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University of Oxford
Department of Engineering Science
Third Year Engineering Design Project 2014/2015
Design of a Car for the Formula
Student Competition
Team Oxford Octane
Alastair Adams-Cairns (St. Edmund Hall)
Robert Bainbridge (St. Catherine’s College)
Justin Hubbard (Hertford College)
Edmund Moss (Somerville College)
Yuntao Zhu (Lincoln College
Talbot Kingsbury (Keble College)
Abstract
Still to be written
Table of Contents
1
Introduction.........................................................................................1
2 Engine....................................................................................................2
2.1 Introduction.......................................................................................................... 2
2.1.1 Objectives & Specification...........................................................................................2
2.2 Engine Selection................................................................................................... 4
2.2.1 FSAE Rules.................................................................................................................. 4
2.2.2 Available Engines........................................................................................................ 4
2.2.3 Decision....................................................................................................................... 5
2.3 Engine Modelling.................................................................................................. 6
2.4 Analysis and Optimisation.................................................................................... 8
2.4.1 Air Intake..................................................................................................................... 8
2.4.2 Throttle....................................................................................................................... 9
2.4.3 Venturi....................................................................................................................... 10
2.4.4 Plenum...................................................................................................................... 13
2.4.5 Forced Induction and Natural Aspiration...................................................................15
2.4.6 Cylinders................................................................................................................... 17
2.4.7 Valves........................................................................................................................ 19
2.4.8 Fuel Injection............................................................................................................. 22
2.4.9 Fuel........................................................................................................................... 23
2.4.10 Air/Fuel and Equivalence Ratio................................................................................24
2.4.11 Fuel Consumption.................................................................................................... 25
2.4.12 Fuel Tank................................................................................................................. 27
2.5 Fine Tuning......................................................................................................... 28
2.6 Conclusion.......................................................................................................... 30
2.7 References.......................................................................................................... 31
3
Thermal Management.........................................................................32
3.1
Introduction..................................................................................................... 32
3.2
Basics of the cooling system............................................................................32
3.3
Cooling system components............................................................................ 33
3.3.1 Coolant pump selection.......................................................................................... 34
3.3.2 Cooling fan selection................................................................................................ 35
3.4
Radiator analysis............................................................................................. 35
3.5
Conclusion....................................................................................................... 38
3.6
References....................................................................................................... 39
4. Aerodynamics....................................................................................40
4.1
Introduction..................................................................................................... 40
4.2
Material selection analysis for the aerodynamic package................................40
4.2.1 Introduction............................................................................................................. 40
4.2.2 Material properties................................................................................................... 41
4.2.3
Manufacture......................................................................................................... 41
4.2.4
Multi-criteria decision analysis..............................................................................43
4.3
Undertray......................................................................................................... 44
4.3.1
4.3.2
Introduction.......................................................................................................... 44
Theory.................................................................................................................. 44
4.3.3
4.3.4
4.3.5
4.3.6
4.4
Wings............................................................................................................... 51
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
4.4.7
5
Computational fluid dynamics..............................................................................45
Diffuser angle analysis......................................................................................... 48
Ground clearance analysis....................................................................................50
Conclusion............................................................................................................ 51
Introduction.......................................................................................................... 52
Top speed performance........................................................................................52
Aerofoil selection.................................................................................................. 54
Rear wing............................................................................................................. 56
Front wing............................................................................................................ 56
Cornering performance......................................................................................... 57
Conclusion............................................................................................................ 59
4.5
The complete aerodynamic package..............................................................60
4.6
Conclusion....................................................................................................... 61
4.7
References....................................................................................................... 61
Chassis and Packaging........................................................................62
5.1
Introduction..................................................................................................... 62
5.2
Design Procedure............................................................................................. 63
5.2.1 Decision Making (Space frame vs. Monocoque).......................................................63
5.2.2
Regulations and Dimension Specifications...........................................................64
5.3
Materials.......................................................................................................... 67
5.3.1
5.3.2
5.3.3
5.3.4
5.3.5
5.4
Analysis of the Chassis.................................................................................... 81
5.4.1
5.4.2
5.4.3
5.4.4
6
Comparison of Materials.......................................................................................... 67
Composite Materials............................................................................................. 68
Material Selection.................................................................................................... 74
Composite Sandwich Structures...............................................................................77
Methods for Manufacturing Composite Materials.....................................................79
Finite Element Analysis (FEA)...................................................................................81
Impact Testing the Chassis.......................................................................................82
Torsion Test.............................................................................................................. 83
Rollover stability test............................................................................................... 84
5.5
Packaging......................................................................................................... 85
5.6
Conclusion....................................................................................................... 88
5.7
References....................................................................................................... 90
Suspension, Steering, Tyres and Brakes...............................................91
6.1
Introduction..................................................................................................... 91
6.2
Suspension....................................................................................................... 91
6.2.1
6.2.2
6.2.3
6.2.4
6.2.6
6.2.7
6.2.8
6.3
Suspension type....................................................................................................... 91
Setting Suspension Geometry..................................................................................92
Dynamic Suspension Simulation..............................................................................94
Actuation methods................................................................................................... 95
Spring-Damper Calculations.....................................................................................96
Suspension System Fabrication................................................................................98
Anti-roll bar.............................................................................................................. 99
Steering........................................................................................................... 99
6.3.1 Ackerman Steering Principle..................................................................................100
6.3.2 Steering Properties................................................................................................ 101
6.3.3 Upright Fabrication................................................................................................ 102
6.4
Tyres.............................................................................................................. 104
6.4.1 Tyre Options........................................................................................................... 104
6.4.2 Tyre Size................................................................................................................ 105
6.4.3
6.4.4
6.4.5
3.4.6
6.5
Brakes............................................................................................................ 112
6.5.1
6.5.2
6.5.3
6.5.4
6.5.5
6.6
Rim Selection......................................................................................................... 106
Tyre Theory............................................................................................................ 107
Tyre Simulation...................................................................................................... 109
Tyre Friction Ellipse................................................................................................ 111
Brake Discs............................................................................................................ 113
Brake Callipers....................................................................................................... 114
Pedal Box............................................................................................................... 115
Braking Force Calculations.....................................................................................116
Heat Simulation..................................................................................................... 118
Conclusion..................................................................................................... 120
7. Electrical and Control System (Yuntao Zhu).........................................121
7.1 Introduction...................................................................................................... 121
7.2 Engine Control Unit (ECU).................................................................................121
7.2.1
7.2.2
7.2.3
7.2.4
7.2.5
7.2.6
7.2.7
Introduction............................................................................................................. 121
ECU......................................................................................................................... 122
Control of Air/Fuel ratio........................................................................................... 123
Ignition timing control............................................................................................. 125
Cooling control........................................................................................................ 125
Electronic throttle control (ETC)..............................................................................126
Sensors.................................................................................................................... 127
7.3 Braking Control System (Stability Control).......................................................129
7.3.1 Electronic Stability Program (ESP)...........................................................................129
7.3.2 Anti-lock Braking System......................................................................................... 131
7.3.3 Traction Control System (TCS).................................................................................135
7.4 Battery System................................................................................................. 135
7.4.1
7.4.2
7.4.3
7.4.5
7.4.6
7.4.7
7.4.8
Introduction............................................................................................................. 135
Battery.................................................................................................................... 136
Battery Management............................................................................................... 137
Alternator................................................................................................................ 139
Shutdown system.................................................................................................... 140
Brake Light.............................................................................................................. 141
Overall system circuit diagram................................................................................141
7.5 Conclusion........................................................................................................ 142
7.6 Reference......................................................................................................... 144
8. Drivetrain..........................................................................................145
8.1. Introduction..................................................................................................... 145
8.2. Gearbox........................................................................................................... 145
8.2.1 Gearbox Comparison............................................................................................... 145
8.2.3 CVT Selection.......................................................................................................... 148
8.2.4 CVT Guard............................................................................................................... 149
8.3. Differential....................................................................................................... 150
8.3.1 Necessity and dual CVTs.......................................................................................... 150
8.3.2 Differential type comparison...................................................................................150
8.3.3 Limited Slip Differential Selection............................................................................151
8.4. Chain Drives.................................................................................................... 151
8.4.1. Chain drive, belt drive and driveshaft.....................................................................151
8.4.2 Ratio calculation...................................................................................................... 152
8.4.3 Chain and sprocket selection...................................................................................153
8.5. Half Shafts and Constant Velocity Joints..........................................................154
8.5.1. Half shaft material selection...................................................................................154
8.5.2. Half shaft sizing...................................................................................................... 155
8.5.3 CV Joints.................................................................................................................. 156
8.6 Conclusion........................................................................................................ 156
8.7 References........................................................................................................ 157
9. Simulation.........................................................................................158
9.1. Introduction..................................................................................................... 158
9.2. Software.......................................................................................................... 159
9.3. Driving Force Simulation.................................................................................159
9.3.1.
9.3.2.
9.3.3.
9.3.4.
Overview................................................................................................................ 159
Drivetrain............................................................................................................... 159
CVT......................................................................................................................... 160
Engine and Clutch.................................................................................................. 161
9.4. Driver.............................................................................................................. 162
9.4.1.
9.4.2.
9.4.3.
9.4.4.
Requirements......................................................................................................... 162
Velocity look up...................................................................................................... 162
Braking point calculator......................................................................................... 163
Velocity Control...................................................................................................... 165
9.5. Brakes............................................................................................................. 165
9.5.1. Brakes subsystem.................................................................................................. 165
9.6. Drag and rolling resistance.............................................................................. 166
9.6.1. Drag....................................................................................................................... 166
9.6.2. Rolling resistance................................................................................................... 166
9.7. Rotational inertia............................................................................................. 166
9.7.1. Introduction............................................................................................................ 166
9.7.2. Effective masses.................................................................................................... 167
9.8. Results............................................................................................................. 168
9.8.1. Acceleration event................................................................................................. 168
9.8.2. Autocross event (single lap)...................................................................................169
9.8.3. Endurance event.................................................................................................... 170
9.9. Conclusion....................................................................................................... 170
9.10. References..................................................................................................... 171
10. Project Management and Finance......................................................172
10.1. Introduction................................................................................................... 172
10.2. Project planning............................................................................................. 172
10.3. Finance.......................................................................................................... 172
10.4. Conclusion..................................................................................................... 173
10.5. Appendices.................................................................................................... 174
11
Conclusion.....................................................................................176
Justin Hubbard
1
Hertford College
Introduction
Introduction
Oxford Octane’s 3rd Year Project is a design project based on the Formula Student competition run
by SAE International, previously known as the Society of Automotive Engineers, where the aim is
to produce a Formula-style racing car to compete in an event run annually. It is a globally
recognised competition with 12 different events running in different regions across the globe. Each
student team designs, builds and tests a prototype based on a series of rules, which ensure ontrack safety and encourage clever problem solving. The points for the Formula Student Event,
obtained from the 2015 SAE Rules are outlined in Table 1.1. However, this project was set out as a
design project, with no final construction necessary.
Table 1.1
The scoring system for Formula Student competition
Static Events
Dynamic Events
Technical Inspection
Design
Presentation
Cost and Manufacturing Analysis
Acceleration
Skid Pad
Autocross
Efficiency
Endurance
Total
No Points
150
100
75
75
50
150
100
300
1000
The group was subdivided into more specific roles to try and give the chance for more in
depth research into how to optimise the performance of the car. This resulted with: Alastair
taking control of the engine design, Robert with the aerodynamics and thermal management
design, Justin with the chassis and packaging design, Edmund with the suspension, steering,
tyres and brakes design, Yuntao with the electrical and control systems design and Talbot with
the transmission and simulation design along with the financial aspects of the project. Once
everyone established what their roles entailed, a decision was made about the key aim of the
group. It was decided that the car would consist of an internal combustion engine (ICE) only,
without a hybrid or electric drive system. A theoretical budget of £40 000 was set to construct
a theoretical model of the car, with the main aim of the team being for it to compete with the
top end competitors at the 2015 Formula Student event.
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Alastair Adams-Cairns
St. Edmund Hall
Engine
2 Engine
2.1 Introduction
The Formula Student car will be designed to partake in both static and dynamic events in order to
gain points and compete with other teams whilst keeping within the constraints of the rules set out
by FSAE (Formula Society of Automotive Engineers). [1] The sole source of power to the car is an
internal combustion engine so the design is crucial to the success of the car on race day. In this
chapter, the selection, modelling and optimisation of the engine will be covered as well as the fuel
to power the engine. The engine of choice is a Honda CBR600RR from a motorcycle.
2.1.1 Objectives & Specification
In order to create a useful method for selecting the engine, it is important to specify which
parameters are the most important for the engine. The main objective will be maximising power
available to the car; the reason for this decision will be addressed below. Whilst there are points
available for efficiency of the car, the dynamic event with most points available is the endurance
event where a score is calculated based on the time taken for the car to complete the event. As per
the FSAE rules [1], three times the number of points available for efficiency are available for the
endurance event so maximising the power of the engine will be the number one priority. There is
also an acceleration event for which points are available. An engine with high torque is desirable
for this event as torque is a better measure for determining the acceleration of a car than power, so
selecting an engine with a high torque output as well as high power output will be a priority.
Another objective will be to minimise weight. As described above, performance of the car is very
important and adding any unnecessary weight to the car will only reduce its performance.
As the efficiency of the car carries with it some points, efficiency will be another priority when it
comes to modelling and optimisation, although it is rather less important than engine power output.
Other important considerations are cost, availability and packaging. The project has a budget of
£40,000 and large though that might seem, most of it will be spent on the design and manufacture
of a carbon monocoque chassis, so keeping the cost of the engine down will be important as this is
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St. Edmund Hall
Engine
a key component of the car. The availability of the engine will have to be taken into account too; it
will need to be sourced within a few weeks so that modifications can be made to it. This means any
rare engines are out of the question. Packaging is a factor that is sometimes overlooked. Fitting the
engine and transmission behind the driver as dictated by the FSAE rules [1] will be a challenge as
well so a bulky engine may not fit.
Taking the above into account and looking at cars from previous years that have performed well,
the following engine specification should be adhered to without fail:




