Physics Anonymous - research paper final paper

RESEARCH PAPER FOR NTU SCIENCE SYMPOSIUM
THE PHOENIX
Redefining Roller Coasters
Physics Anonymous:
Bhumika Lamba, Bushra Kareem, Kanika Gakhar and Megha Singhal
4/15/2013
E-mail id: singhalmegha@gmail.com, kanika.gakhar1@gmail.com, kareembushra@gmail.com,
bhumika.lamba5sg@gmail.com

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ABSTRACT
Roller coasters work on a combination of physics principles and concepts. This research paper
aims to “redefine” roller coasters by adding more thrills for the riders and at the same time
making it more efficient and safe.
The Aerodynamics of the coaster has been designed in such a way that the air drag on the coaster
is made minimal, which helps in conserving the possible loss of velocity, as in the case of
conventional roller coasters. Inspired by the mechanism used in sports cars, we used the principle
of downward force, to make sure that the coaster has a strong grip and at the same time,
incorporating the shape of sport cars, we ensured that it moves with great velocity. The physics
behind the working of the wings of birds (e.g.: macaw) is integrated in the roller coaster as well,
so that the power required to climb up steep hills, is reduced, due to the upward thrust created by
the wings. Hydraulic pumps are used so that the energy is provided more efficiently, as this type
of launch does not require the amount of fuel that would be required for other launching
mechanisms. Hydraulic pumps also make the launch smoother. Moreover, the sound energy
produced by the screaming of riders, is also utilized to produce electricity that is in turn used to
run small thrill mechanisms. Even a jet engine has been used, so as to provide a sudden boost
when the coaster begins to lose momentum, which will help create more excitement and allow
riders to enjoy the thrills of the ride to the fullest, till the end of the ride!

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INDEX
1. Introduction  Background theory
 Roller coaster forces
 Roller coasters and your body
2. Improvements  Speed efficiency
 Downward force- Race Car analogy
 Fuel efficiency
 Safety features
3. Innovations  Wings
 Stream-line shape
 Split tail mechanism
 Bendable mid-section mechanism
 Illusions
 Sound energy utilization
 Jet technology
 Point of application
 Working of the jet turbine
4. Basic Structure
5. Mathematical proof
6. Conclusion
7. Bibliography
8. Appendix

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INTRODUCTION
BACKGROUND THEORY OF THE ROLLER COASTER PHYSICS
The purpose of the coaster's initial ascent is to build up a sort of reservoir of potential energy.
The concept of potential energy, often referred to as energy of position, is very simple. Once you
start cruising down that first hill, gravity takes over and all the built-up potential energy changes
to kinetic energy. Gravity applies a constant downward force on the cars.
The coaster tracks serve to channel this force -- they control the way the coaster cars fall. If the
tracks slope down, gravity pulls the front of the car toward the ground, so it accelerates. If the
tracks tilt up, gravity applies a downward force on the back of the coaster, so it decelerates.
When the coaster ascends one of the smaller hills that follows the initial lift hill, its kinetic
energy changes back to potential energy. In this way, the course of the track is constantly
converting energy from kinetic to potential and back again.
This fluctuation in acceleration is what makes roller coasters so much fun. In most roller
coasters, the hills decrease in height as you move along the track. This is necessary because the
total energy reservoir built up in the lift hill is gradually lost to friction between the train and the
track, as well as between the train and the air. When the train coasts to the end of the track, the
energy reservoir is almost completely empty. At this point, the train either comes to a stop or is
sent up the lift hill for another ride.

