A Study of Kinetic Energy Recovery Systems

Fourth Year Major Project

For the Degree of

M.Eng. in Mechanical Engineering

Journal Paper

Iain McLeod Rourke

072383414

A Study of Kinetic Energy Recovery Systems

April 2012

Project Supervisor: Dr. Daniil Yurchenko

School of Engineering and Physical Sciences

Mechanical Engineering

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Year Mechanical Engineering

A Study of Kinetic Energy Recovery Systems i

A Study of Kinetic Energy Recovery Systems

Iain McLeod Rourke

Supervisor: Dr. Daniil Yurchenko

M.Eng. Mechanical Engineering

School of Engineering and Physical Sciences

Heriot-Watt University

Riccarton

Edinburgh

EH14 4AS

Scotland

I Abstract

In an age of high fuel prices and growing environmental concern, research and development

into more fuel efficient vehicles has grown over the last decade. While mainstream car

manufacturers strive to provide their customers with more economic, low carbon vehicles,

members of the motorsport community are beginning to introduce new fuel saving

technologies into racing in an effort to make the sport more relevant and reduce its impact on

the environment. A technology known as Kinetic Energy Recovery Systems (KERS) has

shown great potential in reducing the fuel consumption of vehicles. KERS have been used in

the 2009 and 2011 seasons of Formula-1 and are beginning to emerge in mainstream

production vehicles. The main aim of this paper is to develop a mathematical model of

Heriot-Watt University’s Formula Student Car in an effort to quantify the reduction in fuel

consumption if KERS were to be implemented. The model takes the form of a simulated lap

of a known circuit. The simulation is dynamic and allows the user to investigate different

vehicle setups as well as explore various track layouts.

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A Study of Kinetic Energy Recovery Systems ii

II Table of Contents

I Abstract ............................................................................................................................... i

II Table of Contents ............................................................................................................... ii

III Table of Figures ................................................................................................................ iv

IV Nomenclature .................................................................................................................... vi

1 Introduction ..................................................................................................................... 1

2 Literature Review ............................................................................................................ 1

2.1 A Brief History of KERS ......................................................................................... 1

2.1.1 KERS in Formula-1 .......................................................................................... 1

2.2 System Designs ........................................................................................................ 2

2.2.2 Electrical KERS (Battery Based Design) ......................................................... 2

2.2.3 Mechanical KERS (Flywheel Based Design) ................................................... 2

2.3 How Mechanical KERS Work ................................................................................. 5

3 Objectives ........................................................................................................................ 6

4 Lap Simulation ................................................................................................................ 6

4.1 Vehicle Setup ........................................................................................................... 6

4.2 Acceleration Model .................................................................................................. 8

4.3 Deceleration Model ................................................................................................ 10

4.4 Cornering Model .................................................................................................... 11

4.1 Track Breakdown ................................................................................................... 12

4.2 Velocity Profile ...................................................................................................... 14

4.2.1 Straights .......................................................................................................... 14

4.2.2 Corners............................................................................................................ 16

4.2.3 Feature Time ................................................................................................... 17

4.3 Force Analysis ....................................................................................................... 18

4.4 Using KERS ........................................................................................................... 19

4.4.1 System Implementation .................................................................................. 19

4.4.2 Flywheel Design ............................................................................................. 20

4.5 Energy Storage ....................................................................................................... 21

4.6 Energy Transfer ..................................................................................................... 22

4.1 Power Analysis ...................................................................................................... 23

4.2 Fuel Consumption Analysis ................................................................................... 24

5 Discussion ..................................................................................................................... 25

5.1 Fuel Savings ........................................................................................................... 25

5.2 Brake usage ............................................................................................................ 25

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A Study of Kinetic Energy Recovery Systems iii

5.3 Optimisation ........................................................................................................... 26

5.4 Other uses for Simulation ...................................................................................... 26

6 Conclusion ..................................................................................................................... 26

7 Future Work Plan .......................................................................................................... 27

7.1 Objective ................................................................................................................ 27

7.2 Simulation Improvements ...................................................................................... 27

7.2.1 Engine Capabilities ......................................................................................... 27

7.2.2 Performance Boost ......................................................................................... 28

7.3 Research Methodology (Physical Testing) ............................................................ 28

7.3.1 Determining Resistive Forces on the Car ....................................................... 29

7.3.2 Acceleration/Deceleration Tests ..................................................................... 30

7.3.3 Fuel Consumption Test ................................................................................... 30

7.4 Cost Estimation ...................................................................................................... 31

7.5 Planning ................................................................................................................. 31

7.6 Summary of Future Work Plan .............................................................................. 32

8 Acknowledgements ....................................................................................................... 33

9 Bibliography .................................................................................................................. 34

9.1 Textbooks ............................................................................................................... 34

9.2 Journals .................................................................................................................. 34

9.3 Technical Papers .................................................................................................... 34

9.4 Lecture Notes ......................................................................................................... 34

9.5 Internet Sites .......................................................................................................... 34

10 References ................................................................................................................. 35

11 Appendices ................................................................................................................ 36

11.1 Appendix-A: Simplified Track Layout ............................................................. 36

11.2 Appendix-B: Large Image of STCC_Jyllan ...................................................... 37

11.3 Appendix-C: Additional Graphs ....................................................................... 38

11.4 Appendix-D: Spreadsheet User Guide .............................................................. 40

11.5 Appendix-E: Images of Spreadsheet ................................................................. 43

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A Study of Kinetic Energy Recovery Systems iv

III Table of Figures

Figures

Figure 1: Exploded view of a Flywheel based KERS Unit [] ................................................... 3 Figure 2: Assembled Sectional view of Flywheel based KERS Unit [] .................................... 4 Figure 3: Assembled Flywheel with Scale [] ............................................................................ 4 Figure 4: Potential Locations for Flywheel Hybrid System [] .................................................. 4 Figure 5: Elevation of Formula Student Car [] ......................................................................... 7

Figure 6: End Elevation of Formula Student Car [] .................................................................. 7 Figure 7: Free Body Diagram for Accelerating Formula Student Car ...................................... 8

Figure 8: Free Body Diagram for Decelerating Formula Student Car .................................... 10 Figure 9: Cornering Diagram [] .............................................................................................. 11 Figure 10: Aerial Photograph of Race Track STCC_Jyllan Scale: 1:1250 [] [] .................... 13 Figure 11: Close-up of Turns 4, 5, 6 & 7 ................................................................................ 13 Figure 12: Close-up of Turns 15, 16, 17, 18 & 19 .................................................................. 13

Figure 13: Drive Cycle Breakdown as a Percentage of Total Lap Time ................................ 14 Figure 14: Velocity Diagram for a Straight ............................................................................ 15 Figure 15: Velocity Diagram for a Corner .............................................................................. 16 Figure 16: Layout of the Rear of HW-02 [] ............................................................................ 19

Figure 17: Design of Composite Flywheel [] .......................................................................... 20 Figure 18: Breakdown of Testing Budget ............................................................................... 31

Figure 19: Gantt chart for Proposed Work .............................................................................. 32

Figure 20: Layout and Dimensions of Simplified Track ......................................................... 36

Figure 21: Large Image of Race Track STCC_Jyllan [19] ..................................................... 37 Figure 22: Screen Shot of Sheet-1 ........................................................................................... 43 Figure 23: Screen Shot of Sheet-2 ........................................................................................... 43

Figure 24: Screen Shot of Sheet-3 ........................................................................................... 44 Figure 25: Screen Shot of Sheet-4 ........................................................................................... 44

Figure 26: Screen Shot of Sheet-5 ........................................................................................... 45 Figure 27: Screen Shot of Sheet-6 ........................................................................................... 45 Figure 28: Screen Shot of Sheet-7 ........................................................................................... 46 Figure 29: Screen Shot of Sheet-8 ........................................................................................... 46

Figure 30: Screen Shot of Sheet-9 ........................................................................................... 47 Figure 31: Screen Shot of Sheet-10 ......................................................................................... 47

Figure 32: Screen Shot of Sheet-11 ......................................................................................... 48

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A Study of Kinetic Energy Recovery Systems v

Graphs

Graph 1: Max Cornering Velocities for a Range of Friction Coefficients .............................. 12 Graph 2: Vehicle Velocity for each Feature of the Track ....................................................... 17 Graph 3: Impact on Vehicle Performance ............................................................................... 20

Graph 4: Flywheel Energy Profile .......................................................................................... 22 Graph 5: Flywheel Power Profile ............................................................................................ 22 Graph 6: Power Characteristics during a Lap ......................................................................... 23 Graph 7: Fuel Consumption over the Course of a Lap ........................................................... 24 Graph 8: Total Brake usage over the Course of a Lap ............................................................ 25

Graph 9: Torque/Power Curve for Honda CBR600RR [] ....................................................... 27

Graph 10: Distance-Time Graph for Standard Vehicle ........................................................... 38 Graph 11: Comparison between Kinetic Energy of Standard Car & Car with KERS ............ 38

