Report_Draft2

The Design of a Drivetrain for an
Eco-Marathon Vehicle
Author: Hugh Mc Sweeney
Student No. 13345326
3rd
Year Mechanical Engineering
National University of Ireland, Galway
22/02/2016
Supervisor: Dr. Pádraig Molloy
For Assessment as Part of ME3151

iii
Abstract
The purpose of this report is to describe the design of a drivetrain that will be used in a car built
by a group of NUI Galway Engineering students that will compete at the Shell Eco-Marathon
in London in June. The car will compete in the prototype battery-electric category. This report
describes how decisions were made on different parts of the drivetrain based on calculations,
logistics and costs.
The main priority with a drivetrain is its effect on the energy consumption of the vehicle. The
motor and the way it is used can greatly affect the efficiency of an eco-marathon vehicle. The
gearing selection based on the driving strategy was an extremely important decision and is
discussed at length in this report.
The drivetrain design consists of many parts including power transmission, motor selection and
mounting, wheel build, brake selection and mounting, motor controller and battery mounting
and driving strategy. These all have an effect on each other in some form or another and this
report outlines how decisions were made with these effects in mind.
A common trend throughout the report is the use of Matlab to create mathematical models.
This was done because a project such as this can have constantly changing parts and designs
and it is important that the benefits or disadvantages of these changes can be quickly calculated
and visualized through graphical information.
The report gives a detailed outline of how the most energy efficient drivetrain possible was
investigated, designed and built.

iv
Acknowledgements
There are many people without whom this project would not be possible. Firstly, I would like
to thank all the NUIG Eco-Marathon team members, including students and supervisors for
their dedication to and enthusiasm for this project. I would especially like to thank team
supervisors Dr. Nathan Quinlan, Dr. Rory Monaghan and Dr. Maeve Duffy who continue to
work above and beyond to organise a structure for this project to take place and dedicate endless
hours to its continued improvement. I would also like to thank fellow drivetrain designer Shane
Queenan for his help with the project and his lack of hesitation whenever I required his help or
sought his advice. Shane proved an adept leader of the drivetrain team and provided great
direction to the team members. I would also like to thank drivetrain team members Michael
Carr and Mark Carmody for the pivotal role they played in the building of the drivetrain. A
special mention must also be given to past team members Daniel Fahy and Cian Conlon-Smith
who did superb work in providing a platform, in the form of the GEEC 1.0, from which the car
could be improved upon. Daniel and Cian also gave some great advice on the designing and
building of an Eco-Marathon vehicle. Finally, I would like to thank Dr. Pádraig Molloy and
Ronan Divane for their input on the project. Weekly meetings with them provided a thorough
overview of design work and provided a great deal of guidance as to what was done well and
what could be improved.

v
Table of Contents
List of Figures............................................................................................................................1
List of Tables .............................................................................................................................4
Glossary of Terms......................................................................................................................5
List of Abbreviations .................................................................................................................5
1. Introduction ........................................................................................................................6
2. Technology & Literature Review.......................................................................................7
2.1. Existing Technologies.................................................................................................7
2.2. Useful Literature .........................................................................................................9
3. Design Approach..............................................................................................................11
4. Detailed Design Analysis .................................................................................................14
4.1. Preliminary Testing...................................................................................................14
4.2. Motor Selection.........................................................................................................17
4.3. Driving Strategy........................................................................................................34
4.4. Power Transmission System .....................................................................................40
4.5. Brakes........................................................................................................................47
4.6. Rear Wheel Hub Selection........................................................................................53
4.7. Wheel Bearings .........................................................................................................59
4.8. Rim Selection............................................................................................................61
4.9. Tyres..........................................................................................................................65
4.10. Motor Mounting ....................................................................................................67
5. Safety & Risk Analysis.....................................................................................................69
6. Conclusion........................................................................................................................70
6.1. Design Review ..........................................................................................................70
6.2. Recommendations.....................................................................................................71
6.3. Future Work ..............................................................................................................72
7. Appendices .......................................................................................................................74

vi
7.1. Appendix A ...............................................................................................................74
7.2. Appendix B ...............................................................................................................75
7.3. Appendix C ...............................................................................................................76
7.4. Appendix D ...............................................................................................................80
7.5. Appendix E................................................................................................................81
7.6. Appendix F................................................................................................................81
7.7. Appendix G ...............................................................................................................82
8. Bibliography.....................................................................................................................83
9. Drawings...........................................................................................................................85

1
List of Figures
Figure 1.1: The GEEC 1.0 completing an attempt at the Shell Eco-Marathon in 2015. (Joyce,
2016) ..........................................................................................................................................6
Figure 2.1: An example of a single speed transmission at the 2015 Eco-Marathon. This
particular one had an adjustable mechanism for tensioning the chain.......................................8
Figure 2.2: The University of Central Lancashire's car which used 26'' mountain bike rims. ..9
Figure 3.1: The shell designed by Paul Mannion resulting from studies on the aerodynamic
design of an Eco-Marathon vehicle. (Mannion, 2015) ............................................................11
Figure 4.1: Experiment results showing the relationship between steady-state rolling resistance
and total vehicle mass for three different tyre pressures..........................................................15
Figure 4.2: Maxon RE65 250W DC motor. (Maxon, 2016)...................................................18
Figure 4.3: Maxon RE50 200W DC motor (Maxon, 2016).....................................................18
Figure 4.4: Plot showing speed-torque relationship of RE50, RE65 and Ebay motors given a
maximum current of 10A.........................................................................................................19
Figure 4.5: A plot showing the efficiency of the Maxon RE50 and RE65 motors and the Ebay
motor when running with different torques at a maximum current of 10A.............................21
Figure 4.6: A plot showing the efficiency of the Maxon RE50 and RE65 motors and the Ebay
motor when running with different torques at a maximum current of 10A.............................22
Figure 4.7: A plot showing the relationship between motor efficiency and motor speed for the
Maxon RE50 and RE65 motors and the Ebay motor...............................................................23
Figure 4.8: Vehicle speed as a function of gear ratio at nominal motor speed for the Maxon
RE50 and RE65 motors and the Ebay motor...........................................................................24
Figure 4.9: A graph showing the efficiency of each motor as a function of the motor speed. The
dotted lines show the minimum and maximum speeds that the motor would operate at for the
desired vehicle speeds (6.94m/s (25 km/h) to 9.44 m/s (34 km/h)).........................................25
Figure 4.10: The track topography as supplied by the organisers. The graph shows the
‘chainage’ or distance in to the lap and the level in metres at various points associated with the
map on the next page (Shell Eco-Marathon, 2016). ................................................................26
Figure 4.11: This is a free body diagram of the car on the incline section of the course. .......28
Figure 4.12: Power required for various climbing speeds with dashed lines showing the
maximum power each motor can continuously supply along with the corresponding car
velocity.....................................................................................................................................29

2
Figure 4.13: Power required for various climbing speeds with dashed lines showing the
maximum short-term power each motor can supply along with the corresponding car velocity.
..................................................................................................................................................30
Figure 4.14: Ebay motor efficiency at various vehicle speeds with a black dotted line showing
the exit velocity, 5.5 m/s, from the incline section..................................................................33
Figure 4.15: Maxon RE50 and RE65 motors and Ebay motor efficiency at various vehicle
speeds with a colour associated dotted line showing the exit velocity for each motor. ..........34
Figure 4.16: Relationship between vehicle velocity and time when accelerating from standstill
with the RE50 motor and the Ebay motor. ..............................................................................37
Figure 4.17: London track map (Shell Eco-Marathon, 2016)..................................................39
Figure 4.18: The technique used to draw the sprocket tooth profile. The green border represents
the finished tooth profile..........................................................................................................44
Figure 4.19: Triangle used to derive the equation suitable for a mathematical model for pitch
radius diameter of a sprocket given number of teeth and pitch...............................................45
Figure 4.20: Plot showing the diameter of the driven sprocket at different gear ratios for a ¼’’
pitch chain and a ½‘’ pitch chain.............................................................................................46
Figure 4.21: The 1/4'' chain and sprocket mounted on the rear wheel.....................................47
Figure 4.22: A CAD render of a v-brake mounted between two rear members......................48
Figure 4.23: CAD render of motor mounting on under part of chassis. The red line shows where
the chain comes in contact and exits the shell. ........................................................................49
Figure 4.24: A CAD render of a v-brake mounted at the top of the wheel. ............................50
Figure 4.25: A CAD render of the mounted disc rotor and calliper. .......................................50
Figure 4.26: Free body diagram showing the forces acting on the car during brake technical
inspection.................................................................................................................................51
Figure 4.27: Free-body diagram showing the forces acting on the rotor when the brake is
activated...................................................................................................................................52
Figure 4.28: Free-body diagram showing the force from the calliper acting on the rotor.......52
Figure 4.29: A diagram of a freewheel unit using a ratchet and pawl mechanism (Liou, 2007).
..................................................................................................................................................54
Figure 4.30: A Shimano Dura-Ace track bike rear wheel hub with thread on freewheel unit
capability. (Velodrome Shop, 2016)........................................................................................54
Figure 4.31: A Carbon-Ti road bike rear wheel hub with disc brake compatibility and a built-
in freewheel unit (Carbon-Ti, 2016)........................................................................................55

3
Figure 4.32: A Quando bike rear wheel hub with disc brake and thread-on freewheel unit
compatibility. ...........................................................................................................................56
Figure 4.33: The freewheel unit which threads on to the hub (Ebay, 2016)............................56
Figure 4.34: A CAD render of the driven sprocket mounted on the freewheel unit................57
Figure 4.35: A free-body diagram showing the loads acting on bearing A and bearing B. The
large circle represents the driven sprocket...............................................................................60
Figure 4.36: Diagram showing cross-section of bead seat rim................................................62
Figure 4.37: A CAD render of the wheel hub with swaged spokes attached. .........................62
Figure 4.38: A free-body diagram showing the static loads acting on the wheel....................64
Figure 4.39: Diagram representing chain and sprockets..........................................................67
Figure 4.40: Diagram showing relationship between wraparound angle and tangent angle. ..68
Figure 4.41: CAD render of the mount design for the Ebay motor. ........................................69
Figure 4.42: A CAD render of the mount design for the Maxon RE50 motor........................69
Figure 6.1: The drivetrain of the GEEC 2.0 under construction..............................................72

4
List of Tables
Table 4.1: Maximum recommended continuous currents, torques and power outputs for each
of the motors. ...........................................................................................................................20
Table 4.2: Maximum short-term currents, torques and power output for the RE50, RE65 and
Ebay motors. ............................................................................................................................30
Table 4.3: Wheel torque and traction forces calculated from motor torques for each of the
motors at continuous and short-term draw currents.................................................................31
Table 4.4: Car deceleration calculation results on the inclined section for continuous draw
currents.....................................................................................................................................32
Table 4.5: Car deceleration calculation results on the inclined section for short-term draw
currents.....................................................................................................................................32
Table 4.6: A decision matrix weighting the suitability of various power transmission systems.
..................................................................................................................................................43
Table 4.7: Comparison of factor of safety and weight saving for nuts and bolts made of various
materials...................................................................................................................................59
Table 4.8: Information on three different tyres being investigated. ........................................65

