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FORMULA 1: THE TECHNOLOGY BEHIND THE FORMULA
Muneeb Alvi (mra48@pitt.edu), Zachary Carson (zmc4@pitt.edu)
Abstract – The Formula One (F1) racing sport is currently
leading the way for automotive engineering. However, most
people do not realize that the engineers making the race
cars for the F1 directly impact the modern road cars we
drive every day. The proof can be found in the traction
control systems and aerodynamic designs found on many
road cars. These systems that make cars more efficient and
safer to drive were originally applied heavily in the F1, and
transferred over to the common car due to the F1’s immense
popularity and the continuous testing of these technologies
on the race track. This paper briefly provides an overview
on these past societal and engineering successes from the
F1, and focuses on a potential engineering success titled the
Kinetic Energy Recovery System (KERS), which is currently
exclusive to the F1. Using the Law of Conservation of
Energy, the system attempts to capture energy wasted to
heat during the braking of a car, and store that energy in a
flywheel. This energy can then be called upon later to
temporarily power the car. This system, although exclusively
designed for racing, can theoretically be carried over to the
everyday road car, allowing more efficiency than the current
electrical regenerative brake designs. This paper provides
an in-depth look at a flywheel, the main component of the
KERS system. The implications, barriers, and the potential
for the system’s implementation in modern road cars are
also considered.
European streets resulted in the most famous and
tecnologically advanced racing on the planet.
This sport has now become more than just a competition
for the drivers. Competition also exists with the constructors
of the cars and the motivated engineers who design and
build the F1 cars under harsh standards and restrictions to
prove the engineering worth of their car designs. From
racing through the streets to becoming a part of driving
through the streets for the common man, the F1 is now part
of most people’s lives by becoming “the testing ground for
[advanced automotive] technology” [1]. Due to the F1’s
popularity and rigorous testing of automotive designs,
technologies that were designed first for F1 use, such as
advanced aerodynamics, traction control, and F1 gasoline,
have been implemented overtime into the everyday road car.
Although current F1 technologies, such as the Kinetic
Energy Recovery System, show potential of being
transported to the road car, past F1 technologies that are
currently fitted to modern road cars must be discussed to
communicate a sense of how impactful the F1 has been,
before viewing how much more of an influence the F1 can
deliver.
PAST PROOF TO FUTURE PROMISE
The following technologies illustrate how the automotive
world has changed through the use and design of F1
technologies. Although some of these technologies did not
originate in the F1, they were put through rigorous testing
and design advancements in the F1 race cars that eventually
led to them entering the universal automotive world and
providing safer transportation for race car drivers and daily
commuters.
Key Words – aerodynamics, automotive engineering,
flywheel, formula one, kinetic energy recovery system, shell
gasoline
IN THE F1 COCKPIT
Advanced Aerodynamics
The Formula One (F1) has been described by many as the
greatest automotive sport in the world, but many have their
own reasons as to why. Some declare that it contains the
fastest cars to ever race on a track, and while that may be
true, most do not understand why the sport’s race cars are
the fastest in the world. Others have a more technological
view of the F1’s importance and this view requires the
exploration of the technology used by the F1 to argue just
how influential the F1 has become. When the F1 began just
over fifty years ago, it began as gearheads racing cars on the
streets of Europe with many accidents abound. Taking notice
of these unnecessary accidents with the public, the
Fédération Internationale de l'Automobile (FIA) was created
to formulaize racing with restrictions and standards on a
closed course. Hence the F1 or Formula One was born.
What began as hotheaded racing fanatics going thorugh
Ever since the early 1960s, the F1 has experimented with
advanced aerodynamics [2]. Trying to find a way to reduce
energy loss due to air resistance, engineers in the F1
radically changed the shapes of their race cars, employing
methods such as the ‘now familiar wings [on road cars]’ in
order to create downforce and help stabilize the race cars [2].
Engineers also attempted to shape their cars in such ways as
to reduce air drag and have air flow around the car, rather
than right at it. An impact of such dedicated shaping to
reduce air drag, or the force on the car due to air, can be seen
in the all-electric road car, the Nissan Leaf. Designed to run
at very minimum power requirements, the Leaf must
minimize all power and energy loss in trying to push against
the air. Thus it was designed with advanced aerodynamics in
mind to give the consumer the highest mileage possible of
about 100 miles for every charge of the battery [3].
