Formula SAE Suspension Design
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School of Engineering
Faculty of Engineering, Physical Sciences and Architecture
THE UNIVERSITY OF QUEENSLAND
Bachelor of Engineering Thesis
Formula SAE Suspension Design
Student Name: DANIEL RAYMOND BURT Course Code: MECH4500 Supervisor: Dr. Ross McAree Submission date: 7th November 2003
A thesis submitted in partial fulfillment of the requirements of the Bachelor of Engineering degree program in the
Division of Mechanical Engineering
Daniel Raymond Burt
62 Ellen St Woody Point
QLD, 4019 7 November 2003 Prof. J. M. Simmons Head of School School of Engineering University of Queensland Brisbane Queensland 4072 Dear Sir, I hereby submit my Thesis titled “Formula SAE Suspension Design” for consideration as partial fulfilment of the Bachelor of Engineering degree. All the work contained within this Thesis is my original work except where otherwise acknowledged. I understand that this thesis may be made publicly available and reproduced by the University of Queensland unless a limited term embargo on publication has been negotiated with a sponsor. Yours sincerely, Daniel Raymond Burt 33628055
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ABSTRACT
Formula SAE is a student project undertaken by the Mechanical Engineering department
of the University of Queensland and various other universities in Australasia, America,
Europe and England. It is a competition to engineer and build a racing car to compete in
design and track events.
The objective of my thesis is to analyse the performance of the 2001 and 2002 formula
SAE racing car of the University of Queensland, identify it’s short comings in terms of
suspension/steering geometry, set up and structural integrity and improve the design for
the 2003 formula SAE.
The thesis follows the format of a design analysis. The investigation and analysis of the
performance of the previous 2 years formula SAE race cars of the University of
Queensland is used as a platform as to the complete redesign of the suspension system of
the 2003 University of Queensland formula SAE race car.
It will discuss the design of the suspension and steering for the 2003 University of
Queensland formula SAE racecar in order to optimise its performance and ability to be
tuned to a particular racing course.
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ACKNOWLEDGEMENTS
I would like to express my appreciation to the following people for their valuable
contribution and assistance in the completion of this thesis:
All fellow UQ Racing team mates from both the 2002 and 2003 teams, for their
dedication, passion and extreme time commitment needed to be a part of this formula
SAE team. In particular, George Commins and Francis Evans for their countless hours of
support and technical advice/ input on the suspension design.
Mr George Dick, for his patience, technical tuition, guidance and dedication to the
formula SAE project throughout the year.
The workshop staff; John, Ross, Dave and Neil, for your technical assistance and
attention to the formula SAE project throughout the year.
Graham for time spent using instron to test rod ends strength and spring rates.
Professor Ross McAree for being my thesis supervisor, and being inspirational in his
systematical approach to all engineering problems.
Professor David Mee for being the academic supervisor of the Formula SAE project in
the University of Queensland.
Professor Hal Gurgenci for making the Formula SAE project available to students at the
University of Queensland.
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CONTENTS
ABSTRACT........................................................................................................................ I
ACKNOWLEDGEMENTS ............................................................................................ II
1. INTRODUCTION......................................................................................................... 1
2. COMPETITION & DESIGN OBJECTIVES ............................................................ 2
2.1 Formula SAE Competition............................................................................... 2
2.2 Formula SAE Rules - Suspension/Steering ..................................................... 3
2.3 Formula SAE Rules - Dynamic Events............................................................ 5
2.4 Design Objectives............................................................................................. 11
3. BRIEF LITERATURE REVIEW............................................................................. 12
3.1 Wheelbase & Track .................................................................................. 12
3.2 Roll Centres ............................................................................................... 12
3.3 Pitch Centre ............................................................................................... 16
3.4 Anti-dive, Anti-lift & Anti-Squat ............................................................. 17
3.5 Camber....................................................................................................... 19
3.6 Toe .............................................................................................................. 21
3.7 Steering Geometry .................................................................................... 22
3.7.1 Kingpin Inclination & Castor .................................................................22
3.7.2 Ackerman Steering .................................................................................23
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4. CRITICAL ANALYSIS OF 2001/2002 SUSPENSION DESIGN/SETUP............ 24
5. 2003 SUSPENSION GEOMETRY DESIGN ........................................................... 27
5.1 Wheelbase .................................................................................................. 27
5.2 Track .......................................................................................................... 28
5.3 Roll Centres ............................................................................................... 29
5.4 Anti-dive, Anti-squat, Anti-lift & Pitch Centre...................................... 31
5.5 Anti-roll Rates ........................................................................................... 31
5.6 Steering Geometry .................................................................................... 33
5.7 Kingpin/Castor.......................................................................................... 34
5.8 Camber Gain............................................................................................. 34
6. OVERVIEW OF 2003 SUSPENSION COMPONENT DESIGN .......................... 36
6.1 Suspension Loading .................................................................................. 36
6.1.1 Strain Gauge Testing .............................................................................36
6.1.2 Bump and Braking Shock Factors .........................................................38
6.1.3 Fatigue Design.......................................................................................39
6.2 Wishbone Construction............................................................................ 40
6.2.1 Tubing Selection ....................................................................................41
6.2.2 Rod end Selection ..................................................................................41
6.2.2.1 Testing...............................................................................................42
6.2.3 Insert Design ...........................................................................................44
6.3 Rocker and Upright Design..................................................................... 45
6.4 Spring and Damper................................................................................... 49
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6.4.1 Selection ................................................................................................49
6.4.2 Damper Dynamometer...........................................................................50
6.4.3 Spring Testing........................................................................................51
6.4.4 X-Ray.....................................................................................................52
6.5 Steering Selection...................................................................................... 53
6.6 Accuracy & Adjustment ........................................................................... 54
6.7 Component Placement.............................................................................. 55
6.7.1 Rocker , Spring and Damper and Anti-roll bar Placement .....................55
7. VEHICLE SET UP ..................................................................................................... 58
8. RESULTS............................................................................................................... 60
9. CONCLUSIONS & RECOMMENDATIONS ......................................................... 64
10. BIBLIOGRAPHY............................................................................................. 66
APPENDIX A .................................................................................................................. 67
APPENDIX B .................................................................................................................. 71
Roll Centre Analysis.............................................................................................. 71
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LIST OF FIGURES Figure 2.1: The incredibly small Tokyo Denki Formula SAE racecar was extremely
competitive...................................................................................................................9
Figure 2.2: The 2002 UQ Formula SAE racecar at the Mount Cotton Hillclimb..............10
Figure 3.1 Roll Centre........................................................................................................13
Figure 3.2 Track Variations ...............................................................................................15
Figure 3.3 Pitch Centre ......................................................................................................16
Figure 3.4 Anti-dive ...........................................................................................................17
Figure 3.5 Forces applied to contact patch during braking................................................18
Figure 3.6 Camber..............................................................................................................19
Figure 3.7 Camber Change ................................................................................................20
Figure 3.8 Toe definitions ..................................................................................................21
Figure 3.9 Castor & Kingpin Inclination ...........................................................................22
Figure 3.10 100% Ackerman .............................................................................................23
Figure 4.1 Poor Wear on Front Tires of 2002 Car .............................................................25
Figure 5.1 Front Wishbones are Swept Backwards ...........................................................28
Figure 5.2 Front roll Centre Movement with 1° of roll (All measurements are in inches)
....................................................................................................................................30
Figure 5.3 Rear roll Centre Movement with 1° of roll (All measurements are in inches).30
Figure 5.4 Anti-roll bar Design (only half CAD modelled) ..............................................32
Figure 5.5 Relative Anti-roll Stiffness with Rear Anti-roll Bar Adjustment.....................33
Figure 6.1 Strain Gauge Testing ........................................................................................37
Figure 6.2 Rear Lower Wishbone ......................................................................................40
Figure 6.3 Initial Setup of Rod End Bearing Testing ........................................................42
Figure 6.4 Revised Setup of Rod End Bearing Testing .....................................................43
Figure 6.5 Results of Rod end Bearing Testing .................................................................44
Figure 6.6 Wishbone Insert ................................................................................................45
Figure 6.7 Front Upright ....................................................................................................46
Figure 6.8 Rear Upright .....................................................................................................47
Figure 6.9 Front Rocker .....................................................................................................48
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Figure 6.10 Rear Rocker ....................................................................................................48
Figure 6.11 Risse Racing Jupiter 5 Shock .........................................................................49
Figure 6.12 Damper Dyno Results of 1 Shock ..................................................................50
Figure 6.13 Graph of Results .............................................................................................51
Figure 6.14 Steering Rack in 2003 Racecar.......................................................................53
Figure 6.15 Chassis on Jig for suspension Pickup Accuracy.............................................54
Figure 6.16 Front Spring and Damper Placement .............................................................56
Figure 6.17 Rear Spring/Damper and Anti-roll Bar Placement.........................................57
Figure 8.1 Rear Toe Deflection..........................................................................................61
Figure 8.2 Toe Control Solution ........................................................................................62
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LIST OF TABLES
Table 2.1 Competition Points ..............................................................................................2
Table 4.1 2001/2002 Suspension Parameters ....................................................................24
Table 5.1 Camber Gain Coefficients..................................................................................35
Table 6.1 Actual Spring Rates Results ..............................................................................52
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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1. INTRODUCTION
The University of Queensland was represented for the second time at the third
Australasian Formula SAE competition at in 2002. The previous attempts at the
competition had yielded average results. However, the quality of the racecars of those
teams at the forefront of the competition in 2002 was world class and therefore, the need
for drastic improvement, if the University of Queensland were to be competitive in the
future became evident.