Minimum Peak Power of no less than 65 hp (48.5 kW)
Minimum Torque of no less than 50 Nm
Weight of no more than 60 kg
Cost of no more than £2000
Efficiency will be considered in the design of the engine along with availability and packaging
considerations but these are much more difficult to specify so no figures will be assigned to them in
this specification; however, discretion will be observed when selecting a suitable engine.
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St. Edmund Hall
Engine
2.2 Engine Selection
2.2.1 FSAE Rules
The FSAE rules [1] aim to ensure that every team will be able to compete together with maximum
flexibility of design whilst at the same time trying to keep the competition fair. [1] In particular, the
engine selected must comply with the rules in order for the car to be allowed to enter the Formula
Student competition. The set of rules is extensive but a summary of the key engine rules is
discussed below. The maximum allowable engine displacement is 610 cc. Engines may be
naturally aspirated, turbocharged, supercharged or a combination of the two. All engines must use
a restrictor plate in the intake system with a diameter of 20 mm. The location of the restrictor plate
varies depending on whether the engine is naturally aspirated or whether it makes use of forced
induction. Engines must be four-stroke and can make use of carburetion, low pressure injection
(port injection) or high pressure injection (direct injection). Fuel additives are prohibited and the
maximum allowable sound level from the engine is 110 dB when racing and 100 dB when idling.
[1]
The above rules eliminate large, high power engines, such as those you might normally see in road
or track cars, so attention will be focussed elsewhere.
2.2.2 Available Engines
Short of manufacturing an engine entirely from scratch, something rather complicated and too
difficult to achieve within the time constraints of this project, the maximum allowable engine
displacement of 610 cc limits the available engines largely to those from motorcycles or similar
small vehicles. In order to keep within the specification, an engine would need to be purchased in a
used condition as new ones are too expensive.
Looking at previous competitors’ selections, the two types of engines used come from either
motorcycles or snowmobiles, excluding hybrid and electric power units. This is because more often
than not, these engines tend to be in the 450-600 cc range, which is ideal for meeting the rules.
One such snowmobile engine is the engine from a Yamaha Phazer M-TX which is 499 cc and
produces 80 hp at 12,000 rpm. [2] After further research, it was decided that snowmobile engines
would not be considered for a number of reasons. First, whilst some have a displacement within
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Alastair Adams-Cairns
St. Edmund Hall
Engine
the desired range, many of the engines are two-stroke and most of the four-stroke engines tend to
be a lot larger than 610 cc. [3] Furthermore, whilst researching the engines online, the technical
specifications are rather hard to come by, perhaps due to the fact that fewer units are produced
than motorcycle engines. Not only are snowmobile engines difficult to research but second-hand
snowmobile engines for sale are more difficult to source than their motorcycle counterparts.
Although a big advantage of snowmobile engines is that they often come with a Continuously
Variable Transmission (CVT), which we shall be using as will be explained in a later chapter of this
project, this is not enough to outweigh the disadvantages.
This leaves the decision of which motorcycle engine to choose. The Honda CBR600RR is the most
popular choice amongst Formula Student teams, but a comparison of other similar engines is
worthwhile. Table (1) below is a tabulated comparison of the Honda CBR600RR [4], the Suzuki
GSX-R600 [5] and the Yamaha WR 450F [6]:
Table (1) Comparison of Honda CBR600RR, Suzuki GSX-R600 and Yamaha WR 450F
Engine
Honda CBR600RR
Suzuki GSX-R600
Yamaha WR 450F
Displacement (cc)
599
599
449
Arrangement
4 Cylinder Inline
4 Cylinder Inline
Single Cylinder
Bore x Stroke (mm)
67 x 42.5
67 x 42.5
95 x 63.4
Peak Power (hp)
118.1 @ 13,500 rpm
103 @ 13,550 rpm
58 @ 9,000 rpm
Peak Torque (Nm)
66 @ 11,250 rpm
59.1 @ 11,140 rpm
49 @ 7,000 rpm
2.2.3 Decision
The single cylinder engine was included in Table (1) above because single cylinder engines
provide the greatest thermal efficiency per unit displacement. [7] However, whilst there are a few
engines available with a displacement of around 450 cc, the next largest engines have a
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Alastair Adams-Cairns
St. Edmund Hall
Engine
displacement larger than the maximum allowable 610 cc. The Yamaha WR 450F simply does not
produce enough power for the outlined specification. The Honda and Suzuki engines have the
same displacement but the Honda produces more power and more torque than the Suzuki so this
will be the engine used in the project for modelling and optimisation. Furthermore, used Honda
CBR600RR engines can be sourced very easily from the online marketplace, ebay, for well under
£2000. [8]
Figure 2.1 Honda CBR600RR Engine [9]
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Alastair Adams-Cairns
St. Edmund Hall
Engine
2.3 Engine Modelling
There are two main reasons for engine modelling. The first reason is that by modelling the engine,
we can predict performance without having to carry out actual tests. Testing a full scale model
engine would be costly as well as time-consuming and out of the question for this project. The
second reason for modelling the engine is that we can determine engine parameters that in
practice would be nearly impossible to measure. Furthermore, in the case of an engine, many of
the processes are too complicated to be modelled conventionally. After spending some time
experimenting with a single cylinder model of an engine on a free version of the software, Lotus
Engine Simulation software was acquired from Lotus Engineering Software.
[10]
The Lotus Engine
Simulation software is very powerful and with the use of the handbook, it was possible to begin
analysing the engine of choice. [11]
A model of a stock Honda CBR600RR was constructed with the addition of a 20 mm restrictor in
the intake system. A schematic of the engine taken from the software can be seen below in Figure
2.2:
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Alastair Adams-Cairns
St. Edmund Hall
Engine
Figure 2.2 Schematic of Honda CBR600RR in Lotus Engine Simulation Software
After running a simulation with the engine as above, including the 20 mm restrictor, initially with a
few data points, the software was able to give figures for power, torque, brake specific fuel
consumption (BSFC) and brake mean effective pressure (BMEP), along with many other useful
parameters at different engine speeds. The stock engine with restrictor produced a peak power of
50.4 hp @ 11,400 rpm and a peak torque of 48.9 Nm @ 3,600 rpm. These figures were an early
indication that there was much work to be done to the engine to meet the specification of a
minimum peak power of 65 hp and a minimum peak torque of 50 Nm, whilst also raising questions
about whether to run the engine at peak power or peak torque, bearing in mind that a CVT will be
used. A summary of the performance of this engine simulation can be seen below in Figure 2.3
with Power, Torque, BSFC and BMEP vs engine rpm:
Figure 2.3 Power, Torque, BSFC and BMEP vs Engine rpm for stock engine with restrictor
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St. Edmund Hall
Engine
2.4 Analysis and Optimisation
2.4.1 Air Intake
The first component of the intake system is the air intake. The engine draws in stationary air at
atmospheric pressure through the air intake due to a pressure difference. We can analyse the flow
of air by assuming pipe flow initially in an infinite cross-section before a sudden decrease in crosssection (to a diameter of 40 mm which is the stock size for the Honda CBR600RR).
[9]
The air
intake can be modelled as a sudden change in cross-sectional area which will result in head loss.
The equation for head loss is shown below in Equation (1):
Head Loss=K L × Local Dynamic Head∨h L=K L
ú 2
2g
(1) [12]
where KL is an empirical loss coefficient. For the case described above, the highest value of loss
coefficient is 0.5 and this occurs when the intake is sharp-edged. We can minimise the loss
coefficient by rounding the edges of the intake to achieve a loss coefficient of 0.04 which is small
enough to neglect. A round-edged inlet, as described above, is known as a bell mouth [13] and this
minimises losses; this will be the shape of the air intake which will be used. A diagram of a sharpedged and round-edged or bell mouth inlet can be seen below in Figure 2.4:
Figure 2.4 Comparison of rounded and sharp-edged inlets [12]
2.4.2 Throttle
The next component of the intake system is the throttle. There are a number of throttle valve types
available but the two most popular types will be considered here. The first type of valve is a
butterfly valve which consists of a circular disc on a spindle, housed in pipework. When the throttle
valve is closed, the disc is perpendicular to the direction of flow and blocks the flow through the
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Alastair Adams-Cairns
St. Edmund Hall
Engine
pipe. When the throttle valve is fully open, the disc is orientated parallel to the direction of flow. An
example of a butterfly throttle can be seen below in Figure 2.5:
Figure 2.5 Partially open butterfly throttle [14]
Furthermore, there are losses associated with a butterfly valve; even when open, a butterfly valve
reduces the effective cross-sectional area at the throttle and separation may occur at any of its
edges. [7] An example of how a butterfly valve disturbs the flow can be seen in Figure 2.6 below:
Figure 2.6 Streamlines showing butterfly valve impeding flow when partially open (left) and fully
open (right) [16]
The second type of throttle which will be considered is a barrel valve. A barrel valve consists of a
barrel shaped object housed within pipework. When the barrel valve is closed, it restricts the flow
through the pipe entirely. When the barrel valve is fully open, it does not impede the flow through
the pipe in any way, giving it a great advantage over the butterfly valve. A barrel valve will therefore
be used to minimise losses. An example of a barrel valve fully open, with no obstruction to flow can
be seen below in Figure 2.7:
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Engine
Figure 2.7 Fully open barrel valve [15]
2.4.3 Venturi
The next component of the intake system is the restrictor of diameter 20 mm, as specified by the
FSAE Rules. [1] As a restrictor plate of diameter 20 mm inserted into a pipe of a larger diameter (in
this case 40 mm), also called an orifice plate, would result in large losses from separation, a more
efficient method is needed. A simple but effective way to implement a restrictor is to weld together
two pipes, connected in series between the throttle and the plenum (the next component of the
intake system). The first pipe takes the form of a contractor while the second pipe is a diffuser.
Where the two pipes meet, their diameters will be 20 mm, creating a venturi effect. The design of
the contractor is less important than that of the diffuser because a contractor will not cause any
flow separation. Although there will be no separation in the contractor, there will still be losses; the
equation for head loss is the same as Equation (1), but now we have an expression for KL as per
Equation (2) below:
2
( ( ))
D
K L =0.8 sin θ 1− 1
D2
∧θ=tan −1
D2 −D1
2L
(2) [17]
Figure 2.8 below shows the parameters for Equation (2) above. Taking L = 100 mm, a number
which does not result in too sudden a contraction, [18] we get a value of KL = 0.06 which is similar to
the value for the bell mouth air inlet and is small enough to be neglected. A schematic for the
contractor is shown below in Figure 2.8 and Figure 2.9:
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Alastair Adams-Cairns
St. Edmund Hall
Engine
Figure 2.8 (Left) Schematic diagram of setup described above with parameters corresponding to
Equation (2) [19]
Figure 2.9 (Right) Schematic of contractor pipe taken from software model
The rate at which the diameter of the diffuser pipe increases requires careful attention during its
design. In order to avoid separation, the angle between a line on the inside surface of the pipe and
an imaginary line running parallel to the pipe, of radius equal to the narrower end of the pipe from
the centreline, should be 5-10°. [18] A value between the two, of 8° will be used. The loss coefficient,
KL, has a different expression as shown below in Equation (3):
2 2
( ( ))
D
K L =2.6 sin θ 1− 1
D2
θ=tan −1
D 2−D1
2L
(3) [17]
Figure 2.10 below shows the parameters for Equation (3) above. Taking L = 250 mm, we find that
D2 = 90 mm and KL = 0.036 which is again small enough to neglect. There will also be no
separation in the diffuser. A schematic of the diffuser can be seen below in Figure 2.10 and Figure
2.11:
Figure 2.10 (Left) Schematic diagram of setup described above with parameters corresponding to
Equation (3) [19]
Figure 2.11 (Right) Schematic of diffuser pipe taken from software model
By modelling the engine with and without the inclusion of the restrictor, it is clear that the restrictor
limits the power by a considerable amount. A comparison of peak power output from the stock
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Engine
engine without the restrictor and the engine with the designed intake system and restrictor can be
seen below in Figure 2.12:
Figure 2.12 Graph showing peak power output from engine with (designed intake) and without
(stock) 20 mm restrictor.
As can be seen in Figure 2.12 above, the value for peak power without the restrictor agrees well
with the value given in Table (1) for the Honda CBR600RR engine. This agreement is reassuring
as it means that engine modelling software is producing realistic values that can be used
elsewhere in the project. Moreover, Figure 2.12 above also makes it clear by how much the
restrictor decreases the peak power of the engine. Further optimisation is necessary to meet the
specification. Whereas without the restrictor, the peak power is achieved at maximum rpm, the
addition of the restrictor results in peak power being achieved at just over 11,000 rpm. This
behaviour will be discussed later in the chapter.
2.4.4 Plenum
The next component of the intake system is the plenum. The plenum, combined with pipes at its
exit leading to the cylinders (called runners), completes the intake system. A plenum is a
pressurised chamber containing a fluid (in this case air) at higher pressure than its surroundings.
[20]
In the case of an engine, which has an irregular demand from the cylinders, the plenum works
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to even the distribution of pressure. In the case of the exhaust, a plenum has the added function of
acting as a silencer. The size of the plenum will have an effect on the power output of the engine
but the relationship between the two is not linear. Within a reasonable range, an increase in
plenum size will increase the power output. However, outside this range, any further increase in
size will have little effect on power output. Furthermore, a large plenum will have a negative effect
on throttle response, as a large plenum will take a longer time to fill than a smaller one. In addition,
the pressure inside a larger plenum will decrease resulting in decreased volumetric efficiency,
which is a measure of the effectiveness of the induction and exhaust processes. [23] As well as
power output, a very important consideration regarding plenum sizing is that of packaging. A large
plenum could take up a volume similar to that of the engine itself, meaning that a balance between
power output and size will be needed.
By making use of the Parametric/ Optimiser Tool in the software, it is possible to determine
how power output changes with plenum size. Plenum volumes ranging from 1-12 L were chosen,
with increments of 1 L between each, for use in the simulation. After running a number of
simulations with plenum sizes of less than 5 L, it was clear that power output drops considerably so
any smaller sizes than this were not considered for use with the engine. The results of the
simulation are shown below in Figure 2.13 and Figure 2.14:
Figure 2.13 Engine output power vs engine speed for different plenum sizes
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Figure 2.14 As Figure 2.13 above with focus on the peak power output
In Figure 2.13 and Figure 2.14 above, the red line displays the power output vs engine speed for a
plenum volume of 10 L. When running simulations prior to the use of the Parametric/ Optimiser
Tool, a plenum volume of 10 L appeared to yield the highest peak power output for the engine, so
this volume was used for the software baseline score. However, it is clear from Figure 2.14 that
there are plenum sizes which produce peak power output values above and below that of a 10 L
plenum. An important point to note is that the peak power output in each case is achieved at
around 11,500 rpm and this peak is more prominent than that shown in Figure 2.12. The results
displayed in Figure 2.14 are presented in a more useful format below, in Figure 2.15:
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Figure 2.15 Peak power output vs plenum volume @ 11,500 rpm
It can be seen in Figure 2.15 above that the peak power output is achieved with a plenum volume
of 7 L. Below this volume, the power output decreases rapidly and above it, there is a decreasing
oscillatory behaviour. Taking everything into account, a plenum volume of 7 L will be used to obtain
the maximum power possible; the size of the plenum will not cause a problem and can be
accommodated.
2.4.5 Forced Induction and Natural Aspiration
The final decision with regard to the intake system is whether to make use of forced induction or
whether to have the engine naturally aspirated. We shall analyse both cases below.
Forced induction works on a simple principle whereby a greater mass of air is forced into the
cylinders via some sort of compressor than would otherwise be drawn into the cylinders without a
compressor (natural aspiration) and this results in a charge (air and fuel mixture in a cylinder) with
more potential energy for combustion. One useful application of this is in propeller driven aircraft
that would otherwise lose power at altitude due to a decrease in atmospheric pressure whereas the
forced induction largely negates this. Forced induction can also be very useful for cars with internal
combustion engines as is the case here. There are two common types of compressors:
superchargers and turbochargers. The former are driven directly from the crankshaft of the engine
via a belt which means there is no delayed response, otherwise known as lag. The downside to
superchargers is that they are less efficient than turbochargers. Turbochargers work on the same
principle as superchargers but are driven by exhaust gases in the exhaust manifold. Turbochargers
suffer from lag because there is a delay between throttle depression and the compressor spooling
up from the increased exhaust gas mass flow rate. As the engine will be running at a constant rpm,
the reasons for which will be explained in the CVT section later in the report, it is not a problem that
turbochargers suffer from lag. In addition, turbochargers tend to be more efficient than
superchargers and also offer greater maximum boost pressure. Therefore, the proposal of using a
supercharger can be discarded in favour of analysing turbochargers. A schematic diagram of a
turbocharger implementation is shown below in Figure 2.16:
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Figure 2.16 Schematic diagram of turbocharger implementation in an engine [21]
The limiting factor on the maximum mass flow rate of air being drawn into the engine is given by
conditions of choked flow. In other words, the maximum mass flow rate of air drawn into the engine
is achieved when the flow through the venturi reaches a Mach number of M = 1. [7] [18] If this choked
condition is reached without the use of a turbocharger, then the addition of one will simply add
weight to the engine and have no effect on the peak power produced. Before analysing the
turbocharger any further, it is important to check if the choked condition has already been reached.
It is possible to work out the mass flow rate of air through the venturi under choked conditions (M =
1) using Equation (4) below:
√
γ γ +1
ḿ= Ap
RT 2
( )
− ( γ +1)
2 ( γ−1 )
(4) [22]
Where cross-sectional area of venturi A = 3.14e-4 m2, pressure p = 1e5 Pa, heat capacity ratio
γ
= 1.4, gas constant R = 287 J/kg/K and temperature T = 293 K. Solving Equation (4) above
gives a mass flow rate of air,
ḿ = 0.0927 kg/s under choked conditions. Using this value for
mass flow rate along with Equation (5) below, it is possible to determine the engine rpm at which
choked conditions will occur:
N=
120 ḿ
ρ V s ηvol
Where N is engine rpm, swept volume
density of air
ρ
= 1.90 kg/m3 [24] and
(5) [23]
V s = 0.599e-3 m3, volumetric efficiency ηvol
= 0.88,
ḿ is as above. Solving Equation (5) above gives a value
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of N = 11,300 rpm for choked conditions. This value agrees with the behaviour seen in Figure 2.13.
Figure 2.13 shows that peak power is reached at a similar engine rpm as calculated above using
Equation (5); the flow is choked at this rpm and running the engine at a greater rpm than this will
yield no benefit. It is for this reason that there is no benefit to be obtained by using a turbocharger.
Therefore, the engine will be naturally aspirated and will run at choked conditions to produce
maximum possible power output.
2.4.6 Cylinders
The key component of any engine is its cylinders, where the useful power is produced. The Honda
CBR600RR engine chosen has four cylinders in line with one another. In order to try and smooth
the torque at the crankshaft resulting from combustion and to help balance the engine, the two
outer cylinders move out of phase with the inner two cylinders. The bore (or diameter) of the
cylinders is 67 mm while the stroke (the distance each piston moves within a cylinder) is 42.5 mm.
The bore/stroke ratio is a useful parameter when considering the design of an engine. The
bore/stroke ratio above is 1.576 which is typical of an engine designed for racing; the Renault
engine for the 2014 Formula 1 season, for example, has a bore/stroke ratio of 1.509. [25] The
reason for the comparatively high bore/stroke ratio is to reduce the frictional losses in the cylinders.
The frictional losses increase with increasing piston speed, and thus engine rpm, as can be seen in
Equation (6) below:
N
N
FMEP=0.97+ 0.15
+0.05
1000
1000
(
)
(
2
)
(6) [23]
With frictional mean effective pressure FMEP (bar) and engine rpm N. It is possible to achieve a
given engine displacement by varying either bore, stroke, or a combination of the two; by
increasing the bore size and keeping the stroke small, even at high engine rpm, the piston speed
will be lower and thus frictional losses will also be reduced. Solving Equation (6) above with N =
11,500 gives FMEP = 9.31 bar. Considering the BMEP = 12.39 bar at this speed (taken from the
engine simulation), the engine is losing almost as much power to friction as it usefully produces. It
is for this reason that it is important to keep the piston speed low. Having a large bore has the
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added benefit that there is a larger area available for valves, allowing them to be larger or greater
in number, and a comparatively short stroke reduces crank stresses. [26] A schematic diagram of a
cylinder from the chosen engine can be seen in Figure 2.17 below:
Figure 2.17 Schematic diagram from the engine simulation software showing a cylinder in the
chosen engine with intake valve shown in blue and exhaust valve shown in orange
Another useful parameter to consider is the compression ratio rv. The idealised cycle of an internal
combustion engine with spark ignition is the Otto cycle. The efficiency of the Otto cycle ηOtto
increases with increasing rv as can be seen in Equation (7) below:
ηOtto =1−
1
r
γ −1
v
(7) [23]
The compression ratio for the chosen engine is 12.2:1 [27] which gives an Otto cycle efficiency of
0.63. Increasing the compression ratio will achieve greater efficiency because more mechanical
work can be extracted from a given charge [28]. Unfortunately, the compression ratio cannot be
increased to achieve greater efficiency. This is because increasing the compression ratio could
lead to engine knock, a phenomenon whereby the combustion of a charge in a cylinder does not
coincide with the spark from the spark plug and one or more pockets of air/fuel mixture explode
outside the envelope of the normal combustion front. [29] Engine knock can destroy an engine in
severe cases. Engine knock could be avoided by using fuel with a higher octane rating; the FSAE
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Rules [1] state that E85 is the only other option and its use will be discussed later. If the fuel octane
rating and compression ratio were to be increased, the limiting factor would be high stresses on
mechanical components in the engine, such as the crank and connecting rod. Due to the factors
mentioned above, [7] the compression ratio of 12.2:1 will be retained.
2.4.7 Valves
The valves in an engine allow gas flow into and out of its cylinders. The Honda CBR600RR has
four valves per cylinder, two inlet and two exhaust valves, which are controlled by a double
overhead camshaft or DOHC. A diagram of DOHC implementation is shown in Figure 2.18 below:
Figure 2.18 DOHC arrangement in an engine [30]
A DOHC arrangement gives greater scope for tuning and thus increasing performance. There are
two important things to consider with the design of valve gear, assuming the size and shape of
each valve does not change: valve lift and valve timing. Valve lift refers to the distance a valve
moves between fully closed and fully open positions. Valve timing refers to the angle of the
crankshaft at which the inlet and exhaust valves open and close with respect to top dead centre
and bottom dead centre.
The valve movements are as follows: the exhaust valves open shortly before top dead centre
(BTDC) to allow air to flow into the cylinders on the induction stroke. Next, on the compression
stroke, the inlet valves close after bottom dead centre (ABDC). The exhaust valves then open
towards the end of the combustion stroke, before bottom dead centre (BBDC), which results in a
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loss on the combustion stroke but ensures all combustion products have time to escape. Finally,
the exhaust valves close, at the end of the exhaust stroke, just after top dead centre (ATDC).
The process described above makes up the four strokes of a four-stroke engine cycle. It should be
noted that there is some intake and exhaust valve overlap at top dead centre and this is usually
limited by the clearance between the piston and the cylinder-head. [23] Engines designed for high
performance have a large valve overlap and both inlet and exhaust valves open earlier and close
later than standard engines. [18] [23] After optimisation in the engine modelling software, the valve
timing was determined for the engine of choice. The valve timing diagrams before and after
optimisation can be seen in Figure 2.19 below:
Figure 2.19 Valve timing diagrams before (left) and after (right) optimisation
Whilst valve timing determines when each event takes place, valve lift determines the effective
area for gas flow into and out of the cylinders. Increasing the valve lift above that originally
intended for the engine without changing the piston design and/or connecting rod length could
result in the engine being destroyed if the piston hits a valve and fractures; modifying the valve lift
will not, therefore, be considered. Furthermore, there is a value of valve lift at which the effective
area for gas flow through the valves reaches a maximum; any increase in valve lift beyond this
point will not produce any increase in effective area for gas flow. The valve lift vs crank angle
diagrams for the inlet and exhaust valves can be seen in Figure 2.20 below:
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Figure 2.20 Valve lift vs crank angle for intake (left) and exhaust (right) valves
The effect of the optimised valve timing on the engine power output is considerable and is
graphically represented in Figure 2.21 below:
Figure 2.21 Engine peak power output vs engine rpm for standard and optimised valve timing
2.4.8 Fuel Injection
There are three ways in which to add fuel to air in the engine intake system to create a charge;
carburetion, low pressure injection (port injection) and high pressure injection (direct injection).
A carburettor is a mechanical device used more commonly in older engines to regulate the amount
of fuel going to the cylinders by making use of Bernoulli’s principle which states that for a fluid
flowing in a pipe, the sum of the static and dynamic pressures is constant. If the air intake is
reduced to a smaller diameter at a section, the velocity of the air will increase, while the static
pressure will decrease. A carburettor makes use of this by having a petrol outlet orifice inserted into
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a reduced diameter section of the air intake and tiny petrol droplets are sucked from this orifice by
the low static pressure described above. The droplets are carried along by the flow of air and
ideally, if the air intake is placed close to the exhaust, the heat given off by the exhaust will help to
vaporise the droplets. A diagram of a carburettor can be seen in Figure 2.22 below:
Figure 2.22 Diagram of a Carburettor [31]
As the amount of fuel is controlled by the rate of air flow, the engine will respond slowly if the
throttle is opened suddenly at low engine rpm. The placement of the intake next to the exhaust to
help vaporise the fuel droplets also results in a lower intake air density and thus reduced
performance. [32] Furthermore, the need for another venturi upstream of the throttle results in
losses. For these reasons, a carburettor will not be considered.
Fuel injection is more fuel efficient than carburetion because the fuel flow can be altered according
to the downstream and user-input conditions to produce maximum power. Fuel injectors are
solenoid operated plungers that squeeze fuel through a nozzle to atomise it and are controlled by
engine electronic control units (ECU). Sensors measure engine rpm, intake manifold pressure, air
temperature, coolant temperature and throttle position and the information is fed to the ECU which
then determines how much fuel is needed. The required amount of fuel is injected at the right time
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either into the inlet ports (port or low pressure injection) or into the cylinders directly (direct or high
pressure injection).
Port injection uses injectors at the inlet ports to each cylinder, just upstream of the inlet valves,
whereas direct injection uses injectors located in the cylinder head to inject fuel directly into the
cylinders. Direct injection achieves greater efficiency than port injection because there are no
throttling losses but direct injection requires much more sophisticated and expensive hardware and
software; as the injectors are exposed to higher pressures and temperatures, higher quality
materials have to be used as well as higher precision electronic systems. [23] [33] [34]
The Honda CBR600RR comes with a dual stage fuel injection system which uses low pressure
injection. Fuel injectors are placed at the inlet ports and at the upstream end of the intake runners.
The injectors at the upstream end of the intake runners operate at high rpm and give greater
vaporisation time as well as greater exposure to the turbulent mixing of the flow; this cools the flow
of air and ultimately results in a denser charge, giving more power. [35] As direct injection would
require expensive equipment and significant alterations to the engine, the stock dual stage low
pressure fuel injection system on the engine will be used.
2.4.9 Fuel
The FSAE Rules stipulate that there are two types of fuel available for use: gasoline and E85. If
using E85, the air intake restrictor has to have a 19 mm diameter. [1] E85 is a mix of 85% denatured
ethanol fuel and 15% gasoline, giving it a higher octane rating than standard gasoline. An engine
using a high octane fuel such as E85 needs to have a very high compression ratio. Use of E85 in
an engine designed for gasoline achieves lower fuel economy as more fuel is needed per unit of air
than when using gasoline. E85 is corrosive to the rubber seals often found in fuel systems
designed for use with gasoline so these components may fail prematurely. [36] The Honda
CBR600RR engine is designed for use with gasoline. If E85 was to be used, seals would need to
be changed, the compression ratio would have to be increased (which would increase engine
stresses), a lower fuel economy would be achieved (resulting in the need for a greater amount of
fuel and this would decrease the number of points scored for efficiency) and a smaller diameter air
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restrictor would have to be used (which would make a 10% difference to restrictor area and would
reduce performance). For these reasons, gasoline will be used rather than E85.
2.4.10 Air/Fuel and Equivalence Ratio
The air to fuel ratio (AFR) is the ratio of the mass of air to the mass of fuel in a combustion
process. The condition when there is exactly the right amount of air present to burn all of the fuel is
called stoichiometric combustion. The combustion of gasoline in air produces CO2 and H2O as can
be seen in Equation (8) below:
2C 8 H 18+25 O2 →16 C O 2 +18 H 2 O
(8) [37]
Calculating the AFR using the respective molecular masses of air and gasoline, together with the
equation above, it can be shown that the stoichiometric AFR = 14.7. This means that for total
combustion of 1 kg of gasoline, 14.7 kg of air are needed. [38] Unfortunately, this theory does not
hold in the case of internal combustion engines. The charge of air and fuel in each cylinder will not
be perfectly mixed and the time available at each combustion stroke is short (in the region of a few
milliseconds), especially at high engine rpm. In order to compensate for this, the equivalence ratio,
the ratio of the stoichiometric AFR to the actual AFR, needs to be greater than one.
[23]
The
equivalence ratio is shown below in Equation (9):
ϕ=
AFR stoichiometric
AFR
(9) [38]
If a charge has a greater AFR than stoichiometric, the charge is called lean and the equivalence
ratio is less than one. Conversely, if the AFR is less than stoichiometric, the charge is considered
rich and the equivalence ratio is greater than one. In the case of a lean mixture, all the fuel in the
charge will be burned, leaving some air unburned, resulting in reduced performance. In the case of
a rich mixture, the maximum amount of fuel will be burned in the available air, resulting in lower
fuel efficiency (although a rich mixture helps to cool the engine). This behaviour is shown in Figure
2.23 below:
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Figure 2.23 Response of specific fuel consumption and engine power output with change in
equivalence ratio. [23]
If the mixture of fuel and air becomes too rich, the power output drops. Ideally, the engine should
be run at the highest point on the top curve in Figure 2.23 to produce maximum power, even
though the specific fuel consumption will not be at a minimum. Using the engine modelling
software, this optimum equivalence ratio is Φ = 1.05, providing maximum power.
2.4.11 Fuel Consumption
An important consideration of the engine is the fuel consumption because the fuel and fuel tank will
add weight to the car, decreasing its performance. The brake specific fuel consumption is given for
the engine by the engine modelling software and can be seen in Figure 2.24 below:
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Figure 2.24 Graph of BSFC against engine rpm
The graph in Figure 2.24 above shows that the specific fuel consumption does not increase
dramatically until about 11,500 rpm, the point at which the engine will be operating. At this point,
BSFC = 250.7 g/kW/hr. It is possible to find the amount of fuel needed in the endurance race by
using Equation (10) below:
V =P × BSFC ×t ×
1
ρf
(10)
With the volume V in litres, power P in kW, brake specific fuel consumption BSFC in g/kW/hr, time
t in hours and the density of fuel ρf = 0.71e3 kg/ m^3. [37] In order to determine the value for t (the
time the car will take to complete the race), the lap time will need to be taken into account along
with a weighting for throttle position within each part of the track. A safety factor will be used so the
discrepancy in lap times between the first and subsequent laps can be ignored. In a lap completed
in 36 seconds, as will be shown later in the report, roughly 16 seconds are spent at full throttle, 8
seconds at mid throttle, 6 seconds at low throttle and 6 seconds are spent braking. Working on the
assumption that under braking and at low throttle, the BSFC goes down to 10% of the value at full
throttle and when at mid throttle, BSFC goes down to 40% of the value at full throttle, the
equivalent time spent at full throttle can be worked out. [18] For the 27 lap endurance race, the
equivalent time t in hours can be calculated using Equation (11) below:
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27
( 16+0.4 ( 8 ) +0.1(6+ 6) ) =0.153 hours
3600
(11)
Using the value of t calculated in Equation (11), and using the values given by the engine
modelling software, it can be shown that the required amount of fuel for the endurance race V =
3.91 litres; this is the worst case as the density of fuel used was a minimum value. Using a safety
factor of 1.3, to account for any waiting at the start of the race and driving to and from the pits, a
fuel tank of 5 litres will be necessary.
2.4.12 Fuel Tank
In order to comply with the FSAE Rules, [1] a fuel tank made of rigid material must not carry any
structural loads but it can be any size and can be made of any material. The fuel tank should lie
entirely within the monocoque chassis and a firewall must separate the tank from the driver to
reduce the risk of burns. A suitable material is carbon fibre as this is lightweight and provides
rigidity. Carbon fibre is an expensive material to buy and to work with but there are products
available that meet the requirements. The carbon fibre fuel tank used in Formula Seven is suitable
for Formula Student and this will be the tank used for the car. At a cost of £400, the tank is not
cheap but comes equipped with a fuel pump. [39] A picture of the fuel tank can be seen in Figure
2.25 below:
Figure 2.25 Carbon fibre fuel tank to be used
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2.5 Fine Tuning
At this stage of the design considerations, the engine is giving maximum power output; the flow is
choked at the venturi so no more air is able to get into the cylinders during each cycle. This is a
good result considering the specification. However, it should be possible to optimise the intake and
exhaust runner lengths, making use of resonance tuning. Resonance tuning would not increase the
power output of the engine but would reduce the engine rpm at which the maximum power is
produced, thus lowering fuel consumption. This would make the car lighter as it would need to
carry less fuel, which in turn would increase its performance. Resonance tuning works as follows:
as valves open and close, compression and rarefaction waves are induced in the compressible fuel
and air mixture in the intake and exhaust runners. When the waves reach the end of the runners
they are reflected. If the length of the runners is just right, the waves act to increase volumetric
efficiency. The available benefits are very sensitive to engine rpm. A diagram showing the
operation of resonance tuning can be seen in Figure 2.26 below:
Figure 2.26 Diagram displaying the operation of resonance tuning [40]
Figure 2.26 above shows an inlet valve open at stage 1. At stage 2, the inlet valve is snapped shut
and a compression wave forms. This compression wave travels along the pipe at stage 3. At stage
4, the compression wave is reflected at the end of the pipe and travels back down the pipe at stage
5. At stage 6, the compression wave arrives at the open inlet valve at just the right time to force
more air and fuel mixture into the cylinder than would otherwise be the case, increasing volumetric
efficiency. The same principle applies to the exhaust side of the engine, but instead a rarefaction
wave arrives at the exhaust valve at just the right time to help draw the burnt mixture from the
cylinder, also known as scavenging.
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A diagram showing the effect of the timing of the arrival of pressure waves on volumetric efficiency
for the intake valve can be seen in Figure 2.27 below:
Figure 2.27 Diagram displaying the effect of timing on volumetric efficiency [23]
Figure 2.27 shows that the pressure waves must arrive at just the right time to maximise volumetric
efficiency, so precise calculation of the timing is needed. [41] The same considerations apply to
silencers, where the geometry of the silencer can be made such that pressure waves cancel each
other out, reducing the noise level whilst also minimising the restriction to flow. [23]
A further consideration for manifolds is the layout of the intake and exhaust runners. In order to
maximise the effects of resonance tuning, the system should avoid sending pressure waves from
separate cylinders into the same pipe at the same time as this will lead to increased losses. Two
obvious options for the arrangement of the exhaust manifold are a four-to-two-to-one (4-2-1) or a
four-to-one (4-1) connection. Only the latter reaps the benefits of resonance tuning at high engine
rpm so the 4-1 arrangement will be used. The layout of the intake system is less problematic and
will make use of a one-to-four (1-4) system.
[23]
An example of the intake layout with the inclusion of
a plenum (‘intake chamber’) and a throttle can be seen in Figure 2.28 below:
Figure 2.28 Intake system with 1-4 intake runner arrangement [23]
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2.6 Conclusion
After all optimisation, the final engine power output is shown in Figure 2.29 below:
Figure 2.29 Final peak power output vs engine rpm
As can be seen in Figure 2.29 above, the engine gives a peak power output of 96.9 hp
(72.2 kW) at 11,500 rpm; this is well above the specified 65 hp. The engine also exceeds the other
criteria set out in the specification. The torque achieved at 11,500 rpm is 59.1 Nm which is greater
than the 50 Nm specified. Despite the requirement of a 20 mm restrictor, the power produced after
optimisation is close to the stock engine power output compared with the restricted engine with no
optimisation. At 32 kg, it is well within the 60kg weight specification.
[42]
The Honda CBR600RR
engine is easily sourced from ebay for less than £2000. [8] Efficiency has been taken into account
throughout, including during the selection of a 5 L fuel tank. Packaging is also important and where
possible, the size of components has been kept to a minimum whilst maximising power. The fact
that the car will use a CVT means the engine is able to run constantly at 11,500 rpm, producing
96.9 hp at all times; this will make the car highly competitive. In practice, the actual values for
power and torque may vary from the theoretical values given in the engine modelling software; if
the project included the actual manufacture of the car and its components, testing on track could
be done and the performance optimised using telemetry. The Honda CBR600RR appears to be a
good choice of engine.
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2.7 References
[1] http://www.fsaeonline.com/content/2015-16%20FSAE%20Rules%20revision
%2091714%20kz.pdf
[2] http://www.topspeed.com/motorcycles/motorcycle-reviews/yamaha/2013-yamaha-phazer-m-txar131346.html
[3] http://en.wikipedia.org/wiki/Snowmobile
[4] http://en.wikipedia.org/wiki/Honda_CBR600RR
[5] http://en.wikipedia.org/wiki/Suzuki_GSX-R600
[6] http://www.motorcyclespecs.co.za/model/yamaha/yamaha_wr450f%2003.htm
[7] Private communication with Professor Richard Stone
[8] http://www.ebay.com/itm/Honda-CBR600RR-CBR-600RR-Engine-Motor-2008-07-09Guaranteed-Low-miles-/121594369273
[9] http://www.motorcycle-usa.com/115/396/Motorcycle-Article/2003-Honda-CBR600RR-FirstRide.aspx
[10] http://www.lotuscars.com/engineering/engineering-software
[11] https://lotusproactive.files.wordpress.com/2013/08/getting-started-with-lotus-engine-simulation.pdf
[12] P4 Fluid Mechanics Lectures: Dr. P McFadden, HT2012
[13] http://en.wikipedia.org/wiki/Bell_mouth
[14] http://www.bosch-mobility-solutions.de/de/de/_technik/component/PT_PC_CNG_AirManagement_PT_PC_Compressed-Natural-Gas-02_12737.html?compId=980
[15] http://sohc.nl/pictures/engine/%5B2010-03-25%5D_parts/roller_barrels_01.jpg
[16] Flow Characteristics and Performance Evaluation of Butterfly Valves Using Numerical
Analysis: IOP Publishing, doi:10.1088/1755-1315/12/1/012099
[17] Flow of Fluids Through Valves, Fittings and Pipe: Crane 1982
[18] Private communication with Professor Ray Lohr
[19] Contraction, Expansion, Pressure Drop: Saeid Rahimi, 2011
[20] http://en.wikipedia.org/wiki/Plenum_chamber
[21] http://auto.howstuffworks.com/turbo2.htm
[22] http://www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html
[23] Introduction to Internal Combustion Engines: R Stone, Macmillan 1992
[24] Engineering Tables and Data: A Howatson, P Lund, J Todd, Department of Engineering
Science, 2009
[25] http://www.f1fanatic.co.uk/2013/06/21/renault-reveals-2014-f1-engine/
[26] http://en.wikipedia.org/wiki/Stroke_ratio
[27] http://www.aperaceparts.com/tech/2009hondacbr600rr.html
[28] http://en.wikipedia.org/wiki/Compression_ratio
[29] http://en.wikipedia.org/wiki/Engine_knocking
[30] http://commons.wikimedia.org/wiki/File:Four_stroke_cycle_power.png
[31] http://journeytoforever.org/biofuel_library/z-image/dranefig5-1.jpg
[32] How Things Work, The Universal Encyclopedia of Machines: Paladin, Granada Publishing
Limited, 1972
[33] http://en.wikipedia.org/wiki/Fuel_injection
[34] http://en.wikipedia.org/wiki/Indirect_injection
[35] http://www.honda.com/newsandviews/article.aspx?id=1775-en
[36] http://en.wikipedia.org/wiki/E85
[37] http://en.wikipedia.org/wiki/Gasoline
[38] http://en.wikipedia.org/wiki/Air%E2%80%93fuel_ratio
[39] http://www.formula-seven.com/shop-products/carbon-fiber-fuel-tank/
[40] http://rennlist.com/forums/944-turbo-and-turbo-s-forum/784852-ultra-high-flow-low-cost-8vhead-project-12.html
[41] http://www.autozine.org/technical_school/engine/Intake_exhaust.html
[42] http://cbrforum.com/forum/cbr-600rr-12/enigne-weight-cbr600rr-25219/
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Management
St. Catherine’s College
3
Thermal Management
3.1
Introduction
Thermal
The thermal management of a formula student race car is a vital component in the performance of
the car. The car needs to have an adequate cooling system, which has a capacity proportional to
the power output of its engine. The primary function of the cooling system is to maintain proper and
reliable engine performance within an optimal temperature range. In order to design the cooling
system the relevant 2015 Formula SAE competition rules must be reviewed. The main limitation
states that any “water-cooled engine must only use plain water” [1].
Operating below the minimum engine temperature can cause excess use of fuel and corrosion of
the engine and cooling system. Operation above the maximum engine temperature decreases the
oil viscosity causing wear, excessive oil consumption and decreased mechanical power output. It
is therefore vital to maintain control over the engine temperature. The first variable to consider
when designing an engine cooling system is the required heat loss. A commonly used rule is
shown in the equation below [2]:
1
1
1
Fuel Energy= HP+ Heat + Cooling System Load
3
3
3
Effectively one third of the heat produced by the engine is converted into mechanical work; one
third is lost to ambient air as exhaust and frictional heat. The final third is required to be removed
by the cooling system. This is a reasonable estimate; internal combustion engines are inefficient,
usual efficiency of about 25 % to 30 % [3] and the waste heat removed from the engine is fairly
evenly split between the hot exhaust gases and the cooling system. For this car the power output
is 72 kW leading to a cooling load of 24 kW.
3.2
Basics of the cooling system
In general two basic types of cooling systems exist. They both transfer heat from the engine block
to the ambient air. The two methods for removing heat are air or liquid cooling. Air cooling works by
relying on air flowing directly over hot parts of the engine to dissipate heat. Cooling fins can be
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Thermal
Management
used to increase the effective cooling area that heat transfer can occur across. This method is
limited to low power engines as they can only dissipate small amounts of heat. Liquid cooling relies
on parts of the air cooling method in combination with the use of a coolant, usually water, flowing
through the engine as an intermediate medium to remove heat and achieve more effective cooling.
The limitations of air cooling can be made evident by comparing air and water, air has a lower heat
capacity and less than a tenth the conductivity [4]. Thus air cooling requires unrealistically high air
flow velocities and an extremely large heat exchanger surface area to achieve the same level of
cooling. Liquid cooling is therefore used in formula student race cars.
Figure 3.1 Engine cooling system [5]
Following the SAE rules the coolant used here is plain water. A thermostat or the engine control
unit, ECU, is used to maintain the engine temperature. It controls the power to the coolant pump; if
the engine is overheating the thermostat will increase the power and thus increase the flow rate of
the coolant through the engine and vice versa. When designing a cooling system there are three
different variables to work with: the coolant flow rate through the engine block; the airflow rate
through the radiator and the heat transfer capability of the radiator.
3.3
Cooling system components
There are a number of different components within a cooling system which can be chosen and
designed to ensure the desired values of the variables above. The coolant flow rate is set by a
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Thermal
Management
range of different pumps and is controlled by either a thermostat or an ECU, which vary the flow
rate depending on demand. The airflow rate through the radiator will vary depending on the overall
shape of the body work, side pods, and positioning of the radiator. It can also be increased by
attaching a fan to the radiator. The radiators heat transfer capability relies on a number of different
variables which will be looked at in more detail later.
3.3.1
Coolant pump selection
The initial decision regarding the coolant pump is whether to use a mechanical or an electrical
pump. A mechanical pump is traditionally used in cars. It works by taking mechanical energy from
the engine, in the form of a spinning rubber belt, and uses it to drive an internal pump mechanism.
This results in a decrease in either the cars power output or fuel economy or both as it is running
off energy directly from the engine. The mechanical pump spins all the time at a speed proportional
to the engine speed. As a result coolant is sometimes being pumped when the engine is not at a
temperature which requires cooling. Conversely an electrical pump runs on the battery power and
can be controlled through an ECU .This is significantly more accurate as coolant flow rate through
the engine is set depending on a given temperature range. The drawbacks of electric pumps are
that they are more expensive and typically are not as powerful.
The electrical system has been chosen, as is the case for most formula student teams, mainly due
to the higher level of control, ECU – section 7.2.5, typically smaller size of the pump, and
improvements of around 3.7 kW over a mechanical system. The chosen pump is the Davies Craig
EWP80 [6], costing £135 and weighting 0.9 kg. This pump has a maximum flowrate of 80 L/min.
Figure 3.2 A graph showing pressure and current vs flow for the pump, provided by Davies Craig [6]
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Management
St. Catherine’s College
Thermal
3.3.2 Cooling fan selection
Cooling fans are used to control the airflow velocity over the radiator. The airflow velocity affects
the ability to transfer heat; slower airflow has a higher exit temperature hence a higher average
cooling temperature because more heat transfers by convection. A higher average cooling
temperature means that less heat is transferred from the coolant to the air. Faster airflow velocities
will increase the differential between the coolant and the cooling air; it will have a lower average
cooling temperature, and therefore increase the capability to transfer heat.
For this formula student race car the Jegster 40533 – Jegster fan and shroud kit [7] has been
chosen. This kit contains a fan with a 12” diameter with the ability to produce an airflow rate of
1200 CFM. The shroud reduces losses in thrust from the tips of the fan blades. The kit costs £98
and has a weight of 1.5 kg.
3.4
Radiator analysis
Nomenclature:
cp, water – water specific heat
cp, air – air specific heat
ṁwater –water mass flow rate
ṁair – air mass flow rate
CW – heat capacity of water
CW =ḿwater c p , water
CA – heat capacity of air
C A =ḿair c p ,air
Cmin – minimum heat capacity
Cmax – maximum heat capacity
hwater – heat transfer coefficient for the water
hair – heat transfer coefficient for the air
q – heat transfer rate
qmax – maximum possible heat transfer rate
ε – effectiveness
NTU – number of transfer units
Th, inlet – inlet temperature of the hot fluid
Tc, inlet – inlet temperature of the cold fluid
Aex – external surface area
Ain – internal surface area
UA – overall heat transfer coefficient
Cr – heat capacity ratio
Cr =
Cmin
Cmax
The radiator is a heat exchanger used for cooling the internal combustion engine. Heat exchangers
are implemented to allow the process of heat exchange between two fluids that are at different
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St. Catherine’s College
Thermal
Management
temperatures and separated by a solid wall; in this case the two fluids are the coolant (water) and