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Roller Coaster Forces
The weight of our body that is due to the gravitational force we feel towards earth isn't this
downward pull -- it's the upward pressure of the ground underneath you. The ground stops your
descent to the center of the planet. It pushes up on your feet, which push up on the bones in your
legs, which push up on your rib cage and so on. This is the feeling of weight. At every point on a
roller-coaster ride, gravity is pulling you straight down.
When you are riding in a coaster car that is traveling at a constant speed, you only feel the
downward force of gravity. But as the car speeds up or slows down, you feel pressed against
your seat or the restraining bar.
You feel this force because your inertia is separate from that of the coaster car. When you ride a
roller coaster, all of the forces we've discussed are acting on your body in different ways.
Newton's first law of motion states that an object in motion tends to stay in motion. That is, your
body will keep going at the same speed in the same direction unless some other force acts on you
to change that speed or direction. When the coaster speeds up, the seat in the cart pushes you
forward, accelerating your motion. When the cart slows down, your body naturally wants to keep
going at its original speed. The harness in front of you accelerates your body backward, slowing
you down.

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Roller Coasters and Your Body
When a coaster car is speeding up, the actual force acting on you is the seat pushing your body
forward. But, because of your body's inertia, you feel a force in front of you, pushing you into
the seat. You always feel the push of acceleration coming from the opposite direction of the
actual force accelerating you. This force feels exactly the same as the force of gravity that pulls
you toward the Earth. In fact, acceleration forces are measured in g-forces, where 1 g is equal to
the force of acceleration due to gravity near the Earth's surface (9.8 m/s2
, or 32 ft/s2
).
The coaster constantly changes its acceleration and its position to the ground. When you
plummet down a steep hill, gravity pulls you down while the acceleration force seems to be
pulling you up. At a certain rate of acceleration, these opposite forces balance each other out,
making you feel a sensation of weightlessness -- the same sensation a skydiver feels in free fall.
If the coaster accelerates downward fast enough, the upward acceleration force exceeds the
downward force of gravity, making you feel like you're being pulled upward. If you're
accelerating up a steep hill, the acceleration force and gravity are pulling in roughly the same
direction, making you feel much heavier than normal. If you were to sit on a scale during a roller
coaster ride, you would see your "weight" change from point to point on the track.
At the top of a hill in a conventional coaster, inertia may carry you up, while the coaster car has
already started to follow the track down. Let go of the safety bar, and you'll actually lift up out of
your seat for an instant. Coaster enthusiasts refer to this moment of free fall as "air time."
Having understood these concepts, we decided to improvise and implement our own innovative
mechanisms.

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IMPROVEMENTS
Speed Efficiency
The body of the passengers causes a lot of air drag in the motion of the roller coaster
Earlier: in the conventional roller coasters, the bodies of the passengers provide an
obstruction in the air flow by introducing the aerodynamic force of air drag. This reduces
the speed of the roller coaster by the end of the ride. The roller coaster lifts itself on a
hilltop to gain potential energy from the energy provided by the hydraulics, chain lift or
catapult systems. But the conversion of potential energy into kinetic energy is not 100%
efficient. About 35% of the potential energy is lost due to air drag while its descent. The
reduced speed of the roller coaster makes it impossible for roller coaster to ascend the
high loops. That is why, the height of the loops of the roller coaster decrease gradually
after the first loop.

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Efficient design of the roller coaster
Now: We altered the design of the roller coaster in such a way that half of the body of the
passengers stays inside the structure. Their legs go into the streamlined nose of the roller coaster,
which is efficient as it reduces air drag. The same wind load instead of creating air resistance
now slides smoothly over the streamlined nose of the roller coaster. This mechanism is useful in
increasing the speed when the coaster converts the potential energy to kinetic energy while
descending from hill top. The part of the body that comes in contact with the air is the face (in
order to feel sudden strokes of air on ascent and descent which is necessary for an exciting
experience) and one-fourth part of the upper body. This allows raising their arms into the air.
Downward Force
RACE CAR ANALOGY
Air drag is reduced
due to its streamlined
structure
The wing at the end allows the air to pass over smoothly
which reduces the drag force.
The jet engineThe air suction opening

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Down force is a downward force produced by air pressure, which creates a stronger
pressure between the tire and the surface on which the machine runs. The principle
involved is the same as the one that gives lift to airplanes, but in reverse.
Aerodynamic force results from differences in pressure on the sides of the moving object.
Low pressure is created on the surface on which the machine runs. And the higher
pressure above the structure. The most common methods for increasing the down force of
a vehicle involve reducing the air pressure underneath the vehicle.
The red area shows the intensity of down force underneath the racing car.
The graph below shows the pressure coefficient maximum at the middle.

