~ROLLER COASTER PHYSICS~
The Science Behind the Thrills
Turning Points in Roller Coaster History
The very first “roller coasters” were created in Russia in the
1600’s, and were nothing like the typical roller coaster that comes
to mind today. People rode down steep ice slides on large sleds
made from either wood or ice that were slowed with sand at the
end of the ride. These sleds required skill to navigate down the
slides, and accidents were frequent.
A Frenchman tried to cash in on the popularity of the Russian ice
slides by building one in France, but the warm climate quickly
ended his attempts with ice. A waxed wooden slide proved to be
much more feasible, along with wooden wheeled sleds. Just as
with the ice slides, the necessity of navigation skills caused many
accidents, so tracks were produced to keep the sleds in line.
In the 1850’s, the first shot at a vertical loop was made in France.
This “Centrifuge Railway” offered a rail car that would travel
through the loop with nothing keeping it there aside from its own
centripetal acceleration. Government officials quickly shut the
operation down after one accident.
The beginning of American roller coasters was near the end of the
19th century when railway companies set up amusement parks at
the end of their lines to increase business on the weekends. In
1884 the first real roller coaster in America was introduced: a
gravity driven switchback train. Passengers would climb a set of
stairs to board the car, which was then pushed from the station to
travel down a hill and over a few bumps. At the bottom, the
passengers got out and climbed another set of stairs while workers
hoisted the car to the top of the second station. The passengers got
back into the car and rode to the first station on a second track.
Another attempt at a vertical loop was tried in 1898, and was
called the Flip-Flap Railway. However, the loop on this ride was a
circle, as opposed to the clothoid loops that are used in roller
coaster design today. This caused a problem: the forces generated
by the circular loop were so strong that riders’ necks were snapped.
The beginning of the 20th Century saw great leaps in roller coaster
safety. The first roller coaster to employ trains with an up-stop
wheel system that held to the track rather than just sitting atop it
was built in 1912. This was a huge leap as it gave the opportunity
for greater speed and steeper hills. Many coasters were built
through the 1920’s, but the 1929 stock market crash, the Great
Depression and World War II saw a severe decline in their
Disneyland, America’s first theme park, opened in 1955, and
brought with it a new era for amusement parks. Disney introduced
the first tubular steel roller coaster, the Matterhorn, in 1959.
Before this, roller coasters had always been built from wood, but
the steel track was a huge improvement, offering not only greater
stability, but also opening the door for loops and corkscrews.
Gravity and Potential Energy
Gravity is the driving force of a roller coaster. From the moment
the roller coaster train passes the peak of the lift hill, it is the
acceleration due to gravity that brings it back to the beginning.
When the train is released from the top of the lift hill, gravity pulls
it down. The train begins slowly, then picks up speed as it
approaches the bottom of the hill. As it begins to climb the next
hill, the speed decreases. This is because of the acceleration due to
gravity, which occurs at 9.80m/s2 straight down toward the center
of the Earth.
The initial hill, or the lift hill, is the tallest in the entire ride. As the
train is pulled to the top, it is gaining potential, or stored energy.
The higher the lift, the greater the amount of potential energy
gained by the train. This is shown by the equation for potential
Ug = mgh
Where Ug is potential energy, m is mass in kilograms, g is
acceleration due to gravity, and h is the distance above the ground
in meters. Because mass and gravity are constant for the train, if
the height of the train above the ground is increased, the potential
energy must also increase. This means that the potential energy for
the roller coaster system is greatest at the highest point on the
track: the top of the lift hill.
Velocity and Kinetic Energy
As the roller coaster train begins its descent from the lift hill, its
velocity increases. This causes the train to gain kinetic energy,
which is the energy of motion. The faster the train moves, the
more kinetic energy the train gains. This is shown by the equation
for kinetic energy:
K = 1/2mv2
Where K is kinetic energy, m is mass in kilograms, and v is velocity in meters per
second. Because the mass is constant, if the velocity is increased, the kinetic
energy must also increase. This means that the kinetic energy for the roller
coaster system is greatest at the bottom of the highest hill on the track: the bottom
of the lift hill. When the train begins to climb the next hill on the track, the train
starts to slow down, thereby decreasing its kinetic energy.
