good pace but at the same time they wear out at a rapid pace as compared to medium and hard compound tyres. Though, medium and hard tyres tend to last for a longer time, but they don’t provide as much pace as the soft compound tyres. It is eventually the work of the strategist to decide which type of tyre to use depending on various conditions which include weather conditions, fuel burn rate, track degradation and many other factors. Another thing that is of concern to strategists is the amount of fuel that must loaded into the car. Until 2010 refuelling was allowed but due to some bad accidents while refuelling during the race, it was banned by FIA. The more the fuel in a formula one car, more is the lap time it takes to cover one lap. As a result, it is not suggested that the car is filled till its maximum fuel capacity because it will cost team in time and reduce their chances of winning the race38.

Conclusion

Formula-one cars are racing cars. They are single seater, open cock-pit with wheels outside the main body of the car. The engine is behind the driver. These operate at very high speeds. Therefore factors like aerodynamics, weather conditions, type of tyres, heating and cooling effects are important to ensure their desirable performance. This research paper discusses the drag and downforce, which forms the important component of aerodynamics. Downforce is impacted by three theories, namely, the Venturi effect, Bernoulli’s theorem and the Continuity Equation. Not only aspects like downforce, drag and design affect the performance of the car, even the design of the tracks influence the performance of the car. Also, there are various design elements of these racing cars like wings (front and rear), sidepods, tyres and the diffuser. The paper discusses the heating and the cooling effect on the performance of the formula-one car. Further, the impact of weather conditions like rain, wind and freezing temperatures, on the performance of formula-one cars is described.

Acknowledgement

I would like to express my deepfelt gratitude to Dr. Davio Cianci, a PhD graduate in Physics from Columbia University, for guiding me to write this research paper.

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