5
Glossary of Terms
Matlab: A software program for creating mathematical models.
Swaged spokes: Spokes that must be wholly inserted through a hole in the hub before being
attached to the rim.
Shell-Eco Marathon: An annual competition that challenges students to build energy efficient
cars.
Autodesk Inventor: CAD software used for 3-d modelling and engineering drawings.
List of Abbreviations
ODE: Ordinary differential equation
CAD: Computer aided design
SEM: Shell Eco-Marathon

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1. Introduction
The Shell Eco Marathon is a competition that challenges engineering students around the world
to design, build and drive a car that is as energy efficient as possible. There are two main
categories, ‘Prototype’ and ‘Urban Concept’. Vehicles in the ‘Prototype’ category focus on
maximum efficiency while vehicles in the ‘Urban Concept’ category must adhere to stricter
design rules that make them safer for road use and more comfortable for the driver.
In May, 2015, the GEEC 1.0 seen in Figure 1.1, designed and built by a group of student
engineers from NUIG guided by academic mentors, took to the track at the European branch
of the event in Rotterdam to become the first ever Irish built car to compete in the Shell Eco-
Marathon. The Geec 1.0 achieved a score of 287 km/kWh which placed it 23rd out of 52 entries
in the ‘Prototype Battery-Electric’ category. With the aid of the knowledge gained from this
experience, it was decided to build a new car that would compete in the same category of the
event in London in 2016, the GEEC 2.0. It was hoped that with the understanding acquired of
designing energy efficient vehicles from the previous car, and with the team and operating
structure that was put in place, that the GEEC 2.0 would be more competitive with a goal of
finishing in the top half of the cars that registered a score (33 finishers in 2015). This would
require an estimated score of 405 km/kWh based on the 2015 results.
Figure 1.1: The GEEC 1.0 completing an attempt at the Shell Eco-Marathon in 2015.
(Joyce, 2016)

7
This report outlines the mechanical elements of designing the drivetrain for the GEEC 2.0. The
drivetrain encompasses a wide spectrum of items which ultimately are responsible for applying
motion to the car. The following will be discussed in detail in this report:
• Motor selection
• Motor mounting
• Power transmission
• Hub design
• Rim selection
• Tyre selection
• Brakes
• Driving strategy
2. Technology & Literature Review
Existing Technologies
The Shell Eco-Marathon 2015 in Rotterdam provided the then future designers of the GEEC
2.0 with a valuable opportunity to examine the vehicle designs of other teams. The prototype
vehicles at the competition were closely inspected and common trends were noted.
The vast majority of teams used a single-stage chain power transmission system. Aluminium
sprockets were used in most cases. Large gear ratios were not a problem for some teams but
other teams included a chain tensioning device as seen below in Figure 2.1. This would increase
the friction of the chain drive but may have solved a problem with chain slip for these teams.
The effects of a chain tensioning devices on the efficiency of the drive-train could easily be
tested once the car is built. It is also possible that some of these tensioning mechanisms were
being used for testing different gear ratios without having to change the length of the chain.
This would be very useful as changing the chain length can be a time consuming process.

8
Most teams in the prototype category were using 20’’ rims. It is thought that this was done to
accommodate the desired aerodynamic profile of the body. Many teams opted for a spoked
BMX rim while some teams with higher budgets had custom built carbon fiber disc wheels.
These were similar to the wheels used on the PAC-Car II. These wheels are much more
aerodynamic than spoked wheels and this still applies to an extent when the wheels are inside
the shell of an Eco-Marathon vehicle. Custom built disc wheels meant that custom made hubs
were also designed and built. This is currently beyond the manufacturing capability of the
NUIG team but it is definitely something that should be investigated for next year. In hindsight,
the advantages of a custom made hub are numerous as will be discussed later on in this report.
There were a few prototype vehicles present that did not conform to the 20’’ rim diameter. The
‘University of Central Lancashire’ used 26’’ mountain bike rims. The reason for this was so
that thinner 28mm tyres could be mounted in oppose to the 35mm tyres that are typically used
on BMX rims. The team stated that they experienced no problems using these tyres (which
were designed for road bike rims) on a mountain bike rim. This is commonly done with no
trouble by people using mountain bikes on the road. The smaller tyre width allows a higher
inflation pressure which reduces the area of the tyre in contact with the road which results in
lower rolling resistance. Most of the other prototype vehicles were using Michelin tyres that
are specially designed for the Shell Eco Marathon. Tests done by the PAC-Car II team
confirmed that these tyres are among the most efficient available despite the fact that they are
35mm thick. They are designed to be mounted on typical BMX rims. There are two types of
20’’ tyres that Michelin make for this event, both of which were seen at the event in abundance.
Figure 2.1: An example of a single speed transmission at the 2015 Eco-
Marathon. This particular one had an adjustable mechanism for tensioning
the chain.

9
The first type is a clincher tyre, this is a tyre where a separate tube must be inserted and inflated.
The second is a tubeless tyre which, as the name suggests, does not require a separate tube but
instead the walls of the tyre act as barrier keeping air in. The advantages of tubeless tyres are
two fold; they are lighter and they allow higher inflation pressure than a clincher tyre of the
same width.
Disc brakes were used by every prototype team witnessed. This was a surprise because disc
brakes are usually heavier and add rotating weight to the wheel in the form of a rotor. It may
be that some teams tested v-brakes and were not happy with the results but this was not
confirmed. The split between hydraulic and mechanical disc brakes was fairly even. Hydraulic
disc brakes offer higher braking power, modulation and are slightly lighter than a mechanical
disc brake. However, installation and maintenance of mechanical disc brakes is much easier as
it uses cable instead of hydraulic oil. This means that the brakes do not have to be bled and that
adjustment of the pads placement is much faster.
Most teams mounted the motor controller, battery and motor directly behind the bulkhead and
in front of the rear wheel. There was expert use of space with designs packing as much as
possible in to small amounts of space. Motor mounts were typically positioned suitably for a
single stage chain and sprocket. Some of the higher performing teams had motors built in to
the wheels. This requires a high knowledge, skill and budget and it is not likely that a motor
mounting such as that will be possible for the GEEC 2.0.
Useful Literature
Literature dealing explicitly with the design of Eco-Marathon vehicles is rare and that is why
‘The World’s Most Fuel Efficient Vehicle; Design and Development of Pac-Car II’ (Santin, et
Figure 2.2: The University of Central Lancashire's car which used
26'' mountain bike rims.

10
al., 2007) proved so important in the design of the drivetrain for the GEEC 2.0. The book
outlines the design of the Pac-Car II, a hydrogen fuel cell system built by a team of engineering
students at ETH Zurich, that became the world’s most fuel efficient vehicle in 2005 when it
achieved a score the equivalent of 5385 kilometres per a litre of gasoline. First off, the book
gives the reader a good comprehension of all the areas involved in the design of an Eco-
Marathon vehicle. It also provides an insight to the test results accumulated by the team such
as the coefficients of rolling resistance for various tyres. The power transmission system used
by the team is a single stage spur gear with the custom built wheel containing the internal driven
gear teeth near the rim. The drivetrain also consists of a second motor that can be engaged
when more power is required. Although this complexity of design was not probable for the
GEEC 2.0, it did prove interesting nonetheless and it is something to aspire to. Although the
book does not enter into great detail on design calculations, it does provide an interesting
review of how the world’s most fuel efficient vehicle was designed.
For the design analysis of the car, ‘Shigley’s Mechanical Engineering Design’ (Buyanas &
Nisbett, 2015) proved very useful. This book contains useful formulae and examples for
analysing the effects of loads acting on the likes of bolts and bearings. The book also contains
a wide array of tabulated data on the properties of various materials.
For investigating DC motors, the website of DC motor manufacturers, Maxon, proved very
useful (Maxon, 2016). The website gave key formulae for analysing DC motors. It included
information on obtaining speed-torque characteristics, assessing motor efficiency at different
operating points and it supplied useful information about the motors that the company made.

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3. Design Approach
The designing of the drivetrain was highly dictated by the aerodynamic shell. The decision was
made by the team early in the year to use the studies of Paul Mannion which resulted in the
most aerodynamic design possible for a prototype vehicle in the Shell Eco-Marathon by
adhering to the rules. The design, shown in Figure 3.1, also accounted for driver comfort, driver
visibility, cornering stability of the vehicle and the manufacturing process of the design. It was
thought that this would be a good foundation on which to base the rest of the design. This
design was open to slight manipulation as it had to be converted from a monocoque design to
a chassis mounted body. However, it was desired to stay as close to Paul’s design as possible
for aerodynamic benefits.
The chassis was then designed based on the shell design while also taking into consideration
wheel placement, driver positioning, steering components and drivetrain components. The
chassis included a roll bar, behind which space was designated for the rear wheel and the rest
of the drivetrain components. Two rear chassis members allowed the rear wheel axle to be
connected. Between this connection point and the bulkhead, all the drivetrain components
would have to be mounted. This included a power transmission system, a motor, a lithium ion
battery, a motor controller unit and a rear wheel brake. This meant that the space behind the
bulkhead would have to be optimized.
Each part of the drivetrain affected another part of the drivetrain and because of this it was
necessary to make decisions in a logical sequence. Throughout each design decision
manufacturing, installation, maintenance and budget had to be considered. The most important
factor of the drivetrain is efficiency. Motors tend to have the greatest variation in efficiency in
a drivetrain so it was important that the correct motor was chosen and that the rest of the
components were designed to suit this. The correct motor choice was based on the driving
Figure 3.1: The shell designed by Paul Mannion resulting from studies on the
aerodynamic design of an Eco-Marathon vehicle. (Mannion, 2015)

12
strategy and the track details, particularly the track gradient. The next step was transferring
power from the motor to the rear wheel through a chosen power transmission system. This then
allowed the motor mounting to be examined. The power transmission system affected the rear
wheel hub design. It was necessary for the hub to be compatible with whichever power
transmission system was chosen. The rear wheel hub also had to be compatible with the brake
if a disc brake was chosen. The hub also affected the rim choice and the load bearing
mechanism of the wheel. The rim would have to be compatible with a v-brake if a v-brake was
to be used. The placement of the battery, motor controller, chainguard and motor could then
be closely examined.
In designing the car, the safety of the driver was a priority. A good guideline to follow for
designing a safe car was the ‘Shell Eco-Marathon 2016 Global Rules’ (Shell Eco-Marathon,
2016). This included the necessary design information that protected the driver’s safety. Some
of the more applicable rules to designing and building the drivetrain are listed below:
• Article 25
a) (i) Prototype vehicles must have three or four running wheels, which under normal
running conditions must be all in continuous contact with the road.
h) All parts of the drive train must be within the confines of the body cover.
i) All objects in the vehicle must be securely mounted. Bungee cords or other elastic
material are not permitted for securing heavy objects like batteries.
• Article 27
a) A permanent and rigid bulkhead must completely separate the vehicle’s propulsion
and energy storage systems from the driver’s compartment.
c) The bulkhead must effectively seal the driver’s compartment from the propulsion
and fuel system.
d) The bulkhead must prevent manual access to the engine/energy compartment by the
driver.
e) If holes are made in the bulkhead to pass through wires, cables, etc. it is essential that
the wires/cables are protected by a grommet or similar protective material to prevent
chafing or damage. All gaps/holes must also be filled.