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The down force is the inverse application of Bernoulli’s Principle.
Downward force in the structure of roller coaster:
The aerodynamic force creates a down force in the roller coaster that can be used to
maintain the grip in the roller coasters while it takes turns. Down force means better
handling on turns since the tires grip the track more securely. It also helps to increase the
speed of the roller coaster. This is same mechanism as that used in the racing cars.
However, the down force also decreases the speed of the vehicle as suction is created
towards the ground which obstructs it from moving forward with a high speed. But since,
the roller coaster tracks contain a lot of gaps in between, the downward force created
between the wheels and the bottom surface of the roller coaster is very less, although
enough to prevent it from swaying away. The down force contributes 28% such that the
roller coaster stays intact with the track. But, at the same time, the effect of down force
on the speed of the roller coaster is very less. This is so because roller coaster moves with
invariably high speed of 206kmph.

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Graph showing the increase in lateral acceleration with the introduction of downward force. The analogy
is applied at the roller coasters at turns.
Fuel efficiency
Instead of using the conventional chain system, we improvised on the recently released hydraulic
press system. It works on the basic idea of Pascal’s law, which states that pressure created by one
piston is equal to the pressure exerted on the other piston.

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Thus small force applied on the large piston is equal to the large force exerted on the small
piston. This simple concept can be used to launch the roller coaster in a more efficient manner.
If this type of coaster is not launched fast enough to clear the top hat, it will roll backwards down
the tower and along the launch track. An accelerator coaster's hydraulic launch is much smoother
than other launch technologies such as linear motors. While a linear motor-launched train's
acceleration is greatest at the beginning of the launch and decreases throughout the launch, a
hydraulic launch produces nearly constant acceleration throughout the launch.
The coaster's power source is several hydraulic pumps, each capable of producing 500
horsepower (370 kW). These pumps push hydraulic fluid into several accumulators which are
divided into two compartments by a movable piston, with one side filled with hydraulic fluid and
the other with nitrogen gas. The nitrogen is held in large tanks directly beneath the actual
accumulator. As the hydraulic fluid fills the accumulators, it pushes on the pistons, compressing
the nitrogen. The winch is driven by hydraulic turbines, which winds up or winds out the cables
that are attached to the sides of the catch-car. The train connects to the catch-car with a solid
piece of metal known as a "launch dog" that drops down from the center car. During the launch,

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the launch valves in the hydraulic room open. The compressed nitrogen in the accumulators
forces the hydraulic fluid into the turbines that drive the winch, which enables the launch of the
coaster. When the train reaches full speed and all the pressure in the accumulators has been
released, the catch-car, using the same braking configuration as the train, slows down quickly,
due to its light weight. The number of pumps, accumulators, and turbines varies with the speed
the coaster is designed to achieve.
One major advantage of this launch system compared to others is its low power consumption, the
hydraulic pumps run constantly and actually use less energy than most chain lift drive motors.
Moreover, instead of using nitrogen, even carbon dioxide can be used. This can be collected
from various industries’ outputs so as to reduce air pollution as well. Additionally, the hydraulic
fluid can be re-used and thus is cost-efficient. Thus using such a launch system turns out to be a
great advantage.
Safety Issues
 Block system - The main purpose of the block system is to prevent two trains from
colliding with each other. In this system, the track is divided into several sections, or
blocks. Only one train at a time is permitted in each block. At the end of each block, there
is a section of track where a train can be safely stopped to allow the other trains to unload
and/ or reload (either by preventing dispatch from the station, closing brakes, or stopping
a lift). This mechanism is automated and uses sensors to detect the trains at each
particular block.
 Wheels - Each rail has wheels on the top, bottom, and on one side. Together with the
other rail, this prevents the train from physically being able to go off the track. Under -
friction wheels also keep riders safe if the coaster were to stop; even while inverted.