University of Pittsburgh
Swanson School of Engineering
April 14, 2012
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Muneeb Alvi
Zachary Carson
Traction Control
In the F1, the traction control system on a race car constantly
checks if the tires are moving faster than the vehicle is
passing the road, and if this is true, the engine limits the
power to certain wheels to minimize traction loss and
maximize grip [4]. Although traction control works in more
advanced ways in the F1, modern road car traction control
systems are quite sufficient in providing safer transportation
during rainy and snowy seasons, or other dangerous
conditions.
Shell Power
One technology that came from the F1 and went literally
into road cars is Shell V-Power. By having a history of
providing race cars in the F1 with gasoline, Shell has taken
the formula that it used to power the mighty cars of the F1
and with limited tinkering, provided customers at most gas
stations with Shell V-Power: a gasoline that was designed by
Shell during their participation of designing fuels for F1 cars
in the past, and is very similar to the same fuel Shell utilized
in the F1. The gas is enriched with nitrogen and has higher
capabilities than other fuels in reducing friction in the engine
of a car, which allows more efficient power output and
durability of the engine [5]. This final technology completes
a brief overview of past technologies implemented in
modern road cars, but before moving onto the possibility of
another F1 technology becoming shared with road cars, a
summary of the F1’s impact can be made in one powerful
example.
FIGURE 1
ANALYZING THE FERRARI 458 ITALIA’S AERODYNAMIC FEATURES [6]
ENERGY IS CONSERVED
The Kinetic Energy Recovery System (KERS), currently
employed exclusively in the F1, presents much potential to
be applied in modern road cars. Taking advantage of the fact
that energy can be neither created nor destroyed, but only
transferred from one form into another, energy that is lost to
heat when an F1 car brakes is instead stored by the KERS
system in a storage device, a method resulting from the Law
of Conservation of Energy [7]. That energy can later be
called upon to power the car for short bursts of time.
Obviously this would be a great beneficiary to the road cars
of today, who lose most of their energy that emanates from
braking. Allowing such a system to enter the automotive
world and allowing people to buy cars with the KERS would
provide better gas mileage and assist in reducing the use of
gasoline all together.
The storage devices for the captured energy in the KERS
system can range from capacitors to flywheels. Due to the
magnitude of information and the emphasis that the F1 cars
place on the use of flywheels, other forms of energy storage
will not be further discussed.
Putting it Together
The fairly recent launch of Ferrari’s latest supercar, the
Ferrari 458 Italia, has shown the world just how the F1 can
go from the race track to the road car. In addition to
containing all three discussed technologies, the 458 also
contains paddle shifters and a driver focused cockpit. These
features were greatly inspired by Ferrari’s experience in the
F1 [6]. Figure 1 to the right shows one of these F1
technologies by displaying a crucial feature to the Ferrari, its
F1 inspired aerodynamics. Being an epitome of the most
efficient and elegant design, the 458 embodies a vision of
just what the F1 can provide for modern road cars by making
them more advanced and efficient in every way possible
from driver orientation to design orientation. The Ferrari 458
Italia summarizes up till now, what the F1 has provided for
road cars. Still much is to be provided with the current
potential existing in the F1 exclusive technology, the Kinetic
Energy Recovery System.
The Sum of the Parts
It’s important to take note of how the KERS does not consist
of just one unit, but consists of multiple components
working together to capture and release energy. Figure 2 that
follows displays this fact.
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Zachary Carson
FIGURE 2
SETUP OF A KERS SYSTEM IN AN F1 CAR [8]
FIGURE 3
FLYWHEEL INTERIOR CUTOUT [9]
The above diagram illustrates the process and setup of a
KERS system in a standard F1 car. According to the figure,
when the charging phase begins, the rear brakes (1) release
kinetic energy, or energy resulting from a change in motion
(in this case, slowing the motion of the car). Then the
electric alternator captures that energy as it is told to do so
by the CPU (3). Lastly that energy is transferred and stored
in the storage device (2). With the press of a button on the
steering wheel (4), the driver can release that energy in the
storage unit and obtain approximately 80 additional
horsepower for about seven seconds a lap [8].
One component from the diagram is crucial in allowing
the system to function, the storage and release device. Even
without it, energy can still be transferred but not stored. This
storage is the key aspect of why this system is debated for its
transfer to a road car, clean and renewable energy that can
partially replace gasoline. In the KERS, a flywheel is a
mechanical method of storing the energy, and due to its
unfamiliar nature, must be described in detail to understand
just how the KERS system is able to capture, store, and
release energy.