Graph 12: Acceleration-Time Graph for Standard Vehicle .................................................... 39 Graph 13: Force Required by the Engine; Without and With KERS ...................................... 39

Tables

Table 1: General Information of Formula Student Car HW-02 ................................................ 6 Table 2: Positions of Major Components .................................................................................. 8 Table 3: Testing Budget .......................................................................................................... 31

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A Study of Kinetic Energy Recovery Systems vi

IV Nomenclature

Symbol Quantity Value Units

Δ Change in Quantity [-] [-]

KELinear Linear Kinetic Energy of the Vehicle [-] J

η Total Efficiency of the Flywheel 70% - 80% [-]

KERotational Rotational Kinetic Energy of the

Flywheel

[-] J

IFlywheel Mass Moment of Inertia of the Flywheel [-] kgm2

ωFlywheel Angular Velocity of the Flywheel [-] Rad/s

mTotal Total Mass of the Vehicle Including

driver, Including KERS

[-] kg

v Linear Velocity of the Car [-] m/s

RFlywheel Radius of the Flywheel [-] m

FCentripetal Centripetal Force Exerted on the

Rotating Flywheel

[-] N

ρ Density of Flywheel Material [-] kg/m3

h Thickness of the Flywheel [-] m

CG Centre of Gravity [-] m

mi Individual Mass of Components [-] kg

xi yi zi Position of Individual Masses with

Respect to a Datum

[-] m

Fy Forces in the y Direction [-] N

m Total Mass of the Vehicle Including

driver, Excluding KERS

300 kg

g Acceleration due to Gravity 9.81 m/s2

NR Force Normal/Perpendicular to the Rear

Tyres

[-] N

NF Force Normal/Perpendicular to the

Front Tyres

[-] N

Fx Forces in the x Direction [-] N

a Linear Acceleration of the Vehicle [-] m/s2

FR Frictional Force on the Rear Tyres [-] N

FF Frictional Force on the Front Tyres [-] N

R Radius of Tyres 0.25 m

α Angular Acceleration of the Tyres [-] Rad/s2

MFW Moments about the Centre of the Front

Wheels

[-] Nm

IWheels Moment of Inertia of the Front Wheels

Excluding Axle

[-] kgm2

μ Coefficient of Friction Between the

Tyres and the Track Surface

Ranges from 0.9-1.5 [-]

MF Moments About the Point where the

Front Tyre makes Contact with the

Track

[-] Nm

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A Study of Kinetic Energy Recovery Systems vii

c Height of Centre of Gravity from the

Track

[-] m

b Distance (in the x Direction) from the

Centre of Gravity to the Front Axle

[-] m

d Distance (in the x Direction) from the

Centre of Gravity to the Rear Axle

[-] m

aMax Maximum Acceleration/Deceleration [-] m/s2

r Corner Radius [-] m

ω Angular Velocity of Car Whilst

Cornering

[-] Rad/s

N Car Normal Force [-] N

vMax Maximum Linear Velocity of the Car

While Cornering

[-] m/s

u3 Velocity at the End of the Feature [-] m/s

u1 Velocity at the Start of the Feature [-] m/s

a1 Positive Acceleration of the Car [-] m/s2

sT Total Feature Displacement [-] m

u2 Acceleration/Deceleration Transition

Velocity

[-] m/s

s1 Displacement from the Beginning of the

Feature to the

Acceleration/Deceleration Transition

[-] m

a2 Negative Acceleration of the Car

(Deceleration)

[-] m/s2

s2 Displacement from the

Acceleration/Deceleration Transition to

the End of the Feature

[-] m

t Time Taken to Negotiate a Feature [-] s

FRes Total Resistance Force Acting on the

Vehicle

[-] N

FD Drag Force Acting on the Vehicle [-] N

CD Drag Coefficient of the Vehicle [-] [-]

ρa Density of Air 1.225 kg/m3

A Effective Drag Area [-] m2

FRR Rolling Resistance of the Vehicle [-] N

CRR Coefficient of Rolling Resistance [-] [-]

FEng Force that the Engine must Produce [-] N

Iz-z Mass Moment of Inertia of the Flywheel

Rotating Around the z-z Axis

[-] kgm2

m1 Mass of Flywheel Material 1 [-] kg

R1 Radius of Inner Section of Flywheel [-] m

m2 Mass of Flywheel Material 2 [-] kg

R2 Radius of Outer Section of Flywheel [-] m

ρ1 Density of Flywheel Material 1 [-] kg/m3

ρ2 Density of Flywheel Material 2 [-] kg/m3

KEFlywheel Kinetic Energy Stored in the Flywheel [-] J

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A Study of Kinetic Energy Recovery Systems viii

BR Rear Braking Bias 30% [-]

KECar Linear Kinetic Energy of the Car [-] J

s Displacement [-] m

Average Power Requirement for a

Feature of the Track

[-] W

Average Velocity of the Vehicle over a

Feature of the Track

[-] m/s

dv Differential Element of Velocity [-] m/s

Power Required by the Engine when

KERS are Operational

[-] W

Power Required by the Engine when

KERS are Not Operational

[-] W

Power Absorbed/Dissipated by the

Flywheel

[-] W

Fuel Consumption Rate for a Feature of

the Track

[-] l/s

Efficiency of the Car’s Engine 40% [-]

cal Calorific Value of Fuel 36,960,000 J/l

FC Fuel Consumption for a Feature of the

Track

[-] l

n Upper Bound of Summation [-] [-]

α, β, γ Coefficients used to Calculate Resistive

Forces on the Vehicle

[-] [-]

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A Study of Kinetic Energy Recovery Systems 1

1 Introduction

With rising fuel prices it is becoming increasingly expensive to run a car. In an effort to

combat this problem there is an ever growing demand for “Green Energy” and the

development of new technologies to increase the efficiency of road vehicles, and decrease

their impact on the environment. The efficiency of a car is not only dependant on the

efficiencies of the individual components, but is also dependant on the way in which the car is

being driven. The infrastructure of towns and cities has made the public accustomed to

driving in a certain way. There are currently various technologies emerging to increase the

efficiencies of modern cars. Modern car manufacturers have developed technologies such as

smarter fuels and “stop-start technology” to reduce the fuel consumption of vehicles.

Currently passenger vehicles use 61% of the transport fuel consumed in the UK [1]. Electric

cars are emerging, although the technology has not yet developed enough for them to rival

traditional IC (Internal Combustion) engine cars. The general public will still be reliant on

traditional transport for some years to come.

A technology known as “KERS” (Kinetic Energy Recovery Systems) was developed by

Formula-1 teams for use in the 2009 season and is now being introduced into new road

vehicles and other forms of motorsport.

2 Literature Review

KERS works by recovering some of the braking energy that would ordinarily be dissipated as

heat. Energy can be recovered in an electrical system in the form of charge stored in a

battery, or as rotational kinetic energy in the form of a rotating flywheel (mechanical system).

This recovered energy can then be used to increase the acceleration of the car (Formula-1 and

motor racing) or to reduce the demand on the car’s engine and increase vehicle efficiency

(road vehicles).

2.1 A Brief History of KERS

2.1.1 KERS in Formula-1

In early 2008, Formula-1 began to test and develop a technology known as Kinetic Energy

Recovery Systems or regenerative brakes. KERS were originally intended for mainstream

use in road vehicles. However, the cost required to fully develop this technology was too

high for car manufacturers. Formula-1 teams have an extremely large financial budget as well

as state-of-the-art technology and experienced engineers [2]. For this reason many F1 teams

chose to develop and implement KERS in their cars for the 2009 season. In general the

systems did not perform as well as was expected, with many teams encountering problems (in

particular, aerodynamic problems and trying to control how the units interfaced with the car’s

already complex electronic control unit (ECU)). For this reason, all racing teams agreed not

to use KERS in the 2010 season [3].

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The Federation Internationale L’Automobile (FIA), Formula-1’s organising body has set

some clear regulations to govern the use of KERS within a race. The regulations are in place

to ensure that the cars remain as safe as possible. The regulations state that 400kJ can be

recovered/delivered at a maximum rate of 60kW each lap [4]. KERS are used in F1 as a

“Push to Pass” device that allows drivers to recover braking energy and use it on the straights

to aid in overtaking.

The underlying purpose of technological developments within Formula-1 (as well as making

races more interesting) is for the technology to lead to advancements in the fuel efficiency of

road cars.

At present, KERS do not commonly feature in the Formula Student event. Some experienced

teams [5] have begun to use KERS, however as yet the technology is not widespread. As

systems become more affordable and as teams become more familiar with the technology, the

use of KERS will become more common.

2.2 System Designs

Two different KERS designs emerged in the 2009 season:

1. Electrical-Battery based KERS

2. Mechanical-Flywheel based KERS

All but one team decided to run with the electrical KERS with Williams being the only team

to use the flywheel design [6].