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 Air Brakes - Roller coasters have a brake system that uses compressed air. These are
computer operated but do have an emergency brake in case of emergencies.
 Programmable logic controllers - monitor every aspect of a coaster's operations. They
regulate the ride's speed, ensure that trains never come too close to one another, and alert
human operators to technical glitches or track obstructions.
 Restraints - This can be either a simple lap bar or could be an over-the -shoulder restraint.
These are usually held in place by redundant hydraulic cylinders (so that if one of them
fails, then the bar will still stay locked).
 Various testing mechanisms before the roller coaster gets launched like rider envelopes,
and thorough testing of tracks, wheels, emergency brakes, axles and bolts for any loose
parts or contamination. Sandbags/ human dummies and volunteers are also used to make
sure the coaster is fit for riders.
 Also, ride designers must carefully ensure the accelerations experienced throughout the
ride do not subject the human body to more than it can handle. The human body needs
time to detect changes in force in order to control muscle tension. Failure to take this into
account can result in severe injuries such as whiplash. The accelerations accepted in
roller coaster design are generally in the 4-6Gs (40–60 m s−2) range for positive vertical
g force, and 1.5-2Gs (15–20 m s−2) for the negative vertical g force. This range safely
ensures the majority of the population experiences no harmful side effects.

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INNOVATIONS
Wings
Acknowledging the enormous amount of power required in making a coaster climb up a steep
high hill, and inspired by bird’s as well as airplane’s wings, we designed a set of mobile wings
that spread out during climb, and oscillate up and down, so as to provide upward thrust.
This works on three basic principles:
1) Stream-Line Shape
As seen in an airplane, the wing is stream-lined. It is shaped in such a way, that the air
moving above it, moves faster than the air moving below it, thus creating a low pressure.
Due to this imbalance in pressure, an upward force or thrust is experienced, as a result of
which the body moves upward.

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And following this concept, if streamlined wings can be placed at a suitable angle along
the sides of the coaster, then during climb, the air moving along its stream-line shape will
create an angular thrust, thus making the climb easier.
2) Split Tail Mechanism
As observed in a bird’s wing, the tail is split or has slits that enable wind to pass through the
rear end of the wing. This concept can be applied here as well. We designed our wings in
such a way that it allows for the wind to pass through the end, while trapping air in the fore-
end. The fore end traps air and pushes it downward. Applying Newton’s Third Law of
Motion, we know that an equal and opposite force will be exerted on the wing. This provides
for an upward force. Moreover, this trapped air creates a zone of high pressure, again
creating a pressure imbalance, leading to an additional upward force.
At the same time, during the retracing movement of the wing i.e. when the wing moves back
upward, it allows air to pass through the slits so as to reduce air drag and enable quick
movement.

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3) Bendable Mid-section Mechanism
Just as a bird’s wing is bendable in the middle, we designed our wing with a bendable mid-
section.
Its main application is seen during the retracing motion of wing. It allows for changes in
shape while going up i.e. it folds in a V shape and allows air to pass through its center. This

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not only helps in reducing air drag by overcoming friction due to air during backward motion
of the wing, but also helps in creating a pressure imbalance, as shown in the diagram, which
again gives rise to an upward force or thrust.
Thus, we finally designed stream lined – split tail – half bendable – wings attached at the
sides of the roller coasters, which pop out when the coaster is going up high hill and oscillate
up and down so as to create a constant lift or thrust force in the upward direction. These
wings will use up some amount of power to oscillate up and down, however, in relation to
the power required for pulling up a coaster using chains and other means, this is very little.
Also, they close in once the coaster starts moving downwards.
Illusions
Roller coasters are all about the thrill, and a brilliant way of creating this thrill is by introducing
as element of surprise! Inspired by optical illusions, we designed our tracks in certain spots, in
such a way, that the rider thinks something is going to happen while the opposite happens.