the ambient air. The analysis applied here was first carried out on a stock aluminium radiator [8]
where every dimension was known. This was extended to design a new radiator which fits the
needs of the formula student race car being designed. In order to save both time and money the
designed radiator was then compared to radiators available on the market and the most similar one
was chosen. The method of analysis used is based on the effectiveness – number of transfer
units, NTU, method described in “Fundamentals of Heat and Mass Transfer” [9] and has been
summarised below.
In order to define the effectiveness one must first determine the maximum possible heat transfer
rate [9].
q max=C min ( T h ,inlet −T c ,inlet )
ε=
q
qmax
The number of transfer units is a dimensionless parameter that is widely used for heat exchanger
analysis. The overall heat transfer coefficient is needed to be known in order to find the NTU [9].
1
1
1
=
+
UA h air Aex hwater A¿
NTU =
UA
C min
For each heat exchanger there is a specific form of the effectiveness – NTU relation. In this case a
cross flow (single pass) heat exchanger is being used with both fluids unmixed. The relationship
between effectiveness and NTU is shown below [9].
ε =1−exp ⁡[
( C1 ) ( NTU )
r
0.22
{exp [ −C ( NTU ) ] −1 }]
0.78
r
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St. Catherine’s College
Thermal
Management
The dimensions of the stock aluminium radiator initially analysed are given in table 3.1. The values
of both the external and internal surface areas can be calculated and were found to be 34.2 m2 and
3.14 m2 respectively.
Table 3.1 Radiator dimensions [8]
Lradiator
(m)
Hradiator
(m)
Wradiator
(m)
Wtube
(m)
Htube
(m)
Lfin
(m)
Wfin
(m)
Hfin
(m)
Ntube
Nfin
0.6635
0.4572
0.0603
0.0254
0.0021
0.0040
0.0584
0.0001
86
780
A simulation of the cooling system was made in Matlab, in which the mass flow rates of both the
water and the air could be varied to show how they affect the heat rejected by the cooling system.
This cooling system with the stock aluminium radiator could only achieve the required heat loss, 24
kW, with a mass flow rate of water equal to or greater than 1 kg/s and a mass flow rate of air equal
to or greater than1.3 kg/s. The chosen pump has a maximum flow rate of 1.33 kg/s which is over
that required, however this is a simplified model and in practise it would be advised to be further
away from the pumps working limit. The mass flow rate of air cannot be achieved by the chosen
fan. Therefore the radiator needs to be redesigned.
Figure 3.3 Surface plot for stock radiator
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St. Catherine’s College
Thermal
Management
The heat transfer rate for the radiator can be amplified by increasing both the internal and external
surface areas. In addition to this the overall size of the radiator needs to be reduced to allow it to fit
within the car’s body work. In order to achieve this decrease in size and increase both the surface
areas, the number of tubes and the total fin surface area within the radiator must both increased.
The redesigned radiator has achieved a frontal area of 0.0758 m2 with Aex = 40 m2 and Ain = 4m2.
Matlab was used to show the change in the heat transfer rate.
Figure 3.4 Surface plot for redesigned radiator
In order to save both time and money a radiator with similar dimensions has been found. The
Suzuki LTR450 Aluminium Radiator 2006-2009 [10] meets the needs of this formula student car. The
radiator has an overall size of 17.44” x 9.02” x 4.65”, weights 2.27 kg and cost £130.
3.5
Conclusion
The cooling capacity of a formula student car is a very difficult thing to model. In the areas where
less specific analysis has been done, other formula student teams’ results and choices have
influenced the ones made here. This provides a factor of safety as they have been tried and tested,
producing real results. Where the analysis in this report goes into more detail a level of safety has
again been taken into account. Hence making sure that the simplifications and assumptions made
in the analysis will not lead to failure on the track. Thermal management needs particular care as a
car without a properly working cooling system will be unsafe for use.
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Robert Bainbridge
Management
St. Catherine’s College
Thermal
3.6References
[1] 2015 Formula SAE Rules, T8.1, 2015, p. 61
[2] Day, J., “The Bosch Book of the Motor Car,” 1975, p. 67
[3] [Online] http://en.wikipedia.org/wiki/Engine_efficiency
[4] [Online] http://en.wikipedia.org/wiki/internal_combustion_engine_cooling
[5] [Online] http://www.repairpal.com/cooling-system
[6] [Online] http://www.daviescraig.com.au
[7] [Online] http://www.jegs.com/i/Jegster/550/40533/10002/-1
[8] Carl, M., Guy, D., Leyendecker, B., Miller, A., Fan, X., “The Theoretical and Experimental
Investigation of the Heat Transfer Process of an Automobile Radiator” 2012, p. 10
[9] Incroera, DeWitt, Bergman, Lavine, “Fundamentals of Heat and Mass Transfer”, vol. 6, 2007, p.
686
[10] [Online] http://www.mishimoto.co.uk/suzuki-ltr450-aluminium-radiator-06-09
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Robert Bainbridge
4.
4.1
St. Catherine’s College
Aerodynamics
Aerodynamics
Introduction
Aerodynamics is a major part of any race car. The overall aims are to create as much downforce,
negative lift, whilst keeping the aerodynamic drag on the car to a minimum. Maximum downforce is
desired because it increases the normal loads on the tyres, increasing the grip, without the
corresponding addition of mass. The downforce is limited by its corresponding drag; in most cases
increasing the downforce on a car will increase its drag. So the design of the car must be
optimised. This optimisation will vary depending on the nature of the track. For a fast track with
fewer turns minimising the drag and thus having less downforce will be the optimal design and vice
versa for a corner heavy track.
Formula Student is a competition where cars from competing teams will be judged to determine the
best overall car in terms of cost, reliability and performance. The competition is split into static and
dynamic events. The dynamic events test the cars performance in different scenarios such as
autocross, acceleration and endurance. The endurance event is worth the most points, 300. For
this reason the analysis carried out in this chapter is based on maximising the cars performance in
this event. Meaning downforce is prioritised to increase cornering speed resulting in faster lap
times.
Methods of simulation such as computational fluid dynamics have been developed and used here
to help overcome the problems associated with aerodynamic optimisation of an entire car. It is the
objective of this chapter to design the aerodynamic package of a formula student racing car. As
well as determine the material from which these aerodynamic features will be manufactured.
4.2
Material selection analysis for the aerodynamic package
4.2.1
Introduction
In this section the different materials from which the aerodynamic package will be made are
considered and analysed. The analysis is mainly considering three parts of the package; the two
side pods and a single piece nose cone. The reasons being are that these pieces are for one the
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Aerodynamics
largest and therefore contribute the most to the overall mass of the car, as well as requiring the
most structural strength because failure will lead to an unusable car. For each material the weight,
strength, cost and ease of manufacture are considered. A final decision is made using multi-criteria
analysis based on the aforementioned design criteria.
4.2.2 Material properties
The options have been narrowed down to four different materials, one metal alloy, two composites
and a polymer.
Materials
Table 4.1 Properties of the different materials
Cost of raw
Young’s
materials
Density
Modulus
(£/kg)
(kg/m3)
(GPa)
UTS
(MPa)
ABS Plastic
0.54[1]
1040[2]
2.2[2]
45[2]
Aluminium Alloy
(7075-T6)
1.21[3]
2700[3]
70[3]
570[3]
CFRP
73.85[3]
1500-2000[4]
150-250[4]
1000-1500[4]
GFRP
2.62[3]
1500-2500[4]
80-100[4]
~1000[4]
Acrylonitrile butadiene styrene (ABS) has been selected due to its availability, formability, low cost
and low weight. Its weight is even lower than that of carbon fibre reinforced polymer (CFRP).
CFRP is very strong, however this comes at a price as it is by far the most expensive of the four
materials. Glass fibre reinforced polymer (GFRP) has comparable strength and is a lot cheaper.
The construction process for both CFRP and GFRP is very expensive and time consuming. The
aluminium alloy is the second most economical material and has a simple yet relatively
dimensionally inaccurate manufacturing process.
4.2.3 Manufacture
The construction of the body parts follows a different process depending on the type of material
used. It is important to consider each manufacturing method in detail as they vary in the
complexity, price and accuracy. The accuracy is of high importance because the shapes of the
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Aerodynamics
aerodynamic body parts designed in this chapter need to be manufactured with high dimensional
accuracy to act as the experimental results have predicated.
ABS is a thermoplastic which can be vacuum formed into the desired shapes. This process
involves heating a sheet of ABS until it becomes workable and then draping it over a mould. The
edges are sealed against the mould; a vacuum pressure is then applied from under the mould,
forcing the plastic onto the mould increasing dimensional accuracy. The part then pops off the
mould as pressure is released [2]. This method is a very cost effective way of producing parts; the
moulds themselves are inexpensive and can be constructed from a range of cheap materials such
as medium density fiberboard (MDF) or polystyrene foam. The cycle can range from 2-10 minutes
per part. The downsides to this method are that a lot of material waste is produced and it cannot
guarantee that a constant wall thickness is maintained, which means the strength of the parts may
be impaired. Companies such as “Airforme” [5] provide the service of producing vacuum formed
parts. The total cost of their services for the required body parts is estimated at £200.
High performance parts made out of CFRP are often manufactured using the process of vacuum
bagging as it prevents small air bubbles forming in the material which will reduce strength. A
polished and waxed fiberglass, carbon fibre or aluminium mould has a release agent applied to it.
The fabric and resin can then be applied; the vacuum is pulled and set aside to allow the piece to
harden. There are three different ways to apply the resin to the fabric in a vacuum mould. Dry
layup is the preferred method as it has the least amount of resin waste and can produce the
lightest constructions [6]. The cost of manufacture has been estimated from an online supplier [7];
producing the moulds and purchasing the equipment will be around £1000. GFRP has a very
similar manufacturing process. The difference between these two composites is the cost of the raw
materials. This manufacturing method is expensive in terms of both money and time, each part
needs one to two days to cure, but it will produce dimensionally accurate parts. The materials used
are also a lot stronger.
Finally aluminium sheet is considered. A specialist is required to work large aluminium sheets into
the desired shapes; costing a similar amount to the composite manufacturing procedure.
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St. Catherine’s College
Aerodynamics
Construction of the parts out of aluminium would take less time than the composites however it is
very hard to get a similar level of dimensional accuracy during the metal shaping process.
4.2.4 Multi-criteria decision analysis
Multi-criteria decision analysis is a tool for appraising and ranking alternative options against a
given set of weighted objectives and criteria. The relevant decision making criteria (strength, cost,
weight, ease of manufacture, dimensional accuracy) are assigned a weight from 1-5, one being
unimportant and five important. Each material is then given a rating against these criteria; one is a
low score and five high. The ratings and weights are multiplied and totalled for each option. The
material with the highest weighted score is selected and used to construct the aerodynamic
package.
Table 4.2 Multi-criteria analysis for material selection
Criteria
Weight
ABS Plastic
Aluminium Alloy
(7075-T6)
CFRP
GFRP
Rating
Score
Rating
Score
Rating
Score
Rating
Score
Strength
4
1
4
3
12
4
16
3
12
Cost
1
5
5
3
3
1
1
4
4
Weight
5
5
25
1
5
5
25
3
15
Ease of
Manufactur
e
3
4
12
3
9
3
9
3
9
Accuracy
5
4
20
2
10
5
25
5
25
Total
66
39
76
65
The weightings have been set with the aim of winning the Formula Student competition. Therefore
the criterion which affects the car’s performance is a priority. The weight and dimensional accuracy
of each component are directly related to on track speed and have therefore been weighted the
highest. Due to the large budget and time scale set out in this report both cost and ease of
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St. Catherine’s College
Aerodynamics
manufacture are considered less important criteria and have been weighted to reflect this. CFRP
has the highest weighted score, largely due to its low density and dimensionally accurate
manufacturing process, and is therefore chosen as the material used for the parts which make up
the aerodynamic package.
4.3
Undertray
4.3.1 Introduction
The undertray of a formula racing car is designed to accelerate the airflow under the car, creating
an area of low pressure, thus increasing downforce whilst creating minimal drag. A shaped piece of
body work at the rear of the car, known as the diffuser, draws the air out from under the car. The
car is essentially sucked onto the track increasing the level of grip available through the tires. In
terms of creating the aerodynamic package of a formula student racing car the largest addition in
downforce whilst keeping the drag to a minimal comes from the design of the undertray. This
design can be split into two key areas of analysis: the ground clearance, gap between the
underside of the car and the road, and the diffuser angle, the angle the diffuser makes with the
road.
4.3.2 Theory
The gap between the underside of a car and the road it is traveling along is known as the ground
clearance. The size of this gap can be optimised in order to exploit an effect known as the ground
effect. This effect uses a number of fluid mechanics principles to create downforce. As the air flows
under the car the cross sectional area available for the passing air between the car and the ground
decrease, according to the principle of continuity the air must accelerate. As a result pressure
under the car drops, shown by Bernoulli’s equation [8] for steady incompressible flow along a
streamline:
1 2
p+ ρ v + ρgz=constant
2
Where:
v = velocity
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Robert Bainbridge
St. Catherine’s College
Aerodynamics
p = pressure
ρ = density
z= elevation
g = acceleration due to gravity
A region of low pressure is created under the car. The pressure on top of the car is unaffected; a
pressure difference across the car is produced resulting in a net downward force. The critical
ground clearance can be found by setting up a two dimensional model of the undertray of the car in
Ansys CFX, a computational fluid dynamics software package.
A diffuser eases the high velocity airflow underneath the car back to the velocity of the ambient
atmosphere and helps fill in the area behind the car reducing the drag and increasing downforce.
As the airflow leaves from beneath the car the diffuser also imparts upward momentum on the air
which further increases the downforce produced [9]. The aim is to find the critical diffuser angel at
which the underbody airflow decelerates and expands providing as much pressure recovery as
possible without causing flow separation as this will induce drag.
Figure 4.1 Air flow under a rear diffuser [10]
4.3.3 Computational fluid dynamics
Computational fluid dynamics, CFD, is a branch of fluid mechanics that uses numerical methods
and algorithms to solve and analyse problems that involve fluid flow [11]. A CFD software package
called Ansys CFX was used in this report to find the critical ground clearance and the critical
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Aerodynamics
diffuser angle. All CFD software follows the same methodology; usually split into three sections
preprocessing, the simulation and post processing. During preprocessing the geometry of the
problem is defined, using computer aided design (CAD). The volume occupied by the fluid is split
into discrete cells, a process known as meshing. The physical model and the boundary conditions
are then defined. This involves defining the equation used in the simulation and specifying the fluid
behaviour and properties at the boundaries of the problem. The simulation is started and the
equations are solved interactively. Once the simulation is complete a post processor is used to
analysis and visualise the resulting solution [11].
The geometry shown in figure 4.2 was used to find these critical values. The length of the model, L,
and the front angle, θfront, were estimated from the chassis model as 2300mm and 12.50
respectively. The ground clearance, δ, and the diffuser angle, θd, were varied independently in
order to optimise them both.
θd
θfront
δ
L
Figure 4.2 The geometry used for the undertray simulations
Ansys CFX has been used in this report to create an unstructured mesh, which can be identified by
irregular connectivity. In order to run a two dimensional simulation in CFX, it is required to run the
simulation in three dimensions with the mesh only one cell thick. Three bodies of influence were
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Robert Bainbridge
St. Catherine’s College
Aerodynamics
set up to vary the density of the mesh for the different regions of interest. Two of these had
element sizes of 1e-2 m and 4e-2 m analysing the flow around the entire tray and the downstream
flow respectively. The region between the road and the car has the finest mesh, element sizing of
2e-3 m, as understanding the behaviour of the flow through this gap is of most importance.
Figure 4.3 The overall mesh generated in CFX
Figure 4.4 Shows the variation of mesh densities for the different bodies of influence
The inlet airflow velocity was set at 23.94 ms-1, flowing from left to right, this is the average
simulated velocity for one lap. To show that the tray is moving relative to the ground; the ground is
defined as a moving wall with a velocity of 23.94 ms-1 again going from left to right. Once the
simulation has been run, Ansys CFX can be used to analyse the results. The pressure and velocity
variations can be modelled on contour maps as shown in figures 4.5 and 4.6. It is then possible to
calculate the total downforce and drag on the downward facing sections of the tray per meter width
of the car.
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St. Catherine’s College
Aerodynamics
The simulation is limited by the fact it is two dimensional, the model does not simulate the lateral
movement of the air into the diffuser. This lateral movement decreases the downforce generated
by disrupting the airflow under the car. The pressure distribution on the underbody is likely to be
semi-elliptical, max along the centre line and zero at the edges, so the average downforce should
be over half the two dimensional value.
Figure 4.5 Contour plot showing pressure variation for a 60 mm gap and a 60 diffuser angle. Light
blue is low pressure, dark red high
Figure 4.6 Contour plot showing the u direction, horizontal, velocity component of the airflow for a
60 mm gap and a 60 diffuser angle. Dark red is high velocity and light blue low.
4.3.4
Diffuser angle analysis
The initial plan of analysis was to set the diffuser angle to 12.50 and run the simulation with
different gap sizes, recording the downforce and drag produced. The gap which produced the most
downforce whilst keeping drag to a minimum would then be selected. With the gap set a number of
simulations could then be run again, this time varying the diffuser angle. This process proved to be
unfeasible. The geometry resulted in a critical ground clearance of 200 mm, which is far greater
than the clearance expected. This difference is primarily due to over predicting the diffuser angle,
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Aerodynamics
which lead to the flow becoming detached from the diffuser and forming eddies and vortices.
1000
Downforce (N)
100
500
Drag (N)
0
-500
50
0
0 50 100150200250
0
Ground Clearance (mm)
50
100 150 200 250
Ground Clearance (mm)
Figure 4.7 Plots of downforce and drag against ground clearance, θd = 12.50 airspeed = 23.94 ms-1
The approach was therefore reversed. The ride height was estimated partly from the rules; they
state that the car must have a wheel travel of at least 50.8 mm, 25.4 mm jounce and 25.4 mm
rebound [12]; and partly from consulting the individual in charge of the suspension. A ground
clearance of 60 mm was used. The diffuser angles tested ranged from 20 to 12.50.
600
500
400
Downforce (N)
300
200
100
0
0
2
4
6
8
10
12
14
Diffuser Angle (degrees)
Figure 4.8 Plot of downforce against diffuser angle, δ = 60 mm airspeed = 23.94 ms-1
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Aerodynamics
60
50
40
Drag (N)
30
20
10
0
0
2
4
6
8
10
12
14
Diffuser Angle (degrees)
Figure 4.9 Plot of drag against diffuser angle, δ = 60 mm airspeed = 23.94 ms-1
From the plot in figure 4.8 it is clear that a diffuser angle of 60 produces the most downforce. As
discussed, when the angle is increase beyond this value separation of flow occurs and the
downforce drops. An angle of less than 60 reduces the diffuser’s ability to create low pressure
under the car and so the downforce decreases. It can be observed from figure 4.9 that there is an
angle which produces the minimum drag. This angle found to be 40 but due to the negligible
difference in drag between 40 and 60, 1.1N, the optimal design has a diffuser at an angle of 60.
4.3.5 Ground clearance analysis
With the diffuser angle set to 60 the simulation was run again this time varying the gap between the
underside of the car and the road, δ. δ ranged from 20 mm to 120 mm. The air speed remained at
23.94 ms-1.
The critical ground clearance was found to be 100 mm, having a gap larger than this produces less
downforce because the cross sectional area the airflow travels through has increased in size,
therefore the air velocity reduces and, as shown in section 4.3.2, the pressure will rise. The reason
for the downforce decreasing when the gap is smaller than 100 mm is less clear. It can be partly
put down to the geometry of the model. When the air flow hits the front angular section it creates a
little lift, as the gap is reduced the pressure on this section grows and the magnitude of the lift
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Aerodynamics
increases. The rise in lift begins to outweigh the increasing downforce when the gap is smaller than
100 mm; reducing the front angle, θfront, will reduce this lift.
700
600
500
400
Downforce(N) 300
200
100
0
0
20
40
60
80
100
120
140
Ground Clearance (mm)
Figure 4.10 Plot of downforce against ground clearance, θd = 60 airspeed = 23.94 ms-1
80
70
60
50
Drag (N)
40
30
20
10
0
0
20
40
60
80
100
120
140
Ground Clearance (mm)
Figure 4.11 Plot of drag against ground clearance, θd = 60 airspeed = 23.94 ms-1
Although the critical ground clearance has been shown to equal 100 mm and figure 4.11 shows
that increasing the gap size will decrease the drag; the chosen ride height is 60 mm. The chosen
ride height has taken into account the three dimensional flow characteristics, lateral air flow under
the car. Reducing the gap prevents lateral air flow and thus will prevent the associated reduction in
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Aerodynamics
downforce. If simulated with more complex geometry less lift is expected because the nose cone
and front wing of the car will be designed to guide the airflow under the car without producing any
unwanted lift. For these reasons a smaller ground clearance was chosen.
4.3.6
Conclusion
It must be borne in mind that this is a heavily simplified model; adjustments have been made,
where necessary, to account for these simplifications. In reality the diffuser will have a gradual
change in angle as the air leaves from under the car which prevents flow separation and further
increases the downforce. The undertray will usually have tunnelling to help guide the airflow under
the car and prevent the lateral movement of air into the diffuser. The chosen design values are δ =
60 mm and θd = 60.
4.4
Wings
Nomenclature
V – car velocity
A – frontal area
R – corner radius
CD – drag coefficient
CL – lift coefficient
F – driving force
P – engine power
mc – totals mass of car
ρair – density of air
g –gravitational acceleration
µ - coefficient of friction
D – drag force,
L – lift force,
4.4.1
1
L= ρair V 2 C L A
2
1
2
D= ρair V C D A
2
Aw – wing planform area = span x chord
Introduction
Most formula style race cars will have a front and rear wing, both of which can consist of either
single or multi elements. For this low speed race car it is necessary to evaluate whether the on
track benefits of running the car with a wing package is worth the additional fuel consumption,
associated with overcoming the drag, and the added cost of manufacture. To appreciate the desire
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Aerodynamics
to run a car with a wing package; it is important to understand how a wing creates lift or downforce.
Think of an aeroplane’s wing, the cross sectional shape, the wing profile, is designed in such a way
that the air traveling over the top of it is accelerated. Resulting in a drop in air pressure, a pressure
difference is created across the wing. The higher pressure below essentially pushes the wing
upwards generating lift. In formula race cars these wing profiles are turned upside down. The
effects are reversed and the wing is pushed towards the ground generating downforce. Wings can
provide a huge amount of downforce at the expense of drag which effects top speed performance
and increases fuel consumption.
4.4.2
Top speed performance
The penalty for adding a wing package is the significant addition of drag; this is mainly caused by
the rear wing. Drag effects the cars top speed and it is important to evaluate how much on the
track performance can be sacrificed. The track courses designed for the Formula Student
competition have a limited velocity and thus the added drag limit can be evaluated. The process
involves finding the highest allowed drag coefficient, CD, Max, by following the steps set out by Pehan
and Kegl [13]:
1.
2.
3.
4.
Calculate the theoretical top speed, Vmax, without wings.
Decide the desired top speed with the addition of wings.
Calculate the difference in power absorption between these two cases.
This difference will be donated to the wings to overcome drag and create
downforce.
5. Calculate the CD, Max value that this represents.
The acceleration of a car can be described using Newton’s second law of motion, Force = mass x
acceleration. In the horizontal direction the car experiences a driving force, F, produced by the
engine and a resistive force, D, the total drag force (the rolling resistance is part of the
transmission losses).
1
mc x́=F− ρair C D A V 2
2
When traveling at top speed equilibrium between the driving force and the drag force is reached,
the acceleration is zero. The engine power can be expressed in terms of the car’s velocity and
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Aerodynamics
driving force. This equation can then be rearranged to calculate the theoretical top speed without
wings.
√
V max = 3
2P
ρair C D A
The formula student racing car without wings has a frontal area of A = 1.0 m2 and an estimated
drag coefficient of CD = 0.7. The engine produces 97 bhp however with a transmission efficiency of
85 % the driving power left P = 82.5 bhp = 61.5 kW. With ρair = 1.225 kgm-3 the maximum speed is
Vmax = 52.3 ms-1. The target top speed on track for this racing car is 38 ms-1, so to ensure the car
has some top end acceleration a maximum speed of 45 ms-1 is desired. By rearranging the
equation above the required power, Preq, to achieve said maximum speed was found to be Preq =
39.1 kW. The power difference, (ΔP = P – Preq) 22.4 kW, is the power that is being donated to the
wing in order to get downforce. It must be remembered that donating this power to the wing will
increase full consumption as the engine must always overcome the additional drag.
The front wings do not generate significant drag, so when calculating the maximum drag coefficient
only the rear wing is considered. First estimates of the initial size and shape of this wing must be
made. Ensuring the dimensions fit the design requirements and they are within the rules of the
competition; the chord line has been estimated at 300 mm and the span 1000 mm, thus a wing
planform area of 0.3 m2.
C D , Max =
2∆ P
ρair A w V 3
The maximum drag coefficient was found to be 1.3. The next step is to select a suitable aerofoil
and finalise the front and rear wing dimensions and orientations.
4.4.3
Aerofoil selection
The wings used in Formula 1 contain a number of aerodynamic elements. These multi element
wings enable more control over the airflow and provide a greater lift coefficient, at the expense of
drag. It has been decided that the level of complexity required when analysing multi element wings
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Aerodynamics
and the added cost and difficulty of manufacture outweighs the benefits. In this report only single
element wings are considered.
XFLR5 is an analysis tool for aerofoils operating at low Reynolds numbers and has been used to
select a suitable aerofoil for the wings. The software is usually used for analysing aerofoils used by
gliders. As discussed above the aerofoils used in formula racing operate the same however they
are inverted. It is important to remember XFLR5 will calculate a positive lift coefficient implying a lift
force is generated, when run upside down the aerofoil lift coefficient will have the same magnitude
but it will be negative, generating downforce.
The maximum allowed drag coefficient is quite large meaning aerofoils with proportionally large lift
coefficient have been analysed. Four high lift aerofoils were selected from an online catalogue [14]:
Eppler E423, Chuch Hollinger CH 10-48-13, Modified Wortmann FX 74-CL5-140 and Selig S1223.
XFLR5 was used to find out which of the aerofoils has the highest lift coefficient, it was run with
angles of attack, alpha, ranging from 00 to 150 and the air velocity ranging from 15 ms-1 to 38 ms-1.
Figure 4.12 Plots of CL against alpha for the E423 (left) and the CH 10-48-13 (right)
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St. Catherine’s College
Aerodynamics
Figure 4.13 Plots of CL against alpha for the FX 74-CL5-140 (left) and the S1223 (right)
For all four aerofoils the lift coefficient varies with the angle of attack. It can be seen in figures 4.12
and 4.13 that there is a critical angle of attack for each aerofoil where it produces its maximum lift
coefficient, known as the stall angle of attack. Below the critical angle, as the angle of attack
increases, the coefficient of lift increases. As the angle of attack increases the air flow over the
upper surface begins to separate from the surface, the separation of the flow moves from the
trailing edge towards the leading edge. At the critical angle the flow is more separated and the
aerofoil produces its maximum coefficient of lift. Increasing the angle further will stall the aerofoil,
flow becomes fully separated and the lift coefficient drops [15]. The Selig S1223 aerofoil generates
the highest lift coefficients and has therefore been selected for the wings.
4.4.4
Rear wing
The rear wing was modelled using XFLR5. The same estimates as before were used for the span
and chord line, 1000 mm and 300 mm respectively. The angle of attack was set to 100; a couple of
degrees lower than the critical angle of attack to give a margin of safety against stalling.
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Aerodynamics
Figure 4.14 3D model of the rear wing, the purple lines represent streamlines
The rear wing has a lift coefficient of CL = -1.32 and a drag coefficient of CD = 0.18. The
streamlines in figure 4.14 represent the path traced out by a massless particle moving with the
flow. The figure shows large vortices, swirling air currents, at the tips of the wing; created as air
spills from the high pressure side to the low pressure side of the wing creating drag and a
reduction in downforce. End plates are implemented to prevent this spilling of air, reducing vortices.
This lessens the drag and increases downforce.
4.4.5
Front wing
The front wing is designed to balance the downforce produced by the rear wing. It is therefore
possible to find the required lift coefficient for the front wing by resolving the forces experienced by
the car [13]. Three assumptions were made during this calculation: the rear wing’s location is such
that the downforce it produces works through the axis of the rear tyre (lr = 0 m); the drag produced
by the front wing is negligible (Lf = 0 N); and the cars centre of mass and downforce generated by
the under tray act at equal distances from the axis of the front and rear tyres (a = b). It is also
desired to have an even weight distribution between the front and rear tyres resulting in the front
and rear tyre reaction forces being equal (Nf = Nr). The calculation was done with the car traveling
at top speed, 45 ms-1.
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Aerodynamics
Figure 4.15 Free body diagram of forces acting on the car [16]
The front wing will have the same profile, span of 1200 mm and chord line of 300 mm. The rear
wing drag is Dr = 67 N and the downforce is Lr = 491 N. The drag on the front wing can be
calculated using equilibrium considerations on the free body diagram in figure 4.15.
R ( ↑ ) N f + N r−mg−Lf −Lr=0
M CW ( front axle ) (a+ b)Lr + ( hr−hf ) Dr + amg=l f Lf + ( a+b ) N r
Implementing the assumptions and combining the two equations gives the downforce.
Lf =
( hr−hf ) D r + a Lr
l f +a
Lf = 343 N, corresponding to a lift coefficient of CL = - 0.77. Taking the ground effect into
consideration will lower the required lift coefficient. This coefficient can easily be achieved by a
single element wing at a low angle of attack.
4.4.6
Cornering performance
The major benefit from equipping a race car with a wing package is the better grip in the tyres, this
added normal load through the tyres will increase the theoretically maximum allowed velocity in
cornering. Beyond this velocity the car will lose grip and the resulting track time will suffer. This
increase in performance can be inspected and a decision can be made on whether to run the car
with a wing package or not.
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Aerodynamics
A Matlab simulation was run, calculating the maximum cornering velocities with and without the
wing package. The maximum velocity is the velocity for which the centripetal force is equal to the
frictional force. Assuming constant coefficient of friction; the resultant downward force, Fz, is the
sum of the weight and the aerodynamic force; and a corner is a 900 turn with a constant radius, R,
we have:
1
mV
μ F z=μ mg− ρ C L A V 2 =
2
R
(
)
2
The equation can be rearranged to give V. The track information handout [17] indicates the corner
radius will vary from 12 m to 65 m.
Figure 4.16 Graph showing variations in maximum cornering velocity with corner radius with and
without the wing package.
The relative performance was then plotted using Matlab to show the improvement made to the
cornering velocity. The relative performance is equal to the cornering velocity of the set up being
analysed divided by the cornering velocity of the car with no wings. It gives a quantitative indication
of the improvement made.
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Robert Bainbridge
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Aerodynamics
Figure 4.17 Graph showing variations in relative performance with corner radius with and without
the wing package
The simulation shows that the improvement to the car’s performance increases with larger corner
radii; indicating that the benefits are much more significant if the track primarily comprises of these
sorts of corners. The track layout [17] is known; over 50 % of the corners have a radius equal to or
larger than 60 m. Figure 4.17 shows that using the wing package designed will improve the
cornering velocities of these large corners by over 25 %.
4.4.7
Conclusion
The aim of this section was to decide whether or not to run a car with a wing package. Would the
on track benefits outweigh the cost? The reason a lot of time has been put into this problem is
because the wings are highly complex structures and require a lot of time and money to
manufacture. As the engine is efficient enough to spare the added fuel consumption and the track
layout used in this competition suits a wing package of this type; it has been decided the benefits
do outweigh the costs and this wing package has been chosen for manufacture. Carefully
budgeting and preplanning means space has been found in the budget to incorporate these wings.
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4.5
St. Catherine’s College
Aerodynamics
The complete aerodynamic package
In this report the areas where the biggest gains in terms of on track performance can be made
have been looked at in the most detail. However the aerodynamic package should always be
considered as a whole and when it comes to simulating the race car the overall coefficients need to
be known. The nose cone, body, side pods and wheels all contribute their own coefficients. This
section aims to find suitable estimates for these coefficients.
The nose cone controls the airflow over and under the rest of the car. The nose cone and the body
of the car have been designed to have as close to a teardrop shape as possible. Teardrop shaped
bodies are extremely streamlined and it is the desire by most formula student teams to get as close
to this overall shape as possible. From a simulation run using a simplified model; CL and CD of the
body and nose were found to be -1.53 and 0.122 respectively. To account for the simplicity of the
model these values were adjusted to make them more realistic.
C L =−1.2 C D =0.2
The wheels of a formula student race car have to be uncovered resulting in the wheels being one
of the primary contributors to the aerodynamic coefficients. Uncovered wheels come into direct
contact with airflow. The wheels have a radius of 261 mm; their drag coefficient can be equated to
two to three times that of a cylinder with the same radius.
C L =1C D =0.45
The sidepods contribute significantly to the overall drag of the car and produce a little lift. Ducted
sidepods have been selected in this report because they have a significantly improved flow rate of
air through the radiator over sidepods without cooling ducts. These ducted sidepods have
coefficient equal to:
C L =0.13 C D=0.4
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4.6
St. Catherine’s College
Aerodynamics
Conclusion
The overall coefficients of the car, including the wing package, are simply combined with addition:
C L =−2.16 C D =1.23
Here A, in the equations for lift and drag, if referring to the frontal area of the car. The value of L/D
for a formula student car with high wheel drag, wings and underbody, operating nearer the CL max
than L/D max will be in the range of -1 to -2. For this car L/D is -1.76 and therefore seems
reasonable. It is clear to see that downforce has been prioritised in this report; the car has quite a
large drag coefficient. However as proved in this chapter the increased downforce will lead to
quicker cornering velocities, resulting in faster lap times. The overall aerodynamic performance of
the car can still be improved with the use of features such as gurney flaps, undertray tunnelling and
skirting. Improvements can still be made after manufacture; wing angles and the ride height can be
adjusted to find the optimum positions on the track.
4.7
References
[1] [Online] http://plasticker.de/preise/pms_en.php?show=ok&make=ok&aog=A&kat=Mahlgut
[2] [Online] http://www.fstotal.com/thermoformed-abs-plastic-bodywork-on-rb13-university-of-newsouth-wales-redback-racing-team-2/
[3][Online] http://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-ofmaterials-fall-1999/modules/props.pdf
[4] Howatson, A., Land, P., Todd, J., “Engineering Tables and Data”, 2009, p. 46 – 48
[5] [Online] http://www.airforme.co.uk/
[6] [Online] http://en.wikipedia.org/wiki/Carbon-fibre-reinforced_polymer
[7] [Online] http://www.acpsales.com/home.html
[8] Douglas, J., Gasiorek, J., Swaffield, J., “Fluid Mechanics”, vol. 4, 2001, p. 142
[9] [Online] http://en.wikipedia.org/wiki/Diffuser_(automotive)
[10] [Online] http://www.racecar-engineering.com/technology-explained/diffusers-engineeringbasics-aerodynamics/
[11] [Online] http://en.wikipedia.org/wiki/Computational_fluid_dynamics
[12] 2015 Formula SAE Rules, T6.1.1, 2015, p. 57
[13] Pehan, S., Kegl, B., “Aerodynamic Aspects of Formula S Racing Car”, 2002, p. 1112
[14] [Online] http://www.airfoiltools.com/
[15] [Online] http://en.wikipedia.org/wiki/Angle_of_attack
[16] Dahlberg, H., “Aerodynamic development of Formula Student race car”, p. 5
[17] Howey, D., McGilvray, M., Lohr, R., “Formula Student 3YP – Simulation of vehicle
performance”, 2014
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5
Chassis and Packaging
5.1
Introduction
Chassis
The chassis is the main physical framework of a vehicle, being compared to an animal’s skeleton
in the way it is responsible for both protecting everything contained within, for example the engine,
transmission and driver, and for it to support all the vehicular components and the payload placed
upon it, whether it be providing a cell for the driver or a connection point to the suspension and
wheels. The aim for the chassis is to be rigid enough not to deform too greatly when the car is in
use, such as cornering and accelerating, as this would make the effects of fine-tuning suspension
redundant. On top of rigidity, safety is a crucial aspect to be considered, especially in the case of
dealing with a racing car, which is put under more extreme conditions than a normal car.
The chassis can be constructed as a separate frame and body. The frame is designed to support
the weight of the body and absorb all of the loads imposed by the mechanical components and the
terrain. The body contains and protects the cargo (everything contained by the body). Alternatively,
the chassis can be constructed as an integrated frame and body, known as a monocoque. This is
where the frame and body are combined into a singular, one-piece structure to perform both the
aims of protecting the cargo and supporting and absorbing all loads imposed on the vehicle. The
design of the chassis needs to strictly observe the Rules and Regulations of the FSAE, which will
be referenced and checked off in this report when compared to the actual design of the chassis.
The main aims of the chassis, decided by the group, are to be to minimise the mass due to the
majority of points in the FSAE Rules and Regulations being given to performance in the endurance
race. This has been coupled with a financial viability. Even though these two aims appear to clash,
with the generous budget of £40 000, the mass minimisation has been made the priority as long as
the budget isn’t exceeded. Aerodynamics do play a role in racing car chassis design, however
since the speeds being reached are not expected to exceed 80 mph and average speed around 55
mph it has been assumed that in depth optimisation of the chassis’ aerodynamics will result in
minimal improvements to the performance other than trying to minimise the frontal area.
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5.2
Hertford College
Chassis
Design Procedure
5.2.1 Decision Making (Space frame vs. Monocoque)
The design process began by looking on the formula student website and comparing all the
designs from previous years, directing the majority of focus on the winner from last year as it is
assumed that their design was the best across the board to end up winning the whole thing as the
ability of the drivers cannot be easily compared. Before proceeding, a decision had to be made as
to what type of chassis to make. This brought up three options: a tubular space frame, a full
monocoque made up of composite material and a half monocoque made up of a composite
material majority attached to a rear tubular space frame. Multi Criteria Analysis was used.
Table 5.1
Multi Criteria Analysis for the Chassis
Manufacturing
Cost
Mass
Process
Weighting
2
5
2
Tubular Frame
5
1
4
Half Monocoque
2
3
2
Full Monocoque
1
5
1
Design/Analysis
Process
3
5
1
2
Torsional
Stiffness
4
3
4
5
Total
50
42
54
The criteria considered were weighted according to their relevance to both this particular project
and the group aims. So mass was decided to be the most crucial, whereas the manufacturing
process was not of great importance due to this only being a design project and not actually
constructing the car in real life. The design and analysis process represents how easy it would be
to model the chassis using Solidworks, as this is the tool that has been made available for us to
use and that we have previous experience in using. A full monocoque was the resultant winner
from the Multi Criteria Analysis. The flow chart in Figure 5.1 represents the step-by-step approach
used when designing and optimising the vehicle.
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Hertford College
Figure 5.1
Chassis
Design Flow Chart
5.2.2 Regulations and Dimension Specifications
As mentioned previously, the design of the vehicle needs to meet the specifications stated in the
‘2015 FSAE Rules’. These vary from the minimum length of the wheelbase, being 1525 mm, to the
need for the vehicle to be an open-wheeled and open-cockpit with four wheels not in a straight line.
The definition of open-wheeled is defined in the FSAE Rules in Article 2: T2.1 where the wheels
cannot be obstructed from the side view and when viewed from vertically above 180˚ of the wheels
must be unobstructed. Figure 5.2 shows the ‘keep out’ zone which is defined by extending two
vertical lines 75 mm both in front and behind the outside diameters of each of the tyres.
Figure 5.2
Open-wheeled visualisation [1]
In order to ensure the cockpit opening is of adequate size, a template defined in Article 4: T4.1
Cockpit Opening, shown in Figure 5.3, needs to be inserted vertically into the cockpit to a height of
350 mm above the monocoque floor, this essentially for safety as it represents the ease of escape
for the driver in case of an incident.
While the cockpit opening needs to be of adequate size for a driver to get in and out easily, the
driver’s cell needs to be large enough to fit a 95th percentile male. The dimensions for this are
specified to the following: a circle of diameter 300 mm will represent the head, the centre of which
will be positioned at 280 mm away from the centre of a circle of 200 mm to represent the shoulder
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Hertford College
Chassis
and Packaging
area. The hip region will again be represented by a circle of 200 mm where the centre of which will
be located at 490 mm away from the circle representing the shoulders. The rearmost point of the
pedal is to be positioned at a minimum of 915 mm away from here. This configuration is shown, in
blue, fitting into the driver’s cell in Figure 5.4.
Figure 5.3
Cockpit Opening Template
The chassis, according to section T3.10, must include both Main and Front Roll Hoop structures
securely integrated into the primary structure so that the driver’s head and hands must not contact
the ground in any rollover situation, each has to be made up of a single piece of uncut, continuous,
closed section steel tubing. The main hoop must have bracing supports at a minimum of 30˚ to the
vertical and attached at a minimum of 160 mm from the top-most surface of the main hoop. The
Front Hoop bracing must protect the driver’s legs and extend beyond the driver’s feet and be
attached at a minimum of 50.8 mm below the top-most surface of the Front Hoop. The construction
of the Roll Hoops is to protect the driver’s head in case of a roll over incident. This is proven by
there being a gap of at least 50 mm between the driver’s helmet, and a line projected from the top
of the Front Hoop to the top of the Main Hoop and another line from the top of the Main Hoop down
to the rearmost point of the Main Hoop Bracing. These are all shown in Figure 5.4, outlined with
the template of a 95th percentile male in position.
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Hertford College
Chassis
95th percentile male dimensions in driving position with roll bar clearances
Figure 5.4
One of the many safety requirements specifies a firewall separating the driver compartment from
all components of the fuel supply, engine oil and liquid cooling system is necessary. This firewall
must have no gaps, made from a non-permeable, rigid, fire-resistant material and extend high
enough to protect the neck of the tallest driver defined by extending high enough upwards and/or
rearwards so that the bottom of the helmet isn’t in direct line of sight with any of the necessary
components. Both the main bulkhead and the seat of the car make up the firewall in this design,
which even though aren’t made of a fire resistant material, apply the rigid surface onto which to
apply Teknofibra
[2]
heat resistant tape. This tape made of a material derived from carbon fibre with
very high insulating properties, along with an adhesive layer that increases its strength with
temperature. The conductive properties of this tape range from 0.026 W/mK at 0 ˚C to 0.045 W/mK
at 400 ˚C. This tape has a special surface on one side of embossed aluminium to reflect heat.
Figure 5.4 shows the driver’s seat extending high enough to protect the neck of a 95 th percentile
male, adhering to Article 4: T4.5 in the FSAE Rules.
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and Packaging
5.3
Hertford College
Chassis
Materials
5.3.1 Comparison of Materials
A good way of comparing materials against specific properties is by using a material selection chart
or property map. For example, it is of interest to compare the stiffness of a material against its
density, as this is of most importance in this design.
Figure 5.5
Property Map of Young’s Modulus against Density [3]
Sticking with the priorities decided earlier, the material for the chassis needs to be as stiff as
possible to maintain good torsional stiffness and as light as possible to try and minimise mass. On
the map, the stiffest materials are at the top of the chart and the lightest are towards the left hand
side of the chart. This reaffirms the choice of composite materials for the main body of the chassis,
as the composites region is very near the top and is the furthest left of all the materials of which a
chassis could be made of, as wood isn’t good for the use in motorsport due to its anisotropic
behaviour. This means that the properties of the material vary greatly depending in which direction
it is being tested. Composite materials show anisotropic behaviour as well, only it is easier to alter
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and customise these to suit the desired properties in the manufacture of composite materials,
which will be explained in further depth in the next section.
5.3.2 Composite Materials
Composite materials are mixtures of two or more fundamental materials. Usually one forms a
continuous material, known as a matrix, within which a material, usually microscopic, is embedded.
The term composite materials are used to describe situations where two constituent materials have
been mixed together physically, rather than different components appearing naturally as different
phases in an alloy, such as spontaneous mixture of ferrite and cementite that appears on cooling of
steel. Composite materials can be based on matrices of metals, ceramics and polymers, but by far
the most common composites employed, and the most relevant to motorsport are those based on
polymer matrices.
Usually it is the filler particles that have the most attractive mechanical properties and the function
of the matrix is to act as a glue to hold the particles together.
Looking at the lump of composite material, in Figure 5.6, of total mass m = mm+ mf and total
volume v = vm + vf, where the subscripts m and f referring to the matrix and the fibres respectively.
Figure 5.6
The Rule of Mixtures (RoM):
Lump of composite material [4]
   f  f  (1  f ) m(5.1) where
f 
vf
v
(1  f )  m  m
v and
v
This basically uses the volume fraction of fibres in the material to superpose the densities of both
the matrix and the fibres in order to get the overall density of the combination of the two. The Rule
of Mixtures can be used for more properties of the composite material, such as the stress, strain,
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Poisson’s ratio and the Young’s Modulus. These can vary depending on the orientation or the axis,
which the material is being measure, owing to the anisotropic behaviour of composite materials.
Due to the composite material being utilised in motorsport, the filler used will take the form of
continuous cylindrical fibres which are embedded in a matrix which needs to be capable of bonding
to the fibres in either a mechanical or a chemical manner. In unidirectional (UD) continuous fibre
composites, all of the fibres are oriented in the same, single direction. For now, analysis of a UD
lamina will be considered, building up to the analysis of a laminate, which consists of multiple UD
laminae oriented in different directions to try and create more isotropic behaviour.
Three orthogonal reference axes are used to define the directions: with the 1-direction being
parallel to both the fibres and the lamina, the 2-direction being perpendicular to the fibres and
parallel to the lamina and the 3-direction being perpendicular to both the fibres and the lamina.
Using the theory outlined in An Introduction to Composite Materials
[5]
, the composite material
properties can be calculated. These properties, detailed below, are to be calculated and used in
the analysis of the chassis, but first the equations need to be formed for the varying properties of
interest.
Axial Stiffness
As the composite materials are bonded together, a no sliding condition can be applied so that they
have the same lengths parallel to the bonded surface, resulting in both constituents exhibiting the
same strain.
1   f 1 
 f1