Components of a Traditional Flywheel
Being a mechanical system, safety comes first. Therefore,
most of the components of a flywheel are housed in a steel
case [9]. The steel case attempts to “dissipate radial kinetic
energy from any rotor debris and ensure safety in the event
of mechanical failure” [10]. The container/shaft within the
case contains various components including the hollow glass
and carbon fiber rotor, a concentric motor/generator (which
will now be referred to as the M/G), and certain bearings [9].
Going from the most crucial components to secondary
components of the flywheel, the first and most important
component is the rotor. The hollow rotor is situated around
the center of the shaft. Along with almost every other
component, it is aligned along a vertical axis. Located within
the hollow rotor is the circular M/G mentioned earlier. There
are more components yet to be discussed. Because listing
them now has little significance, their discussion will be in
accord with their purposes in aiding flywheel function,
external to the core M/G and rotor relationship.
Rotor and M/G Relationship
STORAGE OF ENERGY: THE FLYWHEEL
The relationship between the rotor and the M/G is crucial to
the process of energy storage. The purpose of the M/G is to
obtain transferred energy, and then use that energy to do
work on the rotor. This in turn, causes the rotor to spin,
usually at rates over 60,000 revolutions/minute (rpm) [11].
The M/G takes the energy given to it, uses it to do work on
the rotor and the rotor begins to spin with an almost
equivalent amount of kinetic energy. Depending on the
amount of energy given to the rotor, the rotor spins at
different rates, thus containing kinetic energy due to the
rotating motion. The kinetic energy contained within the
rotor agrees with the following (1).
A flywheel is a storage system that consists mostly of
moving or mechanical parts. The interior and exterior of a
flywheel body are shown to the right in Figure 3.
KE = (1/2)Iω2 .
3
(1)
Muneeb Alvi
Zachary Carson
Equation (1) shows that the energy contained within a rotor
is dependent on the inertia of the rotor and the angular
velocity. Thus the more massive the rotor, the higher the
inertia, and the faster the rotor spins, the higher the kinetic
energy that will be stored. As a result and in accordance with
(1), 75% of the flywheel energy is stored between half the
maximum rotor speed and the maximum rotor speed [9].
Because the rotor may reach speeds up to 60,000 r/m,
stability and safety must also be added to the system.
of the rotor’s rotational speed. The rotor would then stop
relatively fast and dissipate its kinetic energy. Thus in order
for a flywheel system to store energy for extended periods of
time, the friction must be reduced to an absolute minimum.
The friction caused by the contact of the glass and
carbon fiber rings with each other is consolidated by
elastomeric material placed in between the rings [9]. This
allows the stress of one ring to be separated from the stress
of another right beside it, resulting in less friction and more
stability.
The friction due to the presence of air is at an absolute
minimum as the entire flywheel shaft is vacuumed until the
air pressure within is a stable 1x10-7 bar [12]. An air
molecule in such an environment would have to travel 30
miles before encountering another [12].
With the aid of carefully placed magnets and an almost
frictionless interior, the rotor can spin for much longer
periods of time, and thus hold energy for much longer
periods of time. This setup, along with carbon and glassbased rings, allows the rotor to reach speeds of over 60,000
rpm with a vibration value of a maximum 0.5 mm in the
vertical direction [10] [9]. Thus the maximum amount of
storable energy in a flywheel system is determined by the
rotor’s mass and angular (rotational) speed, in addition to
how much stability it receives.
Stability
Safety has already been accounted for with the steel case.
Stability in a flywheel shaft is aided with by the use of
magnets. In the container and on the ends of the shaft of the
flywheel are carefully placed emergency magnetic bearings
to allow precise mechanical adjustment of rotor speeds [9].
The rotor, which is mounted on a nonmagnetic steel shaft,
also contains magnets mounted on its surface [10]. These
magnets aid in reducing wobble within the rotor.
In addition to the magnets, stability also increases by
allowing the rotor to be made of different materials. The
concentric rings constituting the rotor are made of glass and
carbon fiber. The stronger material, carbon fiber, is placed
on the regions of the rotor receiving the most stress and the
glass is located on regions receiving the least stress [9]
Figure 4 below shows a rotor “wound of glass and carbon
fiber rings” [9].