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As we all know, by Fermat’s Principle, when light travels from denser to rarer medium, it bends
away from normal and travels faster. We also know that light chooses the quickest route and not
the shortest route.
Thus, if we make certain parts of the track extremely cold, using mini coolers below the tracks,
we can create a region of dense medium. As the air above this is warmer and rarer, it provides
the shorter route for light. This causes the light to bend over the cold patch. However, our eye
perceives it along a straight line. This results in the formation of an image in our brains above the
real image, or in scientific terms, a superior image.
You can see how person thinks the train is going to go straight ahead but it turns downwards,
making it more unexpected.
In Natural phenomenon, Superior mirages can have a striking effect due to the Earth's curvature.
Were the Earth flat, light rays that bend down would soon hit the ground and only nearby objects
would be affected. However, since the Earth is round- if their downward bending curve is about
the same as the curvature of the Earth, light rays can travel large distances. Thus, we can amplify

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the effect of our illusion, by setting it up in a region where the tracks curve, so that the rider
thinks the tracks continue straight ahead, whereas they actually surprise him by turning down!
The reason why we chose to create a superior image rather than an inferior image is that superior
images tend to be more stable, as cold air has no tendency to move up and warm air has no
tendency to move down. Moreover, if an inferior image is created, it would create the illusion of
an image below the real image, thus having a reverse effect. The rider would think the tracks are
going to turn much before they actually turn, thus ruining the surprise element. Additionally,
Inferior images are not stable. Hot air rises, and cooler air descends, so the layers will mix,
giving rise to turbulence.
Thus using simple coolers below the tracks, at curvatures, we can create optical illusions that
delude the riders and introduce an element of surprise.
Sound energy utilization
Sound is measured in decibels. If the sound wave is equal or more than 120%, it is categorized as
screaming. Screaming is one of the aspects that is conventionally linked to rollercoasters, and we
will be utilizing this energy so as to ensure optimum utilization of sound energy.
We will be using piezoelectric speaker to generate electricity from sound energy. The process,
however, can't be "scaled up" for power generation. Electricity can be generated directly from
sound energy by piezoelectric effect. The way it works is that the mechanical energy of sound is
applied directly to a crystal (or possibly a ceramic) with strong piezoelectric characteristics, and
the crystal will generate a small amount of voltage in response to the application of that

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mechanical energy (sound). What we are doing is "squeezing" the crystal. A squeeze will
generate a small voltage for the duration of the squeeze. When the crystal is released, another
small voltage will be generated in the opposite polarity. As stated, the piezoelectric conversion of
mechanical energy (sound) directly to electricity is something we can only do on a small scale.
The relation between sound and power can be understood with the help of a simple chart:
dB Change Voltage Power Loudness
3 1.4X 2X 1.23X
6 2.0 4.0 1.52
10 3.16 10 2
20 10 100 4
40 100 10,000 16
The working of the principles above in the roller coaster:
The Microphones are present inside a tunnel in which due to reverberation and less outside noise,
makes it more effective. When people scream, a mike situated inside the tunnel will detect it and
the signals are then converted to electric signals. These signals are sent to the transistors, which
are like amplifiers, and they convert electric signals to electric power. The power is used by the
LED lights connected in series (red light like eyes). If there is enough power generated, the
motor connected in parallel to the lights will also start working, this motor will cause generation
of smoke using a smoke machine. So at this point “more you scream more thrills you can enjoy”.
This is the circuit diagram used as a reference to build the above described circuit.

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Further piezoelectric speakers are present at all points on the track, which continuously use the
sound to vibrate the crystal, and electricity is produced this electricity is collected and used by a
cooler situated at the point where the mirage effect will be used.
There are three special sensors on the track that will record the amount of sound received at that
point. Each one will have a camera to take a photo of the seated riders. All three cameras will
click the photo, but the point where maximum sound is detected will be selected and the
corresponding photo clicked by that camera will be sent to the system. This will ensure that the
moment of maximum excitement and screaming, is captured and cherished!