With regard to the suspension and steering systems there was still a lot of room for
improvement. The 2002 racecar still maintained many of the handling characteristics of
the 2001 vehicle. The terminal under steering nature of the 2001 racecar continued in the
2002 vehicle, only to a slightly less extent.
The limitations to the modifications able to be made with regard to chassis geometry
somewhat restricted Riseley [6] from achieving anything other than small changes in
suspension geometry. The main focus of the redesign in the 2002 University of
Queensland racecar was to rectify the critical errors made in 2001. Errors that were
imposed due to the inexperience of the team, being it’s first year. Some of these errors
were roll centres that ended under the ground, drive shafts at a large angle in the static
rest position and both wishbones and rod end bearings in bending.
The complete reanalysis of the suspension design for the 2003 racecar was undertaken
and is the basis of this thesis. The rectification of the terminal under steering nature from
the previous racecars, for the 2003 racecar, was obviously essential for the success of the
2003 formula SAE team.
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2. COMPETITION & DESIGN OBJECTIVES
2.1 Formula SAE Competition
The Formula SAE competition is a international competition, run by the Society of
Automotive Engineers, for students to conceive, design, fabricate, and compete with a
small formula -style racing car. The competition is comprised of static and dynamic
events. The competition events test the vehicles engineering design, and performance.
EVENT
Points
Static Events
Presentation 75 Engineering Design 150 Cost Analysis 100 Dynamic Events
Acceleration 75 Skid -Pad Event 50 Autocross Event 150 Fuel Economy Event 50 Endurance Event 350 Total Points
1000
Table 2.1 Competition Points
A full version of the rules can be downloaded from the Australasian Society of Engineers
web page at www.sae-a.com.au/fsae/rules. Some extracts of the important parts of the
rules, pertaining to the suspension/steering design are explained in the following.
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2.2 Formula SAE Rules - Suspension/Steering
The strict rules pertaining to the suspension and steering system of the car are as follows.
3.1.2 Wheelbase and Vehicle Configuration
The car must have a wheelbase of at least 1525 mm (60 inches). The wheelbase is
measured from the center of ground contact of the front and rear tires with the wheels
pointed straight ahead. The vehicle must have four wheels that are not in a straight line.
3.1.3 Vehicle Track
The smaller track of the vehicle (front or rear) must be no less than 75% of the larger
track.
3.2.1 Ground Clearance
Ground Clearance must be sufficient to prevent any portion of the car (other than tires)
from touching the ground during track events.
3.2.2 Wheels and Tires
The wheels of the car must be 203.2 mm (8.0 inches) or more in diameter.
The tires can be any size or type. Tire or wheel type, compound or size may not be
changed after the static judging has begun. Tire warmers are not allowed. No traction
enhancers may be applied to the tires after the static judging has begun.
3.2.3 Suspension
The car must be equipped with a fully operational suspension system with shock
absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4
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mm (1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. The judges reserve
the right to disqualify cars which do not represent a serious attempt at an operational
suspension system or which demonstrate unsafe handling.
3.2.4 Steering
The steering system must affect at least two wheels. The steering system must have
positive steering stops that prevent the steering linkages from 2003 Formula SAE® Rules 12
locking up (the inversion of a four-bar linkage at one of the pivots). The stops may be
placed on the uprights or on the rack and must prevent the tires from contacting
suspension, body, or frame members during the track events. Allowable steering free play
will be limited to 7 degrees total measured at the steering wheel.
3.4.8 Roll Over Stability
The track and center of gravity of the car must combine to provide adequate rollover
stability.
3.4.8.1 Tilt Table Test
Rollover stability will be evaluated using a pass/fail test. The vehicle must not roll when
tilted at an angle of 57 degrees to the horizontal in either direction corresponding to 1.5
G’s. The tilt 2003 Formula SAE® Rules 31 test will be conducted with the tallest driver in the
normal driving position.
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2.3 Formula SAE Rules - Dynamic Events
There are 5 different dynamic events in the competition. Four of which rely on the
dynamic performance of the racecar. Those being, the acceleration, skid -pad, autocross
and endurance events.
Since formula SAE racecars are, in essence, engine power restricted due to a regulations
air intake restrictor sizing, the suspension package is paramount to the success of a
formula SAE vehicles dynamic performance.
The successful design of a performance suspension sys tem is based on performance
compromises, which will be discussed in later chapters. However, before these
compromises can be assessed in the interest of performance in the competitions dynamic
events, these dynamic events must be well understood. A breakdown of what these events
involve follows.
5.4 ACCELERATION EVENT
5.4.1 Acceleration Objective
The acceleration event evaluates the car’s acceleration in a straight line on flat
pavement.
5.4.2 Acceleration Procedure
The cars will accelerate from a standing start over a distance of 75 m (82 yards) on a flat
surface. The foremost part of the car will be staged at 0.30 m (11.8 inches) behind the
starting line. A green flag will be used to indicate the approval to begin, however, time
starts only after the vehicle crosses the start line. There will be no particular order of the
cars in each heat. A driver has the option to take a second run immediately after the first.
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5.5 SKID-PAD EVENT
5.5.1 Skid-Pad Objective
The concept of the skid-pad event is to measure the cornering ability of the car on a flat
surface while making a constant-radius turn.
5.5.4 Skid-Pad Layout
There will be two circles of 15.25 m (50.03 feet) diameter in a figure eight pattern. The
circle centers will be separated by 18.25 m (59.88 feet), and a driving path 3.0 m (9.84
feet) in width will be marked with pylons and a chalk line just outside the pylons. The
start/stop line is defined by the centers of the two (2) circles. A lap is defined as traveling
around one (1) of the circles from the start/ stop line and returning to the start/stop line.
5.5.6 Skid-Pad Procedure
The cars will enter perpendicular to the figure eight and will take one full lap on the right
circle to establish the turn. The next lap will be on the right circle and will be timed.
Immediately following the second lap, the car will enter the left circle for the third lap.
The fourth lap will be on the left circle and will be timed. Immediately upon finishing the
fourth lap, the car will exit the track. The car will exit at the intersection moving in the
same direction as entered. A driver has the option to take a second run immediately after
the first.
5.6 AUTOCROSS EVENT
5.6.1 Autocross Concept
The concept of the autocross event is to evaluate the car's maneuverability and handling
qualities on a tight course without the hindrance of competing cars. The autocross course
will combine the performance features of acceleration, braking, and cornering into one
event.
5.6.2 Autocross Procedure
There will be two Autocross-style heats, with each heat having a different driver. The car
will be staged such that the front wheels are 2 m behind the starting line. The timer starts
only after the car crosses the start line. There will be no particular order of the cars to
run each heat but a driver has the option to take a second run immediately after the first.
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Two (2) timed laps will be run (weather and time permitting) by each driver and the best
lap time will stand as the time for that heat. The organizer will determine the allowable
windows for each heat and retains the right to adjust for weather or technical delays.
Cars that have not run by the end of the heat will be disqualified for that heat.
5.6.3 Autocross Course Specifications & Speeds
The following specifications will suggest the maximum speeds that will be encountered on
the course. Average speeds should be 40 km/hr (25 mph) to 48 km/hr (30 mph).
Straights: No longer than 60 m (200 feet) with hairpins at both ends (or) no longer than
45 m (150 feet) with wide turns on the ends.
Constant Turns: 23 m (75 feet) to 45 m (148 feet) diameter.