13
• Article 34
g) The installation of effective transmission chain or belt guard(s) is mandatory.
• Article 43
a) Vehicles must be equipped with two independently activated brakes or braking
systems; each system comprising of a single command control (lever(s) working
together or foot pedal), command transmission (cables or hoses) and activators
(callipers or shoes).
• Article 42
a) Only front wheel steering is permitted.
• Article 43
c) The rear system must work on each wheel, unless they are connected by a common
shaft in which case they can have a single system.
• Article 43
e) The effectiveness of the braking systems will be tested during vehicle inspection.
The vehicle will be placed on an incline with a 20 percent slope with the driver inside.
The brakes will be activated each in turn.
• Article 124
Definition: For their attempt to be validated, teams must complete 8 laps in a maximum
time of 43 minutes with an average speed of approximately 25 km/h. The total distance
to cover is 17.920 km (8 laps of 2240 m less the distance between start and finish line).
Attempt: Each team will be limited to four official attempts: the best result will be
retained for the final classification. When the vehicle crosses the start line, an attempt
is counted. Even if the vehicle stops near the start line, a new start will not be granted
for the attempt in question.

14
4. Detailed Design Analysis
Preliminary Testing
In order to begin calculating what power would be needed from the motor, an experiment was
carried out using GEEC 1.0 to estimate the steady state rolling resistance of the car. Although
the new car will be lighter and more efficient, the experiment was done to provide an early
estimation of the region that the steady state rolling resistance will be in. The experiment
consisted of tying a rope on to the chassis of the car at one end and tying it to a force gauge at
the other end. A person holding the force gauge then walked along, pulling the car with the
force gauge. The person pulling the car then called out the force gauge reading every 4 to 5
seconds as another person made note of it. A third person made note of the ticking frequency
of the wheel and prompted the person pulling the car if the pace was consistent or not. The
person pulling the car waited 10 seconds before take-off before calling out values. This would
ensure that the values for steady state rolling resistance were not taken from the acceleration
phase. The experiment was carried out at four different weights; just the car (80 kg), the car
and driver (138 kg), 148 kg and 158 kg. The experiment was also run at three different tyre
pressures; 40 psi (underinflated), 50 psi (recommended) and 60 psi (overinflated) to examine
the effect of tyre inflation on the rolling resistance of the car. The results obtained were as
shown in Figure 4.1.

15
The results provide some useful information and mostly comply with what would’ve been
expected before the experiment. The tabulated results are available in Appendix A. As shown
in Figure 4.1 the steady state rolling resistance generally reduces with increasing tyre pressure
and also with increasing mass. However the experiment didn’t completely comply with theory.
It would’ve been expected that the results would comply with eqn. 4.1:
𝐹𝐹𝑟𝑟 = 𝜇𝜇𝜇𝜇𝜇𝜇 eqn. 4.1
Where: 𝐹𝐹𝑟𝑟 = rolling resistance (N)
𝜇𝜇 = coefficient of friction
𝑚𝑚 = mass (kg)
𝑎𝑎 = acceleration (m/s2
)
Results pertaining from this formula would take on a linear pattern but this is not the case with
the results obtained in the experiment. It is thought that the inaccuracies are due to the force
gauge. A project supervisor also suggested that the steady-state rolling resistance may vary
with velocity. The experiment will be re-done after obtaining a more accurate and digital force
gauge.
0
2
4
6
8
10
12
14
70 90 110 130 150 170
SteadyStateRollingResistance(N)
Total Mass (kg)
Steady-State Rolling Resistance vs. Mass
40 psi
50 PSI
60 psi
Figure 4.1: Experiment results showing the relationship between steady-state
rolling resistance and total vehicle mass for three different tyre pressures.

16
The experiment did reveal some useful characteristics. It showed the general effect of
increasing tyre pressure. Running the tyre underinflated results in an increased rolling
resistance and running it overinflated results in a decreased rolling resistance when compared
with the recommended tyre pressure. This suggests that there would be advantages of running
the car with an overinflated tyre but this has to be balanced with the risk of blowing a tyre while
out on the track. As the competition allows four attempts, it may be a good tactic to run the car
with an overinflated tyre only after a good score has already been posted in an earlier attempt.
The results also show that decreasing the weight of the car is critical in reducing rolling
resistance. This must be kept in mind when designing the drivetrain and other components of
the car.
From the experiment, a rolling resistance of 2.8 N at race conditions was estimated for the
steady state rolling resistance of the car for calculation purposes. The aerodynamic drag on the
car at 32 km/h (8.9 m/s) was also calculated using eqn. 4.2:
𝐹𝐹𝐷𝐷 =
1
2
𝐶𝐶𝐷𝐷 𝜌𝜌𝑣𝑣2
𝐴𝐴 eqn. 4.2
Where, 𝐹𝐹𝐷𝐷 = drag force (N)
𝐶𝐶𝐷𝐷 = coefficient of drag
𝜌𝜌 = density of fluid (kg/m2
)
𝑣𝑣 = velocity (m/s)
𝐴𝐴 = frontal area (m2
)
By consulting with the team designing the body of the car and from reading the FYP completed
by Paul Mannion (Mannion, 2015), an average coefficient of drag of 0.09 was used along with
a frontal area of 0.44m2
. The aerodynamic drag calculated was 2.38 N. The total force resisting
the movement of the car at a steady-state of 30 km/h is then the sum of the steady-state rolling
resistance and the aerodynamic drag acting on the car. This calculated is 5.18 N. This complies
with the track data from the GEEC 1.0 which gives an average resistance of 5 N. As it is vital
that the car is not underpowered and that the motor isn’t too overloaded and burned out, a factor
of safety of 2 was applied to the total resisting force acting on the car, bringing the figure to
10.36 N. This would ensure that the car is not underpowered along with the fact that the GEEC
2.0 is expected to be lighter and more efficient. Of course this is only an estimation of the
steady state rolling resistance and aerodynamic drag on the car, used to pick a motor power

17
bracket, but this can be more accurately found through testing when the car is built. By making
models of the car on Matlab, the car’s various properties can easily be changed to form new
results.
Motor Selection
It was desired that the car would reach speeds of up to 34 km/h (9.45 m/s) on flat terrain so that
a coasting strategy could be implemented, and using a resisting force of 10.36 N, the required
power was calculated to be 97.9 W using eqn. 4.3.
𝑃𝑃 = 𝐹𝐹𝐹𝐹 eqn. 4.3
Where; 𝑃𝑃 = power (W), 𝐹𝐹 = force (N), 𝑣𝑣 = velocity (m/s)
This does not mean that a motor in the region of 97.9 W is desirable. This is just the power
required when the car is in a steady state of motion on flat parts of the course with no wind
velocity. The car will decelerate and accelerate many times during the race for various reasons
and this will require a higher output power than the one calculated above. To avoid burning out
the motor in these acceleration phases, the electrical team suggested investigating motors in
the region of 200 W to 250 W on the back of the obtained results. It was also suggested that
the team choose a motor with a rated voltage of 24 V because many electrical components are
easily found with this rated voltage. A DC motor was necessary because of the need to precisely
control the amount of current being applied.
Two motors were identified as possible candidates from high efficiency DC motor
manufacturers and competition sponsors, Maxon, who supply motors for the vast majority of
high performing teams at the Shell Eco-Marathon. The first motor identified was the ‘RE50’
(€522), shown in Figure 4.3. This is a 200 W motor with a maximum efficiency of 94 %. The
second motor identified was the ‘RE65’ (€795), shown in Figure 4.2. This is a 250 W motor
with a maximum efficiency of 83%. These motors are the highest powered of the highly
efficient RE range. It may seem apparent at first that the more efficient motor is the obvious
choice. However, this is not the case. The range of efficiencies that the motors will operate at
need to be considered along with other factors such as the gear train required.

18
The course map, released in November, revealed that there are inclines on each lap of the track.
This meant that the motor may have to be of greater power than originally thought. This will
be discussed in further detail later on. For this reason, the motor that was used for the GEEC
1.0 was considered. This is a cheap unbranded motor found on ‘Ebay’ that was used because
the purchased Maxon motor had been accidentally burned out during testing. This motor is a
350 W DC motor rated for 24 V and so will provide plenty of power for the terrain. The motor
is still in good condition having only been used a handful of times and so it was assumed to
have an efficiency close to its efficiency as new.
Permanent magnet DC motors obey a linear speed-torque relationship. When the motor is at
zero torque, it is at its no load speed and when the motor is at stall torque, it is at zero speed.
However, when operating for long times overheating can become an issue and calculations
carried out by the team designing the electrical drive system for the GEEC 2.0 showed that the
Maxon motors could safely draw 10 A from the battery over a long period of time without
overheating. The results showed that up to 15A can be drawn from the Maxon motors for short
periods of time, and that they would require 4/5th
operation at 10 A for every 1/5th
spent at 15
A. Testing showed that these values were 15A and 18.7A for the Ebay motor. However, the
lithium ion battery purchased for last year’s car can only supply 18A of current and it was
desired that this battery would be used again. Torque from a dc motor is directly proportional
to the current applied while angular velocity is proportional to the applied voltage. The linear
speed-torque relationship was plotted on excel using the stall torque and no load speeds
supplied by the manufacturers which can be seen in Appendix A and Appendix B. The
equations of these lines was then noted from the excel graph. This was repeated with the torque-
Figure 4.2: Maxon RE65 250W DC motor.
(Maxon, 2016)
Figure 4.3: Maxon RE50 200W DC motor
(Maxon, 2016)

19
current relationship of each of the motors using the no load currents provided by the
manufacturers.
A mathematical model of the motors was then constructed which accounted for the maximum
recommended current which resulted in a flat torque characteristic as shown in Figure 4.4.
The maximum continuous operating torques were found for each of the motors. This was done
by finding the torque value at 10A for each motor using the torque-current relationship found
in Excel. These torque values were then inserted in to the speed-torque relationship for each of
the motors. This allowed the maximum power output to be found using eqn. 4.4. The results
were tabulated and are shown in Table 4.1. A surprising result here is that the 200W rated
RE50 motor can produce a higher continuous power than the 250W rated RE65 due to its ability
to output higher motor speeds. As was expected, the 350W Ebay motor was capable of
outputting the highest continuous power.
𝑃𝑃 = 𝑇𝑇𝑚𝑚 𝜔𝜔𝑚𝑚 eqn. 4.4
Figure 4.4: Plot showing speed-torque relationship of RE50, RE65 and Ebay
motors given a maximum current of 10A.
0 100 200 300 400 500 600 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Motor Speed-Torque Relationship
Torque(Nm)
angular velocity (rad/s)
RE50
RE65
Ebay