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Jet technology
POINT OF APPLICATION (Analogy drawn from aeroplanes)
After half of the ride is over, the impact of air resistance brings a significant decrease in the
speed of the roller coaster. At this point of time, the compressed air from passage can be
combusted with the burning fuel as the air goes into the combustion chamber.
In order to counteract the massive effect of air resistance on the speed of the roller coaster while
moving from downhill to uphill during the loops at the end; the wind load acting on the roller
coaster can be used to drive the roller coaster with a high speed. Thus, the obstructive effect of
air resistance is used in jet mechanism to increase the speed of the moving roller coaster.
WORKING OF THE JET TURBINE
The suction fan in the beginning of the tube sucks the high pressure air inside. The high pressure
wind that hits the lower surface of the moving roller coaster can be made to gush through a tube
OPEN TUBES FOR
ENTRY OF HIGH
PRESSURE AIR
THE COMPRESSED
AIR FROM THE
TUBE GOES INTO
THE EXHAUST JET
ENGINE

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that gradually compresses the air on its passage. This will create a high pressure at the tail of the
roller coaster. The low pressure created at the nose of the roller coaster due to the suction of air
will increase the speed of the roller coaster aerodynamically.
The air expands and rushes out of the turbine with a great force. The streaming jet of the gases
produced backwards results in a forward acting thrust which drives the turbine fan which in turn
drives the suction fan in the front. The force produced by the gas released can be used to drive
the roller coaster faster and make it more enjoyable till the end of the ride as well. The boosters
will combust the oxygen present in air.
All jet engines, which are also called gas turbines, work on the same principle. The engine sucks
air in at the front with a fan. A compressor raises the pressure of the air. The compressor is made
up of fans with many blades and attached to a shaft. The blades compress the air. The
Thermal representation of the pressure in jet engine showing its working

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compressed air is then sprayed with fuel and an electric spark lights the mixture. The burning
gases expand and blast out through the nozzle, at the back of the engine. As the jets of gas shoot
backward, the engine and the aircraft are thrust forward. The combustion will happen inside the
chamber such that the flame doesn’t extinguish. This stage ensures the minimal usage of
combustion process at the end for a less time.

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BASIC STRUCTURE
THE INITIAL ROLLER COASTER TRACK
In the diagram of the roller coaster shown above:
1 - At the time of descent from the elliptical loop, the passengers will be made to pass
through the tunnel which contains the sound sensors. Since, the passengers are expected to
scream the highest at this point; the tunnel will allow the reverberation of the screams. This
would amplify the intensity of sound energy of the passengers received by the sound sensors.
Since, Intensity is proportional to the power produced; more intensity of sound energy will
produce the maximum power through the piezoelectric effect.
1
.
2 3
4

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2- The down force between the tacks and the floor of the roller coaster will allow the cart
to stay in intact with the track. Thus, along with the inertia of the roller coaster to move forward,
the centripetal force on the coaster will ensure the safety of the passengers.
3-The mirage effect due to the cooling of the track comes into effect at this moment of
the ride. This is when the roller coaster reaches the peak of the hill.
4- The light weight fiber and expandable wings are released from the sideway chamber of
roller coaster cart. The wings are opened beforehand, to utilize the high speed of the roller
coaster in creating the pressure difference, which in turn creates a pull for the roller coaster at
position 5 in the next diagram.