Hairpin Turns: Minimum of 9 m (29.5 feet) outside diameter (of the turn).
Slaloms: Cones in a straight line with 7.62 m (25 feet) to 12.19 m (40 feet) spacing.
Miscellaneous : Chicanes, multiple turns, decreasing radius turns, etc. The minimum
track width will be 3.5 m (11.5 feet).
The length of each run will be approximately 0.805 km (1/2 mile) and the driver will
complete a specified number of runs. The time required to complete each run will be
recorded and the time of the best run will be used to determine the score.
5.7 ENDURANCE EVENT
5.7.2 Endurance Objective
The Endurance Event is designed to evaluate the overall performance of the car and to
test the car’s reliability.
5.7.4 Endurance Course Specifications & Speeds
Course speeds can be estimated by the following course specifications.
Average speed should be 48 km/hr (29.8 mph) to 57 km/hr (35.4 mph) with top speeds of
approximately 105 km/hr (65.2 mph).
Straights: No longer than 77.0 m (252.6 feet) with hairpins at both ends
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(or) no longer than 61.0 m (200.1 feet) with wide turns on the ends. There will be passing
zones at several locations.
Constant Turns: 30.0 m (98.4 feet) to 54.0 m (177.2 feet) diameter.
Hairpin Turns: Minimum of 9.0 m (29.5 feet) outside diameter (of the turn).
Slaloms: Cones in a straight line with 9.0 m (29.5 feet) to 15.0 m (49.2 feet) spacing.
Miscellaneous: Chicanes, multiple turns, decreasing radius turns, etc. The minimum
track width will be 4.5 m (14.76 feet).
5.7.5 Endurance General Procedure
The event will be run as a single 22 km (13.66 mile) heat. Teams will not be allowed to
work on their vehicles during the heat. A driver change must be made during a three-
minute period at the mid point of the heat.
The aim in all events is to complete the circuit in the shortest elapsed time.
Notably the top speed in any event is 105 km/h, which is not considerably fast in the
realm of motorsport. The lack of long straights, maximum of 77.0 m in Endurance and
60.0 m in Autocross, and abundance of tight corners mean that a successful formula SAE
racecar is more likely to be one with a superior and refined suspension package rather
than engine package. Moreover, through observation in the previous formula SAE
competitions, the smallest racecars seemed to be more suitably sized for the circuits
endured in the formula SAE competition. They were able to take different racing lines
and in some instances effectively straight line chicanes thus always carrying more corner
speed also increasing the speed down the straights.
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Figure 2.1: The incredibly small Tokyo Denki Formula SAE racecar was extremely
competitive
In light of this, the racecar must be designed for the particular circuit in which it is to be
raced. The formula SAE competition is of a tight and twisty nature and therefore, the
racecar must be designed to perform on this type of circuit for success.
For example, if a formula 1 or a indy champ car was to be placed in the formula SAE
competition it would barely be able to complete the circuit let alone with respectable
times. Not that a formula SAE racecar is has anywhere near the cornering, braking or
acceleration ability of one of these racecars, they are just not suited to a tight formula
SAE type circuit.
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The racing of the 2002 formula SAE against the other hill climb cars at the mount cotton
hill climb circuit displayed that the 2002 racecar was much more suited to a circuit of a
larger size. It was more stable at the speeds achieved on this circuit as opposed to the
much slower speeds achieved on a tight formula SAE circuit.
Figure 2.2: The 2002 UQ Formula SAE racecar at the Mount Cotton Hillclimb
The competition skidpad, autocross and enduro circuits are more like go-cart circuits,
rather than circuits intended for a formula style racecar. Therefore, the ideal car for the
competition is essentially to be a go-cart with mandatory suspension.
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2.4 Design Objectives
In the previous 2 years the University of Queensland has entered a racecar aimed at just
competing in the competition. This year, 2003 the University of Queensland formula
SAE team is aiming to have a modest attempt at winning the Australasian competition.
The main design objectives for the 2003 formula SAE racecar are to produce a simple,
lightweight and reliable vehicle capable of winning the 2003 Australasian Formula SAE
competition.
The design objectives of this year’s suspension system are formed on somewhat a
different perspective of the competition. The decision to omit the differential, for reasons
discussed in later chapters, has prompted clever suspension design to overcome the
potential problems in doing this. Also, having considered the dynamic events involved in
the formula SAE competition the 2003 design philosophy is to build a go-cart with it’s
mandatory suspension running on the shortest wheelbase limit of 1525 mm.
The effects of all suspension parameters have to be considered and the details of such
design considerations are discussed here within.
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3. BRIEF LITERATURE REVIEW
The purposes of this section is enlighten the reader as to some of the terms used in double
wishbone suspension design and briefly explain the effects of each on the performance of
the vehicle. Some of the terms that are related to double wishbone suspension are as
follows.
3.1 Wheelbase & Track
The wheelbase is the distance between the front and rear wheels. In the formula SAE
competition, the wheelbase is measured from the centre of ground contact of the front
and rear tires with the wheels pointed straight ahead. The track is the distance between
the centreline of the wheels on either side of the vehicle.
3.2 Roll Centres
The roll centre is the instantaneous centre of rotation of the chassis about the ground. It is
determined by the geometric layout of the suspension members. The roll centre is
governed by the instantaneous centres of rotation of the wheels about the chassis. The
picture below shows the instantaneous centres of rotation of the wheels about the chassis
and the determination of the roll centre.
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Figure 3.1 Roll Centre
The roll centre placement has an effect on the weight transfer of the racecar, as well as
the vehicle attitude on cornering.
There are two different types of weight transfer in roll that add to give the total weight
transfer of the vehicle. They are elastic and geometric. The amount of each type of
weight transfer is determined by the roll centre location.
The formula for determining these weight transfers is shown below.
Lateral Suspended Mass Weight “Geometric” Transfer is found by the equation:
LGWT= SM*Lateral Acc*RC Height/Track
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Lateral Suspended Mass Weight “Elastic” Transfer is found by the equation:
LGWT= SM*Lateral Acc*(SM CG Height - RC Height)/Track
Where SM = Suspended Mass, RC = Roll Centre & CG = Centre of Gravity
The elastic weight transfer is the component of weight transfer that is transferred through
the vehicles springs. The geometric weight transfer is transferred through the wishbones
and consequently, does not contribute to chassis roll. That is to say, if the roll centre
height were the same as the centre of gravity height, the chassis would not experience any
roll at all during cornering.
Another important point is that geometric weight transfer is instantaneous, while elastic
transfer is not due to the transient motion of the spring compression/extension and chassis
roll.
The instantaneous centre of rotation of the wheel of about the chassis determines the
track variation in different situations. It is displayed in the figure below.
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Figure 3.2 Track Variations
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3.3 Pitch Centre
The pitch centre is just as important as the roll centre and is established in essentially the
same manner as the roll centre.
Figure 3.3 Pitch Centre
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3.4 Anti-dive, Anti-lift & Anti-Squat
The following diagram illustrates the calculation procedure of the anti-dive percentage.
Figure 3.4 Anti-dive
The angle B in the diagram is calculated by the evaluation of the forces that are applied to
the tire contact patch as illustrated in the below diagram.
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Figure 3.5 Forces applied to contact patch during braking
The anti-lift and anti-squat geometries are calculated in exactly the same manner.
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3.5 Camber
Wheel camber is important to racecar design. It is illustrated in the following diagram.
Figure 3.6 Camber
Excessive camber gain during driving can detrimental to mechanical grip a racecar can
generate. The camber variations in different driving situations are illustrated in the
following diagram.
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Figure 3.7 Camber Change
The camber variation design involves a trade of between the bump and roll situations. As
illustrated, for no camber gain in the bump situation the instantaneous centre of rotation
of the wheel about the chassis must be at distance infinity from the centre of the vehicle.
I.e. the virtual swing arm length, VSAL = 8 .For no camber gain in the roll situation, the
virtual swing arm length should be half the track.
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3.6 Toe
The variation of the vehicles wheels from parallel to each other is referred to as toe. Toe
is illustrated in the below diagram.
Figure 3.8 Toe definitions
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3.7 Steering Geometry
The steering geometry is one of the most important things to a racecars design.
3.7.1 Kingpin Inclination & Castor
Kingpin inclination and castor are illustrated in the following diagram.