20
Table 4.1: Maximum recommended continuous currents, torques and power outputs for each
of the motors.
The efficiency-torque relationship of each of the motors was then investigated by incorporating
an efficiency relationship in to the mathematical model. Eqn. 4.5 was entered in to the model
so that a relationship between efficiency and motor torque and efficiency and motor speed was
quickly available. To complete this equation it was necessary to find the friction torque of each
of the motors. This was done using eqn. 4.6 (Maxon, 2016). The torque constant is the slope
of the linear relationship between current and torque with current on the x-axis while the no-
load current is as explained before.
𝜂𝜂(𝑇𝑇) =
𝑃𝑃(𝑇𝑇)
𝑣𝑣𝑣𝑣(𝑇𝑇)+𝑇𝑇𝑓𝑓 𝜔𝜔 𝑚𝑚(𝑇𝑇)
eqn. 4.5
Where; 𝜂𝜂(𝑇𝑇) = efficiency for a given torque, 𝑃𝑃(𝑇𝑇) = power for a given torque, 𝑇𝑇𝑓𝑓 = friction
torque of motor (Nm), 𝜔𝜔𝑚𝑚(𝑇𝑇) = motor speed at a given torque (rad/s), 𝑣𝑣 = rated voltage (V),
𝑖𝑖(𝑇𝑇) = current for a given torque (Nm),
𝑇𝑇𝑓𝑓 = 𝑘𝑘𝑇𝑇 𝑖𝑖0 eqn. 4.6
Where; 𝑘𝑘𝑇𝑇 = torque constant (Nm/A), 𝑖𝑖0 = no-load current (A)
The resulting efficiency-torque curve can be seen below in Figure 4.6. It can be seen that the
motor reaches maximum efficiency quickly after zero torque. This complies with what would
have been expected, as Maxon state that DC motors generally reach maximum efficiency at
roughly 1/7th
of the stall torque. The RE50 has higher maximum efficiency at 94% compared
to the RE65’s 87% and the Ebay motor’s 78%. The RE50 also declines in efficiency faster than
the RE65 does. This means that the RE50 is efficient in less torque regions than the RE65 is.
Motor Max. Cont. Current (A) Max. Cont. Torque (Nm) Max. Cont. Power (W)
RE50 10A 0.385 229.54
RE65 10A 0.538 222.52
Ebay 15A 0.854 285.24

21
The model was then altered so that it accounted for the flat torque characteristic at 10A for the
Maxon motors and 15A for the Ebay motor. This model allowed the efficiencies at different
torques for the maximum continuous currents to be easily found. It was also easy to change the
model to the short-term operating currents so that the efficiencies at these levels could also be
investigated if necessary. The torque-efficiency relationship with a flat torque occurring at 10
amps is shown in Figure 4.6. This plot shows that the maximum efficiencies remain the same.
It also shows that the Maxon motors have a much more dramatic drop in efficiency at lower
torques than the Ebay motor does.
0 2 4 6 8 10 12 14 16
0
10
20
30
40
50
60
70
80
90
100
Motor Efficiency-Torque Relationship
Efficiency(%)
Torque (Nm)
RE50
RE65
Ebay Motor
Figure 4.5: A plot showing the efficiency of the Maxon RE50 and RE65 motors and the
Ebay motor when running with different torques at a maximum current of 10A.

22
Having obtained the speed-torque characteristics of each motor, the next task was to find out
the optimal gear ratio to operate each motor at for efficiency. Having already made a model of
the motor efficiency-speed, as seen in Appendix C, the motor speed at which maximum
efficiency occurs was noted for each of the motors. It was desired that the car’s average speed
when current is being applied would be as close as possible to the maximum efficiency motor
speed. This would be dictated by the gear ratio as shown by eqn. 4.7 (Maxon, 2016).
𝑣𝑣(𝑅𝑅) = 𝑅𝑅𝜔𝜔𝑛𝑛 𝑟𝑟𝑤𝑤 eqn. 4.7
Where; 𝑣𝑣(𝑅𝑅) = vehicle speed as a function of gear ratio (m/s), 𝜔𝜔𝑛𝑛 = nominal motor speed
(rad/s), 𝑟𝑟𝑤𝑤 = wheel radius (m)
A desired average speed of 29 km/h was first selected following team meetings. Although the
minimum required speed is 25 km/h, an average speed of 29 km/h would allow the driver to
comfortably use coasting to reduce energy used and would also ensure that the car finishes
safely within the minimum time limit, albeit at the cost of slightly higher aerodynamic drag
and friction losses. This was later changed to 29.5 km/h to make the gear ratio even so that
chain sizing would be easier. A maximum speed of 34 km/h (9.44 m/s) and a minimum speed
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
10
20
30
40
50
60
70
80
90
100
Motor Efficiency-Torque Relationship
Efficiency(%)
Torque (Nm)
RE50
RE65
Ebay Motor
Figure 4.6: A plot showing the efficiency of the Maxon RE50 and RE65 motors and
the Ebay motor when running with different torques at a maximum current of 10A.

23
of 25 km/h (6.94 m/s) was chosen as part of the driving strategy. This results in an average
applied current speed of 29.5 km/h. As can be seen in Figure 4.7, there is a very sharp decline
in efficiency at the higher motor speeds. This means that car should not operate beyond the
nominal motor speed as it would have detrimental efficiency results. This means that the car’s
maximum speed of 34 km/h will actually be the most efficient operating point when applying
current.
Figure 4.7: A plot showing the relationship between motor efficiency and motor
speed for the Maxon RE50 and RE65 motors and the Ebay motor.
The gear ratios needed to achieve the highest efficiency at 34km/h (9.44m/s) were found using
eqn. 4.7 with a wheel radius of 254 mm. This wheel size was the maximum possible due to the
shell. The optimal gear ratios for the RE50 and RE65 motor were found to be 16:1 and 11:1
respectively, while the optimal gear ratio for the Ebay motor was found to be 10:1. The vehicle
speed as a function of gear ratio was modelled for each motor along with the optimal gear ratio
as shown in Figure 4.8.
0 100 200 300 400 500 600 700
0
10
20
30
40
50
60
70
80
90
100
Motor Efficiency-Speed Relationship
Efficiency(%)
Speed (rad/s)
RE50
RE65
Ebay Motor

24
It was desired to see how these efficiency curves would affect the operating speed regions of
the car. The efficiency of the motor was plotted against the velocity of the car at the selected
gear ratios and the minimum and maximum speeds that the car would operate at were also
shown on the graph as shown in Figure 4.9.
The RE50 operates over a larger range of motor angular velocities and thus has a larger
efficiency range than the RE65 and Ebay motors do. This is because it has a higher gear ratio.
The effect of this is that it travels further from maximum efficiency than the others do.
However, because it has a higher maximum efficiency of 94% compared to the RE65’s 87%
and the eBay motor’s 78%, its minimum operating efficiency in this case is still higher than
the minimum operating efficiencies of both as seen in Figure 4.9.
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
0
5
10
15
20
25
30
35
Vehicle Speed with DC Motors at Nominal rpm and torque
VehicleSpeed(m/s)
Gear Ratio
RE50
RE65
Ebay Motor
Maximum Vehicle Speed
Figure 4.8: Vehicle speed as a function of gear ratio at nominal motor speed for the
Maxon RE50 and RE65 motors and the Ebay motor.

25
For these calculations it was assumed that the track would be flat. However the course does
contain varying gradients and it is necessary to factor this in when choosing a motor. The track
data reveals that there is a section of the course that increases in height by 8.6m over a distance
of 255m. This is an average gradient of 3.37% with a maximum gradient of 5% as shown in
Figure 4.10.
Figure 4.9: A graph showing the efficiency of each motor as a function of the motor
speed. The dotted lines show the minimum and maximum speeds that the motor would
operate at for the desired vehicle speeds (6.94m/s (25 km/h) to 9.44 m/s (34 km/h)).
0 2 4 6 8 10 12
0
10
20
30
40
50
60
70
80
90
100
Maxon Motor Efficiency-Vehicle Speed Relationship
Efficiency(%)
Vehicle Speed (m/s)
RE50
RE65
Ebay Motor

26
Figure 4.10: The track topography as supplied by the organisers. The graph shows the chainage (i.e. distance in to the lap) and the level in metres at various points
associated with the track map (Shell Eco-Marathon, 2016).

27
It must be considered that the car will not have to overcome this force for the total distance of
the ascent as it will carry speed in to the climbing section. It can be seen in Figure 4.10 that
there is a 663m descent (Pt.19 – Pt.29) just before the large ascent (Pt.29 – Pt.33) on the course.
This will allow the driver to carry maximum speed in to the climbing section. The method
taken to calculate how much this would assist the ascent was to determine what the total energy
needed to complete the ascent was and to take away the kinetic energy of the car entering the
ascent. To find this kinetic energy it was necessary to determine if the descent prior to the hill
would cause the car to roll without the use of the motor. This was done by subtracting the
steady state rolling and aerodynamic resistances from the kinetic energy at the start of the
ascent and the potential energy due to the change in gradient as shown in eqn. 4.8:
𝑘𝑘𝑒𝑒𝑒𝑒 = 𝑚𝑚𝑚𝑚ℎ +
1
2
𝑚𝑚𝑣𝑣𝑒𝑒
2
− (𝐹𝐹𝑟𝑟 + 𝐹𝐹𝑑𝑑)𝑠𝑠𝑑𝑑 eqn. 4.8
Where; 𝑘𝑘𝑒𝑒𝑒𝑒 = kinetic energy of the car due to descent (J), 𝑔𝑔 = acceleration due to gravity
(m/s2
), 𝑣𝑣𝑒𝑒 = entrance velocity (m/s), ℎ = height (m), 𝑠𝑠𝑑𝑑 = distance of the descent
This yielded a result of -1941J which means the car would require 1941J from the motor over
the distance of the descent to even get to the bottom of the ascent (Pt. 29). It was desired that
the car would enter the ascent at as high a speed as possible to give a high kinetic energy on
entering the ascent. The obtained result means that the car can’t carry a higher speed than the
maximum motor speed due to gravitational effects. Using the gear ratios chosen the maximum
speed of the vehicle without detrimental efficiency effects is 34 km/hr (which is actually
maximum efficiency). This means that the motor will have to apply the required energy of
1941J over a time period determined by dividing the distance of the descent by the speed of
the car (34 km/h). This of course yields the power that the motor will have to apply on the
descent to maintain 34 km/h, in this case 27.7 W. All the motors in question are easily capable
of providing this power. The desired value was the power required for the ascent. The kinetic
energy entering the ascent is found using eqn. 4.9 and using the maximum possible speed of
34 km/h found from the descent calculations.
𝑘𝑘𝑒𝑒𝑒𝑒 =
1
2
𝑚𝑚𝑣𝑣2
eqn. 4.9
Where, 𝑘𝑘𝑎𝑎 = kinetic energy of the car entering the ascent (J)

28
Using eqn. 4.9 showed that the car would have a total energy of 4860J when entering the ascent.
The force acting against the car on the incline section was found to be 51N using the free body
diagram in Figure 4.11 and eqn. 4.10:
𝐹𝐹𝑔𝑔 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚(𝜃𝜃) + 𝜇𝜇𝜇𝜇𝜇𝜇𝜇𝜇𝜇𝜇𝜇𝜇(𝜃𝜃) eqn. 4.10
Where, 𝐹𝐹𝑔𝑔 = force due to gravity acting against movement of the car, 𝜃𝜃 = angle of incline (o
),
𝜇𝜇 = coefficient of friction
The sum of the gravitational force, the steady state rolling and aerodynamic resistance on the
car give the total force acting against the car on the incline as seen in eqn. 4.11, in this case
60.36 N. The total energy required to complete the climb was given by multiplying this force
by the length of the climb, 255m, as seen in eqn. 4.12. This gave an energy requirement of
20’283J. The subsequent power requirement was found using eqn. 4.13.
𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐹𝐹𝑔𝑔 + 𝐹𝐹𝑟𝑟 + 𝐹𝐹𝑑𝑑 eqn. 4.11
Where; 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡 = total force acting on the car (N)
𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑎𝑎 − 𝑘𝑘𝑒𝑒𝑒𝑒 eqn. 4.12
Where, 𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡 = total energy required, 𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡 = total force acting against movement, 𝑑𝑑𝑎𝑎 = length
of ascent, 𝑘𝑘𝑒𝑒𝑒𝑒 = energy at start of ascent.
𝑃𝑃 =
𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡
𝑡𝑡
eqn. 4.13
Where, 𝑃𝑃 = power required from motor, 𝑡𝑡 = time on ascent
Figure 4.11: This is a free body diagram of the car on the incline section
of the course.