2.2.2 Electrical KERS (Battery Based Design)

Battery based KERS consist of an electric motor-generator, a super-capacitor and batteries.

These systems exist in hybrid electric vehicles (HEV). A hybrid vehicle has a dual power

train allowing independent use of either the internal combustion engine or electric motor. For

periods of high acceleration, both engines can be used simultaneously to deliver the required

power. During deceleration, the car slows due to the magnetic field in the generator. This

creates a “back E.M.F.” (Electro Motive Force) and the electrical energy is then converted

into chemical energy in a storage battery. When the car accelerates, the battery produces

electrical energy that then powers a motor which sends drive to the wheels. As well as being

relatively heavy, the electrical system is also very inefficient. There are four energy

transitions in this cycle. The transformation of energy from one form to another intrinsically

introduces considerable inefficiencies in the cycle [7]. The efficiency of the regenerative

cycle is just 36% [7]. This effectively means that 64% of the possible recoverable energy is

lost due to the inefficiency of transforming energy into different forms.

2.2.3 Mechanical KERS (Flywheel Based Design)

There are a number of designs that come under the banner of mechanical KERS. Systems

including “Compressor/Turbine” designs and “Torsion Spring” designs have been prototyped.

However, the most popular design and furthest developed is the flywheel design.

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Mechanical KERS involve recovering braking energy and storing it as mechanical energy.

Common mechanical KERS consist of a high speed flywheel, a clutch and a gearing system

(commonly a continually varying transmission (CVT)). Similar systems are used in space

applications to provide “uninterruptable power” [7]. The technology is still very much in its

infancy in road vehicles. The advantage of a mechanical Kinetic Energy Recovery System is

that the energy remains in the same form throughout the regenerative cycle. This gives the

mechanical system a crucial advantage over the electrical based KERS. Mechanical systems

can achieve full cycle efficiencies of over 70% [7] [8]. When the driver wishes to decelerate,

the flywheel is engaged via a clutch. The car slows down due to the inertial load being

applied. The clutch is then disengaged and the flywheel stores this recovered energy in the

form of rotational kinetic energy. This energy can then be reused during periods of

acceleration. The CVT is used to control and regulate the torque, which is transmitted to and

from the flywheel. The CVT and clutch are commonly operated by a set of hydraulically

actuated pistons, controlled by the car’s ECU.

Figure 1: Exploded view of a Flywheel based KERS Unit [9]

Figure 1 shows a flywheel based KERS system coupled to the rear differential. The

differential is modified to accept a coupling gear.

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Figure 2: Assembled Sectional view of Flywheel

based KERS Unit [10]

Figure 3: Assembled Flywheel with Scale [11]

Figure 2 and Figure 3 give an indication of the physical size of the unit. A typical system has

a total mass of 25 kg [8] and a total spatial volume of 13 l [10].

Figure 4: Potential Locations for Flywheel Hybrid System [12]

Figure 4 shows the many possible locations where KERS can be installed. The unit must be

connected to somewhere on the drive-train in order to transmit energy to and from the

flywheel. The optimum location for the system highly depends on the total vehicle design

constraints such as spatial considerations, centre of mass location and transmission efficiency.

It is clear from initial research that a mechanical KERS design has greater potential for

development due to the increased efficiency it has over the electrical system. A review of

several journals and technical papers on similar vehicle simulations has revealed one should

expect a 25% [8] - 35% [1] [a] improvement in fuel economy. This is an improvement of

approximately 10% on the current top performing electric hybrid vehicles [7].

[a] Note: The figure 35% is so large due to the fact that, in the simulation, the vehicle spent a large

percentage of time travelling downhill.

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2.3 How Mechanical KERS Work

In an ordinary car, in order to slow down, the driver must apply the brakes to reduce the

kinetic energy of the vehicle. In conventional brakes, the kinetic energy of the car is

transferred into heat and dissipated to the atmosphere [b]. KERS recovers some of this

braking energy, before it is transformed into heat, and stores it so it can be used during

periods of acceleration

The basic principle behind KERS is the transformation of linear kinetic energy to rotational

kinetic energy.

Equation 1

Not all of the linear kinetic energy will be transformed into rotational kinetic energy, some

will be lost due to system inefficiencies.

Equation 2

The energy stored in a rotational body is given by:

Equation 3

The kinetic energy of a body travelling with a linear velocity is given by:

Equation 4

Substituting Equation 3 and Equation 4 into Equation 2 yields:

(

)

(

) Equation 5

(

) (

) Equation 6

As the mass of the flywheel is increased, the potential to store energy is also increased.

However, moving a heavier flywheel will require the car’s engine to use more power. The

amount of energy that the flywheel can store can be increased if the radius or the angular

velocity is increased. Therefore, the energy capacity of the flywheel can be increased without

necessarily increasing the overall mass of the vehicle by a large amount. In this case, the

limiting factor becomes the free space available in the vehicle. Another limitation to the

energy capacity of the system is the angular velocity of the flywheel. The faster the flywheel

spins, the larger the centripetal load and therefore the stress will be. The centripetal force

acting on a ring element of thickness ΔrFlywheel is given by Equation 7 [13]:

Equation 7

If the maximum stress in the material is exceeded, the flywheel will disintegrate, releasing all

the stored rotational energy. This therefore introduces a safe speed limit that the flywheel

must not exceed.

[b] Note: Some energy is lost due to dynamic losses but the majority of the kinetic energy is dissipated as

heat.

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3 Objectives

The main objective of this project is to develop a simulated lap of a vehicle negotiating a

known circuit. The purpose of this simulation is to investigate the reduction in fuel

consumption if KERS are used. The Heriot-Watt University Formula Student Car was chosen

for analysis. This allowed certain measurements to be taken from the car and used in the

simulation. Furthermore, this provides the team with a dynamic tool that allows for

investigation of varying the vehicle setup and different track layouts.

The mathematical model is based on the application of Newtonian mechanics, equations of

motion as well as energy transfer.

The simulation has been developed in Microsoft Excel due to its simple user interface and its

ability to quickly generate graphs, tables and other forms of data visualisation. This allows

the user to develop the simulation further by introducing more complex models that better

represent conditions in practice [c].

The simulation will be run with the standard car, and then re-run with a regenerative brake

operating to recover energy. This will provide a comparison between the two scenarios,

hence allowing the saving in fuel consumption to be referenced to the standard setup.

4 Lap Simulation

In order to model the performance of the Formula Student car, certain vehicle parameters

have been analysed. Vehicle setup and acceleration/cornering models were created in order to

build a representation of the car’s velocity as it negotiated a known track. Through analysis

of free body diagrams it is possible to calculate the power requirements, and hence the fuel

consumption necessary to complete a lap of the track. To begin, a simplified track was

analysed [d]. Gradually the track and vehicle complexity were increased in order to approach

conditions that may be found in practice.

4.1 Vehicle Setup

In order to develop a suitable acceleration model for the vehicle, the dimensions and layout of

all major components must be considered.

Table 1: General Information of Formula Student Car HW-02

HW-02

Engine Position Rear

Drive Rear Wheel Drive

Vehicle Mass 280 kg

Average Driver Mass 70 kg

Wheel Base 1.6 m

Wheel Track 1.3 m

[c] Note: A brief explanation of the various sheets of the simulation can be found in 11.4 Appendix-D:

Spreadsheet User Guide and 11.5 Appendix-E: Images of Spreadsheet.

[d] Note: An illustration of the simplified track can be found in 11.1 Appendix-A: Simplified Track

Layout Figure 20.

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Figure 5: Elevation of Formula Student Car [14]

Figure 6: End Elevation of Formula Student Car [15]

The position of the centre of gravity is a major contributing factor that affects both the

acceleration of the car as well as the handling. Rear wheel drive racing cars often opt for a

rear centre of gravity in order to increase the normal force on the driven wheels.

The red dots in Figure 5 and Figure 6 represent the position of some of the major vehicle

components. The centre of gravity of the vehicle is calculated by summing the product of all

the individual masses and their distance from a datum.

{ }

∑ ∑{

}

Equation 8

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The datum point for the centre of gravity is shown in Figure 5 and Figure 6 as a green dot

located in the middle of the rear axle and at ground level. The position of the centre of

gravity is measured from this reference point. Table 1 shows the mass and position of some

of the major vehicle components. Not every component is listed but the vehicle’s centre of

gravity can be estimated from knowing the positions of major components.

Table 2: Positions of Major Components

Component Mass X Y Z m∙x m∙y m∙z

(kg) (m) (m) (m) (kgm) (kgm) (kgm)

Left Rear Wheel 12 0 0.25 0 0 3 0

Right Rear Wheel 12 0 0.25 1.3 0 3 15.6

Engine 63 0.5 0.31 0.65 31.5 19.53 40.95

Driver 80 0.9 0.4 0.65 72 32 52

Left Front Wheel 12 1.6 0.25 0 19.2 3 0

Right Front

Wheel 12 1.6 0.25 1.3 19.2 3 15.6

Total 191 Sum 141.9 63.53 124.15

Centre of Gravity 0.74 0.33 0.65

4.2 Acceleration Model

Figure 7 reduces the layout of the vehicle to a system with a centre of gravity at which all the

vehicle’s mass acts. Since the position of the centre of gravity is known, the theoretical

maximum acceleration and deceleration can be calculated.