Figure 3.9 Castor & Kingpin Inclination
The effects of both kingpin inclination and castor are to camber the wheels during
steering. Kingpin inclination cambers the outside wheel positively and castor does the
opposite, cambering the outside wheel negatively. Castor and kingpin inclination trail
both affect the torque experienced at the steering wheel to turn the wheels. If either or
both are excessive the torque required to turn the steering wheel too may be excessive.
Excessive steering input force is not ideal. However, a lack of torque is just as
undesirable. Some torque is required for adequate steering “feel”.
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3.7.2 Ackerman Steering
Ackerman is the term that describes the phenomenon of toe in or toe out during turning.
Perfect Ackerman, or 100% is achieved when both wheel are rotating around the same
instantaneous center as the vehicle. This is illustrated in the diagram below.
Figure 3.10 100% Ackerman
Consequently, the inside wheel has to turn more than the outside to achieve this (toe out).
The more the wheels toe out during turning the greater the Ackerman percentage. Parallel
steering is 0% Ackerman. The Ackerman angle is defined as the difference between the
two steered angles and therefore, the percentage Ackerman is defined as the percentage
of this Ackerman angle to the perfect Ackerman angle.
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4. CRITICAL ANALYSIS OF 2001/2002
SUSPENSION DESIGN/SETUP
The previous formula SAE racecars of the University of Queensland exhibited many
handling issues. The general consensus of all drivers for both the 2001 and 2002
competitions was that the racecar exhibited excessive under steering in both the transient
and steady state cornering.
The first step to the improvement for the 2003 formula SAE racecar is to evaluate or
identify the problems with the cur rent and previous designs/setups.
The suspension parameters in the 2001 and 2002 formula SAE Racecar as they were
designed is as follows.
Parameters 2001 2002 Wheelbase (mm) 1700 1760 Track, front (mm) 1285 1285 Track, rear (mm) 1285 1285 Tire Hoosier 20.0x6.0 - 13, R25 compound Scrub Radius (mm) 42 38 Kingpin Inclination (deg) 0 2.8 Castor (deg) 4 4.8 Castor Trail (mm) 20 21 Roll Centre Height, front (mm) -39.6 18 Roll Centre Height, rear (mm) 15.24 32 Steering Parallel 70% Ackerman Weight Distribution Front Left (kg) 61 70 Front Right (kg) 60 70 Rear Left (kg) 90 81 Rear Right (kg) 90 81 Table 4.1 2001/2002 Suspension Parameters
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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The first thing to notice is that the roll centres were under the ground in 2001. This was
unintentional an occurred as a result of incorrect tire diameter and deflection.
The under steering apparent in both racecars was a result of a rear suspension that was
working well partnered with a front suspension that was not. The castor on either of the
racecars was not great enough to deal with the camber gain in roll that the car exhibited
in the front geometry. The evidence is clear that the front tires were cambering
excessively, when the used front tires are closely examined.
Figure 4.1 Poor Wear on Front Tires of 2002 Car
Some other issues that become apparent with the previous cars are that the roll centres
lateral movement in roll is outrageous. They almost leave the vehicle’s track. This kind of
roll centre movement makes the car difficult for an inexperienced driver to predict. Also,
the manufacturing techniques to acquire the proposed geometry were appalling. The
suspension pick up points were welded to the chassis with a student holding them in
position with pliers, whilst the welder tacked them on. If this kind of inaccuracies are
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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going to be introduced in manufacturing then the roll centre analysis and any other
geometry may as well be forgotten about.
The spring and relative anti-roll rates were initially analysed in 2001, but not tuned with
an anti- roll bar, as the anti-roll bar designed for use in 2001 was a failure. The weight
distribution moved forward in 2002, however, the spring and relative anti-roll rates were
not reanalysed.
The steering was supposed to be 70% Ackerman in the 2002 racecar. Upon extensive
theoretical and practical analysis it was determined that the 2002 racecar actually
realistically had close to parallel steering. The position of the steering rack meant that the
onset of inversion of the inside steering arm was delayed to much to have any effect at
all.
The Torsen differential used on both these racecars is a torque sensitive differential. It
locks up when under torque or a torque bias. The viscosity of the oil inside it determines
the bias in which it locks. Both the drive and braking torques are passed through the
differential so when the racecar is either accelerating or braking the differential is
effectively locked. The formula SAE competition comprises of a tight and twisty circuit
and as such most of the time on corner entry or exit the differential is locked. This point
was illustrated when the differential failed and was permanently locked during the
endurance event of competition in 2002. Not only did this not slow the car at all, it
actually made the car easier to predict on corner entry and exit, due to the lack of
transients of the differential locking.
All these factors of miscalculation, inaccuracy or lack of calculation at all lead to the
average suspension performance of the previous racecars.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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5. 2003 SUSPENSION GEOMETRY DESIGN
The 2003 suspension geometry design is entirely new to that of the 2002/2001 racecars.
The decision to run the car with no differential has had a great effect on the approach of
the goals of the suspension setup.
The omitted differential, meant that if the car would attempt to “Drive through the front
wheels” if the weight transfers weren’t setup such as to prevent it.
The main points of the design of the 2003 suspension was to achieve a lot more than
usual transverse weight transfer (from inside rear to outside front). This was to be
achieved by the use of lots of castor and Ackerman in the steering.
The parameters chosen for the 2003 geometry and an explanation of the effects of these
are described below.
5.1 Wheelbase
The wheelbase was chosen to be the smallest on the rule limit at 1525 mm. This was to
increase the longitudinal weight transfer and increase the turn responsiveness of the car.
The small wheelbase will also benefit the weight transfer, providing more traction in both
braking and accelerating situations. Also, to some degree the car can be steered with the
application of throttle/brake on the onset of under steer or over steer respectively.
The front wishbones are swept backwards rather than even to get the wheelbase down
whist keeping the rear attachment on the front roll hoop. It also allowed the steer to be in
behind the lower wishbone to keep the steering rack low in the car whist avoiding bump
steer.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 5.1 Front Wishbones are Swept Backwards
5.2 Track
The track is at 1200 mm front and 1100 mm rear. This difference in track was chosen to
create more weight transfer in the rear than in the front and lower the difference in
cornering wheel speed in the rear, to compensate for the omitted diffe rential.
The wheelbase to track ratio is then a lot smaller, at 1.27, than 2001 and 2002 with 1.33
and 1.37 respectively. This means that the racecar will possess a lot more agility with it’s
decreased yaw resistance and yawing inertia. This value is more typical of a go-cart and
therefore, will be more suited to the go-cart like circuits this racecar will endure.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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5.3 Roll Centres
Driver feedback was one off the major concerns involved in the placement of roll centres.
It was considered just as important as the effects of the roll centres in weight transfers
and racecar cornering attitude. To achieve accurate and informative feedback to the driver
not only the roll centre placement has to be considered but also the roll centre movement.
The roll centres are above and as close to the ground as feasible making sure they never
pass through the ground, to control weight transfer by making it mainly elastic and
avoiding jacking/change in jacking confusing the driver. The lateral roll centre movement
was also cons idered and almost zero movement was achieved with a ratio of width of
chassis in top to width of chassis in bottom of 1.5. The front roll centre is statically at
35mm and the rear at 38mm. The rear is slightly higher than the front to give the feeling
of under steer initially on turn in. This is due to the track variation in roll. The higher roll
centre in the rear means that the increase in track on the outside of the vehicle in the rear
is greater than that of the front with a lower roll centre. The overall effect is that the
racecar’s chassis rotates with respect to the wheels, ever so slightly, to face the outside of
the turn. Thus creating an under steering type feeling.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 5.2 Front roll Centre Movement with 1° of roll (All measurements are in inches)
Figure 5.3 Rear roll Centre Movement with 1° of roll (All measurements are in inches)
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5.4 Anti-dive, Anti-squat, Anti-lift & Pitch Centre
Just as important to driver feedback is the pitch centre and anti-dive, anti-lift and anti-
squat geometries.
The anti-dive and anti-squat was chosen to stop movement of the pitch centre. There is
10% of anti-dive and 0% of anti-squat. The reason for adding anti-dive and not anti-squat
is because of the considerably larger spring rate in the rear combined with less weight
transfer (i.e. better braking than accelerating). The pitch centre is 1 mm above the ground
and 600 mm forward of mid wheel base and moves only 3 mm up and 384 mm forward
when under full braking of 1.5g.
