Physics of roller coasters

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A roller coaster is a machine that uses gravity and inertia to send a train of cars along a winding track.The track also causes friction [1] The combination of gravity and inertia, along with g-forces and centripetal acceleration give the body certain sensations as the coaster moves up, down, and around the track. The forces experienced by the rider are constantly changing, leading to feelings of joy in some riders and nausea in others. The basic principles of roller coaster mechanics have been known since 1865,[ citation needed ], and since then roller coasters have become a popular diversion.



Instead, the car is pulled to the top of the first hill and released, at which point it rolls freely along the track without any external mechanical assistance for the remainder of the ride. The purpose of the ascent of the first hill is to build up potential energy that will then be converted to kinetic energy as the ride progresses. The initial hill, or the lift hill, is the tallest in the entire ride. As the train is pulled to the top, it gains potential energy, as explained by the equation for potential energy below:

where Ug is potential energy, m is mass, g is acceleration due to gravity and h is height above the ground. Two trains of identical mass at different heights will therefore have different potential energies: the train at a greater height will have more potential energy than a train at a lower height. This means that the potential energy for the roller coaster system is greatest at the highest point on the track, or the top of the lift hill. As the roller coaster train begins its descent from the lift hill, the stored potential energy converts to kinetic energy, or energy of motion. The faster the train moves, the more kinetic energy the train gains, as shown by the equation for kinetic energy:

where K is kinetic energy, m is mass, and v is velocity. Because the mass of a roller coaster car remains constant, if the speed 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 largest downhill slope on the track, typically at the bottom of the lift hill. When the train begins to climb the next hill on the track, the train's kinetic energy is converted back into potential energy, decreasing the train's velocity. This process of converting kinetic energy to potential energy and back to kinetic energy continues with each hill. The energy is never destroyed but is lost to friction between the car and track. Brakes bring the ride to a complete stop.

Inertia and gravity

When going around a roller coaster's vertical loop, the inertia that produces a thrilling acceleration force also keeps passengers in their seats. As the car approaches a loop, the direction of a passenger's inertial velocity points straight ahead at the same angle as the track leading up to the loop. As the car enters the loop, the track guides the car up, moving the passenger up as well. This change in direction creates a feeling of extra gravity as the passenger is pushed down into the seat.

At the top of the loop, the force of the car's acceleration pushes the passenger off the seat toward the center of the loop, while inertia pushes the passenger back into the seat. Gravity and acceleration forces push the passenger in opposite directions with nearly equal force, creating a sensation of weightlessness.

At the bottom of the loop, gravity and the change in direction of the passenger's inertia from a downward vertical direction to one that is horizontal push the passenger into the seat, causing the passenger to once again feel very heavy. Most roller coasters require passengers to wear a safety harness, but the forces exerted by most loop-the-loop coasters would keep passengers from falling out.


showing gravity force and contact force commonly referred to as the g-force CoasterH=2.5rforces.gif
showing gravity force and contact force commonly referred to as the g-force

G-forces (gravitational forces) create the so-called "butterfly" sensation felt as a car goes down a gradient. An acceleration of 1 standard gravity (9.8 m/s2) is the usual force of Earth's gravitational pull exerted on a person while standing still. The measurement of a person's normal weight incorporates this gravitational acceleration. When a person feels weightless at the top of a loop or while going down a hill, they are in free fall. However, if the top of a hill is curved more narrowly than a parabola, riders will experience negative Gs and be lifted out of their seats, experiencing the so-called "butterfly" sensation.

Difference between wood and steel coasters

A wooden coaster has a track consisting of thin laminates of wood stacked together, with a flat steel rail fixed to the top laminate. Steel coasters use tubular steel, I beam, or box section running rails. The supporting structure of both types may be steel or wood. Traditionally, steel coasters employed inversions to thrill riders, whereas wooden coasters relied on steep drops and sharp changes in direction to deliver their thrills. However, recent advances in coaster technology have seen the rise of hybrid steel coasters with wooden structures, an example being the New Texas Giant at Six Flags Over Texas and, wooden coasters that feature inversions, an example being Outlaw Run at Silver Dollar City as well as 2018's addition Steel Vengeance.