Figure 7: Free Body Diagram for Accelerating Formula Student Car

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There is no acceleration in the y direction, therefore the sum of the forces must equal zero:

∑ Equation 9

Equation 10

The sum of the forces in the x direction is equal to ma:

∑ Equation 11

Equation 12

For maximum acceleration to occur, FR→Max→“Slipping”, FF→Min→“Rolling”:

Two front wheels rolling therefore:

Equation 13

Summing the moments around the centre of the front wheels:

∑ Equation 14

Equation 15

Substituting Equation 13 into Equation 15 and rearranging yields:

Equation 16

Rear wheel drive therefore:

Equation 17

Substituting Equation 16 and Equation 17 into Equation 12:

Equation 18

Taking moments about the point where the front wheels come into contact with the road

surface:

∑ Equation 19

( )

Equation 20

( )

Equation 21

Substitute Equation 21 into Equation 18:

( )

Equation 22

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(

( )

( ))

( ) Equation 23

( )

(

( )

( )

) Equation 24

4.3 Deceleration Model

The free body diagram for the decelerating car is shown in Figure 8. The derivation of the

maximum deceleration is performed in a similar way to the maximum acceleration model.

Figure 8: Free Body Diagram for Decelerating Formula Student Car

There is no acceleration in the y direction, therefore the sum of the forces must equal zero:

∑ Equation 9

Equation 10

The sum of the forces in the x direction is equal to ma:

∑ Equation 11

Equation 25

For maximum deceleration to occur, FR→Max→“Slipping”, FF→Max→“Slipping”:

Equation 26

Equation 27

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Substituting Equation 26 and Equation 27 into Equation 25:

Equation 28

( ) Equation 29

Substitute Equation 10 into Equation 29:

Equation 30

Equation 31

4.4 Cornering Model

There is a maximum velocity with which the car can negotiate each corner. This maximum

velocity is governed by the corner radius and the coefficient of friction between the tyres and

the track surface. Traction will be broken and the vehicle will start to slide when the

centripetal force exceeds the frictional force applied by the tyres. Therefore the maximum

velocity for each corner will occur when the centripetal force equals the frictional force.

Figure 9: Cornering Diagram [16]

Equation 32

Equation 33

Equation 34

√ Equation 35

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Graph 1 shows the maximum cornering velocities for a range of different coefficients of

friction. It is observed that the coefficient of friction between the tyres and the road surface is

a major contributing factor to the maximum velocity at which the vehicle can safely traverse

the corner. The coefficient of friction for tyres is difficult to predict and subject to change

throughout the lap. The coefficient of friction is highly dependent on the temperature of both

the tyres and the road surface, tyre pressure and the load which is on the tyres [17]. This leads

to an uncertainty in the value of the coefficient of friction. The best way to determine the

coefficient of friction of the tyres would be through experimental testing. A typical range for

the coefficient of friction of tyres used buy the team is 0.9-1.5 [18] [e].

Graph 1: Max Cornering Velocities for a Range of Friction Coefficients

4.1 Track Breakdown

In order to model the performance of the car, the race track must be broken down into

individual features (Corner or Straight). Figure 10 shows the layout of one of the tracks

which was analysed. Figure 11 and Figure 12 show detail of certain areas of the track. The

lengths of straights and corners as well as corner radii are required in order to calculate the

maximum velocities for each feature of the track.

The red line on Figure 10, Figure 11 and Figure 12 represents the track’s “centre line”. The

simulation can be used to investigate different “racing lines” to assess the fastest route around

the track.

[e] Note: The coefficient of friction that is currently being used in the simulation is 1.2

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200

Ve

loci

ty (

m/s

)

Radius (m)

Max Cornering Velocities

μ1=0.9

μ2=1.2

μ3=1.4

μ4=1.5

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Figure 10: Aerial Photograph of Race Track STCC_Jyllan Scale: 1:1250 [f] [19]

Figure 11: Close-up of Turns 4, 5, 6 & 7

Figure 12: Close-up of Turns 15, 16, 17, 18 & 19

Once a full analysis is carried out, it is possible to identify key track characteristics. Figure

13 breaks down the vehicle’s performance and displays the velocity regimes as a percentage

of the total lap time. Figure 13 gives an overview of general track characteristics, whereas

Graph 2 analyses the vehicle’s velocity as a function of time and gives a more detailed

representation of the car’s performance.

[f] Note: A larger image of Figure 10 can be found in 11.2 Appendix-B: Large Image of STCC_Jyllan

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Figure 13: Drive Cycle Breakdown as a Percentage of Total Lap Time

4.2 Velocity Profile

Now that the acceleration model and track dimensions are known, it is possible to construct a

velocity profile for the vehicle travelling round the track while ensuring that each corner is

taken at a safe speed.

4.2.1 Straights

Each straight must be split up into an acceleration zone and a deceleration zone. The

maximum possible velocity at the end of a straight can be calculated using the equations of

motion:

Equation 36

√

Equation 37

A corner will always follow a straight, so the value obtained in Equation 37 must be checked

against the maximum allowable velocity for the next corner given in Equation 35.

{

Equation 38

If a corner follows a corner and the second corner is of a smaller radius than the first, then the

car must negotiate the first corner at the maximum velocity of the second. This is due to the

fact that race cars generally do not brake while cornering, as the vehicle can be difficult to

control due to the uneven loads on the tyres. Therefore, the braking must be done on the

straight before the first corner.

If the case arises that u3 > vMax then the straight must be split into an acceleration zone and a

deceleration zone.

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Figure 14: Velocity Diagram for a Straight

Figure 14 shows the vehicle accelerating (a1) from point 1 to point 2, then decelerating (a2)

from point 2 to point 3 to ensure the corner is taken at a safe speed. To build an accurate

velocity profile of the car, the unknowns: u2, s1 and s2 must be calculated.

The vehicle’s initial velocity, u1 is known and it accelerates to u2 with an acceleration a1.

√ Equation 39

The vehicle then decelerates from u2 to u3 with a deceleration a2.

√ Equation 40

√

Equation 41

Let Equation 39 = Equation 41:

√ √

Equation 42

Equation 43

Using the relationship:

Equation 44

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Substituting Equation 44 into Equation 43:

( )

Equation 45

( )

Equation 46

This value for s1 can now be used in Equation 39, to calculate u2, and in Equation 44 to

calculate s2. This approach can be used for each straight on the track where u3 > vMax.

4.2.2 Corners

Corners will either be taken at constant velocity, or accelerated through until the vehicle

reaches the maximum velocity for the corner. If u1 < vMax then there will be a period of

acceleration followed by constant velocity.

Figure 15: Velocity Diagram for a Corner

Figure 15 shows the vehicle accelerating from point 1 to point 2, then travelling at a constant

velocity for the rest of the corner. The constant velocity that the vehicle travels at will be

equal to the maximum velocity of the corner (or next corner if corner 2 has a smaller radius

than corner 1). Using Equation 39 it is possible to calculate the length of the acceleration

zone.

√

Equation 39

Equation 47

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If s1 ≥ sT, then the vehicle will accelerate through the whole corner. If s1 < sT, then the car

will accelerate over a distance of s1, and then travel at constant velocity for the remainder of

the feature, s2.

4.2.3 Feature Time

The time taken to complete a feature can be calculated in one of two ways. When a = 0, use:

Equation 48

When 0 > a > 0, use:

Equation 49

Now that the velocity for each section of the track, and the time taken to complete each

feature is known, it is possible to construct a full velocity profile.

Graph 2: Vehicle Velocity for each Feature of the Track

Graph 2 shows the velocity of the car for all points of the track. Positive gradients are areas

of acceleration, negative gradients are areas of deceleration and lines of zero gradient are

constant velocity zones. This velocity profile is the fastest possible way that the vehicle can

negotiate a lap of the track. This simulation assumes zero driver error i.e. no late/early

braking and no deviation from the race line. This simulation also assumes constant

acceleration. In reality the vehicle’s acceleration will change depending on which gear the

engine is in.

0

5

10

15

20

25

30

0 20 40 60 80

Ve

loci

ty (

m/s

)

Time (s)

Velocity vs. Time

Car Velocity

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4.3 Force Analysis

During the course of a lap, the vehicle will be in one of three velocity regimes:

Constant Velocity

Acceleration

Deceleration

During constant velocity regimes, the resultant force on the vehicle is zero. Therefore, the

engine must produce enough force to overcome all the losses in the system. The main

resistance forces acting on the vehicle are frictional forces and drag forces.