5.5 Anti-roll Rates
The anti-roll rate not only determines the amount the chassis rolls during cornering but
the relative anti-roll rates, front to rear, determine the weight transfer characteristics of
the racecar. Many racecar engineers refer to the relative roll stiffness as the “magic
number”. Changing the relative anti-roll rate front to rear is the single most effective way
of establishing a balanced racecar. By changing the relative anti-roll rate and hence the
relative weight transfer, the overall mechanical grip can be sacrificed at one end of the
racecar to improve the other, until a balance is achieved.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 5.4 Anti-roll bar Design (only half CAD modelled)
The relative anti-roll rate can be adjusted by the single rear anti-roll bar. The adjustment
in the anti-roll bar goes from 87 N.m/deg rotation to 424 N.m/deg rotation. This
adjustment is achieved by adjustment in the lever arm length to the anti-roll bar. This
allows a range of relative anti-roll rate ratio of 44% (softest anti-roll bar setting) to 32%
(stiffest anti-roll bar setting) or 49% with out anti-roll bar.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Roll Stiffness
0.3
0.320.340.36
0.380.4
0.42
0.440.460.48
0.5
0 100 200 300 400 500
Rear Anti-roll Bar Stiffness (Nm/deg roll)
% F
ron
t A
nti
-ro
ll S
tiff
nes
s
Figure 5.5 Relative Anti-roll Stiffness with Rear Anti-roll Bar Adjustment
5.6 Steering Geometry
The choice of the percentage of Ackerman steering geometry to run is complicated. It is
well documented that the addition of pro Ackerman (over 100%) or toe out will achieve
better turn in response. Turn in response was something that was severely lacking in the
previous UQ formula SAE racecars. However, from tire slip angle analysis, the perfect
Ackerman to run would be approximately 70% for steady state, depending on the tire.
Yet, in the opinion of many racecar engineers, the unloading of the inside tire in turning
is so great that having the inside tire at the optimum slip angle is not really that important.
In fact, trading down from the optimum lateral grip on the inside tire, which may in be
almost nothing due to it’s severe unloading, is not much to compromise for the gains in
turn in response achieved with pro Ackerman. With this in mind the steering is adjustable
from 80% to 120% Ackerman. Interchangeable steering arms on the uprights achieve this
adjustment.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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5.7 Kingpin/Castor
The kingpin was chosen to be 0° as kingpin positively cambers the outside wheel when
steered and an acceptable scrub radius of 30 mm could be achieved with out the use of
kingpin. 7° of castor was chosen to promote a considerable amount of transverse weight
transfer.
5.8 Camber Gain
The camber gain in roll and dive was chosen considering the kingpin, castor and
spring/anti-roll rates as well as the trade-off for different driving manoeuvres. The trade-
off between roll and dive was evaluated front and rear. It was decided that roll was more
important than dive to improve cornering ability whilst lowering the need for negative
static camber to keep the loaded wheel not positively cambered. Eliminating substantial
static camber also helps with accelerating and braking situations. The front is less biased
towards favouring roll as the castor helps in steering to maintain good camber attitude
whilst cornering.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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The following values of camber gain where obtained in the new geometry.
Front Rear
Camber coefficient in bump (° / 10 mm bump) 0.5 0.6
Camber coefficient in roll (° / g) 0.42 0.38
Table 5.1 Camber Gain Coefficients
These values were analysed in suspension analyser to achieve 0° camber on the two
outside, loaded wheels in corner. This was achieved by estimation of the steering angle in
various radius corners at different lateral acceleration levels. Ultimately, the values were
entered into a excel spreadsheet for ease of evaluation of the different situations. The
above values were deemed to be the best compromise based on the evaluations of the
spreadsheets results.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6. OVERVIEW OF 2003 SUSPENSION
COMPONENT DESIGN
6.1 Suspension Loading
One of the main goals of the 2003 design was to reduce the mass of the vehicle as much
as possible without compromising structural integrity. With a competitive formula SAE
racecar being approximately 220 kg (almost 2/3 of the existing 2002 University of
Queensland racecar), a lot of weight was to be removed. This was only going to be
achieved by making all components of the vehicle designed to be on the limit of failure
for their maximum potential loading. Before a design on the limit of failure could be
established, with respect to the suspension components, the exact details of the loading
needed to be understood with great detail and accuracy.
The forces on the suspension members as well as upright and rocker loading could be
evaluated by considering the maximum accelerating, braking and cornering loadings.
However, the evaluation of the distribution of the loading to various wheels in different
driving manoeuvres and the factor of safety to apply to this loading with respect to shock
and bumpy road surfaces still needed to be established or explored in great detail.
6.1.1 Strain Gauge Testing
The evaluation of these factors was established, or at least better understood, by the use
of strain gauges measurements on all suspe nsion members on the left hand side of the
existing 2002 University of Queensland racecar during testing sessions conducted on the
16th and 24th of April, 2003.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 6.1 Strain Gauge Testing
The strain gauge testing was conducted using an existing strain gauge amplifier built by
Barry Alsop. It had 2 channels with Dataforth SCM5B38 strain gauge modules and a low
pass filter. The two-pole low pass filter was of 3 Hz and the sample rate was 30 samples
per second. The data was recorded by a laptop with a 8 bit A/D converter National
Instruments DAQ card. The software doing the logging was a Lab view module. The
strain gauges were dual element rosettes with one gauge in the axis of strain and one
across the axis. The one across the axis was for temperature compensation of the
wheatstone bridge. They were placed on one side of each member only. The rod ends and
spherical bearings meant there was theoretically no bending in any of the members. So
strain gauges on one side of the beam were adequate for measuring the
tension/compression the beams experienced.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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The other two resistors, which completed the wheatstone bridge where chosen with the
same temperature coefficient by heating the resistors and measuring the change in
resistance.
The offset nulling for the wheatstone bridge was done at the track with the car on the
ground. Therefore the vehicles resting weight was considered 0 strain for all members
including pushrods.
Calibration of the strain gauges was performed by hanging various weights on one end of
each member, with the other end suspended from the roof.
A testing circuit was designed to test the various driving manoeuvres of the vehicle were
performed in a range of various testing runs. The maximum recording time of the
datalogger was 3mins.
6.1.2 Bump and Braking Shock Factors
The evaluation of the braking and shock factors with the use of the strain gauges was
quite effective. The comparison of the actual loading in driving situations to the
theoretical loading in these situations was extremely informative. The steady state
cornering loads were as expected, illustrating the fact that little or no lateral grip
generated on the inside wheel. However, the most interesting facts to come from this
testing were that there was always a peak in the wishbone loading on the application of
heavy braking. This shock peak in most cases being 2 times that of the steady state
braking loading. Also, the circuit in which testing was conducted on this particular day
had a few bumps and potholes, which inevitably got driven over at considerable speed.
The pothole generated loadings 5 times that of the steady state in the pushrods and
steering links.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.1.3 Fatigue Design
The evaluation of fatigue frequencies for the design of the aluminium uprights and
rockers (aluminium components designed against fatigue failure) was also to be
established by the strain gauge data.
However, the strain gauge amplifier utilized, had a 3 Hz low pass filter incorporated. The
problem being that the suspension fatigue da mage frequencies would be of a considerably
larger than the 3 Hz filter. To cut a long story short the frequency spectrum plot was
established only to realize that the results of the analysis were entirely useless.
The frequencies seen in this frequency spectrum plot for a cornering manoeuvre are
ridiculous and entirely useless in the analysis of fatigue of any of the suspension
components.
In future, if the loading frequencies are to be considered in design, frequencies of at least
up to 100 Hz should be recorded. As the wheel rotational frequency at the vehicles top
speed of 140 km/h is 23.6 Hz or 148.28 rad/s, giving a factor of four to overcome aliasing
effects.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.2 Wishbone Construction
Wishbones were constructed of two sections of circular hollow tubing, two rod end
inserts, two rod ends and a spherical bearing housing with spherical bearing. The
wishbone that has the pushrod/pullrod connected to it also has a connecting plate
assembly.
Figure 6.2 Rear Lower Wishbone
The single most important consideration with the construction of the wishbones is that
the direction of all members passes through the node of the spherical bearing housing,
especially that of the pushrod/pullrod. The failure to do so will leave wishbone members
in bending and consequently lead to excessive loading and failure. This fact was realized
in 2001 with the failure of the rear lower wishbones in bending.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.2.1 Tubing Selection
The Selection of tubing was based on the maximum loading both in tension and
compression. The material chosen for the wishbones was racetech 4130 chromoly, with a
yield strength of 650 MPa. The list of available tubing in this series was restricted. ¾”
tube was to be retained from the previous years designs to give the required stiffness of
the suspe nsion wishbones, so the wall thickness required was all that needed to be
determined. In tension, simple normal stress calculation was used and in compression,
Euler’s buckling theorem was used to establish the onset of buckling. Considering the
maximum loading of 10468.8 N in tension, 18183.3 N in compression and maximum rod
length of 0.5 m in the 2003 geometry design incorporating the before mentioned shock
factors, the tubing was chosen to be ¾” CHS with 0.9 mm wall thickness. This tubing
size would see a stress of 278.622 MPa and with a critical buckling load of 40155 N, the
onset of buckling was likely to occur.