Conservation of Energy
Energy cannot be created or destroyed, but it can be converted from one form to
another. For the idealized roller coaster, all energy is conserved through
conservative forces, such as gravity. As the train accelerates down the lift hill,
potential energy is converted into kinetic energy. When the train ascends another
hill, the kinetic energy is converted into potential energy again. This is
conservation of mechanical energy, and it continues throughout the entire ride.
The total mechanical energy for the train is shown by the equation:
Where E is the total mechanical energy, K is kinetic energy, and U is potential
energy. From this, the equation for conservation of total mechanical energy can be
Ei = Ef
Ki + Ui = Kf + Uf
Where Ei is total initial mechanical energy and Ef is total final
mechanical energy. This shows that the total initial mechanical
energy equals the total final mechanical energy for the system. It
is because of this phenomenon that a roller coaster is called a
“coaster.” After the initial input of energy to carry the train up the
lift hill, the roller coaster simply coasts through the rest of the ride.
For a non-idealized roller coaster system, not all of the energy is
conserved. Friction is the main cause of energy leaks in the system
and the reason why mechanical energy is not fully conserved for a
real roller coaster. This is because friction is a nonconservative
force. Nonconservative forces are forces that cause a change in
total mechanical energy. Friction opposes motion by working in
the opposite direction. The friction between the train and its tracks
as well as between the train and the air take energy out of the
system, slowing the train and creating both heat and sound. This
effect is most noticeable at the end of the ride as all remaining
kinetic energy is taken out of the system though brakes. Because
of the energy leaks due to friction, each successive hill or loop on a
roller coaster must be shorter than all the hills or loops previous to
it, otherwise the train will not have enough energy to make it all
the way over.
Curves are an essential part of a roller coaster, and centripetal
acceleration is part of moving in a circular path. Therefore,
centripetal acceleration is also an essential part of a roller coaster.
Centripetal acceleration points toward the center of the circular
path of the train, but is felt by passengers as a force pushing them
to the outer edge of the circular path. This feeling is often
described as centrifugal force, although there is no actual force
pushing or pulling passengers away from the circle. The
“centrifugal force” is actually your body’s inertia, or its resistance
to the train’s change in direction: your body wants to continue in a
straight line and attempts to do so as the train turns. Luckily, your
body is strapped into the roller coaster train, otherwise your body
would continue in the straight path that the train was following
before it entered the curve.
The equation for centripetal acceleration is:
ar = v2 / r
Where ar is centripetal acceleration, v is velocity in meters per
second, and r is the radius of the circle in meters. This means that
the higher the train’s velocity, the greater the centripetal
acceleration. This also means that the smaller the curve of the path
being traveled, the greater the centripetal acceleration. Because of
this, many high-speed roller coasters use banked turns rather than
the flat ones that are safe for slower speeds. Banking the turns in a
roller coaster gives you the feeling of being pushed into your seat
rather than being thrown to the side of the car.
G-forces are used for explaining the relative effects of centripetal
acceleration that a rider feels while on a roller coaster. Consequently, the
greater the centripetal acceleration, the greater the G-forces felt by the
passengers. A force of 1 G is the usual force of the Earth’s gravitational
pull that a person feels when they are at rest on the Earth’s surface; in
other words, it can be described as a person’s normal weight. When a
person feels weightless, as in free fall or in space, they are experiencing
0 G’s. When the roller coaster train is going down a hill, the passengers
usually undergo somewhere between 0 and 1 G. However, if the top of
the hill is curved more narrowly than a parabola, the passengers will
experience negative G’s as they rise above the seat and get pushed down
by the lap bar. This is because gravity and the passengers’ inertia would
have them fall in a parabolic arc. G-forces greater than 1 can be felt at
the bottom of hills as the train changes direction. In this case the train is
pushing up on the passengers with more than the force of gravity because
it is changing their direction of movement from down to up. G-forces
that are felt when changing direction horizontally are called lateral G’s.
Lateral G’s can be converted into normal G-forces by banking turns.
Roller coasters today employ clothoid loops rather than the circular loops of earlier roller
coasters. This is because circular loops require greater entry speeds to complete the loop.
The greater entry speeds subject passengers to greater centripetal acceleration through the
lower half of the loop, therefore greater G’s. If the radius is reduced at the top of the
loop, the centripetal acceleration is increased sufficiently to keep the passengers and the
train from slowing too much as they move through the loop. A large radius is kept
through the bottom half of the loop, thereby reducing the centripetal acceleration and the
G’s acting on the passengers.
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