Equation 50

At the moment this simulation does not take into account the effects of drag. This is because

the drag coefficient (which is velocity dependent) and the effective area can be difficult to

estimate.

Equation 51

The best way to estimate the drag forces on the vehicle would be through experimental testing

of the car. The frictional resistance on the vehicle is made up of rolling resistance and

internal losses from the individual components in the drive-train. The rolling resistance of a

vehicle is given by:

Equation 52

Again, the best way to determine the frictional losses in the system is through experimental

testing. Once values for the losses are determined, these values can then be used to refine the

simulation.

When the vehicle is accelerating, the engine must produce enough force to overcome the drag

and friction losses, and also provide enough force to accelerate the vehicle. The required

force can be determined by analysing Figure 7 and Equation 11.

∑ Equation 11

Equation 53

Equation 54

During deceleration, it is assumed that the engine is idle. Therefore, the engine is not

required to produce any force on the vehicle during deceleration regimes.

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4.4 Using KERS

4.4.1 System Implementation

Figure 16: Layout of the Rear of HW-02 [20]

In order to simulate the KERS being used, a location on the vehicle must be decided. The

current design of HW-02 does not have a great deal of free space. The only area with ample

free space is the “rear plate” of the vehicle shown in Figure 16. Placing the system in this

area has two main advantages:

1. The device will be placed near the rear wheels of the vehicle. This will move the

vehicle’s centre of mass further towards the rear. This will increase the normal force

on the rear wheels and hence, increasing the grip of the driven wheels.

2. The system is placed very close to the rear differential and drive-shafts. This allows

for the system to be coupled to the drive-train of the vehicle by means of a “step-up

gear” [g].

One disadvantage of this location is: Most racing cars have braking biased towards the front

of the vehicle [h]. This means that a smaller percentage of braking energy is available for

recovery in this location.

[g] Note: Refer to Figure 1 for a diagram of how this may be accomplished.

[h] Note: A typical braking bias for the Formula Student car is 70% front, 30% rear.

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Graph 3: Impact on Vehicle Performance

Graph 3 shows the effect of moving the centre of mass towards the rear of the vehicle. The

increased normal force on the rear wheels gives the car a slightly larger maximum

acceleration therefore, increasing the maximum velocity at certain points on the track.

4.4.2 Flywheel Design

The flywheels used by Formula-1 teams are made from a steel hub with carbon fibre wound

round the outer rim. This results in a lightweight design with a relatively high mass moment

of inertia.

Figure 17: Design of Composite Flywheel [21]

Figure 17 shows the flywheel simplified to two materials with density ρ1 and ρ2 respectively.

The moment of inertia can be calculated by simplifying the shape to two cylinders.

(

)

Equation 55

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The masses of the different materials can be calculated using the relationship:

Equation 56

Equation 56 can then be used to express Equation 55 in terms of densities:

(

(

))

Equation 57

A well designed flywheel will have a lightweight hub and denser outer ring. This will allow

most of the mass to be concentrated at the rim of the wheel, resulting in a higher mass

moment of inertia. The outer rim of the wheel also experiences the largest stresses therefore,

the choice of material must be strong enough to endure the large loads.

4.5 Energy Storage

The simulation is designed such that the flywheel will recover energy during every

deceleration zone, then use that stored energy when the vehicle is accelerating or travelling at

constant velocity. In this simulation the KERS are used as an aid to improving fuel

consumption only. The system is not used to boost the acceleration of the vehicle

To decelerate the car, its kinetic energy must be reduced [i]. Some of this energy will be

transferred into heat by the front brakes and the rest will be done by the rear brakes and

flywheel.

Equation 58

Equation 58 shows the maximum energy the flywheel can recover over a given deceleration

zone. This value must be checked against the maximum energy transfer rate and also the

maximum allowable stored energy in the flywheel, to ensure that the value calculated in

Equation 58 is below both.

During acceleration, the maximum amount of energy the flywheel can discharge is equal to

the change in kinetic energy of the vehicle.

Equation 59

Again, this value must be checked to ensure the maximum energy transfer rate is not in

breach.

During areas of constant velocity the maximum amount of energy that the flywheel can

deliver is equal to the work done by the frictional forces acting on the car.

Equation 60

[i] Note: To ensure the car slows down safely it is important that the braking bias is adhered to.

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Graph 4: Flywheel Energy Profile

Graph 4 shows the energy that is stored in the wheel as the car negotiates the track. The

larger the car’s change in velocity, the greater the potential for recovering energy.

4.6 Energy Transfer

By differentiating the function in Graph 4 with respect to time it is possible to develop the

power characteristics of the flywheel.

Graph 5: Flywheel Power Profile

Graph 5 shows how the flywheel is performing on different areas of the track. Positive areas

represent the flywheel “charging” (storing energy) and negative areas represent the flywheel

“discharging” (dissipating energy).

0

5

10

15

20

25

30

35

0 20 40 60 80 100

Sto

red

En

erg

y (k

J)

Time (s)

Energy Stored In Flywheel vs. Time

With KERS(On)

-20

-15

-10

-5

0

5

10

15

0 20 40 60 80

Po

we

r (k

W)

Time (s)

Wheel Power vs. Time

With KERS(On)

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4.1 Power Analysis

Now that the force required for different areas of the track is known, the power requirement

for each feature can be calculated.

Equation 61

During periods of acceleration or deceleration it is necessary to calculate the average velocity.

∫

Equation 62

Equation 63

Using this approach, it is possible to ascertain the required power for each feature of the track.

Graph 6: Power Characteristics during a Lap

Graph 6 shows the power required for each feature of the track. The blue series shows the

power required for the standard car to negotiate one lap of the track. The red series shows

power required when the extra mass of the KERS is added. In this case, the KERS are acting

as “dead weight” to show the extra power that would be required should the system not be

working.

The green series shows the reduction in required engine power due to the use of KERS. The

stored energy within the flywheel is being used to reduce the amount of work the engine

needs to do during acceleration and constant velocity periods.

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When the KERS are operating, the engine can operate at a reduced power, as the flywheel is

also providing the driven wheels with power [j].

{

Equation 64

4.2 Fuel Consumption Analysis

The fuel consumption rate for each feature of the track can be calculated from the power

profile, calorific value of the fuel and the engine efficiency.

Equation 65

Now that the fuel consumption rate for each feature of the track is known, the fuel

consumption for each feature can be found by multiplying the fuel consumption rate by the

time it takes to complete the feature.

Equation 66

The fuel consumption for an entire lap can be calculated by performing a cumulative sum of

the fuel consumption for all the individual features.

∑

Equation 67

Graph 7: Fuel Consumption over the Course of a Lap

[j] Note: The power leaving the wheel is negative by convention, it is therefore added to to

result in a reduced “required power”.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 20 40 60 80 100

Fue

l Co

nsu

mp

tio

n (

l)

Time (s)

Fuel Consumption

Without KERS

With KERS (Off)

With KERS (On)

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Graph 7 displays the fuel consumption of the vehicle on each section of the track. Again, the

blue series represents the fuel consumption of the standard vehicle. The red series shows the

extra fuel that must be consumed due to the increase in vehicle mass.

The green series shows that less fuel is used over the course of a lap due to the KERS

providing a percentage of the power.

5 Discussion

5.1 Fuel Savings

In the above simulation, an 11.97% reduction in fuel consumption is observed. Over the

course of a race, the car will consume less fuel, resulting in fewer pit stops. This can also

allow the vehicle to start a shorter race with less fuel in the tank to reduce the car’s weight.

Where this technology is of a particular advantage is in endurance events and long distance

races.

It was found that the percentage reduction in fuel consumption is highly dependent on the

design of the race track. In the above simulation, the car is decelerating for 15.53% of the

total lap time. If a track with fewer corners is simulated then the amount of time the car

spends decelerating will reduce. This means that the potential to recover energy will reduce.

The use of KERS will become unsuitable in these circumstances, as the recovered energy will

be outweighed by the extra energy required to accelerate the extra mass in the vehicle.

5.2 Brake usage

Due to the flywheel being used as an “inertial brake”, the brake pads themselves will be used

less.

Graph 8: Total Brake usage over the Course of a Lap

-60

-50

-40

-30

-20

-10

0

0 20 40 60 80

Po

we

r (k

W)

Time (s)

Total Brake Power vs. Time

Without KERS

With KERS (Off)

With KERS (On)

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Graph 8 shows the power dissipated by the brakes over the course of a lap. It indicates a

21.22% reduction in the total work done by the brakes. This will increase the life of the brake

pads themselves as they will experience less wear.

There is however a trade-off to the reduction in brake usage. Due to the fact that the brakes

will be used less, the temperature of the brake pads and brake discs will be lower than normal.

This reduction in brake temperature may reduce the braking efficiency of the car [22].

5.3 Optimisation

The ideal flywheel is one with a low mass but with the potential to recover a large amount of

energy. By reducing the mass of the flywheel, the flywheel’s radius must be increased, or its

angular velocity must be increased. In this case the design is constrained by the spatial

volume required and the safe operating velocity of the system. The optimum flywheel design

must be a compromise of the above factors and will differ from vehicle to vehicle.

