Done by:

Aisha ALDhaheri

ALYazia ALnuaimi
11.51

*videos*

http://www.youtube.com/watch?v=j3eqpYgyVJw&feature=related

http://www.youtube.com/watch?v=W7f_t00boqY

*Pictures*

*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 19^th 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 20^th 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 numbers.

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 energy:

U_g = mgh

Where U_g 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 

*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:

E = K + U

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 derived:

E_i = E_f

or

K_i + U_i = K_f  + U_f

Where E_i is total initial mechanical energy and E_f 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.

*Friction*

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.

*Centripetal Acceleration*

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:

a_r =  v² / r

Where a_r 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*

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.

*Clothoid Loop*

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.