29
A Matlab model was made of the descent and ascent so that the variables, such as climbing
speed, could be easily changed. The power required for various climbing speeds was plotted,
as seen in Figure 4.12 along with the maximum continuous powers each motor could output
from Table 4.1.
It can be seen in Figure 4.12 that the power requirements that the motors are capable of
producing result in very low speeds, which means a high torque is required from the motor.
However, it must also be considered that the car will decelerate as it goes up the incline and it
must be insured that it does not decelerate to a standstill. Before checking if it was possible to
get up the incline using these calculations, it was decided to investigate the motors’ capabilities
when they were pulling higher currents for a short period of time. The currents investigated are
shown in Table 4.2. It can be seen in Figure 4.12 that this results in much higher average
velocities on the incline and it is much less likely that the vehicle will decelerate to a standstill
as a result.
3 3.5 4 4.5 5 5.5 6
180
200
220
240
260
280
300
320
340
360
380
Average Velocity (m/s)
MotorPowerRequired(W)
Ebay
RE50
RE65
Figure 4.12: Power required for various climbing speeds with dashed lines
showing the maximum power each motor can continuously supply along with
the corresponding car velocity.

30
Table 4.2: Maximum short-term currents, torques and power output for the RE50, RE65 and
Ebay motors.
The torque output for each of the motors was converted to torque output at the wheel using
eqn. 4.14 below for both the continuous draw currents and the short term draw currents. This
was in turn converted to the vehicle traction force using eqn. 4.15.
𝑇𝑇𝑊𝑊 =
𝑇𝑇𝑚𝑚
𝑛𝑛
eqn. 4.14
Where, 𝑇𝑇𝑊𝑊 = wheel torque, 𝑇𝑇𝑚𝑚 = motor torque, 𝑛𝑛 = gear ratio
Motor Current (A) Torque (Nm) Power (W)
RE50 15A 0.58 337.91
RE65 15A 0.81 327.68
Ebay 18A 1.07 338.91
3 3.5 4 4.5 5 5.5 6
180
200
220
240
260
280
300
320
340
360
380
Average Velocity (m/s)
MotorPowerRequired(W)
Ebay
RE50
RE65
Figure 4.13: Power required for various climbing speeds with dashed lines showing
the maximum short-term power each motor can supply along with the corresponding
car velocity.

31
𝐹𝐹𝑇𝑇 =
𝑇𝑇𝑤𝑤
𝑟𝑟
eqn. 4.15
Where, 𝐹𝐹𝑇𝑇 = traction force, 𝑟𝑟 = wheel radius
None of the traction forces in Table 4.3 are greater than the total resistance on the hill of 51 N
that was calculated earlier. This means that even if the short-term high current is used with the
most powerful motor, the car will still decelerate on the hill.
Table 4.3: Wheel torque and traction forces calculated from motor torques for each of the
motors at continuous and short-term draw currents.
Motor
Motor Torque
(Nm)
Wheel Torque
(Nm)
Traction Force (N)
Continuous
RE50 (10A) 0.38 6.84 25.42
RE65 (10A) 0.54 6.46 25.42
Ebay (15A) 0.85 8.54 33.62
Short-term
RE50 (15A) 0.58 10.44 41.10
RE65 (15A) 0.81 9.68 38.13
Ebay (18A) 1.07 10.7 42.13
It was thus necessary to calculate how much the car would decelerate on the incline with each
of the draw currents shown above. The force accelerating the car was found by subtracting the
traction force from the total force acting against the car on the incline i.e. steady-state rolling
resistance, aerodynamic drag force and gravitational force. The acceleration of the car on the
incline was found using eqn. 4.16 which is an alteration of Newton’ second law.
𝑎𝑎 =
𝐹𝐹 𝑁𝑁
𝑚𝑚
eqn. 4.16
Where; 𝐹𝐹𝑁𝑁 = net force (N), 𝑚𝑚 = mass of vehicle and driver (kg)
This was first done at the continuous draw current and then at the short-term draw currents as
shown below. The entrance velocity calculated earlier was used (9.44 m/s / 34 km/h). The
distance the car would travel on this incline (3.8%) before coming to a standstill was calculated
using eqn. 4.17 (State Examinations Comission, 2009)
𝑑𝑑 = −
𝑢𝑢2
𝑎𝑎2 eqn. 4.17

32
Where, 𝑑𝑑 = distance travelled (m), 𝑢𝑢 = entrance velocity (m/s),
The length of the incline section on the course is 255m as stated earlier. It was thus possible to
find the velocity of the vehicle on exiting the incline using eqn. 4.18 (State Examinations
Comission, 2009). The results were first computed for the continuous draw currents as shown
in Table 4.4.
𝑣𝑣𝑒𝑒 = �𝑢𝑢2 + 2𝑎𝑎𝑠𝑠𝑎𝑎 eqn. 4.18
Where, 𝑣𝑣𝑒𝑒 = exit velocity,
Table 4.4: Car deceleration calculation results on the inclined section for continuous draw
currents
RE50 (10 A) RE65 (10 A) Ebay (15 A)
Total Force (N) -24.05 -25.56 -13.77
Acceleration (m/s2) -0.22 -0.23 -0.13
Entrance Velocity (m/s) 9.44 9.44 9.44
Distance travelled (m) 203.82 191.76 355.90
Exit velocity (m/s) n/a n/a 5.5
It can be seen here that the two Maxon motors, the RE50 and RE65, are incapable of making
it to the end of the incline without decelerating to a standstill. The Ebay motor does make it to
the end but at a very low velocity of 5.5 m/s, which is 52% efficient as seen in Figure 4.14.
This is undesired so calculations were done for each of the motors at the short-term draw
currents using the same method. This provided higher exit-velocities and thus higher
efficiencies. These results are shown in Table 4.5
Table 4.5: Car deceleration calculation results on the inclined section for short-term draw
currents.
RE50 (15 A) RE65 (15 A) Ebay (18 A)
Total Force (N) 9.87 12.85 1.72
Acceleration (m/s2) -0.09 -0.12 -0.07
Entrance Velocity (m/s) 9.44 9.44 9.44
Distance Travelled (m) 496.39 381.41 632.45
Exit Velocity (m/s) 6.85 5.85 7.3

33
The higher draw currents allow the car to get to the top of the incline at exit velocities 6.85 m/s
and 5.85 m/s for RE50 and RE65 motors respectively. The Ebay motor would reach the top
9.04 m/s when drawing 18 A. This results in much higher motor efficiencies as seen in Figure
4.15. Using this driving method the motor would operate at efficiencies of 68.75%, 57% and
66% for the RE50, RE65 and Ebay motors respectively as seen in Figure 4.15.
On the back of these results, a team decision was made to continue analysis with the Maxon
RE50 and the Ebay motors. This was because the Ebay motor has more than enough power to
get the car over the large inclined section. The RE50 has enough short-term power to get over
the incline and is more efficient than the Ebay motor and the RE65. It was decided to design
the rest of the drivetrain so that either motor could be easily interchanged for the other.
0 2 4 6 8 10 12
0
10
20
30
40
50
60
70
80
90
100
Ebay Motor Efficiency-Vehicle Speed Relationship
Efficiency(%)
Vehicle Speed (m/s)
Figure 4.14: Ebay motor efficiency at various vehicle speeds with a black dotted
line showing the exit velocity, 5.5 m/s, from the incline section.

34
Driving Strategy
Driving strategy can have a large effect on the score obtained at the Shell Eco-Marathon.
Although the specific driving strategy will not be found until comprehensive testing has been
done on the car, this chapter will describe the expected driving strategy based on how the car
is expected to behave. A driving strategy will be discussed for both the Ebay motor and the
RE50 motor. Some factors of the driving strategy were already decided when choosing the
motor. For example, it was decided to adapt an average speed of 29 km/h instead of the
minimum 25 km/h that is required to complete the 17.92 km in 43 minutes as stated in the rules.
However there are a lot of other influences on the driving strategy.
The driving strategy used at the 2015 event with the GEEC 1.0 was an ‘accelerate and coast’
strategy. This is the strategy used by most teams. It involves accelerating the vehicle up to a
certain speed and then not applying any current until the vehicle decelerated to a certain speed.
0 2 4 6 8 10 12
0
10
20
30
40
50
60
70
80
90
100
Motor Efficiency-Vehicle Speed RelationshipEfficiency(%)
Vehicle Speed (m/s)
RE50
RE65
Ebay Motor
Figure 4.15: Maxon RE50 and RE65 motors and Ebay motor efficiency at various
vehicle speeds with a colour associated dotted line showing the exit velocity for each
motor.