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CONTINUED ROLLER COASTER TRACK
6- at last, when the unavoidable air resistance reduces the speed of the roller coaster, the jet
engines are activated inside the roller coaster, to maintain the g-forces and to a bring a sudden
high speed at the end of the ride.
5
The height of the second last loop,
instead of being reduced, remains
the same because the air resistance
is overcome by the wing expansion
system.
6

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MATHEMATICAL PROOF
Mathematical Proof for Use of Wings:
If seven pumps, four accumulators and 32 turbines are used, which can produce15.5 MW for
each launch, although only 7500 kW are used, the coaster can be set off with an initial velocity
of around 200 km/hr or 55m/s.
Thus from the simple diagram, we see:
U= 55m/s and assuming mass of the coaster is 1000kg,
Using the third law of Motion, final velocity can be calculated, had the coaster been launched
from a height of 30m
V2
= u2
+ 2aS

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V2
= (55)2
+ 2(10)(30)
V = 60 m/s (app)
Force acting on coaster = Centripetal Force
F= mv2
/r
Assuming that the longitudinal radius of the elliptical is approximately 10m
F = 1000 x (60)2
/10
F = 3.6 x 105
N
Now looking at the climb section in the simple diagram, we see:
U= 60m/s
Again using the third law of Motion, final velocity as the coaster reaches the hill top, can be
calculated:
V2
= u2
+ 2aS
V2
= (60)2
+ 2(-10)(30)
V = 55 m/s (app)
Thus, we see there is a drop in velocity from 60 m/s to 55 m/s. So as to make up for this 5 m/s
loss in velocity, the wing system is used. This prevents use of extra force initially to maintain top
speed during the climb, by reducing drag and creating an upward lift.

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CONCLUSION
Just as the Phoenix rises from the ashes of its predecessor every 300 years, our redefined roller
coaster arises from the conventional designs and mechanisms of roller coasters. It integrates
mechanisms inspired from macaws, sports cars and airplanes. Not only this, it also incorporates
optical illusions as well as sound energy utilization.
Thus, this research paper enabled us to understand the mechanisms behind various natural as
well as man-made forces, and go into the depths behind it, so that we could figure out their
applications in our unique roller coaster.
This redefined roller coaster is worthy of being entitled as ‘The Phoenix’ due to its various
advantages. Hydraulic power has been used by the roller coaster as it produces more efficient
and consistent power output. It helps in giving a smoother launch and with less input provides
maximum output. Also, Sound energy that would not have been used, has been utilized to
generate electricity, which helps in optimizing the output. Moreover, the wings play a major role
in reducing the power required during the upward movement. In addition to this, the flap at the
back of the coaster, which is inspired from the aerodynamics of a sports car, makes sure that
even at high speed, the coaster stays on the track, due to the downward force that creates a strong
grip on the track. The aerodynamics designed for the coaster helps in reducing the air drag
experienced and hence optimizes the output of the coaster as there are lesser restraining forces.

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However, there were some flaws in our work. For example, in the mirage effect, the cool
temperature will be difficult to maintain at a constant rate, and condensation that will result from
the cold temperature, might cause reduction of the friction between the tracks, and this might
turn out to be dangerous. Also, the contraction of the tracks as a result of this cooling, poses a
major problem. In the wing system, an identified flaw was that the space between the two blocks
will have to be quite large to accommodate the wings. This will cause our roller coaster to
occupy a large area, a drawback especially in any space-conscious amusement park. Also, large,
cumbersome wings, or any appendages at all, pose danger of breakage. This is the same case for
the jet engines. In fact, the flame released from the jet engines might heat up the tracks, thus
leading to expansion. Moreover, this flame is a potential threat, and calls for more safety
mechanisms. Additionally, it requires fuel and it is very easy for the jet to get contaminated, due
to flying in dust particles and other impurities, which can make its utilization and maintenance
quite expensive.
The sound utilization process is also not very efficient, as all the sound energy cannot be
efficiently captured and thus only a small amount of voltage will be produced.
However, with a little more research and innovation, these flaws can be overcome, and our
redefined roller coaster will be ready to hit the tracks!