5.4 Other uses for Simulation

As well as being used to investigate savings in fuel consumption, this simulation can also be

used for different means. The simulation can be used as a “driver aid”. The velocity profile

can be used to help drivers determine at which velocity they should be approaching certain

corners and identify the length of braking zones.

The simulation can also be used by the Formula Student team to investigate the effect of

altering certain vehicle parameters such as wheelbase, wheel track and the positions of

different components. With slight alterations to the simulation, the team can investigate

factors such as load transfer and load sensitivity during cornering.

6 Conclusion

This study has shown the positive impact that flywheel based KERS would have on the fuel

consumption of Heriot-Watt University’s Formula Student Car, as well as addressing

potential draw backs. It is expected that the use of KERS will reduce the car’s fuel

consumption by more than 10% depending on track layout and vehicle setup. The Lap

Simulation will continually be updated and modified as a functioning tool for the Formula

Student Team.

Although KERS have proven to be useful, it is foreseen that they will not be implemented in

Heriot-Watt University’s Formula Student car for some time. The Team is very much still in

its infancy and is still learning many of the skills required to produce a successful car.

Introducing KERS into the car’s design does not help the team meet its current goals.

However, as the team gains experience and the technology becomes more widespread, it is

foreseen that KERS will start to be implemented into the design.

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7 Future Work Plan

7.1 Objective

The purpose of this future work plan is to detail methods to improve and validate the current

lap simulation. Further simulation techniques are suggested to increase the scope of the

current simulation. As well as simulation improvements, a preliminary plan for physical

testing of the Formula Student Car is presented. The results of these tests will be used within

the simulation as a method of calibrating it and as a means of validating some of the

calculated results.

7.2 Simulation Improvements

7.2.1 Engine Capabilities

Currently, the simulation calculates the acceleration model of the car based on the mass,

centre of gravity and coefficient of friction between the tyres and the road surface. This

acceleration model is the maximum that is achievable and it is unlikely that the car will

achieve this acceleration for the entirety of the lap.

In practice, one of the greatest factors that affects the vehicle’s acceleration is the

performance of the engine.

Graph 9: Torque/Power Curve for Honda CBR600RR [23]

Graph 9 shows a torque/power curve for the Honda CBR600RR (the same engine that the

team currently uses). During racing, it is desirable to operate between the point of maximum

torque and the point of maximum power. This window is known as the power band. The

output torque varies across the power band therefore, the acceleration of the car will vary

depending on the engine speed. Also, different gears will result in a different output torque.

Thus, the torque delivered to the driven wheels (and hence acceleration of the vehicle)

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becomes a function of engine speed and gear selection. Using these principles, it is possible

to construct a more accurate acceleration model for the car. This new acceleration model is

dependent on the performance of the engine and the road speed of the car (combination of

engine speed and gear ratio, assuming wheels are in pure roll).

7.2.2 Performance Boost

In its current form, the lap simulation is used to calculate the benefits in fuel consumption

should a flywheel based KERS unit be implemented. In this configuration, the energy stored

within the KERS is being used to reduce the amount of energy the engine is required to

produce. A second way this stored energy can be used is as a means of increasing the

acceleration of the car during the straights. It is proposed that a second simulation be made

that analyses this alternative use of KERS.

In this new simulation, the car’s engine would be used to its full capacity, i.e. the KERS will

not actively reduce the fuel consumption of the car. Instead, the stored energy within the

flywheel will be dissipated such that it increases the torque delivered to the driven wheels.

This increase in torque will increase the car’s acceleration for the period of time that the

KERS are being used. This increase in acceleration will increase the vehicle’s maximum

velocity on the straights, and therefore, reduce the overall lap time.

This new aspect to the simulation is potentially difficult to integrate with the current

calculation method in the original spreadsheet. This is mainly due to the fact that the current

spreadsheet works with large time increments (the length of time required to complete a

feature). If the KERS were being used to increase acceleration, it is likely that the stored

energy will be dissipated before one of these time steps has elapsed. In order for the new

simulation to work alongside the current one, the time steps must be broken down into smaller

increments. This may become untidy and cumbersome in Microsoft Excel. Matlab may be a

more appropriate programme to use when carrying out this new simulation.

7.3 Research Methodology (Physical Testing)

In order to validate the simulation, physical testing should be carried out on the Formula

Student Car. To carry out physical testing of the vehicle, the team would need to take the car

to a race track or an air field. Currently the team uses Knockhill Race track near Dunfermline

to carry out dynamic testing. Knockhill have let the team use a small paddock area free of

charge in the past. A longer section of track may be required for a short period of time in

order to carry out some of the dynamic tests. It is possible that Knockhill may let the team

use a longer section of track during down time for a reduced rate. In order to carry out the

testing, the team will require the following equipment:

Formula Student Car

Fuel

Driver

Other Team Members

Laptop

Video-V Box (Data Logger) [k]

[k] Note: The Video-V Box is a piece of data logging equipment that uses GPS satellites to track the

motion of the car.

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7.3.1 Determining Resistive Forces on the Car

The two main resistive forces acting on the car during the race are drag forces and friction

forces (external and internal). It is complicated to analytically calculate these forces

accurately. Another method to determine the resistive forces acting on the car would be

through experiment.

If the vehicle was travelling at a certain speed, then the car was put into neutral, the only

forces acting on the car would be drag and friction. Therefore, the vehicle would begin to

decelerate.

The total resistive force on the car is a function of the velocity at which the car is travelling

[24].

Equation 68

The coefficients α and β are values that describe the frictional forces on the vehicle. Friction

is a combination of the rolling resistance of the vehicle’s wheels as well as internal losses that

may occur in the drive-train and wheel bearings. The coefficient γ is a value that contributes

to drag forces on the vehicle. γ is dependent on air density, effective drag area and the drag

coefficient.

Equation 69

Equation 70

The “skin friction” component of the drag coefficient is also dependent on the velocity of car.

However, the dominant factor in a car’s drag is the component due to form drag and the

“wake” this induces. Typically, form drag is over ten times larger than skin friction for cars.

Therefore, the change in the skin friction drag coefficient will have a small effect on the

overall drag. Thus, γ can be approximated by Equation 70.

The following experimental procedure should be carried out to calculate the resistive force on

the vehicle (the vehicle should be setup for racing conditions before the experimental

procedure is carried out):

1. The driver accelerates to an arbitrary speed (High speed)

2. The driver starts the data logger

3. The driver shifts into neutral gear to disengage the engine

4. The driver must keep the car straight as it decelerates

5. The V box will log the car’s velocity as a function of time

6. A velocity-time plot can then be created in Excel or MatLab

7. Differentiating this function with respect to time will yield acceleration as a function

of time

8. This can then be rearranged to give acceleration as a function of velocity

9. Using F=ma, the total resistive force on the vehicle can be calculated depending on

the car’s velocity

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The above procedure should be repeated several times and an average taken. After the testing

is complete, the resistive force should be integrated into the simulation to produce a more

accurate acceleration model.

7.3.2 Acceleration/Deceleration Tests

Once the new theoretical acceleration model has been built it will be useful to test the validity

of this model by performing an acceleration test. From standstill the vehicle will accelerate

over a set distance. Again, the Video-V box will be used to log the vehicles velocity as a

function of time. The actual acceleration of the Formula Student Car can then be ascertained

and compared against the theoretical model.

A deceleration test, in the form of a skid test, can be carried out to calculate the coefficient of

friction between the tyres and the road surface. The vehicle will start by travelling at an

initial velocity. The brakes will then be fully locked. By measuring the stopping distance it is

possible to find the deceleration of the vehicle. The coefficient of friction can then be

obtained through Equation 31.

The purpose of the above tests is to allow the theoretical acceleration/deceleration models to

be compared against the car’s observed performance. This comparison will show how large

the difference is between the simulation and the car’s actual performance. The results of this

comparison will highlight the limitations of the simulation and show how accurately it

approaches the observed results.

7.3.3 Fuel Consumption Test

One of the major aspects of the simulation is the calculation of the fuel consumption rate of

the vehicle. The fuel consumption rate is calculated by analysing the power that the engine

must produce. The engine’s efficiency and the fuel’s calorific value are assumed in order to

calculate the rate at which fuel is consumed for a given velocity.

The validity of this calculation can be tested by carrying out a physical test of the vehicle’s

fuel consumption. The vehicle should first be filled up with a known volume of fuel. The car

should then travel at a known velocity until the fuel runs out. By measuring the duration of

the test, it is possible to determine the fuel consumption rate of the car. This test should be

carried out across a range of velocities to allow the actual fuel consumption rate to be

compared against the rate calculated in the simulation. By modifying some of the

assumptions made in the simulation, based on the results of the test, it may be possible for the

calculated fuel consumption rate to approach the observed rate.