  m1  m1
Ef
Em
For the composite material of interest, the reinforcing fibres are much stiffer and put under much
higher stresses than the matrix, so there is a redistribution of load. Therefore the overall stress can

be expressed, in terms of the contributions from both the fibres and matrix:
1   f  f 1  (1   f )m1
Combining these two equations and after some rearrangement, the Young’s Modulus is found:

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E1 
Chassis

  f E f  (1   f )E m

(5.2)
This is a proof of the Rule of Mixtures being utilised to find another property of the composite

material as a whole in similar
fashion.
Transverse Stiffness
Calculating the transverse stiffness is more difficult due to the higher concentration of stresses in
the matrix between the fibres, as the stresses aren’t redistributed as well as in the axial state. The
limiting case will be considered of equal stress, so when a stress is applied in the 2-direction
2   f 2   f 2 E f  m 2   m 2 E m
the overall strain is the combination of the total strains of the matrix and fibres in the 2-direction:

 2   f  f 2  (1   f ) m 2
The composite Modulus is given in similar fashion, stress over strain, and after some

rearrangement gives:
  f (1   f )  1

E 2  

E m 
 E f
(5.3)
Shear Stiffness

The Shear Moduli are estimated
in a similar fashion to the axial and transverse stiffness. The shear
modulus is the ratio of the shear stress to the shear strain. Considering 2 directions:
G13   f G f  (1   f )Gm
Poisson’s Ratios
(5.4)

The Poisson’s ratio ij is the ratio the negative strain (contraction) in the j-direction when a stress is
 ij  
applied in the i-direction, shown by
12  21

E1 E 2
j
i . This leads on to two more useful relationships:
(5.5)
and
G23 
E2
2(1  23 )
(5.6)
By using the simple equation for Poisson’s ratio, calculating the constituent strains and then
 the Poisson’s ratios for the 
summing them,
2 directions parallel to the lamina can be produced:
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12  
2
  f  f  (1   f ) m
1
Chassis
(5.7)
Off-axis elastic constants of laminae

The relationship between
ij and ij can be expressed using Einstein Notation: ij=Cijklkl where Cijkl
is a stiffness tensor. However in practice, it can be more useful to express observed strains in
terms of applied stress: ij=Sijklkl where Sijkl is the compliance tensor. If plane stress conditions are
applied, 3   23   31  0 , the reduced compliance tensor is
 S11 S12

S    S12 S22
 S16 S26

S16   E11
  
S26     E212
S66   0

 E121
1
E2
0
0 

0 
1 
G12 
(5.8)
When the lamina is loaded in a direction oriented at  to the 1-direction, the compliance tensor
needs to be both pre and post-multiplied by appropriate rotation tensors to give one transformed


compliance tensor S [6] :

  
  
  
x
 x 




 x 
1
  y   T' S T   y   S   y 
  
  
  
xy
xy
xy
 c 2 s2
2cs 
 2

T    s  c 2 2cs 
 cs cs c 2  s2 
where

T 
' 1
&
(5.9)
 c 2
s2
cs 
 2

  s
c2
cs 
 2cs 2cs c 2  s2 
&
c  cos  , s  sin  .


 or the
These graphs in Figure 5.7 outline
the almost isotropic behaviour
properties when a
laminate is stacked with adjacent plies at 45˚ orientation to each other. So this has been chosen as
the orientation for the stacking of the laminae in this design to try and create as isotropic behaviour
as possible, as a racing car is exerted to varying orientations of force whilst in performance – bias
isn’t needed in just a single direction.
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Figure 5.7
Variation of loading angle  ˚ of Young’s Modulus E and Poisson’s ratio 12 for a
single UD lamina, a cross ply laminate [0˚/90˚] and a [0˚/45˚/90˚/135˚] laminate [7]
Composite Material Strengths

Using the theory outlined in the B8 Composites Notes8, the tensile and compressive strengths of
composite materials can be estimated. The strength depends on the failure strains of both the
matrix and the fibres. Usually, in the case of reinforced fibres in a polymer matrix, the fibres are
more brittle than the matrix as this is the ‘stiffener’ in the composite material; so therefore have a
smaller failure strain compared to the matrix. If the volume fraction of fibres is small (
 f  1), the
effect of the fibres actually weakens the matrix, so there is a critical fibre fraction below which the
matrix is stronger on its own, and above which the fibres start to have a beneficial effect.
Figure 5.8
Graph showing how the strength of composite materials varies with fibre fraction [9]
The right hand side of the graph is shaded in as this is the area of
 f  .7 , which is geometrically
impossible to pack fibres in a matrix of this fraction region. It is only of interest to look into high, but
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realistic, volume fractions of
.3   f  .7
Chassis
, and in this case the maximum stress of the composite
occurs at the maximum stress of the fibres, i.e. when the fibres break. (*) denotes point of failure.
Figure 5.9
Graph showing tensile strength of composite material with high volume fraction [8]
When the fibres fail, the total stress is carried by the composite, which can be calculated by
equating forces in the 1-direction. So the tensile strength through superposition of stresses at f* is
 1*   f  *f  (1  f ) m'
(5.10)
This is the equation for the majority of the bold line in Figure 5.8.
The compressive strength of composite materials is usually lower than the tensile strength due to
the matrix normally having a fairly low shear modulus so “kink bands”
[9]
can form in the matrix
between the fibres. These kink bands impose an axial shear on the fibres, which are notoriously
susceptible to shear failure due to their very high aspect ratio. The transverse compressive and
tensile strengths are much less than the axial ones, due to the presence of fibres with different
elastic properties resulting in local stresses greatly exceeding the average stress. The fibre-matrix
interface is weaker than the matrix as there is a great discontinuity of properties here. In this case
the compressive strength is slightly greater than the close to almost irrelevant tensile strength.
When stresses are applied along non-principal axes, a maximum stress criterion needs to be
applied to all varieties of failure modes that are assumed to be independent of one another. Failure
will occur at the lowest failure stress.
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Chassis
5.3.3 Material Selection
Matrix Selection (Thermosets vs. Thermoplastics)
There are many factors to be considered when choosing the material to make up the matrix of the
composite. There are two types of polymers that are used in composite materials. The first is
thermoplastics (TP), which soften on heating. This is because they are often described as linear
polymers as there aren’t any cross-links between the chains, which is why when it is heated, it
softens as the secondary bonds that bind the chains together melt and it flows like a highly viscous
liquid. This can be done reversibly time and time again. The other type of polymer matrices are
thermosets (TS) which are a combination of two components, a resin and a hardener, which, when
heated together and harden due to a chemical cross-linking reaction causing the liquid to solidify to
form an infusible mass. On reheating, the secondary bonds melt, but thermosets aren’t reversible
as the cross-links prevent true melting so the polymer cannot be hot-worked as further heating just
causes is to decompose.
As confirmed in Principles of Polymer Engineering
[10]
, thermosets are more beneficial for
motorsport as there is quite a high volume fraction of reinforcing fibres in the material. The low
viscosity of the precursor liquid, before it reacts with the hardener, allows the resin to pass through
the closely packed array for thorough wetting of the reinforcing fibres. Also, thermosetting resins
have greater toughness, and with high temperatures possible close to the engine, it would be
impractical to use a reversible material for the matrix if it just ends up melting and returning to a
viscous liquid during performance.
Comparison of properties of polymers [11] [12]
TS/TP
Young’s
Tensile
Compressiv
Failure
Density,
Modulus, E
Strength,
e Strength
Strain,
(Mg/m3)
(GPa)
t*(MPa)
c*(MPa)
*(%)
Epoxy
TS
1.2-1.4
2.1-5.5
40-85
100-200
2-5
Polyesters
TS
1.1-1.4
2.0-4.5
40-90
120
2
Polypropylene, PP
TP
1.2-1.7
1.0-1.4
50-70
40
40-80
Nylons
TP
2.0-3.5
1.4-2.8
50-100
60-110
300
The table clearly shows thermosets to be stiffer, both in the Young’s Modulus and the failure strain
Table 5.2
columns. For motorsport, an epoxy resin is the most popular to be impregnated to the reinforcing
fibres, shown by the very high stiffness.
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Fibre Selection
Hertford College
Chassis
The major reinforcement fibres consist of Glass fibres, Carbon fibres and Aramid fibres. These are
all desired due to their high stiffness and relatively low density. As the main priority for reinforcing
fibres is to be light, usually the specific properties are compared, which is the property of interest
divided by the density of the material, which are included in the Table 5.3.
Comparison of the properties of reinforcing fibres [12] [13] [14]
Diameter Density,  Specific
Specific
(m)
Stiffness, E/
Strength, */
(Mg/m3)
E-Glass
12
2.60
29
0.73
Carbon (High Strength) 7
1.75
143
1.83
Carbon (High Modulus) 7
1.95
200
1.35
Aramid (Kevlar49)
12
1.45
90
2.07
Table 5.3
Failure
Strain, *
2.6
1.1
0.6
2.3
It is all very well comparing the strength and stiffness of a fibre on its own, but what is actually
relevant is the strength and stiffness of the fibres when they are in an epoxy resin – the composite
material behaviour. In the table below are some estimates of the densities, stiffness and tensile
strength of UD laminates made up of 50% fibre volume fraction using the Rule of Mixtures
equations 5.1, 5.2 and 5.10 from earlier.
Table 5.4
Comparison of UD lamina of 50% fibre/epoxy ratio
Lamina Specific
Density,  (Mg/m3)
Stiffness, E/
E-Glass
1.95
20
Carbon (HS)
1.53
82
Carbon (HM)
1.58
120
Aramid (Kevlar49)
1.38
48
Lamina Specific
Strength, */
0.40
1.07
0.79
1.11
Compressive failure can occur through crushing or shearing, but the most likely is through
buckling. The compressive strength can be estimated through the Euler bucking of an individual
fibre, as it can be seen as a very long cylindrical rod.
2
 2E  d
 
 
16  L 
*
b
(5.13)
As the fibres all have very small diameters with respect to the length, buckling is the most likely
method of failure in compression, confirmation of the formation of kink bands. The compressive
strengths of the fibres in a composite material are very comparable to the tensile strengths, shown
in Table 5.4, due to the fibres having some lateral support from the surrounding matrix. However,
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this isn’t the case for Aramid fibres, which posses a compressive strength of around 20% that of its
tensile strength. This is due to the structural formation of the fibres, as it is made up of weak van
der Waals bonds, which are overcome in compression resulting in fibrillation of the fibre and
buckling. This weakness in compression rules out Aramid fibres from selection, as a car will
experience a combination of tensile and compressive forces due multiple combinations of loads
exerted whilst being driven. Carbon fibres are more expensive than the rest, however they posses
the best all round performance for their purpose. High Modulus Carbon fibres have been singled
out as the choice for this design, as the main priority is for good torsional stiffness of the vehicle, so
the slightly lower tensile strength shouldn’t be an issue as it is still strong enough to survive from
the forces exerted on the vehicle under the extreme racing conditions.
The numbers in the text
represent the stages in the
diagram.
Figure 5.10
Processing Acrylonitrile to PAN for manufacture of carbon fibres [15]
Looking into some background of how carbon fibres are made, the most popular method is
outlined in Figure 5.10, which is from organic precursor fibres called polyacrylonitrile (PAN)
[16]
which is formed by polymerisation of acrylonitrile. This is obtained by reacting propylene with
ammonia and oxygen with the use of catalysts (1). Bulk PAN fibres are isolated and then stretched
to align the molecular chains. These stretched fibres are heated where the active nitrile groups
react resulting in a ladder polymer (2). Sustaining the tension on the fibres and heating it in an
oxygen-containing environment causes further chemical reactions to form cross-links (3).
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Further heat treatment of the carbon ring structure at a suitable temperature then produces the
desired characteristics of the fibre, high modulus or high strength, as shown in Figure 5.11 below.
Figure 5.11
Relationship between heat treatment and properties of PAN based carbon fibres [17]
From the graph it can be seen that high strength carbon fibres need to be heated between 14501600˚C, whereas a temperature of more than 2500˚C for high modulus carbon fibres to be made,
which are the ones desired for this design.
5.3.4 Composite Sandwich Structures
In automotive structures, a method for increasing specific strength and stiffness even more is
through creating a sandwich structure. This consists of two thin, stiff faces, known as skins,
separated by a thick, lightweight core to transfer the loads between skins. An adhesive film needs
to be placed between the skins and the core to create some form on continuity between the layers.
For automotive sandwich structures, the skins spread out both the bending loads and the in-plane
loads, whereas the transverse shear forces are to be absorbed by the core. The adhesive film also
experiences degrees of shear force, so needs to be strong enough to prevent the skins from
separating from the core as this will weaken the sandwich structure. The skins will be made up of
the carbon fibre reinforced polymer. As for the core material, when it comes to automotive
structures, there are two main options: foam cores and honeycomb cores.
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Figure 5.12
Chassis
Setup of sandwich panel with honeycomb core [18]
Foam cores are relatively cheap and can be made up of a variety of low-density materials. The
honeycomb core, shown in Figure 5.12, is usually made up of a hexagonally shaped cell structure,
which can be compared to the appearance of the cross-section of a beehive. It offers the best
strength to weight ratio of the core materials due to there being around 90% open space across the
core. The honeycomb core is ideal to be the core for all bulkheads as they are flat and they need to
be appropriately aligned much like fibres to reap the maximum benefits, whereas the foam core is
more easily shaped around curves and more complex geometry.
Table 5.5
Relative property enhancement for sandwich structures
Relative Bending Stiffness
Relative Bending Strength
Relative Weight
Solid Material
1
1
1
[19]
Core thickness t
7.0
3.5
1.03
Core thickness 3t
37
9.2
1.06
Table 5.5 shows, by keeping the skins the same thickness but by increasing the thickness of the
core, how much the properties can be enhanced when adopting sandwich structures. These
strength and stiffness values can only be estimates due to the difficulty in deciding at which variety
of failure mode the sandwich panel structures will fail, for which examples include skin yield, face
buckling, core shear and face indentation. However, it has been proven that sandwiching the
composite materials greatly improves the properties of the structure when they are used as skins in
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the sandwich structure. For this project, Aluminium-5052 honeycomb core will be used for the
bulkhead core, as this has the best stiffness [18] and rigid polyvinylchloride (PVC)
[20]
foam will be
used for the remaining structures’ core, which like thermosets, have a high number of cross-links.
However difficulties occur when trying manufacture sandwich structures with PVC foam cores, due
to the need for high temperatures when curing the composite material skin around it.
5.3.5 Methods for Manufacturing Composite Materials
There are a number of methods for manufacturing carbon fibre reinforced polymers (CFRP).
However, all methods for producing CFRP made of continuous fibres embedded in an epoxy matrix
are very slow and labour intensive. This, along with the great expense usually is a great drawback
of implementing CFRP in an FSAE project, but it does result in a much lighter and stiffer chassis.
There are two options when it comes to the fabrication process of CFRP, where the main similarity
between all of them is that an expanded polystyrene mould of the vehicle needs to be made to lay
the fibres up against, which is then coated with a release film: these options are dry layup or wet
layup. A dry layup is when the matting of reinforcing fibres already impregnated with the epoxy
resin, known as prepreg tape as the resin is already embedded and partially cured, although still
flexible enough to wrap around a mould. Completing the curing of the prepreg cloths can be
completed through two different methods. One is called compression moulding, where the idea is
to apply a reinforced shaped around the lay up mould and then perform a compression on the
prepreg cloths of around 1000 tonnes
[21]
to consolidate the construction and push out all voids in
the material. Heat and pressure is then applied to complete the curing process. The second dry
layup method is called autoclave moulding, where the lay up mould is put in a pressure bag to try
and minimise the volume of voids in the construction. This is then placed in an autoclave, which is
essentially and oven to apply the appropriate temperature and pressure conditions required for
curing. The advantages of this method is that there is usually less wastage of excess resin as it is
already impregnated in the cloth, and as a result can result in lighter constructions. However, the
drawback is that it is very difficult to make large constructions strong enough via this method, as
there is a slight discontinuity between individual cloths being layed. It is more likely to be used for
smaller body parts.
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A wet layup is where the resin needs to be applied to dry cloth of reinforcing fibres. Again, here the
fibre matting is layered onto the mould. There are two methods for applying the resin to the cloth.
The first is to essentially roll the resin into the dry fabric with a roller or brush, and then place the
entirety into a vacuum bag to try and force all of the voids including air bubbles out of the
construction, as any voids in the material will severely weaken the final construction. The second
method is known as vacuum infusion, where the layed up mould is placed in a vacuum bag
immediately, and then the resin is fed through a tube, being pulled through into the bag by the
pressure differential between the inside and outside of the bag and distributes itself uniformly
throughout the dry fabric. Both of these wet layup methods require the mould to be placed in an
autoclave to apply the appropriate pressure and temperature for curing the construction.
Figure 5.13
Vacuum Infusion setup and process [22]
It has been decided that vacuum infusion will be the method of fabrication utilised for this project,
due to its effectiveness in constructing large single pieces, and its slightly less labour intensive
process of applying the resin, but yet still fairly time consuming. It can be seen that it is essential
for the resin’s viscosity to be low so that it can spread and pass through small gaps in the stack of
reinforcement, The release film coated on the mould then allows the CFRP structure to be
separated from the mould. The vacuum infusion setup and process is outlined in Figure 5.13,
where the reinforcement stack is the sandwich structure made up of layers of carbon fibre cloths
separated by the chosen core. As well as the adhesive film, the cores needs to be sealed with a
resin coating to create an impermeable barrier between the core and skins, preventing the resin
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from spreading throughout the core. Also the curing temperature needs to be as low as possible to
prevent the PVC core from decomposing when heated [20], yet still high enough to properly cure the
composite material. A mesh to enhance the resin flow, a peel ply fabric to provide easy removal of
the cured laminate along with a combination of materials to promote resin flow are all included in
the Peel Ply and Distribution Fabric.
5.4
Analysis of the Chassis
5.4.1 Finite Element Analysis (FEA)
Finite Elements Analysis, with background from Korsunsky’s ‘B1 Finite Elements Note’s [23], is the
most widely used computational method for simulating the behaviour of a mechanical system, and
has been used in analysis of static responses of the chassis. The method involves dividing a
domain up into a finite number of smaller more manageable sub-domains known as finite
elements. Each finite element has its own boundary conditions, and the method effectively
equilibrates every finite element to predict the overall response of the whole mechanical system.
This enables the stresses and strains of any geometry to be calculated, however complicated. This
is done by using shape functions, most commonly in the form of mapped triangles, due to its very
simple geometry. A mesh of triangular elements is created, where the size of the triangles, or
alternatively the density of triangles can be defined based on how accurate the calculation is
needed to be – a finer mesh uses smaller elements and leads to more accurate results but takes
more time to compute.
5.4.2 Impact Testing the Chassis
Before analysing the chassis model, the properties of the material need to be calculated and
entered into Solidworks. This was done by defining the shell feature, where the material can be
divided up with each layer treated as a unidirectional lamina, where the position, thickness and
orientation can be specified. This was done for stacking of orientations [0˚/45˚/90˚/135˚]s
throughout the laminate with each layer 0.5 mm thick. The properties of the lamina to be used have
all been calculated using the theory outlined in a previous chapter for a composite material of high
modulus carbon fibre to epoxy resin unidirectional plies of volume fraction 50% and the results are
shown in Table 5.6, using equations 5.1, 5.2, 5.3, 5.4, 5.7 and 5.10.
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Table 5.6
Properties to be entered for simulating the analysis
E1
196 GPa
E2
5 GPa
G12
5 GPa
12
0.3
t
c
1300 MPa
1070 MPa
Chassis

1630 kg/m3
The analysis tests were simulated on Solidworks using the built
 in FEA software.