HAND IN HAND
Now, a question arises as to how the flywheel interacts with
the F1 car to obtain and store the energy. As the M/G in the
hollow rotor provides the rotor with energy, it must obtain
that energy from somewhere, and this is where the braking
of an F1 car factors in. Another design aspect for the transfer
of energy is the connection of the flywheel to the
continuously variable transmission (CVT) within the cars. A
CVT transmission can contain an infinite number of gear
ratios with no steps in between. This is the exact opposite of
most vehicles’ transmissions, which must go between fixed
gear ratios [13].
When the car brakes, the electric alternator (discussed
earlier), captures some kinetic energy, but the electric
alternator cannot store the energy. So the alternator transfers
the energy to the M/G in the flywheel. As a result, the M/G
does the same amount of work on spinning the flywheel.
Once the flywheel begins spinning, has immense
stability, and very little resistance (it is practically in a
vacuum), the energy originally captured by the alternator is
can be used to spin the flywheel in the form of kinetic
energy.
Once the energy is stored, the KERS system must be able
to release it. In order for this to occur, the CVT transmission
of the car connects the flywheel to the drivetrain of the car.
Thus, if the gear ratio of the CVT is moved toward a
position to speed the flywheel up, the flywheel stores
energy. This has the same effect as having the electric
alternator capture and transfer energy that is released from
FIGURE 4
EXPOSED ROTOR MADE OF GLASS AND CARBON FIBER [9]
Alternating between carbon and glass-based materials on the
rotor allows further stability and reliability.
Storing the Energy by Reducing Friction
Now that stability has been added, the goal of reducing
friction remains. Friction results from the rings of the rotor,
and air friction within the flywheel shaft itself. These two
sources of friction, if untreated, would lead to the reduction
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Zachary Carson
the brakes to the M/G that spins the flywheel. However, if
instead the CVT is moved toward a gear ratio that slows the
flywheel down, energy is released [12]. That is what
happens when the F1 driver presses the KERS button on the
steering wheel. One example of a modern F1 KERS system
with a flywheel is shown in Figure 5.
In KERS, mechanical energy, which consists of both
potential and kinetic energy, received from the braking of a
car is stored as mechanical energy in the spinning of a
flywheel with no energy conversion required. Because fewer
conversions are required, flywheel “mechanical hybrid
systems offer advantages of higher efficiencies” [14].
In addition to the conversions of energy needed for
batteries, another loss of efficiency results from the fact that
batteries need to maintain a charge state at least above 90%
to maximize battery life in a traditional regenerative brake
system. The clear advantage of using KERS is in the fact
that, when coupled with a flywheel, F1 cars lose and gain
energy constantly throughout a race. This constant and
frequent gain and loss of energy would have dire
consequences on battery life, but due to the mechanical
nature of a flywheel, has very minimal effects on KERS
energy storage [14]. The efficiencies of both the electrical
hybrid storage system and KERS flywheel storage system
are displayed in Table I and Table II.
TABLE I
EFFICIENCY LOSSES OF BATTERY BASED HYBRID STORAGE SYSTEM [14]
Cause of Efficiency Loss
Efficiency Loss
Mechanical energy into electrical energy
29%
May undertake AC to DC conversion
9%
Electrical energy to chemical energy
10% + 0.003% per minute
Total round trip efficiency
About 31%-34%
FIGURE 5
A KERS SYSTEM DESIGNED BY FLYBRID SYSTEMS [12]
The figure displays a flywheel system designed by Flybrid
Systems for use in F1 cars. It weighs less than 18 kg, is
capable of producing 60 kW, and can provide nearly 400 kJ
per lap [12].
TABLE II
EFFICIENCY LOSSES OF KERS MECHANICAL STORAGE SYSTEM [14]
Cause of Efficiency Loss
Efficiency Loss
Gear mesh loss
1.5%
CVT loss
8%
Flywheel storage loss
2% per minute
Total round trip efficiency
>70%
ADVANTAGES, BARRIERS, AND POSSIBILITIES
To transport a system that is fairly new and scarcely tested to
a road car that has relied mostly on gasoline for years is not
a simple copy and paste. For example, there already exists a
regenerative brake technique in some hybrid road cars and
adding another, more expensive system might raise
concerns. Although much more energy efficient, yet more
costly and experimental, a KERS with a flywheel must be
compared to current methods of efficient transportation,
because although it is used in the extremely demanding
cases of the F1, the technology is not perfect.