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7.4 Cost Estimation

In order to carry out the proposed testing, the following budget has been proposed. The

budget displayed in Table 3 is the estimated cost required for one testing session.

Table 3: Testing Budget

Component Estimated Cost

Knockhill Track Hire £200

Fuel £120

Van Hire £110

Consumables £100

Total £530

Figure 18 shows the breakdown of the proposed testing budget. The testing budget presented

in Table 3 is preliminary at the moment, as track hire has not yet been confirmed with

Knockhill. The required capital depends highly on how efficiently the team carries out the

tests (this will determine how many testing sessions are required).

Figure 18: Breakdown of Testing Budget

7.5 Planning

The testing is proposed to be carried out in the first semester of the 2012/2013 academic year.

To make the best use of time, the testing will start early in the semester and run into week 10.

Currently the team carries out testing on Wednesdays therefore, this schedule has continued to

use Wednesday for the testing slot. The outlined testing will take place alongside other

important testing the team may need to carry out.

38%

22%

21%

19%

Cost Estimation

Knockhill Track Hire

Fuel

Van Hire

Consumables

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Figure 19: Gantt chart for Proposed Work

Figure 19 outlines the proposed schedule that the testing should run to. Planning and test

preparation will take place early in the semester to ensure that the time of current and new

team members is used as efficiently as possible. A series of dynamic testing sessions are

planned and will take place on a weekly basis. The testing sessions shall be used to carry out

the tests detailed above as well as other dynamic tests the team may need to carry out. In the

period of time between each testing session the results from the previous week’s test will be

analysed. The results of these tests will then be built into the simulation. After all the

physical testing of the car is complete, final adjustments will be made to the simulation. The

results of the simulation can then be used to aid the team in making design decisions

regarding the build of the following year’s car.

7.6 Summary of Future Work Plan

This plan outlines a work scope that should be initiated at the start of Semester 1 of the

2012/2013 academic year. A preliminary budget of £530 is proposed for each testing session.

The results of this future work should be used as a method of improving and validating the

current simulation. Using KERS as a performance boost will increase the scope of the

simulation and allow the team to investigate ways in which this will aid racing performance.

By introducing the performance and capabilities of the car’s engine, more accurate

acceleration models can be built. With the introduction of more realistic models, the

simulation will begin to produce results that better approximate the observed conditions. The

results of the physical testing should be used as a calibration method to make the simulation

more applicable to the current car’s design. At the end of this future work scope, the team can

evaluate the obtained results and make a decision on how best to pursue new research into the

use of flywheel based Kinetic Energy Recovery Systems in the design of the Formula Student

Car.

03/09/2012 28/09/2012 23/10/2012 17/11/2012

Planning

1st Batch of Testing

Evaluation of Results & Modifications to Simulation

2nd Batch of Testing


3rd Batch of Testing


4th Batch of Testing


Final Adjustments to Simulation

Use Results to Help Design HW-04

Date

Task

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8 Acknowledgements

1. Dr Daniil Yurchenko: I am sincerely thankful to my project supervisor, Dr Daniil

Yurchenko, for the guidance he has shown throughout the course of my project.

2. Tom Smurthwaite (3rd

Year Mechanical Engineering): I would like to thank Tom

for sharing his experience in creating lap simulations.

3. Bryce Wilson: I would like to extend my thanks to Bryce Wilson, Team Principle

of IFMotorsport Dunfermline Fife. At the start of my project, Bryce was kind

enough to take the time to explain some of the main factors that race teams must

consider when implementing new technology such as regenerative braking.

4. Members of the Formula Student Team: Thanks to members of the 2011-2012

Formula Student Team for sharing their experience and resources.

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9 Bibliography

9.1 Textbooks

Engineering Mechanics; Dynamics; Sixth Edition; J. L. Meriam L. G. Kraige

Tyre and Vehicle Dynamics; Second Edition; Hans B. Pacejka

Race Car Vehicle Dynamics; William F. Milliken, Douglas L. Milliken

Modern Electric, Hybrid Electric, and Fuel Cell Vehicles; Fundamentals, Theory and Design;

Mehrdad Ehsani, Yimin Gao, Sebastien E. Gay, Ali Emadi

9.2 Journals

International Journal of Hydrogen Energy 35 (2010) 8417-8424; Comparison of fuel economies of

high efficiency diesel and hydrogen engines powering a compact car with a flywheel based kinetic

energy recovery system; by Alberto Boretti

Journal of Renewable and Sustainable Energy 3, 013105 (2011); Design and Analysis of Kinetic

Energy Systems for Automobiles: Case Study for Commuters in Edinburgh; by John Walsh, Tariq

Muneer, Ali N. Celik; Published online 11th

February 2011

Application of a Variable Drive to Supercharger and Turbo Compounder Applications; Chris

Brockbank Torotrak (Development) Ltd; 2008 SAE International

Improvements of Vehicle Fuel Economy Using Mechanical Regenerative Braking; Alberto Boretti;

University of Ballarat, Ballarat Australia; 2010 SAE International

9.3 Technical Papers

Full-Toroidal Drive Transmission Systems in Mechanical Hybrid Systems – From Formula-1 to Road

Vehicles; by Chris Brockbank BSc (Hons) & Chris Greenwood BSc (Hons); Torotrak (Development)

Ltd

Hardware Development of a Full-Toroidal Variable Speed Transmission for Pressure Charging and

Other Engine Auxiliary Systems; by C Brockbank, BSc, J Fuller BEng, Torotrak (Development) Ltd

Simulation of the Fuel Consumption Benefits of Various Transition Arrangements and Control

Strategies Within a Flywheel Based Mechanical Hybrid System; W Body BEng MSc, C Brockbank

BSc, Torotrak (Development) Ltd

Introducing the “Rotrak” Variable Speed Traction Drive Centrifugal Supercharger to Fully Exploit

Engine Downsizing; D. J. Burtt and A. P. Kolstrup

Formula 1: Lap Time Prediction; 4th

Year Final Project; I J Wood

9.4 Lecture Notes

Mechanical Engineering Science Machine Dynamics Lecture 3: Vehicles in Motion by Dr. Wei

Wang

9.5 Internet Sites

F1Fanatic.co.uk; URL: http://www.f1fanatic.co.uk/2009/01/11/kers-explained-how-a-mechanical-

kinetic-energy-recovery-system-works/

Wired.com; URL: http://www.wired.com/autopia/2010/10/flywheel-hybrid-system-for-premium-

vehicles/

Racecar-Engineering.com; URL: http://www.racecar-engineering.com/articles/f1/flywheel-hybrid-

systems-kers/

FlybridSystems.com; URL: http://www.flybridsystems.com/index.html

http://www.f1fanatic.co.uk/2009/01/11/kers-explained-how-a-mechanical-kinetic-energy-recovery-system-works/

http://www.f1fanatic.co.uk/2009/01/11/kers-explained-how-a-mechanical-kinetic-energy-recovery-system-works/

http://www.wired.com/autopia/2010/10/flywheel-hybrid-system-for-premium-vehicles/


http://www.racecar-engineering.com/articles/f1/flywheel-hybrid-systems-kers/

http://www.racecar-engineering.com/articles/f1/flywheel-hybrid-systems-kers/

http://www.flybridsystems.com/index.html

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10 References

[1] Journal of Renewable and Sustainable Energy 3, 013105 (2011); Design and Analysis of Kinetic

Energy Systems for Automobiles: Case Study for Commuters in Edinburgh; by John Walsh, Tariq

Muneer, Ali N. Celik; Published online 11th

February 2011

[2] Federation Internationale de L’Automobile (FIA); Press Release; “Teams Comment on F1’s

Environmental Future; 08/10/2008; Ross Brawn, Team Principal, Honda Racing F1;

Adam Parr, CEO, Williams F1; URL: http://www.fia.com/en-

GB/mediacentre/pressreleases/mobility/2008/Pages/f1_environment.aspx Last visited 09/04/12

[3] Formula 1; Kinetic Energy Recovery Systems (KERS); 2012; URL:

http://www.formula1.com/inside_f1/understanding_the_sport/8763.html Last visited 06/04/12

[4] Full-Toroidal Drive Transmission Systems in Mechanical Hybrid Systems – From Formula-1 to Road

Vehicles; by Chris Brockbank BSc (Hons) & Chris Greenwood BSc (Hons); Torotrak (Development)

Ltd

[5] Oxford Brooks University; Hybrid Formula Student Racing Car; URL:

http://www.brookes.ac.uk/about/news/peopleandplaces/students/car Last visited 14/04/12

[6] “Formula 1’s Kinetic Energy Recovery Systems”; About.com Formula 1; by Brad Spurgeon; URL:

http://formula1.about.com/od/car1/a/kers.htm Last visited 09/04/12

[7] International Journal of Hydrogen Energy 35 (2010) 8417-8424; Comparison of fuel economies of high

efficiency diesel and hydrogen engines powering a compact car with a flywheel based kinetic energy

recovery system; by Alberto Boretti

[8] Improvements of Vehicle Fuel Economy Using Mechanical Regenerative Braking; by Alberto