Side Impact Test
The Side Impact Test
[24]
consists of a load of 7 kN applied to the side impact zone which is
specified as the vertical impact zone between the upper surface of the floor and 350 mm above the
ground in the direction of the driver, where the maximum allowable deflection cannot exceed 25
mm and there cannot be failure anywhere in the structure, with a failure considering all modes
including tensile, compressive, shear or buckling.
Figure 5.14
Description of side impact zone for a monocoque
[25]
This Side Impact Test was simulated by the fixing the geometry about where the suspension would
be attached to the chassis on the same side as the applied load. Then multiple 7 kN forces were
applied to the side of the cockpit. The results are shown in Figure 5.15, with the resultant
deflection, showing the maximum deflection of 4.4 mm with the maximum von Mises stress of 136
MPa occurring at the corners of the cockpit opening, not exceeding the yield stress of the material
of around 800 MPa. The Side Impact Test is passed comfortably as it is only required to survive a
single applied load, rather than multiple loads distributed evenly over the impact zone of 7.5 kN.
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Figure 5.15
Chassis
Results of the Side Impact Test
5.4.3 Torsion Test
The torsion test isn’t a test specified in the FSAE Rules, but it is very much of interest as high
torsional rigidity is thought of as the primary function of high performance chassis. This was also
carried out in Solidworks by trying to recreate the effects of cornering on the vehicle. This fixed the
geometry to the rear of the vehicle, and then a torque was created on the front of the vehicle by
applying two equal and opposite directional forces of 5 kN to opposing sides of the front of the car
at a distance of .223 m from the centre of rotation. The diagram showing the resultant
displacement of this process is shown in Figure 5.16, where it can be seen that the maximum
deflection is 5.1 mm, at a distance of 1.2 m from where the geometry is fixed.
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Figure 5.16
TorsionalRigidity
Chassis
Resultant Displacement of the Torsion Test
Torque