35
Acceleration was then applied once more until the car reached the desired speed and this
process was repeated for the duration of the race. This has been shown by many teams,
including the Pac Car II team, to be the most efficient method. This strategy was easy to carry
out at the Rotterdam track because it was mostly flat. However, as mentioned in the previous
section, the London track contains varying gradients throughout. This means that coasting
sections will have to be more carefully chosen so that the motor can provide enough torque to
get up the inclines as discussed in the previous section. It is also important to not accelerate too
fast into bends and have to brake to slow down as this is wasted energy.
In Figure 4.17 a map of the track is shown. The numbers on the track coincide with the gradient
map in Figure 4.10. The car will have to accelerate from Pt. 0/42 on the map below at the
beginning of the race.
The track data from the GEEC 1.0 showed that the car decelerated, on average, 0.04 m/s2
when
coasting. For the purpose of developing a model that can be altered after testing, this
deceleration rate can be used to analyse the GEEC 2.0. The time taken for the car to decelerate
from 34 km/h (maximum motor efficiency used) to 25 km/h (minimum motor efficiency used)
can be found using a simple kinematic equation as shown eqn. 4.19. The distance travelled in
this time can then be found using eqn. 4.2 (State Examinations Comission, 2009). The time
taken for the car to decelerate from 9.44 m/s (34 km/h) to 6.94 m/s (25 km/h) on flat terrain
was calculated to be 62.5 seconds. The car would travel 511.88m in this time.
𝑡𝑡 =
𝑉𝑉𝑓𝑓−𝑉𝑉𝑖𝑖
𝑎𝑎
eqn. 4.19
Where; 𝑡𝑡 = time (s), 𝑉𝑉𝑓𝑓 = final velocity (m/s), 𝑉𝑉𝑖𝑖 = initial velocity (m/s),
𝑎𝑎 = acceleration (m/s2
)
𝑑𝑑 =
𝑡𝑡(𝑉𝑉𝑖𝑖+𝑉𝑉𝑓𝑓)
2
eqn. 4.20
Where; 𝑑𝑑 = distance travelled (m)
It was desired to investigate how long it would take the car to accelerate from standstill to the
maximum speed of 9.44 m/s using a Matlab model. The first step in doing this was finding the
relationship between the motor torque, the motor speed, the stall torque and the no load speed
of the motor using eqn. 4.21 (Maxon, 2016). The no load speeds for the RE50 and Ebay motors
are 623 rad/s and 402.8 rad/s respectively.

36
𝑇𝑇𝑚𝑚 = 𝑇𝑇𝑠𝑠 �1 −
𝜔𝜔 𝑚𝑚
𝜔𝜔0
� eqn. 4.21
Where; 𝑇𝑇𝑚𝑚 = motor torque (Nm), 𝑇𝑇𝑠𝑠 = stall torque (Nm), 𝜔𝜔𝑚𝑚 = motor speed (rad/s), 𝜔𝜔0 =
motor no load speed (rad/s)
The stall torque had to be adjusted throughout the model to account for the flat torque at 10 A
for the Maxon RE50 and at 15 A for the Ebay motor. This stall torque was converted to a force
acting on the wheel with eqn. 4.22 using the radius of the wheel, 0.254 m, and the gear ratio
for the respective motor.
𝐹𝐹𝑊𝑊 =
𝑇𝑇𝑚𝑚
𝑟𝑟𝑤𝑤 𝐺𝐺
=
𝑇𝑇𝑠𝑠
𝐺𝐺𝑟𝑟𝑤𝑤
�1 −
𝜔𝜔 𝑚𝑚
𝜔𝜔0
� eqn. 4.22
Where; 𝐹𝐹𝑊𝑊 = force acting on the wheel (N), 𝑟𝑟𝑤𝑤 = wheel radies (m), 𝐺𝐺 = gear ratio
The motor speed can be converted to vehicle speed using eqn. 4.23 (Maxon, 2016). The total
force propelling the car forward is given by subtracting the total rolling resistance from the
force being applied to the wheel. Since this model seeks to give an accurate representation of
how the car will perform, no factor of safety is applied to the steady state rolling resistance. A
rolling resistance of 5 N is used but this can be changed in the model once testing has been
carried out on the car. The acceleration function is given by eqn. 4.24.
𝜔𝜔𝑚𝑚 =
𝑣𝑣𝑤𝑤
𝐺𝐺𝑟𝑟𝑤𝑤
eqn. 4.23
Where; 𝑣𝑣𝑤𝑤 = linear wheel speed (m/s)
𝐹𝐹𝑤𝑤−𝐹𝐹𝑠𝑠𝑠𝑠
𝑚𝑚
=
𝑇𝑇𝑠𝑠
𝐺𝐺𝑟𝑟𝑤𝑤 𝑚𝑚
−
𝑇𝑇𝑠𝑠
𝐺𝐺2 𝑟𝑟𝑤𝑤
2 𝑚𝑚𝜔𝜔0
𝑣𝑣𝑤𝑤 −
𝐹𝐹𝑠𝑠𝑠𝑠
𝑚𝑚
=
𝑑𝑑𝑣𝑣𝑤𝑤
𝑑𝑑𝑑𝑑
eqn. 4.24
This is a first order ordinary differential equation with the solution shown in eqn. 4.25. A
boundary condition of velocity is zero when time is zero is assumed.
𝑣𝑣(𝑡𝑡) =
𝛽𝛽
𝛼𝛼
(1 − 𝑒𝑒−𝛼𝛼𝛼𝛼) eqn. 4.25
Where; 𝛼𝛼 =
𝑇𝑇𝑠𝑠
𝐺𝐺2 𝑟𝑟𝑤𝑤
2 𝑚𝑚𝜔𝜔0
, 𝛽𝛽 =
𝑇𝑇𝑠𝑠
𝐺𝐺𝑟𝑟𝑤𝑤 𝑚𝑚𝜔𝜔0
−
𝐹𝐹𝑠𝑠𝑠𝑠
𝑚𝑚
The results were plotted using Matlab as seen in Appendix C and are shown in Figure 4.16. It
can be seen here that it takes both motors 80 seconds to reach a maximum velocity 9.44 m/s.
However it takes the RE50 68 seconds to accelerate from 6.94 m/s (minimum operating speed)

37
to 9.44 m/s (maximum operating speed). The Ebay motor achieves this in 55 seconds. This is
advantageous as it would allow coasting to be done more frequently.
As previously discussed it is necessary to enter the big climbing section at the highest speed
possible so that the car has enough energy entering the climb to make it to the top. However,
as the map shows, there is a long bend before this section (26-30). It is important to make sure
that the car can safely negotiate this bend at the desired speed without rolling over. It can be
estimated from the track map that the track undergoes a 90o
turn over a distance of 423m. The
track shape is approximately equal to a quarter of a circle. The turning radius is thus given by
the eqn. 4.26 and gives a turning radius of 269.43m.
𝑟𝑟𝑡𝑡 =
2𝑑𝑑𝑡𝑡
𝜋𝜋
eqn. 4.26
Where; 𝑟𝑟𝑡𝑡 = turning radius (m), 𝑑𝑑𝑡𝑡 = turn distance
The height of the centre of gravity is an important factor when undergoing a turn. The lower
the centre of gravity, the less likely it is that roll over will occur. A wide wheel base will also
reduce the likelihood of rollover. The wheel base is the centre to centre distance of the front
tyres. The current design’s wheel base is 800 mm. It is estimated that the centre of gravity’s
0 20 40 60 80 100 120
0
1
2
3
4
5
6
7
8
9
10
Velocity of DC motors when Accelerating from Standstill
time (s)
velocity(m/s)
RE50
Ebay
Figure 4.16: Relationship between vehicle velocity and time when accelerating
from standstill with the RE50 motor and the Ebay motor.

38
horizontal location of the car will be around the driver’s torso position as the driver is the
highest load acting on the car and the load of the driver is acting over a relatively concentrated
area. The estimated horizontal distance between the centre of gravity and the front axle is
638mm. Paul Mannion, who did a comprehensive study on the design of an Eco-Marathon
vehicle, determined that the vertical height at which rollover begins to occur, assuming no
braking is applied, is given by eqn. 4.27 (Mannion, 2015).
ℎ =
𝑚𝑚𝑔𝑔
2
�1−
𝑑𝑑 𝑎𝑎
𝑙𝑙
�
𝑚𝑚𝑣𝑣2
𝑟𝑟𝑡𝑡 𝑤𝑤
eqn. 4.27
where; ℎ = height of COG at which roll over occurs (m), 𝑑𝑑𝑎𝑎 = horizontal distance between
COG and front axle(m), 𝑙𝑙 = wheel base (m), 𝑟𝑟𝑡𝑡 = turn radius (m), 𝑤𝑤 = track width (m)
At the point of the track in question, the track width is 7.5 m. The desired speed to complete
the turn at is 9.44 m/s (34 km/h). Subbing these values in to the equation along with an
estimated car and driver mass of 120kg gives a maximum allowable COG height of 22.5m.
This is much higher than what the COG height of the vehicle will be. The COG height of the
GEEC 1.0 was 0.35m (Fahy, 2015). Given that the driver is positioned lower in the GEEC 2.0,
this number should be even lower than last year’s car. This suggests that the car will
comfortably be able to take this bend at a speed of 9.44 m/s.

39
Figure 4.17: London track map (Shell Eco-Marathon, 2016).

40
Power Transmission System
One of the primary decisions for the drive train was the power transmission system that would
be used. This choice can have a great effect not only on the car’s efficiency but also on how
simple it is to assemble and maintain the car. This section will discuss the various options that
were available and will detail the pros and cons of each as well as outlining how the ultimate
decision was made.
Due to the high operating speeds of the motors, large gear reductions were required. This meant
that the power transmission system would have to provide a gear reduction. Having researched
the transmission systems available that were capable of gear reduction, the next step was to
narrow down the options by choosing transmission systems that were practically applicable to
the GEEC 2.0 project. This left us with the following five options:
• Spur Gear
• Belt Drive
• Single-Stage Chain Drive
• Multi-Stage Chain Drive
• Planetary Gears.
The spur gear system involves direct contact between machined gear teeth. The teeth mesh
with each other where the pitch circles of each gear are in contact with each other tangentially.
There are two main advantages with spur gears. Firstly, the gear train takes up very little room
from driver gear to driven gear when compared with other transmission types. This is because
the centre to centre distance from each gear to the next is given by the sum of the pitch radii of
the gears. This is the smallest possible distance between two gears operating on one plane. This
was very important in the design of the GEEC 2.0 drivetrain because there was very little room
behind the bulkhead due the aerodynamic shape of the shell. The second main advantage of
spur gears is efficiency. Under correct operating conditions spur gears can obtain efficiency
levels between 97% and 99% (Wmberg, 2016). Spur gears have a recommended maximum
operating ratio of 1:10 per stage. The Pac-Car II (Santin, et al., 2007) used spur gears to great
effect but this involved the construction of a custom wheel with gear teeth built in. This would
be unviable for the GEEC 2.0. One major concern with spur gears is how they would operate
in a moving vehicle with no suspension and how much this would affect their efficiency. Spur
gears are in very close and precise contact and the lack of movement between the stiff gear
heads could be problematic under vibration in the car or any bumps that the car may hit.