6.2.2 Rod end Selection
There are many different rod end manufacturers, producing products of various qualities.
Due to budget restrictions in the project and the kind sponsorship of linear bearings for
rod end and spherical bearings the choice was narrowed to 2 different series, PMG or
RMT.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.2.2.1 Testing
On the 29th of May 2003 rod end testing was undertaken in the materials department. The
testing involved the two previously mentioned rod end bearings series (PMG and RMT).
Intuition and previous design lead to the initial selection of 5/16” rod end bearings were
considered the approximate size required for this application and as such were the subject
of the initial rod end testing.
Specimen 1 (PM5G) was tested with a high tensile bolt through the eye, which was held
by the instron at one end and 4 grade 8 nuts clamped by the instron at the other. See
figure 1. The tensile bolt bent as the load was applied, and therefore the data from this
test is uncharacteristic of the rod end bearing. The deflection measurement taken, by the
instron machine, being that of the rod end and the shaft. This test was deemed a failure
and consequently, the shaft deflection problem had to be rectified for further testing.
Figure 6.3 Initial Setup of Rod End Bearing Testing
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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The other specimens (2-5) were tested with a hardened steel shaft. Also, the nuts at the
other end were not simply clamped in the instron as before. Two (2) grade 8 nuts were
placed on the end of the rod end bearing and in a frame that restrained only the nuts. See
figure 2. The idea here was to only have the amount of thread in the testing as would be
seen as the rod end would be used, so if thread failure was the critical mode of failure it
would be seen in the testing.
Figure 6.4 Revised Setup of Rod End Bearing Testing
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Rod End Testing Results
0
500
1000
1500
2000
2500
3000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Displacement (mm)
Load
(kgf
)
Specimen 1 (PM5G)
Specimen 2 (PM5G)
Specimen 3 (PM5G)
Specimen 4 (RMT5X5)
Specimen 5 (RMT5X5)
Figure 6.5 Results of Rod end Bearing Testing
A smaller rod end in the RMT series could be considered. However, the smallest in this
series is the 5/16” rod end. This being considered, the PM5G 5/16” UNF rod ends were
chosen, as they are strong enough for this application.
6.2.3 Insert Design
The tubing insert is the piece in the end of the tubing that the rod end bearings thread
into. The inserts in the previous two years designs were silver soldered into the tubing.
The design of the insert was of a considerable length due to the need for great surface
area for the silver solder to be effective. A better solution, in my opinion, is to just weld
in the insert. The insert can then be half the length and consequently half the weight.
Consequently, as the tubing is 4130 chromoly, the insert being welded into the tubing
was to be of a similar material. 4340 alloy steel was the only material available.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 6.6 Wishbone Insert
Note: Hexagonal section was used for ease of rod end adjustment.
6.3 Rocker and Upright Design
The rockers and uprights design were to be made from machined billet aluminium 2024-
T351. This alloy was chosen for it’s high strength relative to other aluminium’s, with a
yield strength of 455 MPa, however, the presence of the alloying element copper makes it
suitable for machining.
With the lack of fatigue frequency data, which was to be determined from the strain
gauge data, another type of estimation of fatigue life of the components had to be
evaluated. The estimation of a loading with an alternating amplitude equal to the mean
amplitude was deemed an appropriate approximation.
With the evaluation of this amplitude ratio in the appropriate fatigue strength diagram for
2024-T351 for infinite life gave a maximum stress value of 14.5 ksi or 100 MPa.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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The parts were designed to be as light as possible whilst maintaining stress levels below
100 MPa in the stress concentrators in all loading situations.
Figure 6.7 Front Upright
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 6.8 Rear Upright
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Figure 6.9 Front Rocker
Figure 6.10 Rear Rocker
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6.4 Spring and Damper
6.4.1 Selection
The selection of a mountain bike spring and damper unit is almost unanimous among
formula SAE designs. This is not only because of the fact that they are almost the only
thing commercially available that is suitable. They are compact, light weight, have
interchangeable springs with varying stiffness and have sophisticated and adjustable
damping in both compression and rebound.
Figure 6.11 Risse Racing Jupiter 5 Shock
The particular shock unit chosen for this application was a Risse Racing Jupiter 5. It has
the following features:
• 2 ¼ “ Travel
• External Compression damping adjustment
• External Rebound damping adjustment
• Independent damping circuits for compression and rebound
• Large piston allows for wide damping adjustment range
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• Gas charged eliminates cavitation
• Adjustable preload for fine tuning sag
6.4.2 Damper Dynamometer
The dampers were taken to the damper dyno at fulcrum suspensions to quantify their
individual damping properties. This would allow informed damping set-up decisions. The
damper dynamometer software produces various different graphs, however the graph of
most interest to this project was the force versus velocity graphs. All 4 dampers were
tested individually. The dampers had 14 clicks of compression adjustment and 6 clicks of
rebound adjustment.
Figure 6.12 Damper Dyno Results of 1 Shock
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Some interesting points to note are:
• All 4 different dampers yielded different results on the same settings
• Compression damping is approximately linear
• Rebound damping is approximately linear
• The available range of damping available in these dampers will allow any where
from 50% to 150% of critical damping on the racecar.
6.4.3 Spring Testing
Spring testing was undertaken to establish the real spring rates of the springs obtained.
This was deemed to be a sensible operation, to establish if the rates where as intended by
the manufacturer, as correct spring rates are so critical to the vehicle performance.
Spring Rates
y = 0.0624x - 0.0162
y = 0.0342x + 0.0176
y = 0.0411x - 0.0263
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50 60
Displacement (mm)
Load
(kN
) 225 lb Risse
180 lb Thomas Marsh
225 lb Fox
Figure 6.13 Graph of Results
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Spring Rate 180 lb
Thomas Marsh 225 lb Risse
225 lb Fox
KN/mm 0.0342 0.0624 0.0411 N/m 34200 62400 41100 lb/" 195.3 356.3 234.7
Table 6.1 Actual Spring Rates Results
The Thomas marsh and fox spring rates were close to their designed value. However, the
Risse spring was a lot stiffer than as designed.
6.4.4 X-Ray
The placement of the spring and damper units in the vehicle required that a spherical
bearing be placed in both ends of the damper unit. This presented a major problem as the
bolt needed to secure the damper unit needed to be of adequate size to take the loading
and yet a spherical bearing needed to be sourced that would fit into the tight hole without
too much machining of the damper unit. The spherical bearing chosen was an SKF
GE6C. It allowed a 6 mm high tensile bolt to be used and didn’t require too much
machining for fitment, only 1 mm larger diameter. The machining was not blindly
performed. X-Rays taken in the department of Veterinary Science illustrated just how
close the machining came to interfering with internal passages and mechanical
adjustment components.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.5 Steering Selection
On researching steering rack availability of commercial steering racks. It was deemed
economically viable to purchase a BRT steering rack at $400 US for a 750g it wasn’t
even worth cons idering manufacturing a custom one.
Figure 6.14 Steering Rack in 2003 Racecar
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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6.6 Accuracy & Adjustment
One of the major considerations in the construction of the 2003 racecar was the accuracy
to which the major components were constructed. Particular care was taken in the chassis
construction to ensure that the suspension attachment points were in exactly, or as close
to as possible, in the place as designed. Even the slightest inaccuracy of 1 mm can move
the roll center by up to 5 mm.
Figure 6.15 Chassis on Jig for suspension Pickup Accuracy
All suspension parameters such as camber, castor, wheel alignment, ride height and toe
can adjusted by the rod end thread tuning. In the case of the ride height and toe
adjustments the pushrod/pullrod and toelink members function as turnbuckles with both a
right and left hand thread rod end a for ease of adjustment on the car.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Kingpin inclination on this racecar is 0° and is not adjustable. Making the kingpin
inclination adjustable is a difficult task, without compromising the design. In 2001, a rod
end was used on the upper front wishbone connection to the upright. It was consequently
in bending under braking and inevitably yielded during driving. The only other way to
achieve adjustable kingpin inclination is to shim pack a bracket to the connection point of
the upper wishbone. Both options compromise the lightweight, simple and effective
design and therefore, kingpin inclination adjustment was sacrificed.