AngularDisplacement
2  5.223
 9153Nm/ deg
3 

1 5.10310
tan 

1.2


This is a very good torsional rigidity, satisfying the priority of high chassis stiffness for the design.
5.4.4 Rollover stability test
Rollover stability is specified in Article 6: T6.7 of the FSAE Rules, specifying that the track of the
car along with the centre of gravity of the car must combine to provide adequate rollover stability,
which is tested on a tilt table. The vehicle must not roll when tilted at an angle of 60˚ to the
horizontal, with the tallest driver in the normal driving position. This test involves the calculation of
the position of the centre of mass of the full vehicle. A value for this was calculated through
superposing the result from Solidworks of the overall chassis with all the components, with
additional calculations to take account for the centre of mass of a driver of 77 kg in normal driving
position. For a human, this is positioned just above the hipbone, so at the upper part of the
circumference of the circle representing the hips in the 95th percentile template. The position of the
centre of mass in relation to the z-direction is irrelevant due to the orientation of the tilt table, so it is
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only of interest to see where it is in the x-y plane. This point must be inside the centre of rotation,
defined as the contact point between the outer surface of the tyre and the ground. The coordinates
for the centre of mass of the vehicle are (-17, 284), with the origin positioned on the car centreline
level with the floor of the vehicle. When the vehicle is tilted at 60˚, this is not beyond the rotation
pivot, or alternatively, angled at over 90˚ to the ground about the centre of rotation, shown by lying
right of the horizontal line.
Figure 5.17
5.5
Rollover stability test: vehicle tilted at 60˚ to the horizontal
Packaging
As stated earlier, the role of the chassis includes supporting and protecting everything it carries. So
all the components’ positions and setup need to be taken into account in the design of the car.
There are various options encountered at the initial arrangement of the car, which is weighed up
nicely in Racing and Sports Car Chassis Design [26], such as whether the engine is placed at the
front, middle or back. After careful consideration of the rules and how best to optimise the vehicle
based on research of past FSAE vehicles [27], the vast majority of racing cars adopt a rear wheel
drive setup. So it is quite easy to come to the decision of placing the engine at the back along with
the other main components such as fuel tank, transmission and electrical components to try and
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get as much of the weight as possible over the rear wheels to help the transfer of the power
generated from the engine onto the road. Having all the major components adjacent to each other
also helps the efficiency of the power transfer due to minimising the distance for the transmission
line to cover. An added desire for rearward loading of components is the limited space towards the
front of a refined shaped vehicle with the legs, steering and suspension components filling that
space. Having the heavy components at the back also allows the possibility of a more symmetric
distribution of weight between the wheels compared to the front or the middle, as this would usually
consist of placement alongside the driver. From Race Car Vehicle Dynamics
[28]
, “For best traction
on acceleration out of a corner the drive wheels needs to be evenly loaded”, certainly emphasising
the need for symmetric loading down the car centreline. A symmetric distribution of weight is very
helpful for cornering and so is a low centre of mass for the whole vehicle as this helps reduce
abrupt and significant weight transfer in cornering, which would increase instability in corners the
chances of rollover. Rollover stability can be improved with a wider track base. These are all
factors which are considered with the roll stiffness, which needs to be low enough to try and evenly
distribute the load, but high enough so that the car doesn’t roll too much in the corners so that the
centre of mass is moving too much in cornering. An asymmetrically loaded car can reduce the feel
of control for the driver, as steering would be affected. To accommodate all these considerations,
the chassis was designed to be fairly narrow but long to try and minimise the frontal area of the
vehicle as well as minimising the distance between the ground and the centre of mass.
Working closely with the rest of the team, the floor plan of the main components packaged into the
rear of the car can be organised and is shown in Figure 5.18. The components are colour coded to
help distinguish between them, with engine in silver, the fuel tank in black, alternator in green, the
braking control unit (BCU) in red with there being one for each side of the car, the battery in blue,
the engine control unit (ECU) in yellow and the CVT in white. All these components also need to be
positioned in an efficient way relative to each other for to ease the connections between them.
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Figure 5.18
Hertford College
Chassis
Floor plan of rear compartment containing all the main components
Close contact with Edmund and Robert helped put together the full modelling setup of the car, as
shown in Figure 5.19 where addition of the wings, wheels and suspension are illustrated.
Figure 5.19
Isometric view of assembly including wings, wheels and suspension
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Chassis
The packaging of the car is a very important feature in the design process as serious problems can
be encountered when it comes to building the car – a lack of space in one area could lead to a
completely different design being the optimal.
5.6
Conclusion
The key roles of the chassis have been outlined in this chapter, with special focus on the material
on how composite materials are being used to achieve these. It can be seen why they have been
exclusively adopted in the motorsport industry, with the smallest of improvements in material
properties leading to dramatic improvements in performance.
The approximate cost of making the chassis is estimated in Table 5.7. These were drawn up
mainly through online research, trying to find the cheapest and most practical options. If
construction were to be carried, there would be the possibility of seeking out sponsorship from
some of the companies, leading to this being a possible overestimation. The contingency
represents all unexpected costs, for example the laying up process is quite difficult and a problem
may arise resulting of wasted resources, along with additional materials that may be needed along
the way.
Table 5.7
Finances of the chassis
£4 000
Further research and development could go into better and more efficient fixing of the roll hoops to
composite body; if the car were actually going to be built these problems would be encountered. In
this design they have simply been bolted with reinforcements to the monocoque body.
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Improvements could go into the more accurate modelling of the chassis in the analysis process,
with the fine details of the sandwich panelling being a priority. However, there are obviously limits
to how this model has been tested. Firstly with Solidworks, where the simplicity of modelling the
monocoque without the sandwich layering had to be employed due to the complexity involved in
modelling such a construction on Solidworks requiring a skill level and time that aren’t available at
this level. Simplification also occurred in specifying the material in the program. In theory, the
orientation of the carbon fibre cloths stacking leading to isotropic behaviour seems viable, however
in practice these wouldn’t lead to perfectly isotropic behaviour. There are also limitations to the
Finite Element Analysis used to test the chassis, as it can be difficult to decide or evaluate the
appropriate element size, as in an ideal world the infinitely fine mesh would be used, but for
complicated geometry and large mechanisms, an infinitely powerful machine would be needed to
process. This can lead to information gaps, especially where large stress gradients can occur,
especially at stress concentration points of complicated shapes.
A table summarising the characteristics of the chassis design are contained in Table 5.8.
Table 5.8
Monocoque Chassis Summary
Mass (including chassis, seat and roll hoops)
65 kg
Cost
£20 680
Dimensions (maximum)
1.02x0.75x2.30 m
0.95 m2
Frontal Area
Torsional Stiffness
9153 Nm/deg
Wheel Base
1.60 m
Track Width
1.24 m
Comparing these results to previous years results in the FSAE competitions
[27]
this looks to be
competitive after the design process. Obviously, results would vary with the actual construction of
the vehicle outside of the theoretical world and into the real life when it is put together.
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5.7
Hertford College
Chassis
References
1. 2015 Formula SAE Rules: Article 2, T2.1 Vehicle Configuration, p24.
2. Walkers Garage Limited [Online] http://www.walkers-garage.co.uk/teknofibra.htm
3. University of Cambridge Department of Engineering [Online]
http://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/stiffness-density/NS6Chart.html
4. Tan, J.C., ‘B8 Composites Lecture Notes’, p11.
5. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, pp61-74.
6. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, pp83-87.
7. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, p96.
8. Tan, J.C., ‘B8 Composites Lecture Notes’, p44.
9. Tan, J.C., ‘B8 Composites Lecture Notes’, p45.
10. McCrum, N.G., Buckley, C.P. and Bucknall, C.B., ‘Principles of Polymer Engineering’ Oxford
Science Publications, Second Edition, 1997, p246.
11. Ashby, M.F. and Jones, D.R.H, ‘Engineering Materials 2: An Introduction to Microstructures,
Processing and Design’, Pergamon Textbook, Volume 39, 1986, p242.
12. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, pp31, 33.
13. Howatson, Lund and Todd, ‘Engineering tables and data’, April 2009, pp 45-48.
14. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, pp10, 11, 15, 26, 31.
15. Wikimedia [Online] http://commons.wikimedia.org/wiki/File:PAN_stabilization.PNG
16. Encyclopaedia Britannica [Online]
http://www.britannica.com/EBchecked/topic/468259/polyacrylonitrile-PAN
17. Hull, D. and Clyne, T.W., ‘An Introduction to Composite Materials’, Cambridge Solid State
Science Series, Second Edition, 1996, p14.
18. HexWebTM Honeycomb Sandwich Design Technology [Online]
http://www.hexcel.com/Resources/DataSheets/Brochure-DataSheets/Honeycomb_Sandwich_Design_Technology.pdf
19. University of Cambridge Department of Engineering [Online]
https://www.repository.cam.ac.uk/bitstream/handle/1810/236995/design;jsessionid=468CDCA
AB6C02A246E2B014C4BF6B8FE?sequence=1
20. NetComposites [Online] http://www.netcomposites.com/guide/pvc-foam/91
21. Engineer’s Handbook [Online] http://www.engineershandbook.com/MfgMethods/molding2.htm
22. NetComposites [Online] http://www.netcomposites.com/guide/infusion-processes/57
23. Korsunsky, A., ‘B1 Finite Element Methods Lecture Notes’, pp19-30.
24. 2015 Formula SAE Rules: Part AF – Alternative Frame Rules: Article 4, Structural
Requirements, AF4.1-3, pp76-77.
25. 2015 Formula SAE Rules: Article 3, Driver’s Cell, T3.34 Monocoque Side Impact, p46
26. Costin, M. and Phipps, D., ‘Racing and Sports Car Chassis Design’, Cambridge, 1967, pp3-6.
27. Racecar Engineering Magazine [Online] http://www.racecar-engineering.com/formulastudent
28. Milliken, W.F. and Milliken, D.L., ‘Race Car Vehicle Dynamics’, SAE International, 1995, p41.
29. Steel Tube Direct [Online] www.steeltubedirect.co.uk
30. West System [Online] www.westsystem.com/ss
31. The BPF Expanded Polystyrene Group [Online] www.eps.co.uk
32.The Practical Machinist [Online] www.practicalmachinist.com
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6
Suspension, Steering, Tyres and Brakes
6.1
Introduction
This chapter considers those components of the car which are directly involved in relaying the
controls from the driver in the cockpit to the action of the car on the road. Having an engine with a
high power output is not enough to ensure good car performance, the tyres and suspension
system must be carefully selected to ensure that the power from the engine is transmitted to the
road surface as efficiently as possible. All braking, accelerating and cornering forces must be
transmitted through the tyre contact patch and so tyre selection is one of the most critical factors in
overall car performance. The primary role of the suspension system is to maximise this contact
patch by ensuring the tyres remain in contact with the road at all times, it also works in
collaboration with the steering system to optimise the car’s handling through the corners. The car
must be responsive to the driver’s commands if it is to perform well in the endurance event. The
brakes must be strong enough to meet the formula student regulations and also balanced to give
the driver maximum control.
6.2
Suspension
6.2.1 Suspension type
The first decision to be made with regard to the
suspension is which system to use. Broadly
speaking suspension systems can split into two
groups, dependent and independent systems. In
a dependent system the wheels on each side of
the car move together whereas in an independent
system each wheel is free to move on its own.
Figure 6.2.1A range of different suspension systems (1)
Four wheel independence is highly desirable in a racing car as it means any sudden upsets in the
road surface will be confined to the wheel and tyre that experiences the upset. For this reason
dependent systems such as the ‘De Dion’ tube were disregarded. Common forms of independent
suspension include the MacPherson Strut and double wishbone suspension. The MacPherson
strut is a design which was used in some early racing cars and rally cars, but is not feasible in the
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formula student competition as it is difficult to adjust and the unit is impossibly tall to fit into a really
low car. Double wishbone suspension is by far the most common suspension system in the
modern day, used in everything from road cars to formula 1 (1). It is extremely popular with formula
student teams due to the ease with which the geometry of the system can be altered to optimise
the camber on the tyres and the roll centre of the car. This car will use double wishbone
suspension on both the front and rear of the car.
6.2.2 Setting Suspension Geometry
The principle of double wishbone suspension is based on a four bar chain, where two of the ‘bars’
are upper and lower wishbones, one ‘bar’ is the upright which connects to the wheel and the final
‘bar’ the chassis between the two wishbone connections. The suspension geometry can therefore
be varied in three ways:
1. By changing the length and angle of the upper and lower wishbones.
2. By changing the points here the wishbones connect to the chassis
3. By modifying the dimensions of the upright.
In designing the suspension geometry there are a number of parameters which must be
considered, these parameters are explained below.
Instantaneous Centre, Roll Centre and Roll Axis
The instantaneous centre (IC) of the car is found by extending the paths of the upper and lower
wishbones until they intersect, see figure 6.2.2, it represents a point that the wheel and control
arms rotate about during bump or droop. It is an important parameter as it defines the way in which
the camber (see below) changes with respect to the wheel height.
Figure 6.2.2 Determination of instantaneous centre, roll centre and roll moment arm (2)
From the instantaneous centre, another line is drawn to the contact point beneath the tyre.
Assuming the suspension layout is symmetrical; the point where this line crosses the centreline
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gives the roll centre (RC) of the car. The roll centre defines the point about which the sprung mass
of that end of the vehicle will roll under the influence of a centrifugal force (2). It also represents the
point through which the forces from the tyres act upon the chassis. The position of the roll centre
determines how the cornering loads are transferred through the suspension system. If the roll
centre is a long way above the ground or even above the CoG a ‘jacking’ effect occurs whereby the
sprung mass of the car is lifted due to a moment about the instantaneous centre. If the roll centre
is below ground an opposite effect called ‘packing’ occurs whereby the sprung mass applies extra
load to the suspension system as it attempts to rotate into the road. If the roll centre is at the road
surface all the lateral forces pass from the chassis to the wheels through the damper/springs, so
no lateral loads need to be transmitted through the wishbones (3).
In reality the roll centre is usually set in the range of 15% to 30% of the CoG height (3). Keeping
the roll centre closer the ground reduces the amount of load taken by the wishbones but means
there is a greater roll moment. The final parameter to discuss is the roll axis; this is a line which
joins the front roll centre to the rear roll centre. Typically racing cars have an inclined roll axis (4),
so following conventional wisdom the front roll centre in this car will be lower rear. In the initial
design of the car the lower wishbone is set as horizontal and so the position of the roll centre is
varied by adjusting the angle of the upper wishbone. The plot below shows the relationship
between the angle of the top wishbone and the roll centre, and gives an initial estimate for the
suspension geometry.
Target Roll
Centre
(mm)
Upper
Wishbone
Angle (°)
FRON
T
40
9
REAR
70
12
Figure 6.2.3 Relationship between position of roll centre and angle of upper wishbone
Camber
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Camber is measure of the centreline of a tyre relative to the ground. A neutral camber tyre runs
perpendicular to the road, whereas a negative camber tyre slants in towards the car and a positive
camber tyre slants away from the car. (see figure 6.2.4).
Figure 6.2.4 Illustration of different kinds of camber (5)
Typically formula student cars will run with a static negative camber of 1° to 3° to improve handling.
When the body rolls into a corner the majority of the load is transferred to the outer tyres and so it
is important that the contact patch of the outer tyres is maximised. The camber will change with the
body roll, in an optimised design the outer tyres will be at neutral camber under a maximum
cornering load (see section 6.2.3). Without the negative camber, only the outer edge of the tyre is
loaded during the corner so overall grip is reduced. The disadvantage of setting negative static
camber is that under normal running, only the inner edge of the tyre is loaded, this will result in tyre
wear and reduce overall grip in acceleration and deceleration. There is clearly a trade-off when
increasing the static camber and so the initial target for this car is a relatively conservative -2°.
6.2.3 Dynamic Suspension Simulation
Although parameters may be set whilst the car is stationary, it is important to note that all
parameters will change under loading as the suspension geometry is altered. An initial model was
setup using the targets as specified in 6.2.2 and Lotus suspension analysis software was used to
simulate the suspension response under 30 mm of jounce and 30 mm or rebound. (Jounce is the
upward movement of suspension components and rebound is the downward movement of
suspension components). The model was continuously altered and updated until a satisfactory
suspension geometry was found. The software provides data for a range of suspension
parameters and some of the results are shown in figure 5 and figure 6.
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Camber vs. Roll
Roll Centre
150
100
50
Rear
Heirght ofFront
Roll Centre
Suspension, Steering, Tyres, Brakes
0
-20 0 20
-50
-30 -10 10 30
2
1
0
Front (°) -3 -2 -1
0 1 2 3
-1Rear
Camber Angle
-2
-3
-4
Travel (mm) (Rebound '-ve', Jounce '+ve')
Roll Angle (°)
Figure 6.2.4 Image of final suspension model in
The position of the roll centre is shown in figure 5, clearly there is a variation in the height of the roll
centre depending on whether the system is in jounce or rebound. The handling characteristics of
the car will change as the roll centre of moves; for example, when braking into a corner the front
axle will be loaded and the front suspension will experience jounce, this will lower the roll centre
and therefore produce a greater roll moment.
6.2.4 Actuation methods
One of the main advantages of double wishbone suspension is that it permits us to use a range of
different actuation methods. The simplest solution involves mounting the shock absorber outboard
with the upper spring pivot attached to the chassis and the lower spring connector attached to the
lower wishbone. Or we can mount the shock absorber inboard and actuate it by a rocker arm
(either a pull rod or a push rod), the benefits of each system are summarised in the table below.
Chassis to lower wishbone
 Extremely simple system to setup
 Keeps
BENEFITS
Push-rod / pull-rod suspension
shock absorbers outside of the
main body which may make overall car
packaging easier
 Shock
absorbers are easily accessible if
repairs/ changes need to be made
97
 By
locating the shock absorber in the
wheel the airflow around the wheel is
disrupted less
 The
linkage can be used to modify the
motion ratio for the spring.
Edmund Moss
Somerville College
Suspension, Steering, Tyres, Brakes
LAYOUT
Exported from final Solidworks model
(6)
It was decided to use a pushrod suspension system on the front of the car and more conventional
chassis to lower wishbone system on the rear. At the front of the car there is move available space
to locate the shocks within the body; there is also a greater aerodynamic advantage in taking the
shock out of the flow at the front as the flow at the rear of the car is likely to be already turbulent.
Some teams use shocks from downhill mountain bikes on their cars, but the shocks used on this
car are from a German company called ‘Bilstein Motorsport’ and are specifically designed for
formula student cars. They are slightly more expensive
(£2200) than the alternative but are a good investment
as they are extremely lightweight (760g) and provide a
range of damping/ rebound settings.
6.2.6 Spring-Damper Calculations
The formula student rules specify that (6):
“T6.1.1 - The car must be equipped with a fully
Figure 6.2.8Formula student damper from Bilstein Motorsport
operational suspension system with shock
absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4 mm(1
inch) jounce and 25.4 mm (1 inch) rebound, with driver seated.”
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This car will be designed will a maximum jounce and rebound of 30 mm, so the total travel of the
wheel is 60 mm. The shock being used has a total travel of 47.5 mm so the motion ratio for the
system must be 1.263 where the motion ratio is defined as.
Mo tion Ratio=
Wheel Travel
SpringTravel
The spring travel is found using the following formula, where θ refers to the angle between the
upright and the shock.
Spring Travel=Wheel Travel × cos θ
The optimum angle is found to be 38°. This
solution is fine for the rear of the car where
the shock can be mounted slightly higher,
but at the front the profile of the car is much
lower and there would be no reasonable
place to mount the pushrod. Fortunately,
since we are using push-rod suspension on
Figure 6.2.9Push rod suspension linkage, motion ratio: 101.68/64.22 = 1.58
the front of the car, the motion ratio can be adapted using the dimensions of the linkage. To keep
the car low at the front the pushrod is connected the upright at an angle of 60°, at this angle, 60mm
of wheel travel corresponds to 30mm of ‘push rod’ travel. Therefore the linkage must increase the
motion by a factor of 1.58 (47.5 / 30).
The next step is to find the required spring rate for the shocks using the following formula:
Wheel Rate=
Spring Rate
( Motion Ratio )2
When the suspension system is in its steady state (stationary) the wheels should have 30mm of
available jounce and 30mm of available rebound. Each front wheel supports a load of 589N and
each rear wheel supports a load of 981N, therefore:
Front Wheel Rate=19.6
N
N
Rear Wheel Rate=32.7
mm
mm
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Front Spring Rate=31.2
Somerville College
Suspension, Steering, Tyres, Brakes
N
N
Rear Spring Rate=52.16
mm
mm
6.2.7 Suspension System Fabrication
With the suspension layout decided, a complete model was built in Solidworks to help with the
overall car packaging see figure 6.2.10 and 6.2.11. The wishbones are constructed from carbon
fibre tubes connected to brackets at either end of the upright (to be discussed in the next section).
These brackets are not off the shelf parts and would have to be custom made, but the carbon
tubes are supplied as a kit by Formula 7 and can be cut to any desired length. One important
feature of the design is the connection between the ball joints and the wishbones. The joints are
screwed into the brackets , which means static camber can be easily modified by screwing them
one thread in or one thread out.
Figure 6.2.10 Front suspension assembly
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Figure 6.2.11 Rear suspension assembly
6.2.8 Anti-roll bar
Put in if space
6.3
Steering
The steering system must be designed to give the driver the maximum amount of control over the
car, whilst also providing him with feedback from the road. The steering system is made up of the
steering wheel, the steering mechanism and the linkages that connect to the wheel uprights, the
aim is minimise the overall weight of the system whilst still ensuring that it is strong enough to
stand up to the applied loads. There are a range of different steering that can be used,
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6.3.1 Ackerman Steering Principle
The Ackerman principle is related to the angle of the front wheels as the car corners. As the car
makes a turn, the two front tyres are essentially following two circles whose radii differ by the track
length. As a result the inner tyre must turn at a tighter angle than the outer tyre, with Ackerman
steering geometry this discrepancy is taken into account and the inner wheel is turned further
during a corner. If the two front wheels are setup to run in parallel, then the front inner tyre will not
be able to follow the desired path and so scrub will occur. Although the Ackerman principle has
been trusted for hundreds of years, recent race car builder have begun to disregard it for a number
of reasons. When a car is cornering at speed, each of the tyres develops a slip angle (this will be
covered in more depth in the following chapter) which means that the wheel direction is not the
same as the direction of travel. This modifies the Ackerman picture considerably, figure 6.3.1, the
instantaneous centre of curvature has moved from Point I to Point X.
Figure 6.3.1 Steering layout for
full Ackerman
Figure 6.3.2 Variation in the Ackerman picture accounting for
slip angle
This means the front wheels are now very close to parallel so little or no Ackerman compensation
is required. As a general rule the Ackerman theory applies to slow corners with thinner tyres, but
when the speeds increase and slip angles become a factor, the Ackerman geometry is not as
relevant. For this car, a moderate amount of Ackerman steering will be used, the steering arms will
be angled at 5° with respect to the wheel face.
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6.3.2 Steering Properties
Just as with the suspension setup, a number of properties must be considered when designing the
steering system.
Figure 6.3.3 Diagram showing the various parameters related to the steering geometry (3)
Caster and Mechanical Trail
Caster is measure of the location of the steering axis in reference to the vertical; positive caster
occurs when the steering axis comes in front of the vertical and negative caster occurs when it
comes behind. Positive caster in a car tends to create a lot of align torque and therefore promotes
straight line stability, although this is beneficial, increases in caster will also make the steering
heavier and so should be avoided since his car has no power steering system. The mechanical
trail is the distance between the steering axis and the vertical at the road’s surface.
Toe
Toe is defined as the angular deflection from the vehicles centreline and the centreline of the rim.
Toe-in is when the wheels are turned inwards towards the car, just like large positive caster, toe-in
promotes straight line stability, particularly at high speed. Toe-out has the opposite effect, it
decreases the straight line stability of the car but improves the car’s turn-in response, as the car
approaches a corner, a slip angle is created at the inner tyre more quickly than usual and so the
car is pulled into the bend. Running toe out can be beneficial to some setups, but in general it is
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very difficult to get the balance right, as too much toe out will lead to excess tyre wear and oversteer tendencies (5).
King Pin Inclination and Scrub radius
The king pin inclination is a similar principle to caster but instead of looking at the tyre from the
side, it looks at the tyre from the front. Following the kingpin axis down to the road surface, the
scrub radius is the distance between this point and the centre of the tyre. The greater the scrub
radius the larger the circle the wheel has to rotate about when turned. A large scrub radius leads to
heavy steering whereas a small scrub radius allows the tyre to be swivelled about a point on the
road surface.
The following target parameters were determined by assessing the theory and looking a the set up
of a number of different pre-existing cars.
Parameter
Target
King Pin Inclination
5 – 8 degrees
Scrub Radius
0 - 20mm
Static Toe
0
Mechanical Trail
20 – 40 mm
6.3.3 Upright Fabrication
When it comes to the steering geometry of the car there is perhaps no part more important than
the upright. Steering parameters are almost entirely set through the design of the upright, as a
result it is a part which must be custom made for this project. The first stage of design was simply
to construct a part to join the two wishbones to the wheel. The brake mount and steering arm were
added later in the process. Once constructed the upright was tested along with the wheel assembly
to see confirm that it met the design parameters if it met the design parameters.
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Figure 6.3.4 King pin inclination and scrub radius test.
Figure 6.3.5 Caster and mechanical trail
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6.4
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Tyres
There are a number of companies who provide specialist tyres for formula student competition, the
three main contenders are Goodyear, Hoosier and Avon. (7). All three provide specific tyres but
some companies provide more data on their tyre package than others. This is a pure design
project and so our final results will be based on a simulation, it therefore makes sense to use
Avon’s tyres as they have the most in depth data package and will therefore give us the most
accurate simulation results.
6.4.1
Tyre Options
There are three main types of tyre construction, radial ply, bias ply and bias belted ply, see figure
6.4.1. Unfortunately Avon only supplies a bias ply tyre but it is important to understand the other
tyre types to access the strengths and weaknesses of the tyre selection. Bias ply tyres are made
with the plies running across the tread, typically at an angle between 30° and 40°, the direction is
varied with each layer. Bias belted ply is similar but also contains a belt (usually made of
fibreglass) under the tread which is intended to stabilise the tread and improve the lifespan of the
tyre. Finally, radial ply tyres are made with plies crossing the tread at approximately 90°, they also
contain one or more belts beneath the tread and offer superior performance as the tread runs
flatter on the road and therefore has better grip (8).
Figure 6.4.1 Different tyre construction
methods (9)
Figure 6.4.2 Variations in rolling resistance
coefficient with speed on a flat, smooth road
under rated load and pressure (10)
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One of the major disadvantages of the bias ply tyre is that it typically has a higher rolling resistance
than a radial tyre, as shown in figure 6.4.2. The main cause of rolling resistance in a pneumatic
tyre is hysteresis, as the wheel rotates the area under the contact patch is compressed and the
energy of deformation is greater than the energy of recovery, the energy is mostly lost through heat
gain in the rubber compound. In a bias-ply tyre there is greater energy loss due to the ply structure.
The alternating layers form a diamond pattern, under load the plies flex and stretch the diamond
shaped elements, this in turn produces a wiping motion between the tread and the road which
leads to greater tyre heating (11). Although this has a negative impact on the rolling resistance, it is
not necessarily a bad effect. There could be a performance advantage of having a tyre which heats
up more quickly as tyre adhesion (and therefore overall grip) generally improves with tyre
temperature.
Some of the other advantages of the radial tyre include longer tread life, greater puncture
resistance and greater comfort (12). Although relevant, there factors are not extremely significant
as the formula student events only run for a short period of time and the priority is speed rather
than comfort. The radial tyre may give slightly better handling the bias-ply tyre, but bias-ply is an
acceptable compromise considering they are significantly cheaper and more readily available.
6.4.2
Tyre Size
The first major decision to be made regarding the tyres is which size to use. The formula student
rules (13) specify that all tyres must have a diameter larger than 8’’ (20.32 cm) but in reality most
teams either use 16’’ (40.64 cm) or 20’’ (50.8 cm) tyres so these were the two sizes that were
considered. Tyres are typically specified in the following way: 7.2/20.0-13. All the dimensions are in
inches, the first number represents width of the tyre, the second number represents the overall
diameter and the third represents the diameter of the rims. There are trade-offs between using
larger or smaller wheels. The main advantage of the smaller wheel is the decreased weight; it is
highly desirable to save weight in this area as any rotating bodies on the car have an associated
rotational moment of inertia which will slow the car during acceleration. Solidworks models of a 16’’
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and 20’’ tyre, based off the specified tyre dimensions, were constructed to analyse the difference in
rotational moment of inertia.
7.0/16.0-10
m = 3.8 kg
J = 0.134 kg/m2
7.2/20.0-13
m = 4.9 kg
J = 0.265 kg/m2
Figure 6.4.3 Solidworks models of the two tyre size options, 20’’ and 16’’
As can be seen from figure 6.4.3, the rotational moment of inertia of the 16’’ tyre is roughly half that
of the 20’’ tyre. The difference between running the two tyres equates to an extra 5 Nm of torque
per tyre if the car is accelerating at 1 g. But during 1 g acceleration the transmission will be
outputting over 800 Nm of torque at the rear axle so it is dubious whether the smaller tyres would
have that great an impact. Looking at previous teams there is a reason that the 20’’ tyre is the most
popular; not only is there a greater selection and more available rims in this sizing, the larger
diameter also allows lots of space within the rim for packaging the brakes and wheel hubs. For this
reason the 20” tyres from Avon motorsport were selected.
6.4.3
Rim Selection
The 20’’ tyre is mounted on a 13’’ rim; it is desirable to minimise the weight of the rim to minimise
associated rotational moment of inertia. There are some companies such as ‘OZ Racing’ which
offer a specific wheel package for formula student teams. A summary of their two products is
shown in the table below.
Table 6.4.1
Comparison of the two rims offered by ‘OZ Racing’’
OZ Aluminium Wheel
OZ Magnesium-Alloy Wheel
Mass (per rim)
3.4kg
2.45kg
Cost (per rim)
£183.50
£362
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Clearly there is a trade-off between the cost of the rim and the weight. Although the magnesium
alloy wheel seems an attractive package, the set would cost £715 more than an aluminium set.
After discussing the topic within the team, the decision was made to use the aluminium wheel as
the money saved could be better spent improving other parts of the car (for example building a
carbon monocoque instead of a space frame). A Solidworks model of the aluminium wheel was
built using the specifications from OZ racing and the rotational moment of inertia was found to be
0.0628 kg/m2 .This data was combined with the tyre data and used in the simulation.
6.4.4
Tyre Theory
The tyres generate friction with the road in two ways: Adhesion is the tendency of rubber to stick
to other materials; it is thought to be the result of momentary molecular bonding and energy is lost
in breaking these bonds. Deformation occurs when rubber slides over a rough surface and the
high points on the surface (asperities) penetrate the rubber. As the tyre passes over a peak, each
element of the rubber experiences an increase in pressure as it is loaded (going up the peak) and
then a subsequent decrease in pressure as it is unloaded (coming down the peak) The increase in
pressure during the loading process is greater than the decrease during the unloading process,
and the result is a net resistance (14). Both these frictional effects are incurred because of ‘slip’
between the tyre and the road surface. If the car is accelerating or decelerating, the longitudinal
forces are related to the ‘longitudinal slip’ (sometimes referred to as ‘slip ratio’) as defined by:
i=
V slip
rω
×100 =
−1 × 100
V
V
(
)
Where V is the linear speed of the centre of the tyre, Vslip is the average speed of the rubber within
the contact area, ω is the angular speed of the tyre, r is the rolling radius of the free rolling tyre
(15). A driving torque will result in a positive slip ration as rω > V and a braking torque will result in
negative slip as rω < V. A pneumatic tyre will typically experience maximum tractive force at a slip
of between 15% and 20% (11). Figure 6.4.4 shows how the coefficient of friction varies with the slip
for a braking tyre, notice that a fully sliding tyre results in a lower coefficient of friction so wheel lock
should be avoided where possible. Unfortunately, Avon does not provide data for the peak friction
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coefficient of their tyres, but for the purpose of this project it will be assumed that μ = 1.2 at critical
slip, this is a reasonable estimate considering the results from previous years’ cars and online
research (16).
Figure 6.4.4 Relationship between longitudinal slip and coefficient of friction (under braking) (17)
So far the tyre has only been considered under loading parallel to the direction of travel, but it is
also important to understand how the tyre behaves under lateral loading (in a corner). As can be
seen from figure 6.4.5, under lateral loads there is tread deformation at the contact patch. As a
result the rolling path of the tyre is not in line with the direction of the wheel, this angular difference
is known as the ‘slip angle’. Just as with longitudinal slip, there is a critical slip angle which can
sustain the greatest lateral force (greatest cornering force). For normal road going vehicles this is
approximately 18° whereas for racing tyres it is around 6ۤ° (11). Figure 6.4.6 below shows how the
available cornering force for the Avon tyres varies with different slip angles and under different
loads.
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5.00
4.00
3.00
2.00
1.00
Cornering Force (kN) .
0.00
75kg
150kg
-1.00
-2.00
-3.00
-4.00
225kg
300kg
Slip Angle (deg)
Figure 6.4.5
Figure 6.4.6 Plot of Cornering Force vs. Slip Angle provided by
Deformation of
Avon Motorsport for 7.2/20-13 slick tyre at a camber angle of 0°,
tyre during cornering (18)
pressure 21 Psi and velocity 20 kph. (6)
Oversteer vs. Understeer
During a corner, a slip angle will be generated at both the front and rear tyres, if the slip angles are
the same (and the front and rear are generating similar levels of grip) the car should corner
neutrally. If the slip angle at the rear is greater than angle at the front then the rear tyres will
approach the ultimate grip limit first and so oversteer will occur. If the slip angle is greater at the
front, the car will experience understeer. This car is rear wheel drive and so will have a tendency to
over-steer due to a phenomenon known as ‘power-over-steer’. If the driver presses the throttle
during the corner, extra tractive force is applied to the driving wheels. This extra tractive force
increases the slip angle at the rear wheels and so promotes over-steer (19).
6.4.5 Tyre Simulation
The purpose of a tyre simulation is to identify the working limits of the tyres and thus find the
maximum acceleration and deceleration the tyres can sustain. There are a range of different tyre
models, some based mechanical simulations, and others based on semi-empirical methods such
as Pacejka’s Magic Formula (the most widely recognised tyre simulation technique) (20).
Unfortunately, Avon does not supply sufficient information about these tyres to use Pacejka’s
method but it does provide experimental data referring to slip angle (see figure 6.4.6). In chapter
four of this report, a rough simulation was run to show the positive influence of the wings on the
maximum cornering speed. This simulation is similar but slightly more advanced as it uses
experimental data from Avon and considers the forces on each tyre individually.
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The first step is to find an expression for the load on each tyre in a corner in terms of the velocity of
the car and the radius of the corner. The following calculations reference the parameters in figure
6.4.7; the wheelbase is 1.6 m and the track is 1.2 m. The location of the centre of mass is 0.6 m
from the rear axle and 0.4 m above the road surface; these estimates were taken from the
Solidworks assembly. If car is accelerating toward the centre of the turn at a rate of:
a=
V
r
2
Taking moments about the contact point of the inner tyres gives the following equation
F
¿
1
o+
F 2 o)×T
(¿
T
mV2
¿− Mg × =
×h
2
r
¿
(
)
Front View
Side View
a
MgMg
Tc
Figure 6.4.7 Diagram of the forces acting on the car as it goes round a corner.
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The split between the forces on the outer tyres, F1o and F2o, can be found by factoring in the
longitudinal position of the centre of mass; the forces on the inner tyres are found by applying
vertical equilibrium.
2
(
)
c mg mV h
=
−
F
b +c ( 2
rT )
2
(
)
b mg mV h
=
−
b+c ( 2
rT )
c mg mV h
b mg mV h
Forces on outer tyres : F 1 o=
+
F2 o =
+
b+c 2
rT
b +c 2
rT
2
Forces oninner tyres : F1 o
2
2o
This data is combined with the downforce calculation to find a total load on each wheel in different
cornering situations (see figure 6.4.8). Notice that in some scenarios (for example cornering a 30 m
corner at 30 m/s +), the centripetal acceleration is so great that the inner tyres are completely
unloaded. With the load on each tyre known, the available cornering force at each tyre is found
from the plots from Avon motorsport (see figure 6.4.6) assuming that all tyres achieve 9° of slip.
Force on Rear Outer Tyre
Load
(kN)
Radius
30
Force on Rear Inner Tyre
4.5
1.5
3.5
1.0
2.5
0.5
Radius 60
Radius 65
Load (kN)
0.0
1.5
-0.5 0 5 10 15 20 25 30 35 40
0.5
-1.0
0 5 10 15 20 25 30 35 40
Velocity (m/s)
-1.5
Velocity (m/s)
Figure 6.4.8 Load on the tyres as a function of velocity for a range of different corner radii
Unfortunately, the data from Avon only gives corning force for a few discrete loads (75 kg, 150 kg,
225 kg, 300 kg), so a polynomial line of best fit was used to give an expression for the cornering
force at 9° slip in terms of the vertical load. The available cornering force from all four tyres is then
added together to obtain a total cornering force and this is compared to the required cornering
force
¿
mV 2
. This method makes a number of significant assumptions about the tyre behaviour,
R
for example that both rear and front tyres remain at a constant 9° slip, as a result it is likely there
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are inaccuracies within the calculation and a safety factor of 1.2 is used to give a more
conservative estimate of the maximum corning speeds.
Table 6.4.2 Table summarising the forces acing on each tyre as the car goes round a 30 m
radius corner at various speeds.
Velocit
y (m/s)
18
19
20
21
22
Vertical Loads (kN)
F2o
F2i
F1o
F1i
1.0
5
1.1
0
1.1
6
1.2
1
1.2
7
0.4
0
0.3
8
0.3
6
0.3
3
0.3
1
1.6
6
1.7
3
1.8
1
1.9
0
1.9
9
0.5
8
0.5
3
0.4
8
0.4
3
0.3
8
Cornering Forces (kN)
C2
o
1.6
8
1.7
7
1.8
5
1.9
4
2.0
3
C2i
0.4
5
0.4
1
0.3
7
0.3
3
0.3
0
C1
o
2.4
1
2.4
6
2.5
0
2.5
4
2.5
7
Total
Cornerin
g Force
(kN)
Required
Cornerin
g Force
(kN)
Safety
Facto
r
5.31
3.46
1.54
5.32
3.85
1.38
5.32
4.27
1.25
5.31
4.70
1.13
5.30
5.16
1.03
C1i
0.7
7
0.6
8
0.5
9
0.5
0
0.4
1
The table above is an excerpt from a much larger spreadsheet which tests a broader range of
velocities and a selection of corner radii. In this instance, the table shows us that the maximum
speed the car can go round a 30 m radius corner is 20 m/s. Similar analysis was carried out for the
60 m and 65 m corners and the maximum cornering speeds were found to be 31 m/s and 33 m/s
respectively, these values were then used in the overall vehicle simulation.
3.4.6
Tyre Friction Ellipse
The above calculation assumes that the tyre loading is purely lateral, but in reality the car is also
likely to be accelerating or decelerating during the corner and so will also experience some
longitudinal loading. The friction ellipse is a useful way of thinking about the dynamic interaction
with the tyre and the road when there are both lateral and longitudinal forces present. The concept
is based on the assumption that the tire may slide on the ground in any direction if the resultant
force reaches the tyre’s friction limit. In other words, the tyre can develop a maximum cornering
force or a maximum accelerating/ braking force, but it cannot produce both at the same time. The
ellipse below represents a tyre under a 1kN load. The maximum longitudinal force is calculated
using μ = 1.2, and the maximum lateral force is found from the tyre data from Avon.
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Figure 6.4.9 Friction ellipse of 7.2/20.0-13.0 tyre under a 1kN vertical load
The plot illustrates the friction limit of the tyre; the tyre can sustain a 1.2kN pure longitudinal force
(red arrow) and a 1.594 kN pure lateral force (blue arrow). The purple arrow represents the car
accelerating around a right hand corner. In this case the longitudinal force is 0.993 kN and the
lateral force is 0.934 kN (both considerably less than their limits). If the driver is to optimise the
performance of the tyre he must ‘ride the rim of the friction ellipse’ (2) by balancing the brakes,
steering angle and throttle is to keep the tyre’s resultant line of force just within the boundary circle.
6.5
Brakes
The main function of the brakes is to provide adequate balanced braking forces to all four wheels
so the driver can slow the car in a controlled fashion. The formula student regulations (13) also
specify that the brake system must be made up two independent hydraulic circuits with their own
fluid reserves and must be able to lock all four wheels during a specified test. “Brake-by-wire”
systems are also prohibited.
The decision was made to use a disc brake system on all four wheels with the hydraulic circuits
split between the front and rear wheels. This car will also use a braking control system (see
chapter 7), but the mechanical brake system will still be setup for optimum brake balance so that
the control system is active for as small a time as possible
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6.5.1 Brake Discs
The first decision to be made with regard to the brake discs is whether to use solid or vented discs
(see figure 6.5.1). Vented disc brakes are used on many high end sports cars, they are designed to
dissipate heat more efficiently and so provide better braking performance. The obvious
disadvantage of the vented disc is that it has a greater mass, a fact which cannot be ignored
considering that this is an un-sprung mass that also has a rotational moment of inertia. After
researching previous years’ formula student cars and performing some rough calculations it was
decided to use a solid disc since the braking forces on this car are not great enough to justify the
added weight of a ventilated disc. It was also decided that a 9’’ (22.86cm) disc would be used as
this is a common sizing and can fit comfortably within the 13’’ rim.
Figure 6.5.1 Comparison between solid disc and vented disc
The second topic to consider when discussing brake discs is the material. Ideally it should be
strong enough to sustain high compressive and shear loads, have a high coefficient of friction, be
resistant to wear, have a high thermal capacity and a low density. The problem is that many of
these properties are contradictory, for example it is difficult to find a material with a high thermal
capacity and a low density. Commonly used materials include grey cast iron (cast iron that has a