As is clear from the tables above, the flywheel system
has “measured overall round trip efficiencies of >70% –
[making it] twice as efficient as an electric system,” such as
those currently employed by road cars [14].
Due to a simple design and fewer energy conversions, a
KERS with flywheel system also provides weight benefits
over current electrical regenerative systems. With an overall
weight of just 25 kg (about 55 lbs.), and with the rotor
having a diameter of just 200 mm and length of 100 mm, the
size and weight of the system is not of concern when
discussing its feasibility of being transferred to road cars
[14].
Advantages
The current model of regenerative braking (storing energy
from braking) in modern road cars is an inefficient approach
as it requires converting mechanical energy to electrical
energy and then to chemical energy [14]. This type of
conversion sometimes takes place in road cars that
implement storage of energy in devices such as batteries. In
addition to many conversions taking place during storage,
more conversions must take place to recall stored energy
from a chemical form back into a mechanical from.
Compared to such a system, a KERS-like approach to
regenerative braking has many advantages.
Barriers
Although KERS excels in storing energy, it only captures a
portion of the energy that is given off by the braking of an
F1 car [14]. That fraction of energy translates to about 60
kW of power. However, once the realization occurs that the
original engine output of over 550 kW is unchanged with the
addition of KERS, an additional 60 kW is clearly beneficial
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Zachary Carson
[14]. Furthermore, much debate is occurring regarding
downsizing the engine of an F1 car, and instead allowing the
KERS to be able to output 200 kW [14]. 200 additional kW
is a tremendous amount of power when seen from its
singular source of simply braking. To have this type of
power additions in a road car without spending many
resources such as gasoline would yield large environmental
and efficiency savings.
An additional barrier to KERS’s migration into road cars
is the difference between the horsepower of road cars and
the horsepower of F1 cars. F1 cars have three to four times
the average horsepower of a road car and go much faster.
Because they go faster, F1 cars employ very advanced
brakes that slow them down tremendously fast relative to a
road car and hence, much more energy is released by the
braking of an F1 car than just an ordinary road car. Another
barrier is that the F1 cars that utilize KERS technology
weigh only a fraction of the cars on the road. Once again,
lighter cars mean that the same amount of energy has more
of an effect on F1 cars than on standard, and sometimes
much heavier, road cars. These barriers can be compensated
as (1) shows. The rotors being used in the F1 flywheel
designs are of little mass but rotating at high speeds.
According to (1), that can lead to a sufficient amount of
kinetic energy. But, for a normal road car, the same amount
of energy or even more energy could be achieved with a
larger and more massive rotor, due to more space
availability than an F1 car. This would mean transporting
KERS to road cars would cause some changes in its original
design. Due to this, a design of a KERS for road cars has
been proposed that implements two different modes of
energy recovery. The first mode is for low speed
regeneration (economic) and the second is high speed
performance improvement, for the more powerful vehicles
on the road [14]. Although just an idea for now, a KERS
system with two modes might be sufficient to counter the
weaker and heavier cars of the road.
The last barrier that is worth mentioning is the
preservation of energy for very long or extended periods of
time. Although flywheels can store energy for a relatively
long time, because of the way flywheels function, a rotor
spinning in an almost frictionless environment, means that
the rotor has to eventually lose some spin, and hence energy.
So for now, to store energy for longer periods of time than a
flywheel, a battery is the obvious choice. However, for the
start and stop situations on the road, where energy is coming
and going over short periods of time, a flywheel is more
efficient [14].
original Flybrid Formula One KERS designs that Flybrid
Systems has used in F1 cars. The goal of Flybrid Systems is
to create a flywheel system with a design that can last
250,000 kilometers in road cars. The company also proposes
multiple uses of a flywheel. For example, Flybrid Systems
hopes to use KERS and flywheel design to create a low cost
flywheel system that can perform the launch of a car with
the engine off [11]. A benefit of this is apparent for the start
and stop situations in traffic. Allowing a car to have a full
flywheel ready to discharge its energy while in traffic could
allow the driver to keep the engine off. With Flybrid’s
proposed system, when the traffic begins to slowly move,
the flywheel could alone provide enough energy to move the
car over short distances, perhaps through a separate motor.
This can lead to fuel consumption savings of over 20% [11].