6.7 Component Placement
The placement of inboard suspension components within the chassis is a difficult task
and some of the main points to consider whilst doing so are:
• Aesthetics of Packaging
• Linearity of movement
• Chassis load paths
6.7.1 Rocker, Spring and Damper and Anti-roll bar Placement
As in previous years the springs and dampers where placed with such a ratio to utilize all
the damper travel. This is to maximize the efficiency of the damper and avoid potential
cavitations. The other main concern of the rocker, spring and damper placement is the
linearity of the movement of the spring compression to upright displacement. It is
impossible to get exactly linear movement, however, close to linear movement can be
achieved. The design methodology for this was to place the spring and damper unit with
respect to the rocker in such a way that at full compression/travel they met at right angles.
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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This would mean that the movement would be as close to linear as possible and the
suspension movement would always be getting progressively stiffer rather than softer.
The rear anti-roll bar placement was placed using the same design considerations as the
rocker, spring and damper placement.
Figure 6.16 Front Spring and Damper Placement
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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Figure 6.17 Rear Spring/Damper and Anti-roll Bar Placement
Daniel Raymond Burt ‘Formula SAE Suspension Design’
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7. VEHICLE SET UP
The racecar set up is just as important as the original design. It is in the set up that all the
inaccuracies introduced in the construction of suspension components can be rectified to
ensure the geometry as the vehicle is designed to have is in fact, the same as the geometry
achieved on the vehicle.
A wheel alignment is the first set up operation that is to be performed on the vehicle.
The University of Queensland’s sponsorship with fulcrum suspensions allows free wheel
alignment time on their wheel aligner. This particular wheel aligner performs laser
measurements through many steering angle operations to determine suspension
alignment.
Through the use of mathematics and some logical thinking, all links that are out in the
alignment of the suspension can be rectified in 1 adjustment iteration. The wheel
alignment is performed by the adjustment of rod end bearings at the end of all members
as discussed in the previous chapter.
Some interesting points to note about this wheel alignment set up are:
• Toe is extremely sensitive and must be adjusted after all changes.
• There are no chassis alignment measurements - chassis alignment to straight
suspension still questionable.
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A well-designed suspension system will have plenty of room for adjustment. The
possibilities for adjustment allowable in this racecar are:
• Ride Height
• Castor
• Camber
• Toe
• Spring Rates
• Rear Anti-roll Bar Rates
• Compression Damping
• Rebound Damping
• Anti-Dive Geometry
• % Ackerman on steering
• Tire Pressure
Each setup change has an effect on all other suspension parameters and this must be
considered whilst setting up the racecar.
For example, a ride height change will change the roll centres; Tire pressure will change
the roll centres; Castor will change the roll centres; spring rates will change anti-roll
rates; even damper adjustment will affect anti-roll rates, however, only in the transient
phase. These are only to name a few of the effects of a few possible changes.
Considering this and the fact that the driver’s style is just as an important and integral
part of the vehicles performance, racecar setup is not an easy task and can be a very
daunting task. It requires a lot of experience and the use of intuition and inference.
Unfortunately, due to the late completion of the racecar this year, not enough time has
been allowed to go into too much detail with the setup of the 2003 university of
Queensland formula SAE racecar as was originally intended with this thesis.
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8. RESULTS
The resulting weight distribution on the racecar was somewhat different to as designed.
The original design was for a weight distribution of 50:50. However, the prediction of the
weight distribution of a racecar that didn’t exist at the time is near impossible. The
resulting weight distribution of 53.5:46.5 front heavy, with a 90 kg driver.
This problem had to be rectified before the racecar could be driven/tested successfully.
The spring rates had to be changed from those original designed for (180 lb front, 225 lb
rear), to 235 lb front and 195 lb rear to achieve similar sprung mass frequencies.
Once this was rectified, extensive testing was undertaken.
The first testing session was conducted immediately following the racecar construction
completion on the 8/10/03. This short testing session revealed a lot of minor problems as
well as toe control issues. This was followed by a complete suspension and drive train
strip and crack test. None of the parts had been damaged or showed crack initiation. A
second and much longer testing session was conducted on 10/10/03.
The 2003 car pulls extremely hard with its spool differential and almost flat torque from
5000 rpm. Its turn in response was amazing, and with no suspension tuning other than a
comprehensive wheel alignment at this stage the results were more than pleasing. The
vehicle wasn’t perfectly balanced, being slightly prone to over steer on power
application. However, at this stage the rear anti-roll bar had not been implemented.
With preliminary testing completed the evaluation of the rear toe control and inevitably
redesign and reconstruction of toe link mounting location and toe link. The testing was
simple and involved the application of a torque to the wheel whilst measuring the
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deflection through use of a wheel-mounted laser. The results of the testing revealed that
toe control was in fact an issue.
Rear Toe Deflection
y = 0.0054x + 0.3192
00.20.40.60.8
11.21.41.61.8
0 50 100 150 200 250
Torque (Nm)
Toe (deg)
Figure 8.1 Rear Toe Deflection
With the steady state cornering torque on the wheel in the order of 100 Nm which relates
to a deflection of almost 1 deg, which is outrageous. The problem or reason for the
excessive deflection was the small moment arm to the toe link from the kingpin of 50
mm. The most suitable solution to this problem was to relocate the toe link further up the
upright and chassis, where a much larger moment could be achieved without clashing.
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Figure 8.2 Toe Control Solution
The implementation of the rear anti-roll bar and fixed rear toe control for a testing session
on the 19/10/03 saw a dramatic improvement in the cornering ability of the racecar.
The performance of the 2003 formula SAE racecar is astounding. In comparison to the
2001/2002 racecar it is in another league altogether. With myself as driver skid pad
testing was undertaken. The racecar was setup as it would be in competition, however,
with formula ford tires instead of Hoosier slicks. The skid pad was of an inside diameter
of 15.25 m as in the competition, however, on undulating off camber asphalt. Consistent
times of 5.7s a lap were achieved. Evaluation of the average lateral acceleration for this
yielded a result of 0.99 g’s. Considering that the formula ford tires are no where near as
soft a compound as the Hoosier R25A compound tires as used in previous years and to be
used in this years competition, and that with the Hoosier tires the 2002 racecar achieved a
maximum of 1.14 g’s, as seen in Riseley [6], the resulting performance is going to be
very interesting when the Hoosier R25A compound tires are used.
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The vehicle appears to be performing as designed, sometimes elevating the rear inside
wheel on corner entry. The camber of all wheels seem to be optimal with tire
temperatures, as monitored in the pits, a consistent 41°C across the front tires and 43 °C
across the rear.
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9. CONCLUSIONS & RECOMMENDATIONS
In conclusion, the 2003 formula SAE racecar has proven to be quite successful so far in
testing. The team spirits are high for the upcoming competition with many testing days
scheduled in the month left before the competition.
With regard to the outcome of the suspension design, the results so far look promising
and so far the design is quite successful. There is no right or wrong answer in suspension
design. All suspension parameters have a unique relationship with all the others and as
such they must be addressed as a complete suspension package. With more time tuning
these suspension parameter the car will hopefully go on to be competitive at the formula
SAE competition in Adelaide on the 4th to 7th of December this year.
In all honestly, the successful use of data acquisition systems on racing cars is difficult to
achieve. Measuring the shock position is good for calculating wheel weights and
developing shock speed histograms for shock setup. Tire temperature sensors can tell if
the tires are cambered excessively or over/under inflated. Strain gauges on the suspension
members can help evaluate the shock and bump loading of the member as well as
possibly evaluated fatigue loading frequencies for component design.
Other than this, the evaluation of other parameters with data acquisition is of not such a
straightforward manner.
I guess the point is that the problem is not only in how do you achieve accurate
measurement of other parameters, but also what changes should be made upon knowing
such information.
For example, if optical slip angle sensors were to be used in the future, they can only be
used for academic purposes, considering it’s already known that pro Ackerman works
best on formula SAE cars. The result will tell you that you should be running around 70%
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Ackerman for best performance in the steady state. So the point being why measure it if
it’s not going to prompt a setup change in the car, or achieve anything towards the cars
performance.
The driver is just as much an integral part of the cars performance as the car itself and
must be treated as such. Often driver feedback is a lot more useful than any data ever
could be.