graphite microstructure) and aluminium allow, whilst high end race cars may use more advanced
materials such as carbon ceramics. In their paper ‘Material Selection Method in Design of
Automotive Brake Disc’ (21) M.A. Maleque, S.Dyuti and M.M. Rahman assessed a number of
different materials across a range of physical criteria. Of the materials they tested the winner was
an expensive SiC reinforced Al-Cu alloy, but grey cast iron came in a close second and is
significantly cheaper. As a result grey cast iron discs were chosen, not only are they cheaper than
alternatives, they are far more readily available as the majority of cars use grey cast iron discs.
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Figure 6.5.2 Comparison between, drilled, slotted and drilled and slotted discs
Finally, there are different rotor designs which must be considered, drilled or slotted discs (see
figure 6.5.2). The purpose of both designs is the same, the aim is to allow hot gasses between the
disc and the pad to escape so that the brakes run cooler and stop better. Of the two options the
slotted disc is the better choice, drilling holes in the disc weakens it and drilled discs have a
tendency to develop cracks between the holes. Slotted rotors are also better designed for wet
conditions as they move water away from the rotor more efficiently (22).
6.5.2 Brake Callipers
The role of the brake calliper is to house the brake pads and the pistons. When the driver pushes
the pedal in the cockpit, a pressure is transferred along the brake line via the brake fluid to the
pistons in the calliper; the pistons then compress the brake pads against the disc. There are two
types of brake callipers, floating and fixed callipers. With floating calliper, a bracket is mounted to
the upright but the calliper is free to slide left and right within the bracket. There are only pistons on
the inner side of the disc, as the brakes are applied the force pulls the sliding calliper into position
so that contact is made on both sides of the disc. The advantages of the floating calliper are that it
is usually lighter and more compact than a fixed calliper. A fixed calliper is solidly mounted to the
upright and has pistons on both sides of the disc, depending on their design fixed callipers may
use multiple pistons sorted into pairs. The main advantage of fixed callipers is their superior
braking power and they also provide a better feel through the brake pedal (23). The decision was
made to use dual-piston fixed callipers from Wilwood, the specs are shown in table 6.5.1. Although
these are fixed callipers, they are extremely lightweight as they are specifically designed for
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lightweight race cars, the majority of fixed callipers for sale are designed for much heavier road
going vehicles and so would be unnecessarily robust for this project.
Table 6.5.1
Specifications of Wilwood GP200 Brake Calliper
Piston Bore
31.8mm
Piston Area
7.94cm2
Brake Pad Area (per pad)
14cm2
Mass
0.41kg
Number of pistons
2
6.5.3 Pedal Box
The pedal box is a crucial part of the brake system as it controls the brake balance between the
two hydraulic circuits. As will be explained in the next section, the front wheels require greater
braking forces (and therefore greater line pressure) than the rear wheels. There are two
established ways of varying the brake pressure between the front and rear circuits. The first
involves using different size master cylinders for the front and rear circuits. If the pedal exerts the
same force to each cylinder then the cylinder with the smaller area will result in a higher pressure.
The other method works by using an adjustable bias-bar; this is the bar which connects the end of
the brake pedal to the two cylinders. By varying the angle of the bar the force applied to each
cylinder can be adjusted and so the brake balance can be optimised. For this project both methods
will be used, a bias bar will be initially setup to deliver double the force to the front master cylinder,
and then the cylinder sizes will be selected according to the following calculations. The bias bar
could also be adjusted at a later date to make some more acute adjustments to the brake balance.
The pedal box was purchased from ‘Formula7’ and was selected as it can be made to order with a
range of different master cylinder sizes. The pedal itself acts as a lever arm and gives a
mechanical advantage of 4.4. Taking into account the bias bar, this means the effective mechanical
advantage to the front cylinder is 2.93 and 1.47 to the rear cylinder.
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Figure 6.5.3 Diagram of the pedal box supplied by formula 7 (24)
6.5.4 Braking Force Calculations
As stated in the formula student rules, the brake system must be able to lock all four wheels. This
means that the braking force must be greater must be greater than or equal to the traction limit of
the tyres. As previously stated in section 3.4, the assumed coefficient of friction for the tyres under
braking is μ = 1.2. It is therefore necessary to find an expression for the vertical load on each tyre,
for the purpose of this calculation it has been assumed that the car’s maximum deceleration is
1.2g. Referencing back to figure 6.4.7, the force on the rear axle is F1 the force on the front axle is
F2 and the height of the COM above the road is h. Taking moments about the front axle gives:
( Mg × c ) −( F1 × ( b +c ) )=( M ×1.2 g × h )
Rearranging and performing similar analysis about the rear axle gives expressions for the loads on
the front and rear axles during a 1.4g deceleration.
F1=
Mg
Mg
( c−1.2 h )=0.863 kN F 2=
( b+1.2 h )=2.276 kN
b+ c
b+ c
It is clear that there is a much greater load on the front tyres than the rear tyres when the car is
decelerating. It is crucial that the brakes are balanced to reflect this discrepancy as the car will only
achieve maximum braking at all four tyres reach their friction limit simultaneously. With the load on
each tyre known it is possible to find maximum braking torque generated at each wheel. If the
brakes are to lock-up the wheels, they must be able to produce a torque equal to this value.
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F1
F
× r w =D1 ×r e Front Wheels : 2 × r w =D2 ×r e
2
2
Where D1 is the force acting on the front discs, D2 is the force acting on the front discs, rw is the
radius of the wheel and re is the effective radius of the brake disc. The forces on the discs are due
to friction between the pad and the plate, coefficients of friction vary for different materials but are
usually between 0.35 and 0.42 (25). Taking a worst case estimate of μ = 0.35, it is possible to
calculate the required compressive force from the calliper. Finally the area and number of cylinders
for each calliper is known so it is possible to find the required fluid pressure at the front (P2) and
rear (P1) callipers.
P1=
D1
D2
=2.05 MPa P 2=
=5.43 MPa
2× μ × A
2×μ× A
This pressure must be generated by the master cylinders in the pedal box. It can be assumed that
the driver can press on the brake pedal with approximately 80% of his/her bodyweight, considering
the driver is likely to weigh at least 50kg, it is reasonable that any driver will be able to press the
brake with at least 400N of force. Factoring in the mechanical advantage from the pedal this
means there is an available force of 1173N at the front master cylinder and 587N at the rear
master cylinder. Figure 6.5.4 shows the brake line pressures for the range of different master
cylinders that Formula 7 offer with the pedal box. Looking at the results on the graph a 15.9mm
front cylinder and a 17.9mm rear cylinder were selected.
Brake Linde Pressure vs. Cyliner Bore
9
8
Front Cylinder Pressure
7 Rear Cylinder Pressure
6
Front Pressure Required
5
Brake Line Pressure (MPa)
4
3
Rear Pressure Required
2
1
0
12
15
18
Cylinder Bore (mm)
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Figure 6.5.3 Analysis to find the brake line pressure resulting from a range of different master
cylinders.
6.5.5 Heat Simulation
The following simulation will attempt to find the average disc bulk temperature of one of the front
discs during the endurance test. Fortunately, the Solidworks directory contains a ‘grey cast iron’
material, the two other parameters required to run the simulation are the convective heat transfer
coefficient and heat power applied to the disc during the braking.
The heat
power
applied
Corner
1
Corner
3 to the disc is found by performing an energy balance on the car. During
braking the kinetic energy from the car is converted to thermal energy in the brakes. This study
considers the average heat power applied over one whole lap, which is he total kinetic energy lost
during the three periods of braking, divided by the total lap time. The front of the car experiences
72.5% of the load during braking hence each front disc is supplied with 36.25 % of the total heat
power.
Corner 2
1
2
2
2
2
2
2
M (( V 1 −V 2 ) + ( V 3 −V 4 ) + ( V 5 −V 6 ) ) × 0.3625
2
Average Heat Power Front Disc=
=4.2 kW
t
The coefficient of convective heat transfer is found using the equation for forced convection with
turbulent flow from HLT (26). Where Nu refers to the Nusselt number, Re refers the Reynolds
number and Pr refers to the Prandtl number.
0.8
Nu=0.036 ℜ Pr
hL
k
VLρ
ℜ=
μ
c μ
Pr= p
k
Nu=
1
3
h
L
k
V
ρ
μ
Convective heat transfer coefficient
Characteristic length
Thermal conductivity of air
Air flow velocity
Air density
Dynamic Viscosity of air
cp
Specific heat capacity of air
This formula refers to convection across a flat plate of width ‘L’ with a uniform air flow but a number
of approximations must be made if it is to be applied to this situation. All calculations are made at
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the average lap velocity of 28 m/s. The oncoming air velocity is therefore assumed to be constant
at 28 m/s (in reality the resultant air flow velocity varies across the disc see figure 6.5.4) The
characteristic length for the disc is taken to be ‘D2 – D1’, values for all the other variables are taken
from HLT. The final calculated coefficient is h = 115 W/m2k, although this is a rough calculation, the
final answer is close to figures found during research (27).
Figure 6.5.4 Diagram and plot to show how the resultant flow velocity varies across the disc.
Figure 6.5.5 shows the temperature profile of the disc after a steady state test with the average
heat power applied. The maximum temperature that the disc reaches is 749K or 476°C which falls
within the safe operating limit for cast iron disc brakes (28). This simulation justifies the earlier
decision to use solid discs rather than ventilated discs as overheating is not an issue. A similar
simulation was run on the rear brake discs and in that instance the maximum temperature of the
disc was only 225°C, this may cause problems with the brake balance as cast iron discs typically
perform best in the range of 400°C to 600°C (28). Small adjustments may have to be made on the
bias-bar if this proved to be an issue during testing.
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Figure 6.5.5 Temperature distribution of front brake disc
6.6
Conclusion
Still to be completed
6.7
References
1. Stanniforth, Alan. Competition Car Suspension.
2. Smith, Carrol. Tune to Win.
3. Milliken, D.L. Race Car Vehicle Dynamics.
4. Pat's Column - February. Formula Student Germany. [Online]
https://www.formulastudent.de/academy/pats-corner/advice-details/article/pats-column-february/.
5. Suspension 101. Viking. [Online] http://www.vikingspeedshop.com/suspension-101-cambercaster-and-toe/.
6. SAE Formula Student. Avon Motorsport. [Online] http://www.avonmotorsport.com/resourcecentre/tyre-applications/sae-formula-student.
7. Clarke, Pat. Tyres. Formula Student Germany. [Online]
https://www.formulastudent.de/academy/pats-corner/advice-details/article/tyres/.
8. Tyres. Autozone. [Online]
http://www.procarcare.com/icarumba/resourcecenter/encyclopedia/icar_resourcecenter_encyclope
dia_tires1.asp.
9. All About: Tyres and Wheels. 4Crawler. [Online] http://www.4crawler.com/Diesel/Tires.shtml.
10. Bosch, Robert. Automotive Handbook 2nd Edition.
11. Wong, J.Y. Theory of Ground Vehicles 4th Edition. s.l. : Wiley.
12. Advantages of radial ply tyres over cross ply tyres. Continental. [Online]
http://www.continental.co.za/articles.asp?article=321.
13. FSAE Rules. Formula SAE. [Online] http://www.fsaeonline.com/content/2015-16%20FSAE
%20Rules%20revision%2091714%20kz.pdf.
14. Rubber Friction. Inside Racing Technology. [Online]
http://insideracingtechnology.com/tirebkexerpt1.htm.
15. Tyre-road friction and tyre slip. Tampere University of Technology. [Online]
https://www.tut.fi/ms/muo/tyreschool/moduulit/moduuli_10/hypertext/3/3_1.html.
16. More on Traction for Motorcyclists. [Online] http://www.stevemunden.com/frictiontopics.html.
17. Pave Maintenance. Wikispaces. [Online]
https://pavemaintenance.wikispaces.com/CVEEN+7570-+Spring+2011.
18. Slip Angle. [Online]
http://www.mgf.ultimatemg.com/group2/suspension/chassis_and_handling/slip_angle.htm.
19. Handling. Autozine. [Online]
http://www.autozine.org/technical_school/handling/tech_handling_5.htm#Power-oversteer.
20. Pacejka's Magic Formula. Racer. [Online] http://www.racer.nl/reference/pacejka.htm.
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21. Material Selection Method in Design of Automotive Brake Disc . Maleque, M.A, Dyuti, S and
Rahman, M.M.
22. Cross Drilled vs. Slotted Rotors. Redline 360. [Online]
http://www.redline360.com/garage/brakes-cross-drilled-vs-slotted-rotors-which-is-better.
23. Floating vs Fixed Calipers. Why High End. [Online] http://www.whyhighend.com/floating-vsfixed-calipers.html.
24. Pedal Box - 2 pedals - with master cylinders. Formula Seven. [Online] http://www.formulaseven.com/shop-products/pedal-box-2-pedals-with-brake-master-cylinders/.
25. Brake Lining. Wikipedia. [Online] http://en.wikipedia.org/wiki/Brake_lining.
26. Howatson, Lund and Todd. Engineering Tables and Data. 2009.
27. SolidWorks Education SAE Thermal Distribution. [Online] https://www.youtube.com/watch?
v=tf_WWrHYkSw.
28. Disc Temperatures. AP Racing. [Online] http://www.apracing.com/Info.aspx?
InfoID=36&ProductID=976.
29. Smith, Carroll. Engineer to Win. 1988.
30. Tyre Friction. Inside Racing Technology. [Online]
http://insideracingtechnology.com/tirebkexerpt1.htm.
31. Brakes: Drum vs. Disc. edmunds.com. [Online] http://www.edmunds.com/cartechnology/brakes-drum-vs-disc.html.
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7. Electrical and Control System (Yuntao Zhu)
7.1 Introduction
The electrical and control system plays a crucial role in a formula student racing car even if the car
is equipped with an internal combustion engine. The control system can ensure the optimal
performance of engine and cooling system, also it does make sure the car is under control by the
driver even in harsh conditions. Meanwhile, the engine needs to be started by electrical power,
which can be done by applying a battery system in the car. Therefore, the electrical and control
system is necessary for the formula racing car. The system overview is shown in the figure below,
the system is divided into four subchapters, and the details of each components will be discussed
in those subchapters.
Figure 7.1.1 System Overview
7.2 Engine Control Unit (ECU)
7.2.1 Introduction
An engine control unit (ECU) is a type of electronic control unit that controls a series of actuators
on an internal combustion engine to ensure optimal engine performance. This is done by reading
values from different sensors placed in the engine, comparing the values to the default setting
values in the performance map, then adjusting the engine actuators accordingly.
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7.2.2 ECU
The ECU should fit the engine very well, and it was decided to select an ECU from the
manufacturer. The engine we used is Honda CBR 600rr, it is a 4-cylinder engine and it is using a
Dual Stage Fuel Injection technique.
[1]
In a racing car, at high engine speed, the time for the fuel
injection is very little and only 4 fuel injectors are not enough to satisfy the fuel demand. The Dual
Stage Fuel injection technique can solve this problem by placing a second set of injectors as far
from the intake valve as the length of intake track would permit, and they can inject fuel at higher
rpm to meet the fuel demand.
[2]
Thus, the ECU should be able to control up to 8 injectors with
controls for staged injectors.
Omex710
DTA S80
Link G4+ X
Size (mm)
160*120*40
134*240*46
167*126*42
Weight (g)
400
1130
640
Price (£)
845
915
769
Staged Injection
Yes
Yes
Yes
Cooling Control
Yes
Yes
Yes
Software MAP
Yes
Yes
Yes
In build data
logger
Accessories
(sensors)
Yes
No
Yes
Yes
No
No
Table 7.2.1(1) ECU comparison [3] [4] [5]
The above table shows a comparison of 3 ECUs that were found in the market, they all satisfy the
requirements stated in previous paragraph, and the Omex710 is selected to be the our ECU with
following reasons. It has the smallest size the lightest weight in these three ECUs, and it can
control up to 12 cylinders and up to 12 injectors with controls for staged injectors, which fits the
requirements from the engine. What’s more, the Omex710 is programmable so it can be set to fit
the engine better, and it can provide cooling control for the radiator fan and cooling pump as well.
Last but not the least, the sensors required for the ECU can also be purchased from the same
manufacturer to make sure the sensors are functional to the ECU. [3]
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Figure 7.2.1(1) Omex710 product image [3]
Figure 7.2.1(2) Omex710 function diagram
7.2.3 Control of Air/Fuel ratio
The most important function of ECU is to control the fuel injection to the engine to satisfy the fuel
demand based on the instructions from the driver. The instructions are in the form of electrical
signal coming from different sensors. If the throttle position sensor is showing the throttle pedal is
pressed further down, the mass flow sensor will measure the amount of additional air being sucked
into the engine and the ECU will inject a fixed quantity of fuel into the engine. If the engine coolant
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temperature sensor is showing the engine has not warmed up yet, more fuel will be injected
causing the engine to run slightly ‘rich’ until the engine warms up. [6]
Air-fuel ratio
AFR =
mass of air
mass of fuel
‘Rich’ means the AFR is small, the mass of fuel is much more than the mass of air. If exactly
enough air is provided to completely burn all of the fuel, the ratio is known as stoichiometric
mixture. And for pure octane the stoichiometric mixture ratio is approximately 14.7:1.
λ=
AFR
AFR at stoichiometric
In naturally aspirated engine powered by octane, maximum power is frequently reached at AFRs
ranging from 12.5:1 to 13.3:1 or λ of 0.85 to 0.9. [7] The λ value is monitored by the lambda sensor,
and the ECU maintains the λ to be slightly ‘rich’ for an optimal engine performance but non-optimal
fuel consumption, as shown in the figure below.
Figure 7.2.3(1) Power versus lambda diagram [8]
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7.2.4 Ignition timing control
In a spark ignition internal combustion engine, the engine requires a spark to initiate the
combustion in the combustion chamber. And it is important to calculate the timing of the spark in
advanced since the fuel can not burn the instant spark fires completely. The combustion gases
take a period of time to expand, and the rotational speed of the engine can increase or decrease
the time that an expansion should occur.
[9]
The ECU can adjust the exact timing of the spark to
provide better power and economy, and this is done by reading data from the crankshaft position
sensor and knock sensor, and then calculate the corresponding ignition timing. If the knock sensor
detects a knock, that means the spark occurs too early in the compression stroke, so it will delay
the timing of the spark to prevent this. [6]
7.2.5 Cooling control
The Omex710 can control up to two cooling fans, which is done by monitoring the temperature of
the coolant by the temperature sensor.
[3]
If the temperature goes above a set point, the fan is
turned on, and it is turned back off when the temperature drops below that point. The temperature
can also be controlled by controlling the coolant pump, by changing the speed of the coolant flow
to maintain the optimum temperature.
Figure 7.2.5(1) Cooling Control
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7.2.6 Electronic throttle control (ETC)
The electronic throttle control is an automobile technology which electronically connects the
accelerator pedal (driver) to the throttle (engine), it uses the information from the throttle position
sensor (TPS), accelerator pedal position sensor (APPS), and a variety of other sensors to
determine how to adjust the throttle position.
7.2.6(1) Electronic Throttle Control System [10]
As shown in the figure (1), the ETC is a closed loop control system. The reference signal is the
accelerator pedal position, which indicates where the driver truly wants the throttle to be. The
reference minus the current throttle position to create an error signal, and this error signal indicates
how the throttle position should be changed. The throttle position is changed by controlling the
throttle control motor to open or close the butterfly valve, as shown in the figure (2).
7.2.6(2) Throttle control schematic diagram [11]
7.2.6(3) Toyota ETC schematic diagram [11]
According to the 2015 Formula SAE Rules, at least two separate sensors have to be used as
TPSs, and if an implausibility occurs between the values of the two TPSs, the power to the
electronic throttle must be immediately shut down completely. The implausibility is defined as a
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deviation of more than 10% throttle position between sensors. If a TPS failure occurs, the power to
the electronic throttle must be completely shut down within 50ms. Therefore, the throttle control
technique used by the Toyota is applied in the car to follow the rules. As shown in the figure (3), a
two separate sensor setup is applied to both throttle position detection and accelerator pedal
position detection to improve safety. If the system detects a malfunction, such as the two TPSs are
not matching to each other, or the two APPSs are not matching each other, or the throttle position
being out of range of the correct operation, a fail-safe mode will be immediately employed by the
ECU. The ECU immediately shut down the electronic throttle, and the specific data code will be
stored in the memory of the ECU to help the failure check, and the warning lights in the vehicle
such as check engine light will be illuminated to warn the driver.
Also, in the situation when the car is braking hard, (for example bigger than 0.8g deceleration
without locking the wheels), if the TPSs shows that the throttle is greater than 10% open, the
power to the electronic throttle and fuel pump will be completely shut down by the ECU and this
result in the electronic throttle closing to the idle position.
7.2.7 Sensors
If the ECU can be treated as the ‘brain’ of the control system, then the sensors act as the ‘ears and
eyes’. The sensors convert the physical states of the vehicle into electrical signals, which can be
understood and interpreted by the ECU, and then adjusting the system accordingly. Here, some
crucial sensor mechanisms will be briefly discussed.
7.2.7.1 Position sensor
The position sensor is required for the accelerator pedal position detection and throttle position
detection. Although the structures of accelerator pedal and throttle are different, a potentiometer
that works as voltage divider can be used to measure the position of both accelerator pedal and
throttle. The wiper arm shown in the figure (1) is connected to the accelerator pedal to act as a
APPS and connected to the butterfly valve spindle to act as a TPS. As the butterfly valve opens or
closes, or the rotation of the accelerator pedal, the wiper arm is rotated and causes the output
voltage of the voltage divider changes.
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Figure 7.2.7.1(1) Voltage divider diagram, [10]
Vout=
R2
∗Vref
R 1+ R 2
So the ECU can calculate the relative position of the accelerator pedal and throttle by calculating
the ratio of Vout to Vref.
7.2.7.2 Air mass flow sensor
Figure 7.2.7.2(1) Air mass flow sensor [12]
As shown in the figure (1), a heated wire is suspended in the engine’s air stream, with either a
constant voltage over the wire or a constant current through the wire. When the air flows past the
wire, the wire is cooled. So the resistance of the wire decreases and allowing more current to pass
through the wire. Then the wire is heated up again until it reaches the previous temperature
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(equilibrium). And the air mass flow is proportional to the increased current, and this signal is sent
to the ECU. [12]
7.2.7.3 The Oxygen (lambda) sensor
The lambda sensor can measure the Air to Fuel ratio, so it can be used to monitor whether the
engine is working efficiently and cleanly. The lambda sensor is based on a solid-state
electrochemical fuel cell called the Nernst Cell. Its two electrodes provide an output voltage
corresponding to the quantity of oxygen in the exhaust relative to that in the reference air.
Figure 7.2.7.3(1) The wideband zirconia sensor [13]
7.3 Braking Control System (Stability Control)
The barking control system applied to the car includes three parts: Anti-lock Braking, Traction
Control and Stability program. The purpose of applying these control systems is to make driving
easier, improve the maneuverability of car in corners and harsh conditions (wet condition,
obstacles, etc.).
7.3.1 Electronic Stability Program (ESP)
The main function of ESP is to apply brakes to individual wheels and reduce engine power to
ensure the driver maintains the control of the car if oversteer or understeer occurs.
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Figure 7.3.1(1) Understeer [14]
Figure 7.3.1(2) Understeer with ESP [14]
As shown in the figure (1), the driver is trying to avoid the obstacle and turn the steering wheel at a
high speed. The front wheel does not have enough traction force and slip occurs, so the car is
drifting forward rather than making a turn, and this situation is called understeer. To solve that
problem, two rotational sensors are placed in the car, one for the steering wheel, another one for
the car itself. When the ESP detects that the rotation of the car does not meet the rotation of the
steering wheel, it applies brake force to the one of the rear wheels (depending on the direction that
the driver wants to turn, left rear wheel for turning left and right rear wheel for turning right), as
shown in the figure (2). The brake reduces the forward inertia to stop the drifting so that the car can
turn as driver intended.
Figure 7.3.1(3) Oversteer [14]
Figure 7.3.1(4) Oversteer with ESP [14]
Oversteer normally happens after the understeer. As shown in the figure (3), the driver is trying to
pull the wheels over to keep the car in the left lane after avoiding the obstacle, however the rear of
the car spins out from driver’s intended path. So the ESP applies brake force to the left front wheel
to reduce the torque, as shown in the figure (4).
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7.3.2 Anti-lock Braking System
The anti-lock braking system is a braking control that prevents the wheels from locking up during
braking to avoid uncontrolled skidding, and controls the slip of the wheel precisely around 0.2
during deceleration to achieve maximum braking force. This is done by receiving data from speed
sensor in each wheel and adjusts the braking by sending signal to the hydraulic unit. The ABS
control module constantly monitors the rotational speed of each wheel, if it detects a wheel rotating
significantly slower than the others, it actuates the hydraulic valves to reduce the brake pressure to
that wheel, to stop the locking.
Figure 7.3.2(1) Bosch ABS9 control unit [15] Figure 7.3.2(2) Bosch ESP9 control unit [15]
In the overall simulation (see section 10), the simulation is done with an assumption of ‘skillful
driver threshold braking’, that is the driver can control the brake pedal extremely well to avoid any
slipping, and achieve maximum braking force at the same time. That assumption is achieved by
setting a maximum limit to the braking force to avoid slipping. Without the limitation, slipping occurs
as the wheel speed goes to zero, as shown in the figure (3), the blue colour represent the vehicle
speed and the red colour represent the wheel speed. And the figure (4) shows the slip versus time
plot during the deceleration.
* Note that the slip equation is:
Slip=1−
Wheel angular velocity
Vehicle Speed divided by wheel radius
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Figure 7.3.2(3) Speed versus time plot without ABS Figure 7.3.2(4) Wheel slip versus time plot
without ABS
So slip is 1 means the wheel speed is zero, which means the wheel is locked and the skidding
happens. In the reality, the ABS rapidly applies or releases brake pressure to maintain the braking
force at the threshold braking point, to achieve maximum braking force without slipping. In the
simulation, this is done by controlling the rate of change of brake pressure, as shown in the figure
(5) below.
Figure 7.3.2(5) ABS action simulation
The slip error is the difference between the current wheel slip and the desired slip, and the desired
slip is set to be 0.2 according to the empirical function between slip and friction coefficient, to
maximize the adhesion between the tire and road and minimize the stopping distance with
available friction. Then the error is passed into a Bang-bang controller, which outputs a 1 for a
positive input, and a -1 for a negative input. This tells the ABS whether the wheel requires more
brake force or less brake force. This on/off rate passes through a first-order lag that represents the
delay associated with the hydraulic lines of the braking system, the 5*10^5 is an estimated amount
of brake pressure that the brake can apply or release each time. Then the model integrate the
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filtered rate to yield the actual brake pressure, the upper limit of the integrator is set to be equal to
the maximum brake pressure of our brake system, which is 5.4*10^6. The resulting brake
pressure, multiplied by the piston area and radius with respect to the wheel, is the brake torque
applied to the wheel. Finally the wheel speed is imported into another system to calculate the
current slip. [16]
Figure 7.3.2(6) Overall ABS simulation
The figure (6) shows the overall ABS simulation. The tire torque is the product of friction and tire
radius, and the friction is product of friction coefficient and weight. The experiment shows that the
friction coefficient between tire and road surface is an empirical function of slip, known as mu-slip
curve. During braking, there is no thrust force coming from the engine, so the only force acts on the
car is the friction, which includes air drag and friction force between wheel and road. So the
deceleration of the car can be calculated by friction over mass, and then integrated to get wheel
speed. Then the current slip can be calculated by the wheel speed and car speed, a loop system is
created.
It can be seen from the figure (7) and (8) that the slip varies around 0.2 as expected, the wheel is
not locked during braking and both the time for the deceleration and the stopping distance are
reduced. The 0.2 slip control is the threshold braking technique that all the professional driver are
practicing. The simulation result has proven that the ABS can achieve that precisely, so that the car
equipped with an ABS system can save the driver a lot of trouble during the deceleration and
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ensure the safety. What’s more, the driver normally practices the threshold braking skills on a
normal road condition, so in a different situation such as wet condition or soft road condition, the
coefficients of friction are different in these situations causes the threshold braking skills which
largely based on driver’s experience no longer hold. The ABS, however, can still work precisely in
these conditions since the control is achieved bases on the real-time data and calculations rather
than experience.
Figure 7.3.2(7) speed versus time plot with ABS Figure 7.3.2(8) wheel slip versus time plot
with ABS
It is interesting that, there is a chance that the skilful driver can beat the ABS during deceleration.
As shown in the figure (9), the bump before the activation of ABS indicates the area where a
human can beat the ABS, if the driver is properly threshold braking, properly modulating the brake
pedal force to stop just short of activating the ABS.
Figure 7.3.2(9) Driver versus ABS [17]
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7.3.3 Traction Control System (TCS)
During the acceleration of the car, if one of the wheels is spinning significantly faster than others,
the driver might lose the control of the car due to the unbalance of the speed. With the traction
control system, the control module can sense the unbalance by a speed sensor in each wheel,
then apply brake force to that wheel by sending signals to the hydraulic unit, or even reduce the
power transferred to that wheel.
The traction control system is usually a secondary function of ABS since they have similar principle
of operation, and the Bosch ABS generation 9 includes the traction control. In the overall car
performance simulation, we simulate the action of TCS by limiting the upper saturation values of
the force coming from the drivetrain.
7.4 Battery System
7.4.1 Introduction
Power/W
Current at 14V /A
Ignition
30
2.14
Fuel Injection
70
5.00
Fuel Pump
80
5.71
ECU
30
2.14
Braking Control
30
2.14
Cooling Fan
20
1.43
Cooling Pump
105
7.5
Continuous Power Sum
365
26.07
Brake lights
21
1.5
Engine Starter
3500
250amps*3sec
Table 7.4.1(1) Power estimation [18] [19] [20]
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The above table shows an estimation of the power demand of the car, which includes continuous
power plus intermittent power and the engine starting power, and the equivalent current demand at
the voltage of 14 V. The 14 V is the output voltage of the alternator. The electricity supply in the car
comes from two sources, which are alternator and battery. The battery must be able to supply the
power for the engine initiation and the continuous power demand at low engine speed. And at high
engine speed, the alternator can replace the battery to supply the continuous power demand and
charge the battery.
7.4.2 Battery
There are many types of rechargeable battery in the market, such as lead-acid, lithium-ion,
supercapacitor etc. The lead-acid battery is famous for its high surge currents which can meet the
high current demand from the engine starting, and it is very cheap compared to other two types.
However, it has a low energy-to-weight ratio and a low energy-to-volume ratio, which make the
battery heavy and big. The lithium-ion battery has a very high energy density and a very low rate of
self-discharge, but it is very expensive and volatile, and requires a large battery management
system to protect it.
[21]
The supercapacitor, unlike other rechargeable batteries, can accept and
deliver charge much faster, and tolerate many more charge and discharge cycles (longer battery
life). Therefore the supercapacitor is very popular in electric vehicles or vehicle with kinetic energy
recovery system (KERS). [22]
The main function of the battery in the car is to provide the power for the engine starting, and also
for the continuous power for a short period before the engine is running at a higher than idle rpm.
After that short period the alternator will deliver enough power to the car. Therefore the battery
must be able to discharge current high enough to satisfy the current demand for the engine starting
(normally 250 amps for 3 seconds), and supply the continuous power demand for only a short
period. From these features, the best battery type should be lead-acid battery, which can provide a
high surge current with low cost. Although the low energy-to-weight ratio and low energy-to-volume
ratio make the battery heavy and big, our car does not require too much power from the battery so
a small capacity battery (with smaller size and lighter weight) can satisfy the demand.
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Figure 7.4.2(1) Yuasa NP4-12 lead-acid battery [23]
The battery that is decided to use is Yuasa NP4-12 lead-acid battery with AGM construction type,
which has the nominal voltage of 12 V and a capacity of 4 Amp-Hrs (Ah). It is a lead-acid battery
which can provide high surge currents for starting, and the Deep Cycle feature shows that it can
continuously provide power or a long period of time, also the AGM construction type makes sure
the battery is sealed and increases the energy capacity. The maximum discharge current is 120 A
for 1 second, which is enough for a 4-cylinder engine starting. And the rest of the power, which is
3.79 Ah, can supply the continuous power for 7 minutes, which is definitely enough for the car
before the alternator starts to work. A smaller capacity battery is also considered since the car does
not need that much power, but for a smaller capacity the maximum discharge current becomes
smaller as well, which may not be able to start the engine. The dimension of the battery is
90*70*106 mm, and the weight is about 1.75 Kg, which are both acceptable. [23]
7.4.3 Battery Management
A battery management system (BMS) is an electronic system that can monitor the state of the
battery such as voltage, current, temperature, state of charge etc to prevent it from operating
outside its safe operating area. Since a lead-acid rechargeable battery used, it is necessary to
apply a BMS to prevent the hazardous such as over-heating or over-current in both charging and
discharging, to improve the safety and battery life.
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Figure 7.4.3(1) Battery management system LTC1325 [24]
The final battery management system is a microprocessor-controlled system, LTC1325. It can
measure battery voltage, battery temperature and ambient temperature with internal 10-bit ADC,
and it can provide battery voltage, temperature and charge time fault protection. It also has a builtin voltage regulator for charging if required.
[24]
More importantly, unlike electric car, an internal
combustion engine car does not need too much power from the battery, it is not necessary to build
a huge battery management system to protect the battery. Therefore the microprocessor-controlled
battery management system can provide enough protection, and it is small and light and cheap.
7.4.4 Engine Starting
Figure 7.4.4(1) Engine starting circuit diagram
To start the engine safely, a relay is used to control the starter motor, as shown in the figure about.
The signal port of the relay is controlled by two switches, the starter switch is closed if the driver
starts the car by a key (the push starting is prohibited by the rules), and the brake switch is closed
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if the brake pedal is pressed. This design makes sure the car will not move accidently once the
engine is started.
7.4.5 Alternator
The alternator must be able to provide the continuous power and charge the battery when the
engine RPM is high, and alternator should be as light and small as possible. In order to charge the
battery, the voltage output from alternator should be higher than the nominal voltage of battery.
Therefore 14 V is chose as the voltage output of the alternator, and the continuous current demand
will be 28 A. What’s more, the engine speed is expected to reach 11,500 RPM, so the alternator
must be able to work up to 11,500 RPM.
The alternator in our car is Iskra AAG 35A, as shown in the figure (1). It is a small alternator
designed for stationary engine, with built-in cooling system, regulator and rectifier. As shown in the
figure (2), the alternator starts to work when the engine speed reaches above 1150 RPM, and the
output power can satisfy the car demand when the engine speed reaches about 4000 RPM.
[24]
The engine is expected to reach 4000 RPM in about 1 second after starting, and reach 11,500
RPM in 3 seconds. What’s more, with the continuously variable transmission (CVT), the engine
can run constantly at 11,500 RPM, so ideally the alternator can replace the battery soon after the
engine starting.
Figure 7.4.5(1) Iskra AAG 35A [25]
Figure 7.4.5(2) I-RPM characteristic [25]
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7.4.6 Shutdown system
According to the 2015 Formula SAE Rules
[26]
, every internal combustion engine vehicle must be
equipped with a shutdown system, which includes at least two master switches and one brakeover-travel –switch.
The master switches are used to disable power to all electrical circuits, include battery, alternator,
lights, fuel pump, ignition and electrical controls. The primary master switch must be located on the
driver’s right side of the vehicle, at shoulder height and be easily actuated from outside the car.
The cockpit-mounted (secondary) master switch must be located to provide easy actuation by the
driver in an emergency or panic situation, and it has to be a push/pull emergency switch with a
diameter of 24 mm
The brake over-travel switch is wired in series with the shutdown buttons to prevent the event of
brake system failure such that the brake pedal over travels it will result in the shutdown system
being activated.
.
Figure 7.4.6(1) Primary master switch [26]
Figure 7.4.6(2) Cockpit-mounted master switch [26]
Figure 7.4.6(3) Brake over-travel switch [26]
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7.4.7 Brake Light
According to the 2015 Formula SAE Rules
[26]
, the car must be equipped with a red brake light. The
brake light itself has to have a black background and a rectangular, triangular or near round shape
with a minimum shining surface of at least 15 cm^2. If a single line of LEDs is used, the minimum
length is 150 mm. Therefore the brake light I used is a 12 V LED brake light with a dimension of
16*6*8.5 cm (L*W*H), and it is also approved by the E-market (E4). [27]
Figure 7.4.7(1) Brake light [26]
7.4.8 Overall system circuit diagram
The overall system circuit design is shown in the figure (1) below. The supply voltage is designed
to be 14 V, which is the output voltage of the alternator, and both alternator and battery are the
power source and connected to the 14 V supply line directly. All the electronic devices are selected
to be able to work within a certain voltage range rather than a fixed voltage, therefore even though
the nominal voltage of the battery is 12 V, it is feasible to supply the whole system. The battery is
deactivated from the circuit by the battery management system when the alternator output current
is higher than system demand, and turned into charging mode. The charging mode is terminated
when the battery is fully charged or the alternator failed to satisfy the system demand. Although it is
not clearly drawn in the circuit diagram, all the sensors, cooling fan and pump, fuel pump etc are
connected to the 14 V supply line as well.
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Figure 7.4.8(1) Overall system circuit diagram
7.5 Conclusion
Name
Price (£)
Size (mm)
Weight (kg)
ECU
875
160*120*40
0.4
Braking Control
~900
2200 cm^3
2.7
Alternator
100
3.5
Battery
14
108*123
(diameter*L)
90*70*106
1.75
Battery
Management
Sensors + Wiring
7
Not available
Not available
300
Not available
Not available
Table 7.4.9(1) Overall system cost & weight & size [3] [15] [23] [24] [25]
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A breakdown of the weight, price and size of the whole electrical and control system is shown in
the table above. Although the cost of the electrical and control system is less than one tenth of the
budget, and the size and weight are nearly negligible compared to other parts of the car, it can be
seen from the report that how important the system is to the car. The engine cannot run without the
ECU, most parts of the car cannot start to work without the battery system, and the control system
improve the safety and drivability. To ensure the enough power supply and to prove the necessity
of the control system, several researches and matlab simulations are done during the project.
Every selection of devices, calculations and simulations are done carefully to prove the necessity
of each device being in the system and make sure the system can satisfy the car demand, and will
not bring burden to the car.
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7.6 Reference
[1] http://en.wikipedia.org/wiki/Honda_CBR600RR
[2] http://www.honda.com/newsandviews/article.aspx?id=1775-en
[3] http://omextechnology.co.uk/page8.html
[4] http://www.dtafast.co.uk/S_80_PRO.htm
[5] http://www.linkecu.com/products/engine-management-ecus/g4plus-xtreme
[6] http://en.wikipedia.org/wiki/Engine_control_unit
[7] http://en.wikipedia.org/wiki/Air%E2%80%93fuel_ratio
[8] http://en.wikipedia.org/wiki/Air%E2%80%93fuel_ratio#/media/File:Ideal-stoichiometry.jpg
[9] http://en.wikipedia.org/wiki/Ignition_timing
[10] http://jalopnik.com/how-electronic-throttle-control-works-499966101
[11] https://youtu.be/6bvH9Sv7GkQ
[12]
[13] https://www.youtube.com/watch?v=f-W3FFegUnY
[14] http://en.wikipedia.org/wiki/Oxygen_sensor
[15] https://www.youtube.com/watch?v=L1qt84c2KN0
[16] http://www.bosch-mobilitysolutions.cz/media/db_application/downloads/pdf/safety_1/en_4/abs_esp_generation9_de.pdf
[17] http://uk.mathworks.com/help/simulink/examples/modeling-an-anti-lock-braking-system.html?
refresh=true
[18] http://farnorthracing.com/autocross_secrets9.html
[19] Tom Denton, Automobile Electrical and Electronics Systems,4th edition in 2012,
p205
[20] http://physics.stackexchange.com/questions/57794/calculating-engine-starter-s-energy-use
[21] http://www.daviescraig.com.au/Electric_Water_PumpsEWP80__12V__ELECTRIC_WATER_PUMP___PART_No__8005-details.aspx
[22] http://en.wikipedia.org/wiki/Battery_%28electricity%29
[23] http://en.wikipedia.org/wiki/Supercapacitor
[24] http://www.yuasaeurope.com/images/uploads/uk/downloads/datasheets/NP/NP4-12_UK.pdf
[25] http://cds.linear.com/docs/en/datasheet/lt1325.pdf
[26] http://www.iskra-agv.cz/us/pdf/alternators_aag.pdf
[27] 2015 Formula SAE Rules
[28] http://eu.banggood.com/Wholesale-Warehouse-Universal-12V-LED-Motorcycle-Tail-BrakeLight-License-Plate-Lamp-wp-Uk-942337.html?
currency=GBP&refreshTmp=1&utm_source=google&utm_medium=shopping&utm_content=sa
ul&utm_campaign=motorukw&gclid=CjwKEAjwo5OpBRDU64qO07OXq00SJADn5hYnLljIUNI2y1jZdyiA8ECOKj83APO
Auo0TRFXoulj17RoCvHrw_wcB#
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8. Drivetrain
8.1. Introduction
The role of the drivetrain is to transfer power from the engine to the wheels. The drivetrain should
aim to be as efficient as possible in itself whilst also not restricting the power or efficiency available
from the engine. Throughout this section the ‘efficiency’ is taken to mean only the efficiency of
transferring power through a drivetrain component and does not account for how the drivetrain will
dictate the engine’s efficiency, which is dealt with separately in the gearbox comparison. The
complete drivetrain is shown in Figure 8.1 (the rear wheel hubs will be attached to the outer CV
joints). This chapter will explain why each type of drivetrain component was chosen over other
options, and how each drive ratio was calculated.
Figure 8.1. Complete
Transmission Configuration
8.2. Gearbox
8.2.1 Gearbox Comparison
Specifying the gearbox was
carried
out at an early stage in the
project
as its attributes strongly affect
other
parts of the car. The internal
combustion engine has a peak power point and a good gearbox should allow the engine to operate
close to this point throughout the events, whilst not being too inefficient or heavy itself. Most
Formula Student teams choose either an Epicyclic Gearbox or a Continuously Variable
Transmission (CVT). Both these options were considered as well as a Helical Sliding gearbox, as
found in most road cars.
The three types of the gearbox were compared based on the following five parameters: mechanical
efficiency, the ability of the gearbox to allow the engine to operate close to its peak power and
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efficiency, gear change speed, mass and cost. These parameters were weighted (allocated
weights are shown in brackets) and the gearbox types ranked in Table 8.1. The purpose of this
table was to offer an initial basis for comparison.
Mechanical
Efficiency (3)
Optimal
Engine
Speed (3)
Gear
Change
Speed (2)
Mass (2)
Cost (1)
WEIGHTED
TOTAL
CVT
3
5
5
3
3
43
Helical
Sliding
5
3
2
3
5
39
Epicyclic
5
2
4
4
3
40
Table 8.1. Gearbox comparison table
Since the outcome of the gearbox comparison table is not conclusive, the simulation was used to
compare the acceleration of the less efficient CVT with a more efficient four speed gearbox. Helical
Sliding and Epicyclic gearboxes were considered similar in contrast to the CVT, so the four speed
gearbox simulation is used to represent both Helical Sliding and Epicyclic. From Figure 8.2 it can
be seen that the CVT offers a generally better acceleration than the more efficient helical gearbox,
by virtue of the engine operating at peak power continuously. Performance of the. The time
required for the four speed gearbox to change gear was not accounted for here and would only
favour the CVT further. The CVT is likely to require higher maintenance and not last as long as a