41
Belt drive systems use a toothed belt to transmit power from a driver gear to a driven gear. The
use of belt drives on bicycles is becoming more and more common. This was appealing because
its application in the GEEC 2.0 would resemble its application in a bicycle. The belt drive is
popular because it requires very little maintenance and no lubrication. However, modern
bicycle belt drives have been shown to be up to 34% less efficient than bicycle chains (Bike
Radar, 2016). Another problem was that the necessary belt drivetrain components are not as
readily available as some other power transmission systems. Another concern was the high
tension needed. This would make it difficult to change the motor and sprocket, especially at
the temporary work stand that will be set up at the event in London.
A single-stage chain drive is the most common transmission system used for bicycles. It
consists of linked chains connected in a loop connecting a driver and a driven sprocket. The
series of links means that the chain driven transmission can handle vibration and bumps very
well. The fact that a split link can be used to take the chain on and off makes it easier to change
the sprocket and motor quickly. Roller chains are known to be up to 99% efficient (Santin, et
al., 2007) which ranks them as one of the most efficient power transmission systems. A
question that remained was whether or not the single-stage chain drive would be capable of
providing the large gear ratios required. While getting the necessary sized sprockets
manufactured wouldn’t be a problem, a worry was that that the chain would start slipping on
the smaller sprocket. Chain manufacturers recommend a chain wrap of 120o
on the smaller
sprocket but say this can be reduced to 90o
if good chain tension is carefully monitored
(Diamond Chains, 2016). However most teams at the Shell Eco-Marathon 2015 used a single-
stage roller chain transmission with large gear ratios.
The large gear ratios that could be problematic with a single-stage chain drive could be solved
using a multi-stage chain drive. This involves a driver and a driven sprocket being connected
to two other sprockets which rotate together on the same shaft. This means that the gear
reduction is done over two stages and so the gear ratios between each stage is reduced. It would
also mean that off the shelf road bike cassettes could be used which would help with mounting
the sprocket on a hub due to the machined groove system used in these cassettes and the
freewheel mounts on the hub of a road bike. These cassettes are typically available in tooth
sizes of 11-32 with front chainrings usually coming in a maximum tooth number of 52.
Bicycles typically use a 1/2” chain pitch. If the 10 to 52 gear reduction (ratio 1:5.2) was used
twice consecutively, it would yield a total gear ratio of 1:27.04 using the formula below. This
ratio would be more than enough for the GEEC 2.0 as shown earlier. The different sprocket

42
sizes that come in a cassette would be convenient for testing different gear ratios. A multi-stage
power transmission would require a lot of room which is not the case in the GEEC 2.0 due to
the aerodynamic body closely wrapping the rear wheel. In terms of efficiency, it would retain
the efficiency of the single-stage chain at each stage so that the total efficiency would be given
by eqn. 4.28. This equation was derived using the same logic as an ‘AND’ sequence in
probability and so it would have to be proven through experimentation.
𝜂𝜂𝑡𝑡 = 0.99𝑖𝑖
− 𝜂𝜂𝑏𝑏(𝑖𝑖 − 1) eqn. 4.28
Where, 𝜂𝜂𝑡𝑡 = transmission efficieny, 𝑖𝑖 = number of stages, 𝜂𝜂𝑏𝑏 = efficiency of bearings at each
stage
It is likely that the transmission system being designed would only require two stages as
discussed above. Two bearings would be required at each stage so that the total efficiency
would be the product of the bearing efficiencies and 0.98 (0.992
).
The final option examined was a planetary gear set up. Planetary gears essentially involve the
use of spur gears inside a larger circle with teeth on its inside. Motor manufacturers ‘Maxon’
manufacture planetary gear units designed for use with their motors. A model which would be
suitable for application on the GEEC is the ‘GP 22 HP’ model which achieves the necessary
reduction for the RE50 of 1:16. This gear unit is quoted to have an efficiency of 78% (Maxon,
2016) but as with spur gears, it is hard to know how it would perform in a moving vehicle.
These gears are advantageous because they are very small with a total length of just 48.6mm
and an outer motor housing diameter of 22mm. This makes them far more compact than any
of the other power transmission systems investigated. The whole gear unit also weighs just
68g. There are however some fundamental problems with using this gear type. Firstly, at 78%,
it is not as efficient as most other systems looked at. Also, it is not compatible with the 350W
‘Ebay’ motor. This is problematic as it is not desired to have different transmission systems for
each of the motors as this would make changing the motor a time consuming task which would
be problematic when testing and at the event. Due to the fact that the Maxon planetary gearbox
currently costs €214 (21/02/2016), it is unlikely that the team will have the resources to
purchase another gear unit for the ‘Ebay’ motor. Finally, Maxon’s lead times can be lengthy as
was discovered when previously ordering motors from the company.
Having attained a large amount of data about the potential gear transmission systems, it was
decided to make a decision matrix to aid with picking the best system. This characterised each

43
of the motors’ suitability based on eight of their characteristics and the importance of each
characteristic.
Table 4.6: A decision matrix weighting the suitability of various power transmission systems.
Consideration Spur Belt
Single-
Stage
Multi-Stage Planetary Importance
Cost 8 7 9 8 2 8
Availability 9 4 9 8 7 7
Efficiency 9 4 10 9 6 10
Weight 7 8 7 6 10 6
Adaptability 10 7 9 10 2 7
Maintenance 7 10 7 6 7 5
Size 9 7 7 3 10 7
Application 4 9 9 10 4 8
Total 63 56 67 60 48
Weighted Score 459 392 496 447 336
It can be seen in Table 4.6 that the single-stage roller chain comes out with the highest weighted
score. This represents its consistent high scores across each of the criteria and especially its
efficiency which is rated as the most important characteristic. The spur gear is in a close second
but ultimately the fact that it is unproven in an application similar to the GEEC 2.0 resulted in
a lower score than the single stage chain drive. The other transmission systems fell short of the
scores posted by the single-stage roller chain and the spur gears due to the importance of the
problems discussed earlier.
The main issues with the single-stage roller chain were the wrap around angle on the small
driver sprocket and the room that it would take up behind the bulkhead in the car. It was thought
that if the desired wrap around angle was not achieved, an idler gear could be used. An idler
gear is a small sprocket that does not act as a power transmitter but its purpose is to tension the
chain or to increase the wrap-around of the chain on a sprocket. With this it was decided to
further investigate the application of a single-stage roller chain-drive to the GEEC 2.0.
In order to use a roller chain it was necessary to design sprockets, one that would mount on the
motor (driver) and one that would mount on the wheel (driven). Chains and sprockets with a
½’’ pitch are the most common and are widely available. It was decided to start designing
sprockets based on this. Seeing as the smallest sprocket typically used for bike cassettes is 10

44
teeth, it was decided to first design a sprocket using this size. The tooth profile of the sprocket
was drawn using the technique in Figure 4.18.
From this it was possible to derive an equation for the sprocket diameter using trigonometry to
solve the blue triangle in the diagram above. The extracted triangle is shown in Figure 4.19.
Using the information in this diagram, it is possible to find the pitch radius, r, of the sprocket
using eqn. 4.29. This equation uses the same variable notation as the diagram. For convenience
the pitch circle diameter was used as an estimation of the sprocket diameter.
𝑟𝑟𝑝𝑝 =
𝑝𝑝 sin(𝛽𝛽)
sin(𝜃𝜃)
eqn. 4.29
Where; 𝑟𝑟𝑝𝑝 = pitch radius (m), 𝑝𝑝 = pitch radius (m), 𝛽𝛽 = angle shown in Figure 4.19 (o
), 𝜃𝜃 =
angle shown in Figure 4.19 (o
)
𝑝𝑝 = chain pitch
𝜃𝜃 =
𝑛𝑛
360
Where; n = number of teeth
Figure 4.18: The technique used to draw the sprocket tooth profile.
The green border represents the finished tooth profile.

45
For a 10 tooth ½’’ pitch sprocket, a pitch diameter of 41mm was calculated. This would leave
plenty of room for mounting the driver sprocket on the motor shaft because the RE50 and the
‘Ebay’ motor both have shafts 8mm in diameter. A concern was the size of the rear sprocket in
comparison to the wheel. A Matlab model, seen in Appendix E, was made using eqn. 4.29 that
plotted pitch circle diameters for different gear ratios using a driver sprocket of 10 teeth. It was
seen in Figure 4.20 that the rear sprocket’s pitch circle diameter approached the size of the rear
wheel. 20’’ wheels are used on the car because of their ability to achieve a small steering radius
at the front and to fit in the compact aerodynamic shell at the rear. 28’’ wheels were run in the
model as a solution to the sprocket approaching the size of the wheel. However, as the size of
the wheel increases, so does the gear ratio required to attain the necessary torque levels and so
the sprocket diameter increases in proportion. As a solution, it was decided to examine what
sprocket sizes the use of a ¼’’ pitch would yield. It was seen that the 10 tooth driver sprocket
would be reduced 20.55mm in diameter which would still leave enough room for mounting on
the motor sprockets. The calculations also showed that the driven sprocket diameters were
greatly reduced. The diagram below shows the rear sprocket diameter at various gear ratios for
½’’ pitch and for ¼’’ pitch sprockets using a driver gear with 10 teeth.
Figure 4.19: Triangle used to derive the equation suitable for a mathematical
model for pitch radius diameter of a sprocket given number of teeth and pitch.

46
Figure 4.20: Plot showing the diameter of the driven sprocket at different gear ratios for a ¼’’
pitch chain and a ½‘’ pitch chain
It can be seen from Figure 4.20 that ½’’ pitch driven sprocket’s pitch circle diameter is bigger
than the wheel diameter of 508mm at the desired RE50 gear ratio of 1:16. However, the same
ratio with a ¼’’ pitch chain results in a pitch circle diameter of 307mm. Although ¼’’ pitch
chains are harder to source, they do significantly reduce the sprocket diameter to a point where
there is a safe clearance between the outer sprocket and the outer wheel. An all-round clearance
of 70mm between the outer wheel and the sprocket was desired in case the wheel punctured.
For this reason it was decided that a ¼’’ roller chain would be used and sprockets were
manufactured for this pitch as seen in Figure 4.21.
0 0.05 0.1 0.15 0.2 0.25
0
500
1000
1500
2000
2500
Rear Wheel Sprocket Diameter against Gear Ratio
SprocketDiameter(mm)
Gear Ratio
1/2' pitch
1/4' pitch
Wheel Diameter
Gear Ratio 1/16
Gear Ratio 1/10

47
Brakes
Braking is something that will be kept to minimum during the race because it can cause a large
loss in energy efficiency. At last year’s event in Rotterdam the GEEC 1.0’s brakes were only
used when pulling up to the start-line and again at the end when stopping. This was possible
by allowing the car to slow down by coasting in to sharp corners. However, this may not be
possible at the London track due to the large amount of descents where it may not be possible
to slow the car down (or even decelerate the car) enough through coasting. This makes
functional and reliable brakes a necessity. In addition to this, the competition’s rules state that
the vehicle must be capable of stopping with two independent braking systems on an incline of
20% (2.862o
). This is tested during a pre-event technical inspection by placing the car
stationary on a ramp. This rule is in place to make sure the braking performance of the car is
adequate for driving on the track and so designing a braking system that is capable of passing
this test should be capable of dealing with the braking necessities of the track.
There were two realistic options for braking systems, a v-brake and a disc brake. It was
originally thought that the v-brake was a better option because it would not restrict the wheel
hub options to hubs that were capable of mounting a disc brake rotor. V-brakes are also cheaper
and easier to install and maintain. Disc brakes require fine tuning every time the wheel is
removed and they allow very little room for error due to the close proximity between the
calliper and the rotor. For this reason it was decided to model a v-brake for the full car model.
On attempting to incorporate mounting for this brake on the model with the shell, chassis and
other components, it was seen that the brake either got in the way of the chain or the mounting
was too cumbersome.
Figure 4.21: The 1/4'' chain and sprocket mounted on the rear
wheel.