The use of the program suspension analyzer has some potential problems. It does not take
into account tire deformation whilst simulating vehicle steady state dynamics. The static
deformation of tire can be compensated for, however, a certain degree of inaccuracy is
introduced in the roll center, camber analysis without considering the change in tire
deformation in the various dynamic situations being modeled.
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10. BIBLIOGRAPHY
1. Gillespie, T.D.,1992, Fundamentals of Vehicle Dynamics, Society of Automotive
Engineers, Warrendale, Pa.
2. Juvinal, R.C., Marshek, K.M., 2000, Fundamentals of Machine Component
Design (3rd Edition), New York, John Wiley and Sons.
3. Manhire, O., 2001, Suspension Geometry Design of the 2001 University of
Queensland Formula SAE Racecar, BE thesis, University of Queensland.
4. Maria, P., 2001, Suspension Component Design for Formula SAE, BE thesis,
University of Queens land.
5. Milliken, W.F and Milliken, D.L., 1995, Racecar Vehicle Dynamics, Society of
Automotive Engineers, Warrendale, Pa. USA
6. Riseley, C., 2002, Suspension Optimisation of the 2001 University of Queensland
Formula SAE Racecar, BE thesis, University of Que ensland.
7. Smith C., 1996, Drive to Win , Carroll Smith Consulting Inc, Palos Verdes Estates,
Ca USA.
8. Smith C., 1978, Tune to Win , Aero Publishers Inc, Fallbrook, Ca USA.
9. Smith C., 1975, Prepare to Win , Aero Publishers Inc, Fallbrook, Ca USA.
10. 2003, Hoosier Racing Tires Homepage, [Online], <www.hoosiertire.com>,
[Accessed January 15 2003]
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APPENDIX A
FSAE-A Design Spec Sheet 2003 Competitors: Please replace the sample specification values in the table below with those appropriate for your vehicle and submit this to with your design report. This information will be reviewed by the design judges and may be referred to during the event. --Please do not modify format of this sheet. Common formatting will help keep the judges happy! --The sample value s are fictional and may not represent appropriate design specs. --Submitted data will NOT be made public or shared with other teams.
Car No 41
University University of Queensland
Dimensions Front Rear
Overall Length, Width, Height
Wheelbase 1525 mm
Track 1200 mm 1100 mm
Weight with 68 kg driver 154 kg 154 kg
Suspension Parameters Front Rear
Suspension Type Unequal length A-Arms. Pull rod actuated spring/damper unit
Unequal length A-Arms. Push rod actuated spring/damper unit.
Tyre Size and Compound Type 20.7x6-13 Hoosier R25A 20.7x6-13 Hoosier R25A Wheels 3 Pce, Mag Centre
13"x6"-43mm o/s 3 Pce, Mag Centre 13"x6"-43mm o/s
Design ride height (chassis to ground)
40 mm 40 mm
Center of Gravity Design Height 300 mm above ground Suspension design travel 26 mm jounce/ 26 mm
rebound 26 mm jounce/ 26 mm rebound
Wheel rate 19.5 N/mm 25.4 N/mm Roll rate 0.86° / g, without anti-roll bars Sprung mass natural frequency (in vertical direction)
2.76 HZ 3.15 Hz
Jounce Damping 90% of critical damping @ 30mm/sec
56% of critical damping @ 30mm/sec
Rebound Damping 62% of critical damping @ 30mm/sec
54% of critical damping @ 30mm/sec
Motion ratio 0.9:1 0.96:1 Camber coefficient in bump 0.5° / 10 mm bump 0.6° / 10 mm bump
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Camber coefficient in roll 0.42°/g 0.38°/g Static Toe and adjustment method 0mm toe out adj. by tie
rods 0mm toe in adj. by toe links
Static camber and adjustment method
0° by inboard rod ends 0° by inboard rod ends
Front Caster and adjustment method
7° adjustable by rod ends
Front Kingpin Axis 0° non-adjustable Kingpin offset and trail 30 mm offset, 32 mm
trail
Static Ackerman and adjustment method
100% Ackerman @4.8m turn diameter Adjustment by interchangable steering link arms
Anti dive / Anti Squat AD 10% @ 1.5 g's, adjustable by spacers ( 0%-10% )
0% (parallel)
Roll center position static 35 mm above ground, CL of the car
38 mm above ground, CL of the car
Roll center position at 1g lateral acceleration
35 mm above ground, moves 6.35 mm toward inner wheel (with no steer), central with 15m turn diameter, 6.35mm toward outer wheel with 7m turn diameter
38 mm above ground, moves 2.8 mm toward outer wheel
Steering System location Rear steer, not in line with lower A-arm, yet no bump steer
Brake System / Hub & Axle Front Rear
Rotors Student designed, lasercut from bis80 steel, hub mounted, 230mm dia.
Student designed, lasercut from bis80 steel, spool mounted, 220mm dia.
Master Cylinder PBR, Mechanical bias bar, for balance. Calipers 44.5 mm Wilwood Billet
Dynalite 44.5 mm Wilwood Billet Dynalite
Hub Bearings (2) off SKF6006 (30/55/13), deep groove, 55mm spacing
(2) off SKF6007 (35/62/14), deep groove, 40mm spacing
Upright Assembly CNC 2024_T351, "bolt-on" steering arms (adj ackerman), 60mm toe link
CNC 2024_T351, 60mm toe link
Axle type, size, and material Stationary axle, 4340 HT 46 Rc, Hollow 30mm OD , 20mm ID. Hub 2024_T351.
Stub axle, 4340 HT 46 Rc. Hub, 4340 HT 46 Rc
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Ergonomics
Driver Size Adjustments Fixed seat and steering wheel. Pedal box adjust fore and aft 50mm
Seat (materials, padding) Carbon fibre base, adapted to driver with individual padding (if req)
Driver Visibility (angle of side view, mirrors?)
200° side visibility, rear view mirrors on cockpit sides
Shift Actuator (type, location) L/H electromotive 'button' shifter Clutch Actuator (type, location) Custom hand lever, below steering wheel. Instrumentation
Frame
Frame Construction Steel tube space frame with bonded aluminium panels Material 4130 Chrome Moly tube Joining method and material TIG welded, 100% MPI to AS 1554.5 SP Targets (Torsional Stiffness or other)
Torsional stiffness and validation method
Bare frame weight with brackets and paint
Crush zone material Crush zone length Crush zone energy capacity
Powertrain
Manufacture and Model 1998 Honda CBR600 F3 4 cylinder, custom dry sump, with integral scavenge pump.
Displacement 599 cc Fuel Type Optimax Induction Atmospheric induction Max Power design RPM 10,000 rpm. 56.5Kw (76Hp) Max Torque design RPM 9,000 rpm. 57Nm (42ft.lbs) Min RPM for 80% max torque 5,850 rpm Effective Intake Runner Length 308 mm. 35mm ID. Effective Exhaust runner length 690 mm Primary, 31.8 mm ID. 185mm Secondary,
44.4mm ID . Exhaust header design 4-2-1 equal length, Fuel System (manf'r) Student designed/built fuel injection, sequential Fuel System Sensors IAT, CTS, CPS, TPS, EGO Injector location Above ports and pointing at back of inlet valves Intake Plenum volume 1575 cc (Butterfl y to airhorns). "Symetric" Plenum-
Runners. Compression ratio 12.0 :1 Fuel Pressure 3 bar (static), EV1, 150g/min injectors Ignition Timing MoTec M4 Coolant System and Radiator location
(2) Side pod mounted radiators, with electric fans, and water pum ps.
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Fuel Tank Location, Type Floor mounted aluminum tank between seat and firewall Muffler Carbon fibre canister.
Drivetrain
Drive Type Chain #520 Differential Type Spool Diff Final Drive Ratio 4.00 (13:52) Vehicle Speed @ max power (design) rpm
1st 45 km/h 2nd 65 km/h 3rd 81 km/h 4th 97 km/h 5th 111 km/h 6th 123 km/h Half shaft size and material GKN 21mm OD Joint type GKN Aerodynamics (if applicable)
Front Wing (lift/drag coef., material, weight)
N/A
Rear Wing (lift/drag coef., material, weight)
N/A
Undertray (downforce/speed) N/A
Wing mounting N/A
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APPENDIX B
Roll Centre Analysis
Front Geometry in Suspension Analyzer
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Front Camber Gain with 1° of roll (All measurements are in degrees)
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Front Camber Gain with 1” of dive
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Rear Geometry in Suspension Analyzer
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Rear Camber Gain with 1° of roll (All measurements are in degrees)
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Rear Camber Gain with 1” of dive
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