helical geared gearbox but neither of these factors were considered to be important for Formula
Student as the car will not be used often and there will be ample time for maintenance. Worth
bearing in mind also is Section T8.4.1 of the FSAE rules, which requires CVTs to have a scatter
guard (see Section 8.2.4) as their moving parts are not necessarily contained otherwise. The
minimal extra mass and cost this would entail was not considered significant enough to alter this
comparison. Therefore a CVT was shown to be the best choice of the three gearbox types
considered.
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Figure 8.2. CVT and fixed speed gearbox acceleration comparison
8.2.2 CVT Comparison
There are various CVT technologies that could be used, by far the most common is that invented
by Van Doorne and known as a Variomatic CVT (Figure 8.3) which consists of a belt running
between two double cone pulleys. The pulleys (also known as clutches) are each made from two
cones and by varying the separation of the cones the diameter in contact with the belt can be
altered. This allows for the ratio created between the pulleys to be varied continuously. The
separation is controlled by springs and masses which exploit the change in centripetal force (as the
car accelerates) to shift the clutch cones. This project will not touch further on the mechanics of
how a Van Doorne CVT is controlled but Section 9.3.3 describes how the CVT was simulated and
how it is possible to tune the CVT for optimal lap times. A toroidal CVT was also investigated but
was not considered viable to purchase due to poor variety and availability outside of the passenger
car and truck markets, which are not as mass sensitive as in motorsport. Designing one’s own CVT
was not considered worthwhile, especially when there are adequate belt drive CVTs available at
low cost.
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Figure 8.3. Example of a Variomatic CVT in a low gear and in a high gear[1]
8.2.3 CVT Selection
There are two specifications of the CVT which must be met: maximum power handling capability
and maximum rotational speed (this is especially important given that the engine chosen is capable
of reaching 14000 rpm). Additionally, it is desirable that the CVT is lightweight and has a large ratio
range so that the engine can be operating near peak power for as long as possible. A significant
problem faced when selecting a CVT was the lack of suitable options on the market; CVTs for the
passenger vehicle market are too heavy and those designed for lighter vehicles, such as go karts,
do not have the power capacity necessary for Formula Student. These were still considered on the
basis that two or more could be used in parallel. However when investigating the specifications of
three CVTs, it was clear that using more than one would be too heavy [2] [3] [4] (see Figure 8.4). The
only CVTs identified with sufficient power handling (and not designed for heavier passenger
vehicles) were those made by TEAM Industries. The company offers designs suitable for 11 hp to
160 hp applications and supplies the input and output clutches separately, allowing for a selection
suited to individual needs. An input and output clutch were selected based on the aforementioned
criteria, see Table 8.2 for the individual specifications. The appropriate belt to use with these
clutches is part #29C3596 manufactured by Gates. This set up will offer a generous ratio range of
0.71–6.3:1, allowing the engine to operate at peak power at speeds between 4.5 m/s and 40m/s.
Since the car’s speed will be above 4.5 m/s for all but the very start of any of the events, this
allows for reasonable approximations to be made in the simulation as to how the car will be driven
at very low speeds (see Section 9.3.4).
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CVT comparison of power handling against mass
9
8
7
6
5
Mass (kg) 4
3
2
1
0
0
20
40
60
80
100
120
Max Power (hp)
Figure 8.4. Comparison of how CVT mass varies with power handling capability[2] [3] [4]
Table 8.2. Chosen CVT Specifications
Part
Description
Max Speed
Max Power
Mass
TEAM TP-185-F[4]
Primary Clutch
11000 rpm
100 hp
3.0kg
TEAM TS-241-R[4]
Secondary Clutch
8000 rpm
100 hp
5.0kg
Gates #29C3596[5]
CVT Belt
(sufficient)
>100 hp
0.5kg
Self manufactured
CVT Guard
n/a
n/a
3.0kg
8.2.4 CVT Guard
As per section T8.4.1 of the FSAE rules, belts must be covered by a
scatter shield in case of failure. This can be easily manufactured
although must be made from 3.0 mm Aluminium Alloy 6061-T6
according to section T8.4.3 of the FSAE rules. The mass of this part is
3.0kg when manufactured according to the design show in Figure 8.5.
Figure 8.5 CVT guard designed in SolidWorks
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8.3. Differential
8.3.1 Necessity and dual CVTs
Some means is required to allow the two driven wheels of the car to rotate at different speeds
when cornering. A differential allows for this but, although the usual choice, is not the only way to
accomplish different wheel speeds. It would also be possible to use two CVTs (one per drive
wheel) to adjust the drive ratio accordingly for each wheel. This is not a common practice although
is achievable and a patent[6] exists for a ‘continuously variable differential’ which is essentially two
CVTs in one differential like unit. This set up would allow for torque vectoring by means of
controlling the two CVT ratios, however designing this controller would require a large amount of
time and then need to be tested thoroughly in the real world to verify it’s usability, hence it was not
considered viable for this design project and so a differential will be used. Two CVTs would also be
heavier than a single CVT with a differential (see Figure 8.4 and Table 8.3).
8.3.2 Differential type comparison
There are three main types of differential: open differentials, limited slip differentials (LSD) and
locking differentials. An open differential will allow the two driven wheels to rotate at different
speeds and will apply equal torque to both wheels, but this torque is limited by the wheel with the
least traction. Thus when the weight is shifted away from the inside wheel in a corner, the outside
wheel cannot receive any more torque than can be transmitted to the inside wheel without it losing
traction. A locking differential will offer the same behaviour as the open differential but can be
‘locked’. When locked both wheels are forced to rotate at the same speed, the torque is now
limited by each wheel’s individual grip. A locking differential is not considered suitable for a formula
student car as when locked the car’s cornering capabilities will be immensely inhibited. The limited
slip differential provides somewhat of a middle ground; it partially locks up when there is a
significant difference in rotational speeds of the two drive wheels (for example when one wheel
loses traction and spins). In order to allow the car to make maximum use of the available grip when
accelerating out of corners or even maintaining a constant speed on the faster corners, a limited
slip differential will be necessary. The performance gain over an open differential is likely to be
substantial, and given the low-medium price of limited slip differentials, an open differential was not
considered any further.
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8.3.3 Limited Slip Differential Selection
Table 8.3. Limited Slip Differential specifications and characteristics
Manufacturer
Cost (£)
Mass (kg)
Characteristics
Drexler[7]
1300
2.7
Abrupt lock up, made specifically for Formula Student
Torsen[8]
350
3.9
Abrupt lock up, made specifically for Formula Student
Quaife[9]
1100
6.0
Progressive lock up, made specifically for Formula Student
Westgarage[10]
600
12.5
Progressive lock up, recycled from a much heavier car
There are three commonly used and widely available limited slip differentials (LSD) built
specifically for Formula Student cars: Drexler, Torsen and Quaife. A fourth option from Westgarage
Engineering Services was also investigated; their differential uses the viscous coupling recycled
from a Ford Sierra LSD [10]. There are various different methods by which LSDs operate (eg. clutch
pack, viscous coupling) and this affect how the car handles. The behaviour can be generalised into
those which lockup completely when a certain torque bias is reached (the Drexler and Torsen
behave like this, both with a bias of 2.6:1) and those which progressively transfer more torque to
the wheel with more grip (the Quaife and the Westgarage differentials behave like this). The
decision between these two characteristics, one being easier to drive with, was considered more
important than that of mass and cost. Without being able to test any of these differentials and due
to the limited previous motorsport experience of the team, it was decided to follow what the vast
majority of Formula Student teams choose, which is the abruptly locking Drexler or Torsen
differentials. The choice between the Drexler and the Torsen is purely one of cost against mass.
The Drexler was chosen in the knowledge that the Torsen could be specified instead, at a later
date, if financial constraints required so. The drive ratio of the Drexler is 3.167:1.
8.4. Chain Drives
8.4.1. Chain drive, belt drive and driveshaft
A chain drive would be the usual choice but it is worth mentioning why a belt drive or driveshaft
would not be suitable. Comparative details are outlined in Table 8.4. Although there are rules about
how much noise the car can make, the noise of a chain drive is expected to be far less than that of
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the engine at wide open throttle. Thus the more efficient chain drive makes a good choice,
especially as most of the differentials considered in section 8.3 are offered with a sprocket for
chain drives only. Whilst a driveshaft would perform well it would not fit the geometry of the car,
given that the engine and CVT will be mounted with the crankshaft and CVT clutch axes of rotation
across the car, and again the purpose made Formula Student differentials tend to be provided only
for use with chain drives.
Table 8.4. Comparison between Chain Drives, Belt Drives and Driveshafts
Advantages
Disadvantages
Chain Drive
Efficiency, reliability, availability, sprockets
available on most differentials (most
Formula Student teams use chain drives).
Noisy
Belt Drive
Quiet
Less efficient than chain (~35%)[11]
Driveshaft
Quiet, efficient
Incorrect geometry for this car
8.4.2 Ratio calculation
The engine produces its peak power at 11500 rpm (See Chapter 2.) which is equivalent to 191.67
rev/s. A power balance equation indicates a top speed of over 40 m/s should be possible at peak
power so the necessary chain ratio was calculated so that the CVT is at the top of its range at 40
m/s (any higher and its range would be wasted, limiting the lowest speed at which the car can run
at peak power).
speed =
ω engine
× d wheel × π
r chain ×r CVT ×r diff
(8.1)
Which gives rise to:
cha∈¿=
191.67
× 0.521 π =3.488
40 ×0.71 ×3.167
r¿
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As shown in Figure 8.1 it is necessary to use two chain drives. This first is necessary to reduce the
rotational speed from the engine (maximum 14000 rpm) to below the maximum speed of the CVT’s
primary clutch (11000 rpm) and the second is necessary practically for transmitting power from the
CVT to the differential (See section 8.4.1 and Figure 8.1). So long as the ratio of the primary chain
drive is sufficient to achieve the first of these two constraints, then the ratio
r chain =3.488 can be
split between the two chain drives. To decide how to divide the ratio between the two drives,
consider that it would be desirable to have as little rotational moment of inertia as possible in the
drivetrain. Since the input side of the CVT will only undergo significant acceleration at the very start
of an event, but the output side following every corner, focus should be on making the reduction in
rotational velocity as early as possible in the drivetrain. Therefore it was decided to make the
primary chain ratio significantly higher than the secondary chain ratio. The secondary ratio could
be less than unity but it was decided on a basis of simplicity and ease of sprocket selection to
specify
primary cha∈¿=3.5
r¿
and
r secondary chain =1 .
8.4.3 Chain and sprocket selection
The chain and sprocket must be strong enough to cope with the torque
and speed and it is also desirable for them to be as light as possible.
AFAM offers a wide range of chains and sprockets. Their 520XSR-G
chain suits this application perfectly, being a narrow, lightweight chain
made from steel alloy and built for motorbike racing.
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Figure 8.6 AFAM
XSR series [12]
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Sprockets are usually made of either steel or aluminium, with steel
lasting longer and aluminium being lighter. So for the short,
performance based events in Formula Student an aluminium
sprocket will be more suitable. AFAM offer a range of sprockets
made from surface hardened aluminium 7075 which are designed
Figure 8.7. AFAM Alu
Racing series sprocket [12]
for motorsport. The number of teeth required of each sprocket to
achieve the desired ratios are shown in Table 8.5. It should be noted
that the driven sprocket on the secondary drive must be of sufficient diameter to fit over the half
shafts and onto the differential, else it could be specified to be smaller and lighter.
Table 8.5. Sprocket teeth specification
Primary Chain Drive
Secondary Chain Drive
Driving Sprocket Teeth
10
20
Driven Sprocket Teeth
35
20
Ratio
1:3.5
1:1
8.5. Half Shafts and Constant Velocity Joints
8.5.1. Half shaft material selection
The half shafts, which transmit power from the differential to the wheel hubs (see Figure
8.1) are subject to high, varying stress due to their mechanical proximity to the wheels and
brakes. For this reason it is important that they are manufactured from an appropriate
material. The half shafts must be able to withstand the maximum torque during
acceleration, but also sudden shock loads from driving, for example when a wheel regains
traction after slipping. It is desirable under these conditions to be able to undergo
significant twisting without failing, to allow enough time and movement for the cause of the
shock load to subside. A material with a high ratio of ultimate tensile strength (UTS) to
Young’s Modulus will perform well in this respect, although a very low Young’s Modulus
would allow a lot of twisting. Table 8.6 shows some materials including some commonly
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used for racing half shafts (Steels 4340, 300M and titanium) (28). Steel 300M and titanium
both offer similar UTS to Young’s Modulus ratios. The density of steel is approximately
twice that of titanium, and thus the ratio of both yield strength and UTS to mass is also
similar for both Steel 300M and titanium. These ratios represent roughly how heavy the
half shaft would have to be in order to achieve sufficient strength and resistance to yield.
Since steel 300M and titanium would both offer similar performance, steel 300M was
chosen as it would result in a narrower and easier to package shaft. It is recommended
[13]
to heat treat the half shaft to Rockwell C42/44 standard, and the surface should be shot
peened to Pratt and Whitney axel specification
[13]
to help resist failure due to surface
microcracks, thus increasing the fatigue life of the part. This is achieved during the shot
peening process by introducing residual compressive stresses into the surface of the steel.
Table 8.6. Half shaft material properties [13]
Material
Yield Strength (MPa)
Ultimate Tensile
Strength (MPA)
Young’s Modulus
(MPa)
Steel (SAE 10120CD)
240
565
210
Steel 4130
400
938
210
Steel 4340
470
1434
210
Steel 300M
1586
1862
210
Titanium
880
950
114
8.5.2. Half shaft sizing
The relationship between mass and radius of a half shaft is of the second order, whereas the
torque it can carry is a third order relationship with mass. Therefore a hollow shaft gives more
benefit in mass saving than it does harm in reducing strength, and a wider shaft will have a higher
torque to mass ratio. But, a wider shaft will be physically larger and more difficult to package
around the car’s suspension and brakes. So that the half shafts are easy to package into the car,
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the outer radius was specified to be 10 mm and the inner radius was then calculated in order to
provide sufficient strength. In order to protect against shock loads, but also to ensure that the half
shaft would fail before the CV joint (which can in some circumstances cause the car to swerve
upon failing, particularly with a limited slip differential) it was decided that there should be a safety
factor of 3.5 (CV Joint is 3.75, see Section 8.5.3) against exceeding the UTS, and a safety factor of
2 against yield. For 300M steel this means the shear stress should not exceed 307 MPa according
to the Von Mises yield criterion (8.3). Then the inner radius of the hollow shaft, r, is the last variable
in equation (8.4) where R is the outer radius and T is the torque under maximum steady state
acceleration in a straight line (which is calculated to be 400 Nm, by dividing the maximum driving
force between the two wheels). The inner radius is then calculated to be 6.43 mm or less,
according to equation (8.5). Thus the specification for the half shafts is outer radius 10 mm and
inner radius 6.4 mm.
τ max =
σY
1
×
safety
factor
3
√
2 ×T R4 −r 4
=
π × σY
R
√
r= 4 R 4−
2× R× T
π × σY
(8.3)
(8.4)
(8.5)
8.5.3 CV Joints
Constant velocity joints are necessary to transfer power over a varying angle between the
differential and the half shafts, and the half shafts and the wheel hub. This angle varies as the car’s
suspension travels up and down. An appropriate CV joint manufactured by GKN Motorsport is
available from UK company Trident Racing Supplies specifically for Formula student. These CV
Joints have a capacity of 1500 Nm [14] which provides a 3.75 factor of safety against failure, slightly
greater than that of the half shafts.
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8.6 Conclusion
The drivetrain has been specified to an extent from which the car’s performance can be simulated
to a reasonable level of accuracy. The simulation (see Chapter 9) has shown the car to be able to
compete with the top end of previous competition results and thus the drivetrain is capable of
offering a good level of performance. Furthermore the car has been shown to be adequately
efficient (see Section 2.4.11). Efficiency, being worth 100 points, was given a lower priority than
performance (worth 575 points) in the design. If one wanted to maximise efficiency then they may
wish to consider a helical geared gearbox instead the less efficient CVT, especially given that the
Brake Specific Fuel Consumption graph of the engine ended up being flatter than first thought
(thus reducing the advantage of the CVT being able to operate at peak engine efficiency) (see
Section 2.4.11). However, if this project were to be continued, and given that there is ample
available money (see Section 10.4), then resources could be allocated to the design of a high
speed CVT incorporating a limited slip differential. This would allow the removal of both chain
drives, thus improving efficiency by approximately 4% (see section 9.6.2 for details and references
to chain drive efficiency). The drivetrain design has been presented so that someone wishing to
build the car would easily be able to acquire the major parts necessary, with only the fixings and
mounts requiring further design work (although due care has been taken to ensure the chosen
parts will work and fit together easily). If this project were to be extended then designing the
mounts for each of the drivetrain components to the chassis would be conducted as the next step.
There is some slack in the finance required for the drivetrain, most notably in the differential
selection, where multiple viable (and interchangeable) options have been presented at different
costs and these present some flexibility for costs of any future developments.
8.7 References
[1] http://auto.howstuffworks.com/cvt.htm
[2] http://www.amazon.com/Comet-Industries-Torque-Converter-Kit/dp/B004GHB7PA/ref=sr_1_3?
ie=UTF8&qid=1430685467&sr=8-3&keywords=torq+a+verter
[3] https://www.gokartsupply.com/4044seri.htm
[4] http://www.team-ind.com/index.php/products/cvt/
[5] http://www.amazon.com/Gates-G-Force-29C3596-GrizzlyYFM550/dp/B00JDN4D76/ref=sr_1_2?ie=UTF8&qid=1430685803&sr=8-2&keywords=gates+
%2329c3596
[6] Patent no. US4963122A
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[7] http://www.drexler-motorsport.com.au/Submenus/products/FormulaSAE.html
[8] http://torsen.info/fsae/fsaefaq.htm
[9] http://www.quaifeamerica.com/downloads/Quaife-Catalogue2014.pdf
[10] http://www.westgarage.co.uk/downloads/brochure1.pdf
[11] www.friction-facts.com/media/wysiwyg/Gates_Carbon_Belt_Drive_rev.pdf
[12] www.afam.com/images/downloads/catalogue/afam_cat_2014.pdf
[13] Engineer To Win, 1984, Carroll Smith
[14] http://www.tridentracing.co.uk/racing-supplies/index.asp?page=gkn-driveline-cv-joints-100
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9. Simulation
9.1. Introduction
As this is a design only project, the simulation serves a particularly important purpose in
allowing for testing and comparisons to be made throughout the development process,
and indicating how the car’s performance through the different events will be affected. The
core components of the simulation were developed at an early stage in the project so that
it could be used by the whole team to simulate the impact their work was having on the
car, and how sensitive its performance was to different changes such as mass, power and
frontal area. Decisions had to be made about what was and wasn’t worth simulating, and
how close to reality components of the simulations ought to be given the resources (most
notably time) available. Figure 9.1 shows the core of the dynamic simulation; the resultant
force on the car is calculated and then used to find the acceleration which is integrated
twice (not shown) to find velocity and position. Each of the contributing forces is handled
by its own subsystem simulation. The simulation is capable of outputting any parameter
that has been modelled, including velocity, throttle position, traction and gear ratio. Outputs
were in the form of graph plots against time or position, which give valuable information as
to how the car is behaving at various points around the track. The simulation also served
as a platform for developing the Anti-Lock Braking system (See Chapter 7).
Figure 9.1. Elements used to calculate resultant force on the car
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9.2. Software
When choosing which piece of software to create the simulation in, three options were
considered: MATLAB, both Simulink and MATLAB, and Visual Studio using C++. The
MATLAB language is significantly more familiar to the majority of team members than C++,
and Simulink’s visual representation of the simulation is recognisable and easy to work
with, whilst being more than adequate for the level of simulation required. For these
reasons it was decided to create the simulation using Simulink (a MATLAB package) and a
short MATLAB script for storing the car’s parameters and making plots of the results.
9.3. Driving Force Simulation
9.3.1. Overview
The driving force represents the tractive force produced as a result of the torque in the half shafts,
which is ultimately produced by the engine. Figure 9.2 shows an overview of how the simulation
arrives at a driving force from the engine and what information is required to make these
calculations and, in the case of the driver, decisions, which is dealt with separately in section 9.4.
Figure 9.2. Simulation flow leading to driving force
9.3.2. Drivetrain
The drivetrain is the subsystem which outputs the driving force seen in Figure 9.1, and takes
velocity and engine output as its inputs. The drivetrain subsystem is also used to calculate the
engine speed (working back from the car’s velocity) to avoid having to model the engine as its own
dynamic system. Figure 9.3 shows how the drivetrain takes the engine torque and multiplies it by
the ratio for each drivetrain component (the triangles represent gains) with the CVT being another
subsytem. The drivetrain simulation is not concerned with the velocity of its components as it was
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not considered necessary to model the state of the drivetrain (other than the CVT ratio), although
the rotational moment of inertia has been taken into account (See Section 9.7).
Figure 9.3. Torque flow through Drivetrain subsystem
9.3.3. CVT
Van Doorne style CVTs usually operate on principles of centrifugal action to alter the effective
diameter of the two clutches and hence the gear ratio. The rate at which the gear ratio changes
with velocity can be altered by changing the clutch masses. For the purpose of the simulation a
value for clutch mass m was used as a gain from velocity to gear ratio (see Figure 9.4). It should
be noted that this is not a real value of mass, but merely a gain which demonstrates the effect of
the clutch mass; there exists a real mass value which would result in optimal performance but this
project did not go beyond proving its existence (see Figure 9.5). Thus, the units of the simulation’s
m are s/m and not kg. The gear ratio must be saturated between the limits of the chosen CVT
(section 8.2.3). The ratio is then used to multiply the torque through the gearbox as well as
calculate the engine RPM which is necessary for the engine simulation. This CVT simulation yields
a good representation of how the drivetrain would behave, although it could be developed to
incorporate the dynamics of how the CVT is actually controlled, if further accuracy were required.
Figure 9.4. CVT simulation subsystem
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Figure 9.5. Lap time sensitivity to CVT clutch mass
Lap
time (s)
m (CVT clutch mass) (s/m)
9.3.4. Engine and Clutch
The Simulink model uses the engine data from Chapter 2 and therefore all is required here
is to look up the available torque at a given RPM from a lookup table (data shown in Figure
9.7), and multiply that by the demand from the driver as in Figure 9.6. It can be seen in
Figure 9.7 that the torque below 4000 rpm is both constant and does not match that from
Chapter 2. This constant 30 Nm torque acts as an approximation for the conditions of
either a slipping clutch or slipping rear wheels. Actually simulating these conditions was
considered a complicated task not worth investing much time in for what is only the first
few meters of the events and can be approximated easily by applying an effective engine
torque below 4000 rpm. This should provide a reasonable approximation so long as the
driver is either slipping the clutch or spinning the wheels below this engine speed. This
assumption is deemed reasonably valid thanks to the selection of a continuously variable
transmission with a large ratio range of almost 10. Thus this approximation only need be in
effect until the car reaches 4.5 m/s (see Section 8.2.3). If the simulation was to be used for
a different event with a large amount of low speed sections, then this is an area that might
be worth developing, along with the tyre simulation in Section 6.4.5, to more accurately
represent low speed and traction loss situations.
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Engine Torque (Nm)
Engine speed (rpm)
Figure 9.6. Engine Simulation
Figure 9.7. Simulink lookup table for engine torque
9.4. Driver
9.4.1. Requirements
Whilst the rest of the simulation is concerned only with how the car responds to inputs, the driver
must ‘decide’ what those inputs are and be able to make the ‘decisions’ similarly to how a real
driver would. The simulation is one dimensional in that corners are simply areas of the track with a
speed limit. Thus the driver has control only of the brakes and the engine, and must use these to
ensure the correct speed through corners, and maximum speeds on straights. For this a means of
finding the braking point prior to a corner is necessary, as well as means to know the cornering
speed.
The fastest way to use the available traction to navigate a corner in a race would be to brake
progressively less into the apex and then progressively apply the throttle after the apex. The
simulated driver will not make mistakes, so to err on the side of caution and produce slightly lower
than optimally achievable lap times, the driver will complete all braking prior to the corner and then
complete the corner at a constant velocity. This also greatly simplifies the simulation, but retracts
little from its usefulness as a design tool.
9.4.2. Velocity look up
In the same way that the engine torque is available on a look up table, so is the target velocity. The
driver subsystem has inputs of velocity and position. The latter is used in a lookup table to find the
target velocity of that section of the track. This target velocity is then the demand for a PI controller
which uses the current velocity of the car as feedback (see Section 9.4.4). So that the car reaches
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the appropriate cornering speeds at the beginning of any corner, the look up table can be manually
adjusted so that the demand is brought forward to an earlier position (and thus the speed is
reached in time for the corner). This method was not used in the final simulation, for the braking
point calculator see Section 9.4.3. As can be seen from Figure 9.8, which is an output made
following some changes to the car, the manual braking point approach can result in braking far too
early for the corners (or equally far too late!) thus requiring the braking points to be altered by trial
and error every time something changes on the car. Whilst this was useful in the early stages of
the project to get an idea of speeds and times, it does not serve well the purpose of the simulation
which is to get quick results across several different setups so that parameters can be tuned.
Figure 9.8. Example of how manual braking points can result in inefficient use of track space
9.4.3. Braking point calculator
As explained in Section 9.4.2, there is a need for a means of calculating the braking point for each
corner during the simulation. This was derived analytically by solving the differential equation:
Fresultant =−drag−brakes−rolling resistance
Fresultant =
−1 2
ρ v A C d −1.2mg−μ r mg
2
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(9.1)
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−1 2
ρ v A Cd
dv
2
=
−(1.2+ μ r )g
dt
m
(9.3)
By means of the substitution:
dv dx dv
dv
=
=v
dt dt dx
dx
(9.4)
To achieve an equation for braking distance in terms of current and upcoming corner velocities:
v2
∫ dx=∫ ρ v 2 A C
v1
2m
−v
d
dv
+ ( 1.2+ μr ) g
ρA C d 2
v + ( 1.2+ μ r ) g)
2m 1
ρA Cd 2
∆ x=ln
v + ( 1.2+ μr ) g −ln ¿
2m 2
(9.5)
⁡(
(
)
(9.6)
Figure 9.9. Braking distance required to approach a 10 m/s corner. This is equation (9.6) plotted
with v1 = 10 m/s and v2 as the independent variable
The value for braking distance (9.6) is compared with the current distance to an upcoming corner
and the driver will continue to accelerate so long as
distance ¿ corner>braking distance . An
example of the threshold is shown in Figure 9.9. This method enables the user to alter how the car
is set up and run simulations without having to go through the process of first establishing the
unique braking points. Notice how the braking points in Figure 9.10 are such that the speed limited
corners are arrived at with the correct velocity but without wasting time before the corner travelling
unnecessarily slowly. The simulations used to produce both Figure 9.8 and Figure 9.10 are
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identical in all respects except from the method of establishing braking points. Although the manual
method (Section 9.4.2) could be tuned to produce the same output as Figure 9.10, this process
would typically take a few minutes and be required each time anything on the car was altered.
Figure 9.10. Example of how the analytical braking point solver uses track space efficiently
9.4.4. Velocity Control
With the desired velocity available from look up tables, the driver’s level of accelerating and
braking are then determined through a proportional-integral (PI) controller in closed loop. The
outputs are saturated and directed toward the engine subsystem (see Figure 9.2) for positive
values and the brakes subsystem for negative values. For the chosen method of driver operation
(all braking on straights), it is desirable that the driver either be demanding maximum acceleration
or maximum braking in the straights. To achieve this a large proportional term was chosen in order
to saturate the controls in the straights. Too large a proportional term would occasionally cause
instability in the corners, where a constant speed must be held. To alleviate this a small integral
term was added to reduce the error brought about by a smaller proportional term, although this
was found to have minimal impact on lap times.
9.5. Brakes
9.5.1. Brakes subsystem
The brakes subsystem is simply a gain which maps the demand from the driver onto the braking
force achievable from the brakes. The maximum braking force was decided to be
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Section 6.5.4) and this was achieved by saturating the output, although the total force slowing the
car could be greater than this due to drag. A more substantial simulation of the tyres was covered
in Section 6.4.5, and an anti-lock braking system was developed separately in Chapter 7.
9.6. Drag and rolling resistance
9.6.1. Drag
The aerodynamics of the car were studied in Chapter 4, in which values for frontal area
coefficient of drag
A
and
C d were determined. These values can be used to calculate the force on the
car due to air resistance by means of equation (9.7), where
ρ is the density of air. This equation
is used in a feedback loop using the current velocity of the car.
Fd =0.5 × v 2 × Cd × A × ρ
(9.7)
9.6.2. Rolling resistance
The force due to rolling resistance contains both constant terms (due mainly to tyre deformation)
as well as linear terms (due mainly to viscous effects in the transmission). Given that a CVT was
chosen, there are considerably less oiled gears and the only substantial viscous losses will be in
the differential and CV joints (it is assumed that the engine’s power figures are measured at the
crankshaft and thus viscous losses in the engine are already taken into account). It was therefore
decided to treat rolling resistance as a constant force, depending on the tyres and the car’s weight.
From studying Figure 6.4.2 and to account for additional slight contributions to rolling resistance
from effects other than tyre deformation, the value for
μr
was chosen to be 0.2, and rolling
resistance is accounted for using equation (9.8) .The losses in the transmission will instead be
accounted for as an inefficiency multiplier, the values of which are shown in Table 9.1.
Frr ¿ m× g× μr
Part
Inefficiency multiplier
Chain Drive
[1]
CVT
[2]
(9.8)
Chain Drive B
[1]
Differential
0.98
0.88
0.98
0.96
A
Table 9.1. Efficiencies of drivetrain components
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[3]
CV Joints
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9.7. Rotational inertia
9.7.1. Introduction
So far the simulation has treated the car as a single mass subject to a resultant force. In reality
there are many masses on the vehicle which are rotating as well as moving through space. Their
rotational velocity requires energy and this should be accounted for as the effect on the
acceleration of the car can be substantial. Rather than simulating the rotational velocity of each
component and the torques accelerating them, the rotational moment of inertia was calculated for
each drivetrain component and then converted into an effective mass, which can be added to the
real mass of the car for the purpose of calculating the acceleration. Thus the new formula will be
equation (9.8) where
me is the total effective mass of the drivetrain components and wheels.
a=
F
m+me
(9.8)
9.7.2. Effective masses
The effective mass of each component was estimated using first the formula for the rotational
moment of inertia of either a solid disk (9.9) or a hoop (9.10), depending on the component. Then
equation (9.11) was used to convert these values into effective masses, where n is the gearing
ratio between each component and the wheels, and r is the radius of the tyres.
2
ma
2
(9.9)
J =m a2
(9.10)
J=
J × n2
me = 2
r
(9.11)
Not all drivetrain components however will be accelerating throughout the entire lap. All
components on the engine side of the gearbox will, for the most part, only be accelerated once (at
the start) and then maintain a roughly constant rotational velocity for the remainder of the event (as
a result of the CVT ratio adjusting continuously). Therefore, it is necessary to include a means to
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alter the effective mass due to rotational inertia once the roughly-constant condition is reached.
Table 9.2 shows calculated estimates for the effective masses brought about by the different
drivetrain components. Those listed in italics are to be ‘switched off’ once the engine passes a
certain speed which it will not then fall below again during an event. This is achieved in the
simulation by using a switch which changes the effective mass of the car when the engine speed
passes a threshold, which is set at 11000 rpm.
Table 9.2. List of effective masses of drivetrain components due to rotation
Component
Effective mass due to rotational inertia (kg)
Engine and flywheel
260
Primary chain drive
40.0
Primary CVT clutch
15.6
Secondary CVT clutch
3.73
Secondary chain drive
1.17
Differential
0.21
Half shafts (x2)
0.00
Constant velocity joints (x4)
0.01
Wheel rims (x4)
4.72
Tyres (x4)
17.0
Total (all components)
Total (from CVT output to wheels)
342.44
26.84
9.8. Results
9.8.1. Acceleration event
The acceleration event is a 75 m straight line sprint with the score being based on elapsed time.
The simulation predicts a time of 3.849 s will be required to complete the sprint, with a speed of
32.08 m/s at the finish line. The distance covered is shown plotted against time in Figure 9.11.
Unlike the circuit events, it is simple to compare this time against previous results since the
acceleration event is the same at every Formula Student venue. The points are calculated with
respect to the fastest time, which in 2014 was 3.439 s achieved by ETH Zurich [4]. The formula
used for the acceleration score is equation (9.12) [5], where Tyour is the achieved time, Tmin is the
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elapsed time of the fastest car and Tmax is 150% of Tmin. The acceleration score that would have
been achieved in 2014 by the simulated time of 3.849 s is 52.15, out of a possible 75 points. This
would have corresponded to 3rd place in the acceleration event [4].
71.5×
Acceleration score=
Tmax
−1)
( Tyour
+3.5
Tmax
−1
Tmin
(9.12)
Figure 9.11. Shows the time taken to complete the 75m acceleration event
9.8.2. Autocross event (single lap)
The autocross event is a single lap of the track from a standing start. Up to 100 points are scored
on how quickly the lap is completed. For the allocated circuit (see Chapter 1), the simulation
predicts an achievable lap time of 37.83 s, with an average speed of 26.96 m/s and a maximum
speed of 38.62 m/s. Figure 9.12 shows the velocity over the single lap, with the driver’s control
demands also plotted where a value of 10 corresponds to maximum demand.
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Figure 9.12. Velocity and driver demands over the course of one lap from a standing start
9.8.3. Endurance event
The endurance event is worth the most points of all events (300) and consist of 27 laps of the
track. Therefore the majority of optimisation work that made use of the simulation was carried out
using the results from the endurance lap time. The simulation predicts an achievable lap time of
36.05 s with an average speed of 28.30 m/s and a top speed of 39.19 m/s. This suggests a total
time for the endurance event would be 16 minutes and 15 seconds. Figure 9.13 shows the velocity
over a typical lap of the endurance event, the driver’s control demands are again plotted where a
value of 10 corresponds to maximum demand. The reduction in mass due to fuel burn was not
taken into account on a lap by lap basis because it was shown to only cause a 30 ms difference in
lap time, which makes less than a second of difference over the course of the event. However a
reduced mass figure was used for the simulation of the much shorter acceleration and autocross
events.
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Figure 9.13. Velocity and driver demands over the course of one lap which follows a previous lap
9.9. Conclusion
The simulation has proved invaluable throughout this design project as it allows the trial of different
setups with feedback within a few seconds. This has allowed for educated decisions to be made by
every team member, based on what forces and speeds the car is undergoing, and how alterations
affect lap times. Finally, the simulation has provided results for the dynamic events for the final
iteration of design (see Table 9.3), allowing for comparison among other design projects and, in
some cases such as the acceleration event, previous Formula Student competitions. It is difficult to
compare the autocross and endurance event results with previous competitions due to the
allocation of a new track design for this project. Therefore a valuable piece of future work would be
to use the simulation to produce results for the tracks used in previous competitions. As for future
developments to the simulation, the next step would be to model each component of the drivetrain
individually with their own velocity states. This would provide a more accurate representation of the
drivetrain and allow for some improved decisions in certain areas, such as differential choice,
where a lack of real world experience (or more accurate simulation) made the decision difficult.
The results proved most sensitive to the chosen cornering speeds, much more so than any single
aspect of the car’s physical specification. Therefore in order to improve on the results in Table 9.3
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further investigation could be made into how the car may be able to make best use of the track
space as opposed to assuming each corner will be driven at constant radius. Furthermore, the
simulation could be developed to allow for braking during corners. For fuel consumption figures it is
necessary to consult Section 2.4.11, which has made use of the simulated throttle demand.
Table 9.3. Simulation results for the three time tested dynamic events
Event
Result
Time / Points
75 m acceleration test
Time
3.849 s)
Points scored (2014)
Lap time
52 out of 75 points (3rd place)
37.83 s
Top speed
38.62 m/s
Average speed
26.96
Endurance time
975 s
Fastest lap
36.05 s
Top speed
39.19 m/s
Average speed
28.25 m/s
Autocross sprint
Endurance (27 laps)
9.10. References
[1] Optimisation of the chain drive system on sports motorcycles, 2004, Burgess and Lodge
[2] www.zeroshift.com/pdf/ Seamless%20AMT%20Offers%20Efficient%20Alternative%20To
%20CVT.pdf
[3] http://web.mit.edu/2.972/www/reports/differential/differential.html
[4] http://events.imeche.org/docs/default-source/Results-2014/fs_uk_2014---accn.pdf?sfvrsn=2
[5] http://students.sae.org/cds/formulaseries/rules/2015-16_fsae_rules.pdf
10. Project Management and Finance
10.1. Introduction
Everyone working on this design project was doing so alongside numerous other commitments,
thus effective project management was key to ensuring effective teamwork. Meetings were held
twice weekly where possible, and means to communicate and share as a group were established
using the internet for times when meeting in person was not possible, or for between meeting
communications. Strict attention was paid to the project’s budget throughout. In the early stages
cost estimates were shared within the team by means of an online spreadsheet, which provided
everyone with a clear picture of the then rapidly changing financial situation.
10.2. Project planning
The project spanned two eight week terms (during which the team could meet in person) and two
five week breaks (during which most of the team could not meet in person). There was a fixed
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meeting every Monday during the eight week terms, during which a time was agreed for a further
meeting later in the week to discuss progress. Often this decision could not be reached during the
meeting and the organisational tool www.when2meet.com was used which overcame this problem.
The first half of the first term was dedicated to initial delegation of roles, research into what was
required from these roles, and presentation to the team of how each member planned to achieve
their section of the design. At this point a schedule was drawn up to aid the order of future work
carried out and reduce the time a team member may have to wait for another to complete their
work, the schedule also helped in keeping everyone on track, with the end goal in mind. The
schedule was constructed from a precedence diagram which allowed for a well-informed Gantt
chart to be drawn (see Appendix 9(A)). This proved to be effective although in future the group
could benefit from stricter adherence to and more frequent evaluation of the schedule.
10.3. Finance
The budget for this design was £40,000. It was decided to include in this a 15% contingency of
£6000, although this was reduced to a £2000 contingency in the later stages of the project when
there was far less uncertainty. This budget allowed the purchase and manufacture of some more
expensive parts not feasible on a minimal Formula Student budget, but still required tight control so
that the selection of too many expensive parts did not result in the budget being exceeded. For
many situations, the worth of parts was managed on a basis of assessing different viable options
that could be used interchangeably, then making the final choice later once the financial standing
was clearer. For example the choice to use a GFRP body was made following the initial cost
estimates and smaller decisions such as differential choice (see Section 8.3.3) were made towards
the end of the project once it was clear that there was going to be sufficient room in the budget. A
spreadsheet of part costs (as well as other details) was kept using an online Google Document
(See Table 10.1) so that all team members could update and assess the project’s finances.
10.4. Conclusion
The final cost is £5261 under budget (not including the £2000 final contingency) and this money
should be put to further improving the performance of the car. Components which were at first
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thought to be too expensive to custom design and manufacture may now be considered for a novel
design. One example of this is the continuously variable transmission and limited slip differential,
which could potentially be manufactured as a single unit to improve efficiency.
Part
Cost
(GBP
)
Mass
(kg)
Part
Cost
(GBP)
Mass (kg)
Brakes - Calipers
500
1.7
Chain Drives
150
1.6
Brakes - Discs
200
10
Half Shafts & CVJs
800
5
Steering Rack
700
1
Oil & Grease
50
1
Suspension - Arms
2200
3
CVT (estimate)
1000
8.5
Suspension - Dampers
2500
4
ECU Omex 710
845
0.4
800
16
Chassis
20000
60
Front Wheels
287.9
6.8
Driver (with gear)
200
77
Rear Wheels
287.9
6.8
Engine
900
32
Body Work - Nose Cone
600
1
Fuel Tank + Fuel
55
8
Body Work - Side Pods
800
2
Fan
98
1.5
Coolant Pump
135
0.9
Pedal Box
700
2
Hoses & Attachments
100
0.1
Fasteners (bolts etc.)
100
1.5
Radiator
130
2.27
50
3
1300
4
600
3
34638.8
254.57
Tyres
LSD Differential
Table 10.1. Cost
breakdown
CVT guard
Wings
TOTAL
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10.5. Appendices
Appendix A
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181
Yuntao Zhu
11
Lincoln College
Conclusion
Conclusion
The aim of the project was to design an internal combustion engine car to be competitive in the
2015 Formula Student Competition. It can be seen from the report that the project is finished under
budget and on schedule, a number of innovative designs have been implemented in to the car to
enhance the performance and the overall simulation give an estimation of the car performance.
A powerful engine with a precise engine control plus an innovative design of transmission ensures
a powerful thrust force. The aerodynamic parts of the car body are scientifically designed to reduce
the drag, and the braking control reduces the braking time and distance. Different aspects of the
racing car are considered to improve the overall performance. The overall simulation results show
that the car is competent for the formula student competition. The simulation predicts an
endurance time of 16 minutes and 15 second, and a 75 meters sprint of 3.849 s which would have
achieved an acceleration score of 52.15 out of 75 in the 2014 Formula Student Competition.
If the project could be continued, the simulation could be developed to achieve a more realistic
result. If the manufacture of the car is possible, some experimental data could also be collected.
Since the project is currently under budget, the rest of the budget could be spent on the
improvement of the car based on the simulation results and experimental data.
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