48
When the motor mounting was changed so that the chain did not come in contact with the
brake, the chain was coming in contact with the shell. It was attempted to mount the motor on
the under part of the chassis. This allowed a v-brake with minimal mounting to be placed
between the two rear members as shown in Figure 4.22. However when this was done on the
cad model, the chain came in contact with the shell as seen in Figure 4.23. It was attempted to
achieve motor mounting in a position that the shell would allow without moving the v-brake
too much but it was not possible. The only other option was to mount the brake a further
distance from these two rear members.
Figure 4.22: A CAD render of a v-brake mounted between two rear members.

49
Two mounting bars were placed vertically on each of the rear members so that the brake was
located at the top of the wheel as seen in Figure 4.24. There was enough room between the
wheel and the shell to allow this but it was decided that the mounting members were adding
too much weight to the car. For this reason it was decided to start researching the availability
of hubs where the mounting of a disc brake rotor and a freewheel unit is possible. Having
sourced a hub, the disc brake was modelled and mounted on the CAD model of the car to make
sure that it would not come in contact with anything. This was done successfully as shown in
Figure 4.25.
Figure 4.23: CAD render of motor mounting on under part of chassis. The red
line shows where the chain comes in contact and exits the shell.

50
It was necessary to calculate the disc brake’s ability to stop the car on a 20% ramp. The rules
necessitate that the rear brake is capable of stopping the car on its own. The free-body diagram
in Figure 4.26 shows the forces acting on the car when it is on the ramp. The angle of the incline
is 2.9o
and the mass of the car and driver is estimated to be a conservative 120kg. It is assumed
Figure 4.24: A CAD render of a v-brake mounted at the top of the
wheel.
Figure 4.25: A CAD render of the mounted disc rotor and
calliper.

51
that there is no slip between the tyres and the surface of the ramp and the car’s mass is treated
as a point mass acting at its centre point as shown in Figure 4.26. Using eqn. 4.30, the total
force pushing the car down the incline was found to be 59.56 N. Using the next equation, the
torque acting on the wheel was calculated as 15.13 Nm. The disc rotor is rotating on the same
axis and at the same speed as the wheel and so eq. 4.31 determines that a torque of 15.13 Nm
has to be applied by the calliper on the rotor to stop the car from rolling down the incline
assuming that there is enough.
𝐹𝐹𝑖𝑖 = 𝑚𝑚𝑚𝑚 sin 𝜃𝜃 eqn. 4.30
Where; 𝐹𝐹𝑖𝑖 = force due to incline (N)
𝑇𝑇𝑊𝑊 = 𝐹𝐹𝑖𝑖 𝑟𝑟𝑊𝑊 eqn. 4.31
Where, 𝑇𝑇𝑊𝑊 = torque acting on wheel, 𝑟𝑟𝑊𝑊 = wheel radius
The forces acting on the rotor when the brakes are applied are the wheel torque and the friction
force of the brake pads on the rotor. The free-body diagram in Figure 4.27 shows the forces
acting on the rotor and the directions they are acting in. The effective radius of the rotor is the
distance between the centre of the brake pads and the centre of the rotor.
Figure 4.26: Free body diagram showing the forces acting on the car during brake
technical inspection.

52
The braking torque was found using eqn. 4.32. A coefficient of friction of 0.4 (Twiflex, 2016)
was assumed for semi-metallic brake pads and an aluminium rotor, the most common
combination for bikes using disc brakes.
𝑇𝑇𝐵𝐵 = 𝐹𝐹𝑓𝑓 𝑟𝑟𝑒𝑒 𝑒𝑒𝑒𝑒 eqn. 4.32
Where; 𝑇𝑇𝐵𝐵 = brake torque (Nm), 𝐹𝐹𝑓𝑓 = friction force (N), 𝑟𝑟𝑒𝑒𝑒𝑒𝑒𝑒 = effective brake radius (m)
The friction force is found by using the eqn. 4.33 which includes the calliper force applied on
each side of the rotor by the calliper as shown in the free body in Figure 4.28.
Figure 4.27: Free-body diagram showing the forces acting on the
rotor when the brake is activated.
Figure 4.28: Free-body diagram showing the force from
the calliper acting on the rotor.

53
𝐹𝐹𝑓𝑓 = 𝜇𝜇𝑓𝑓 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐 eqn. 4.33
Where; 𝜇𝜇𝑓𝑓 = coefficient of friction, 𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐 = calliper force
It was thought that the brake lever that would come as part of a bike disc brake package would
be placed the steering wheel. The maximum force that a human can apply to a hand lever was
estimated to be 137 N (NASA, 2016). This is 5th
percentile male data for an elbow angle of
66.7o
. It was also desired to avoid hydraulic brakes as these require a high knowledge and skill
level to install and maintain and can be a lot harder to fine tune than a disc brake that uses
cables. These disc brakes are called ‘mechanical’ disc brakes and are typically cheaper than
hydraulic disc brakes. Bicycle brakes work off the principle of mechanical advantage. The
force is applied by the user some distance down the brake lever and around the pivot point of
the lever which essentially applies a moment about the end of the brake cable. This typically
results in a force transmission ratio of about 40 (Oertel, Neuburger, & Sabo, 2010). The calliper
force was calculated to be 5480N using eqn. 4.34.
𝐹𝐹𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐹𝐹𝐿𝐿 𝑅𝑅𝑡𝑡 eqn. 4.34
Where; 𝐹𝐹𝑐𝑐 𝑐𝑐𝑐𝑐 = brake calliper force, 𝐹𝐹𝐿𝐿 = applied lever force, 𝑅𝑅𝑡𝑡 = brake transmission ratio
This force is then converted to braking torque at the rotor using the equations above. The
smallest diameter (and lightest) of disc rotors for bikes generally available is 160mm. This
would provide an effective braking radius of about 150mm. This gives a braking torque of 329
Nm which provides a factor of safety of 21.7. This shows that disc brakes will provide more
than enough braking force for the car to pass the braking test at the technical inspection.
Rear Wheel Hub Selection
Coasting/freewheeling is the most efficient state an eco-marathon car can be in because it is
using no energy from the battery. In order to implement a coasting strategy it is necessary for
the rear sprocket to be attached to a freewheel unit. These units allow the wheel to keep
spinning while the sprocket is not being turned by the motor. The most common freewheels
for bicycles use a ratchet and pawl mechanism. Figure 4.29 shows how the freewheel
mechanism operates using the ratchet and pawl mechanism. A is the ratchet wheel, B is the
lever holding the driver pawl, C. D is another pawl that does not act as a driver but does ensure
motion of the freewheel is in one direction only, anti-clockwise in this case.

54
Various methods of configuring a sprocket with freewheel capabilities were discussed. The
first and easiest option would have been to source a high spec track bike wheel hub, such as
the high performance Shimano Dura-Ace hub shown in Figure 4.30 and to attach a thread on
freewheel mechanism. However, due to the fact a disc brake had to be used due to room
constraints, it was necessary to use a wheel hub that was compatible with a disc rotor. This
excluded the track bike wheel hub as these can’t be purchased with disc brake compatibility.
The next option was to move to a high-performance road bike hub with disc brake compatibility
as seen in Figure 4.31. The dilemma with this was that the freewheel unit was already built in.
Figure 4.29: A diagram of a freewheel unit using a
ratchet and pawl mechanism (Liou, 2007).
Figure 4.30: A Shimano Dura-Ace track bike rear wheel hub with thread
on freewheel unit capability. (Velodrome Shop, 2016)

55
These units typically use grooves to keep the sprockets in place with the end sprocket threading
on to keep all the sprockets tightly against the wheel hub. This would mean that the rear
sprocket would have to have these same grooves machined in to it. After discussing this with
Mr. Bonaventure Kennedy, an NUIG lab technician, it was determined that this precision of
machining could not be achieved in-house. It was desired to do the in-house to keep costs down
and an alternative method was suggested. This alternative method involve using two used bike
sprockets which any bike shop would be happy to give away and to spot weld them to either
side of the car sprocket with the centres aligned. These bike sprockets would have the grooves
pre-machined in to them and so would hold the car sprocket in place. The problem with this
method was that it would be difficult to get the desired precision of alignment between the
driver and driven sprockets
The final option was a rear bike hub made by a company named ‘Quando’, shown in Figure
4.32, that was sourced on Ebay which was compatible with disc brakes and a thread on
freewheel unit as seen below. The quality of the bearings in the hub was not presumed to be
very high due to the price of the hub (€26). However, the bearings could be changed for higher
performance bearings later on if desired. It was decided that this was the best option because it
had a quick build time, was cost-effective and was a reliable solution to the problem.
Figure 4.31: A Carbon-Ti road bike rear wheel hub with disc brake
compatibility and a built-in freewheel unit (Carbon-Ti, 2016).

56
The next step was to find a thread-on freewheel unit. A rear wheel freewheel unit, shown in
Figure 4.33 designed for electric scooters was sourced. The unit simply threaded on to the to
the ‘Quando’ hub.
Figure 4.33: The freewheel unit which threads on to the hub
(Ebay, 2016).
Figure 4.32: A Quando bike rear wheel hub with disc
brake and thread-on freewheel unit compatibility.

57
As seen in Figure 4.33, there are four 6mm diameter holes on the freewheel unit that allow the
attachment of a sprocket. Corresponding holes were drilled in to the rear sprocket and a centre
hole the same diameter as the outer diameter of the main body of the freewheel unit was
machined out. This allowed the freewheel unit to be inserted in to the sprocket and made it
possible to join the freewheel unit to the sprocket using fasteners. It was desired that the
sprocket could be taken on and off easily for maintenance purposes. For this reason, nuts and
bolts were used to secure the sprocket to the freewheel unit as seen in the CAD render in Figure
4.34.
The four bolts connecting the freewheel unit to the sprocket would be loaded in shear stress
from the chain rotating the sprocket. It was necessary to check that the maximum possible
operating torque of 10.7 Nm at the wheel would not be enough to shear the bolts. This torque
was converted to the shear force by dividing it by the distance from the outer part of the wheel
to the centre of where the bolt would be. The steel metric bolt with the lowest yield strength
found was an ‘A-2 Stainless Steel’ bolt which has a quoted minimum yield strength of 210
MPa (Buyanas & Nisbett, 2015). The yield strength of the material under shear stress was
found by making a Matlab model using the distortion energy theory, eqn. 4.35 (Buyanas &
Nisbett, 2015). The Matlab model would allow different bolt quantities and materials to be
examined. The area of the bolts under shear stress was found eqn. 4.36. It was assumed for
calculation purposes that the stress was equal across the area of each of the bolts. The shear
stress and factor of safety was then found using eqn. 4.37
Figure 4.34: A CAD render of the driven
sprocket mounted on the freewheel unit.

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