Besides lowering fuel consumption, this could have large
impacts on the reduction of CO2 emissions.
Different from the complexities of an F1 car, Flybrid
Systems also hopes to simplify the KERS system by
allowing it to be automatic, rather than at the push of a
button as is done in the F1 [11]. A computer controlled
automotive system is extremely efficient and allowing a
computer to normalize between gasoline and flywheel as
energy sources would allow much more efficiency than any
human can provide.
Lastly, after so many advances in the field of KERS and
flywheel technology, Flybrid Systems also demonstrated the
reliability of a flywheel system in through a crash test. In a
test that took place at Cranfield Impact Centre, a F1 car
containing a spinning flywheel crashed with a deceleration
of more than 20 g [11]. This is a deceleration of about 196
m/s^2, fatal to most people. However, after the crash the
“flywheel was still spinning at high speed and was
completely undamaged” [11]. This detail is important,
because when discussing so much potential for a system like
KERS that utilizes advanced and expensive technology, it is
comforting to know that a head on crash will likely not
waste all of that potential. This further supports KERS
development for a road car, because on the road accidents
are very frequent. The KERS and flywheel system would
also not damage the car as well due to the KERS’s light
weight and compact design.
Figure 6 shows a possible KERS with a flywheel system
designed by Flybrid Systems to fit standard road cars.
Although not available to the masses, Flybrid Systems hopes
to deliver a KERS to road cars in volume by the year 2014
[11].
Possibility
As described by its advantages and the barriers it must face,
a KERS in a road car is far from a dream. Companies such
as Flybrid Systems have been working with car makers like
Jaguar Cars to develop flywheel hybrid systems for
everyday road cars. Their designs are currently pursuing the
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Zachary Carson
http://www.auto123.com/en/racing-news/f1-technology-kers-deviceexplained?artid=107912
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[12] Sam. (2011, April 24). “Flywheel hybrid systems (KERS).” Racecar
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FIGURE 6
POTENTIAL KERS DESIGNED BY FLYBRID SYSTEMS FOR ROAD CARS [11]
THE FUTURE IS IN THE FORMULA
From the 1960s to 2012, the F1 has not just been the most
advanced racing sport, but also the most beneficial.
Providing technology such as the rear wing spoiler, traction
control, and possibly delivering the KERS, the F1 is more
than just a sport: it is an outside view of the automotive
world years from now. The F1 shows how almost limitless
engineering in slightly controlled restrictions can result in
continued advancement of the automotive world. One
example can be seen with the possible implementation of the
KERS. Although not in a transferable form yet, the KERS
can lead to the development of a hybrid vehicle that disposes
of the current inefficiencies of gasoline and battery powered
vehicles. After exploring such impacts of the F1 and the
KERS, one cannot help but wonder how the world would be
commuting today, if instead the F1 directly made our cars.
ADDITIONAL RESOURCES
A.N. Celik, T. Muneer, & J. Walsh. (2011, February 11). “Design and
analysis of kinetic energy recovery system for automobiles: Case study for
commuters in Edinburgh.” Journal of Renewable and Sustainable Energy.
[Online].
Available:
http://jrse.aip.org/resource/1/jrsebh/v3/i1/p013105_s1?view=fulltext
K. Ernst. (2011, November 29). “Mazda's Regenerative Braking System
Switches Batteries For Capacitors.” Motor Authority. [Online]. Available:
http://www.motorauthority.com/news/1069983_mazdas-regenerativebraking-system-switches-batteries-for-capacitors
(2011, May 17). “Future Porsche 911 models to use KERS.” Auto123.
[Online]. Available: http://www.auto123.com/en/news/future-porsche-911models-to-use-kers?artid=131378
L. Gang, F. Jian-cheng, and T. Ji-qiang. (2010). “Superconducting Energy
Storage Flywheel-An Attractive Technology for Energy Storage.” Journal
of Shanghai Jiaotong University (Science). [Online]. Available:
http://www.springerlink.com/content/x7738n14507g0277/fulltext.pdf
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ACKNOWLEDGEMENTS
We would like to thank the writing center for taking the time
to look through our mistakes and help us transform them
into something that supported our argument. We would also
like to thank Hans Mattingly for the criticisms and critiques
that were given to us since we turned in our first abstract,
only to help and improve our paper ever since. Lastly, we
would like to thank our chair and co-chair who met our
standards for great help in return for expecting great things
from us.
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