P a g e | 32
BIBLIOGRAPHY
We would like to thank the NTU Science Symposium Team for giving us the opportunity
to research and learn so much in the field of physics. We would also like to express our
profuse gratitude to our physics teacher, Miss Deepika Sodhi, for her constant help and
guidance.
We referred to the following links for our research paper:
 Coastersandmore.com - Roller Coaster magazine:: Kanonen - Great firepower at Liseberg
 David K. Lynch & William Livingston (2001). Color and Light in Nature - 2nd ed..
Cambridge, UK: Cambridge University Press. p. 58. ISBN 978-0-521-77504-5.
 a b c An Introduction to Mirages by Andy Young
 https://www.youtube.com/watch?v=4jKokxPRtck
 http://www.youtube.com/watch?v=Vyeb6oiEBTw
 http://electronics.howstuffworks.com/gadgets/audio-music/question309.htm
 http://users.ntua.gr/dpiperid/MyWebPage/Contructions/Amplifiers/MicrophoneAmpEN.h
tm
 http://www.ectinschools.org/page.php?ps=2&p=39
 http://www.electroschematics.com/5643/sensitive-clap-switch/
 http://wiki.wiring.co/wiki/Sound_Sensors
 http://www.gcaudio.com/resources/howtos/voltageloudness.html
 https://en.wikipedia.org/wiki/Roller_coaster
 https://www.youtube.com/watch?v=3sS4nT5odP4

P a g e | 33
 http://www.denenapoints.com/blog/6-important-roller-coaster-safety-features-you-need-
to-know.cfm
 http://www.learner.org/interactives/parkphysics/parkphysics.html
 http://www.ehow.com/info_8091277_roller-coaster-safety-features.html
 www.science.howstuffworks.com/engineering/structural/roller-coaster3.html
 http://www.motorsportworld.tv/wiki/index.php/AERO_PUSH
 www.diracdelta.co.uk
 www.rapidracer.com
 www.images.yourdictionary.com
 http://encyclopedia2.thefreedictionary.com/Bernoulli's+principle
 Dunnicliff, John (1988, 1993). Geotechnical Instrumentation for Monitoring Field
Performance. Wiley-Interscience. p. 117. ISBN 0-471-00546-0
 Arthur Schuster, An Introduction to the Theory of Optics, London: Edward Arnold, 1904
online.
 Ghatak, Ajoy (2009), Optics (4th ed.), ISBN 0-07-338048-2
 Feynman, Richard. The Feynman Lectures on Physics, Vol. 1. pp. 26–7.

P a g e | 34
APPENDIX
Fermat's principle:
The principle of least time or Fermat’s Principle states that the path taken between two points by
a ray of light is the path that can be traversed in the least time. A more modern statement of the
principle is that rays of light traverse the path of stationary optical length with respect to
variations of the path. In other words, a ray of light prefers the path such that there are other
paths, arbitrarily nearby on either side, along which the ray would take almost exactly the same
time to traverse.
Bernoulli’s principle:
Bernoulli’s principle states that “As the velocity of a fluid increases, the pressure exerted by that
fluid decreases.”
1. Application in Airplanes: Bernoulli's Principle of Lift
Air Planes are able to fly because of lift which is what holds an airplane up. Lift is created by
differences in air pressure explained by Bernoulli's principle. It states that air moving fast has a
lower air pressure than air moving slower underneath.
The way the airplane's wings are shaped forces the air going over the top of the wings to speed
up in order to reach the end edge of the wing at the same time as the air traveling under the wing.
The bottom air has to travel a shorter difference to the end of the wing so that the air does not
have to travel fast.

P a g e | 35
These varying speeds create a difference in pressures. This air pressure difference exerts a
upward force on the wings that keeps the airplane in the air.
2. Ground effect in racing cars
Race cars use the principle to keep their wheels pressed to the ground as they accelerate. A
race car's spoiler—shaped like an upside-down wing, with the curved surface at the bottom—
produces a net downward force. They apply the Bernoulli’s principle in opposite direction.
Piezometer
A piezometer is either a device used to measure static liquid pressure in a system by measuring
the height to which a column of the liquid rises against gravity, or a device which measures the
pressure of groundwater at a specific point. A piezometer is designed to measure static
pressures, and thus differs from a pitot tube by not being pointed into the fluid flow.

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