Boretti; University of Ballarat, Ballarat, Australia; 2010

[9] Image Source: Autopia; KERS Comes to Cars as Jaguar Tests Flywheel Hybrid; Article written by

Chuck Squatriglia; 28th

October 2010;

URL: http://www.wired.com/autopia/2010/10/flywheel-hybrid-system-for-premium-vehicles/ Last

visited 28/10/11

[10] Image Source: Flybrid Systems; http://www.flybridsystems.com/F1System.html Last visited

13/04/12

[11] Image Source: “Full-Toroidal Variable Drive Transmission Systems in Mechanical Hybrid Systems –

From Formula-1 to Road Vehicles; Chris Brockbank BSc (Hons) & Chris Greenwood BSc (Hons)

Torotrack (Development) Ltd; Fig. 2

[12] Image Source: “Simulation of the Fuel Consumption Benefits of Various Transition Arrangements and

Control Strategies Within a Flywheel Based Mechanical Hybrid System”; W Body BEng MSc, C

Brockbank BSc, Torotrak (Development) Ltd; Fig. 1

[13] Equation Source: URL: www.aspes.ch/publications/EnerComp1.pdf Last visited 02/04/12

[14] Original Image Source: Chassis and suspension design FSRTE02; by A. van Berkum DCT 2006.23;

Figure 6.23: Side view of suspension box placement and pushrod plane sections; Page 83

[15] Original Image Source: Chassis and suspension design FSRTE02; by A. van Berkum DCT 2006.23;

Figure 4.6: Suspension layout with camber change rate; Page 42

[16] Image Source: Open Clipart Library; URL: http://openclipart.org/tags/car?page=6 Last visited

06/04/12

[17] Adhesion, Hysteresis and the Peak Longitudinal Tire Force; Raymond M. Brach, PhD PE; Brach

Engineering, LLC; University of Notre Dame 2006

[18] Hoosier Race Tyres; URL: http://www.hoosiertyre.co.uk/ Last visited 14/04/12

[19] Image Source: Drawing Title: STCC_Jyllan; Scale: 1:1250; Drawn by Graham Smith Apex Circuit

Design Ltd; Date: 30/08/11

[20] Image Source: Heriot Watt University Formula Student Team HW-02

[21] Original Image Source: Ret-Monitor.com; KERS; KERS Spreads its Wings;

URL: http://www.ret-monitor.com/articles/1009/kers-spreads-its-wings/ Last visited 13/04/12

[22] F1 Technical; “Brake System”; “Cooling System”; by Tomba; 3rd

June 2008; URL:

http://www.f1technical.net/articles/2 Last visited 12/04/12

[23] Sport Rider; Torque/Power Curve for a Honda CBR600RR; URL

http://www.sportrider.com/dyno/146_sportbike_dyno_charts/photo_92.html Last visited 16/04/12

[24] How Stuff Works; How can I Measure the Drag on a Car; URL:

http://auto.howstuffworks.com/question497.htm Last visited 15/04/12

http://www.fia.com/en-GB/mediacentre/pressreleases/mobility/2008/Pages/f1_environment.aspx

http://www.fia.com/en-GB/mediacentre/pressreleases/mobility/2008/Pages/f1_environment.aspx

http://www.formula1.com/inside_f1/understanding_the_sport/8763.html

http://www.brookes.ac.uk/about/news/peopleandplaces/students/car

http://formula1.about.com/od/car1/a/kers.htm


http://www.flybridsystems.com/F1System.html

http://www.aspes.ch/publications/EnerComp1.pdf

http://openclipart.org/tags/car?page=6

http://www.hoosiertyre.co.uk/

http://www.ret-monitor.com/articles/1009/kers-spreads-its-wings/

http://www.f1technical.net/articles/2

http://www.sportrider.com/dyno/146_sportbike_dyno_charts/photo_92.html

http://auto.howstuffworks.com/question497.htm

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11 Appendices

11.1 Appendix-A: Simplified Track Layout

Figure 20: Layout and Dimensions of Simplified Track

Figure 20 is the simplified track that was simulated before the more complex analysis.

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11.2 Appendix-B: Large Image of STCC_Jyllan

Figure 21: Large Image of Race Track STCC_Jyllan [19]

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11.3 Appendix-C: Additional Graphs

Graph 10: Distance-Time Graph for Standard Vehicle

Graph 11: Comparison between Kinetic Energy of Standard Car & Car with KERS

0

200

400

600

800

1000

1200

0 20 40 60 80

Dis

pla

cem

en

t (m

)

Time (s)

Distance vs. Time

Without KERS

0

20

40

60

80

100

120

140

0 20 40 60 80 100

Kin

eti

c En

erg

y (k

J)

Time (s)

Kinetic Energy vs. Time

Without KERS

With KERS

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Graph 12: Acceleration-Time Graph for Standard Vehicle

Graph 13: Force Required by the Engine; Without and With KERS

-10

-8

-6

-4

-2

0

2

4

6

8

0 20 40 60 80

Acc

cele

rati

on

(m

/s2 )

Time (s)

Acceleration vs. Time

Without KERS

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80

Forc

e (

kN)

Time (s)

Required Force vs. Time

WithoutKERS

With KERS

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11.4 Appendix-D: Spreadsheet User Guide

Below is a short description of the purpose of each calculation sheet within the simulation.

The author should be contacted directly regarding specific questions related to the simulation.

Sheet-1: “Car Setup”

This sheet allows the user to enter vehicle specific information such as:

Wheelbase

Coefficient of Friction

Braking Bias

The location of components and their mass are also entered on this sheet in a similar format to

that found in Table 2. The sheet will then calculate the position of the centre of gravity (with

and without KERS).

Sheet-2: “Centre of Gravity”

The values entered in Sheet-1 are then arranged into a free body diagram. Quantities such as

mass moment of inertia of the vehicle’s wheels and total weight are also calculated.

Sheet-3: “Maximum Acceleration”

This sheet solves the free body diagram for two cases:

Maximum Acceleration

Maximum Deceleration

Normal and frictional forces are calculated for each case (with and without KERS).

Sheet-4: “Flywheel Setup”

The user can design the flywheel in this sheet. Flywheel dimensions and material properties

are entered, resulting in the simulation calculating the mass of the system as well as the mass

moment of inertia. This sheet also has the option of introducing a “safe angular velocity” and

cycle efficiency.

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Sheet-5: “Track”

In this sheet the user will enter accurate track dimensions. The track must be split into

“features”:

Straight: With total length

Corner: With arc length and corner radius

The simulation then uses the acceleration models created in Sheet-3 to calculate the velocity

profile for the car as it travels round the track. This sheet is based on Equation 32 to Equation

49.

Sheet-6: “Track KERS”

This sheet performs a similar task to Sheet-5 however, Sheet-6 uses the acceleration model of

the car when the KERS are introduced.

Sheet-7: “Track Graphs”

Sheet-7 begins by using “INDEX Formulae” to rearrange some of the information (velocities,

distances and times) in Sheet-5. The information is then further rearranged using complex

“Array Formulae”. The purpose of these operations is to present the information in such a

way that Excel is able to display graphs relating to different quantities. The graphs displayed

in this sheet allow the user to visualise how the car is performing at certain areas of the track.

This sheet is also responsible for calculating the fuel consumption and power requirements of

the car.

Sheet-8“Track Graph KERS”

Sheet-8 works in much the same way as Sheet-7 but calculates values based on the car using

KERS.

Sheet-9“Comparisons”

This sheet compares the data collected in the previous two sheets so the user can draw a

comparison between the two cases. In this sheet the user is able to find a graphic

representation of the fuel consumption and read off the savings should KERS be used.

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Sheet-10“Cornering Velocities”

This sheet is used purely for reference. The user can enter different values for the coefficient

of friction and the graph will display maximum cornering velocities for a range of radii.

Sheet-11“Differences”

Sheet-11 graphically displays the differences in velocity, acceleration and kinetic energy.

These differences in the stated quantities occur because the vehicle mass and location of the

centre of gravity have changed between the two cases. This sheet is again for reference and

portrays some of the information in a clearer format.

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11.5 Appendix-E: Images of Spreadsheet

Several “screen shots” of the various sheets of simulation are shown in the following section.

Sheet-1: “Car Setup”

Figure 22: Screen Shot of Sheet-1

Sheet-2: “Centre of Gravity”


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Sheet-3: “Maximum Acceleration”


Sheet-4: “Flywheel Setup”


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Sheet-5: “Track”


Sheet-6: “Track KERS”


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Sheet-7: “Track Graphs”


Sheet-8“Track Graph KERS”


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Sheet-9“Comparisons”


Sheet-10“Cornering Velocities”


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Sheet-11“Differences”


A Study of Kinetic Energy Recovery Systems

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