As better technology became available, engineers began to use computerized design tools to calculate the forces and stresses that the ride would subject passengers to. Computers are now used to design safe coasters with specially designed restraints and lightweight and durable materials. Today, tubular steel tracks and polyurethane wheels allow coasters to travel over 100 miles per hour (160 km/h), while even taller, faster, and more complex roller coasters continue to be built.

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Roller coaster Ride developed for amusement parks

A roller coaster is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. People ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world. LaMarcus Adna Thompson obtained one of the first known patents for a roller coaster design in 1885, related to the Switchback Railway that opened a year earlier at Coney Island. The track in a coaster design does not necessarily have to be a complete circuit, as shuttle roller coasters demonstrate. Most roller coasters have multiple cars in which passengers sit and are restrained. Two or more cars hooked together are called a train. Some roller coasters, notably Wild Mouse roller coasters, run with single cars.

Vertical loop

The generic roller coaster vertical loop, where a section of track causes the riders to complete a 360 degree turn, is the most basic of roller coaster inversions. At the top of the loop, riders are completely inverted.

Launched roller coaster

The launched roller coaster is a modern form of roller coaster. A launched coaster initiates a ride with high amounts of acceleration via one or a series of linear induction motors (LIM), linear synchronous motors (LSM), catapults, tires, chains, or other mechanisms employing hydraulic or pneumatic power. This mode of acceleration powers many of the fastest rollercoasters in the world.

Mindbender (Galaxyland)

The Mindbender is an Anton Schwarzkopf looping roller coaster opened in 1985 at Galaxyland Amusement Park, a theme park located in West Edmonton Mall, in Alberta, Canada. At 44.2 m (145 ft) in height, it is the tallest indoor roller coaster in the world as of 2020.


Do-Dodonpa (ド・ドドンパ), formerly known as Dodonpa (ドドンパ), is a steel roller coaster located at Fuji-Q Highland in Fujiyoshida, Yamanashi, Japan. Manufactured by S&S – Sansei Technologies, the launched coaster uses compressed air to propel its trains. It opened on 21 December 2001 as the fastest roller coaster in the world with the fastest acceleration, reaching a top speed of 172 km/h (106.9 mph) in 1.8 seconds. The fastest speed record was previously held by Superman: The Escape and Tower of Terror, both of which accelerated to 160.9 km/h (100 mph) in 7 seconds. The ride was refurbished in 2017, removing the top hat element in favor of a vertical loop and increasing its speed and acceleration to 180 km/h (111.8 mph) in 1.6 seconds. Steel fabrication was provided by Intermountain Lift, Inc.

Patriot (Worlds of Fun)

Patriot is an inverted roller coaster located at Worlds of Fun in Kansas City, Missouri. Manufactured by Bolliger & Mabillard, the inverted coaster opened to the public on April 8, 2006. It features four inversions, a height of 149 feet (45 m), and a track length of 3,081 feet (939 m).

Tatsu Flying roller coaster at Six Flags Magic Mountain

Tatsu is a steel flying roller coaster designed by Bolliger & Mabillard at the Six Flags Magic Mountain amusement park located in Valencia, California, United States. Announced on November 17, 2005, the roller coaster opened to the public on May 13, 2006 as the park's seventeenth roller coaster. Tatsu reaches a height of 170 feet (52 m) and speeds up to 62 miles per hour (100 km/h). The roller coaster is also the world's tallest and fastest flying coaster; is the only flying roller coaster to feature a zero-gravity roll; and has the world's highest pretzel loop. It was the world's longest flying coaster until The Flying Dinosaur at Universal Studios Japan surpassed it in March 2016.

<i>Superman: Ultimate Flight</i>

Superman: Ultimate Flight is the name of three flying roller coasters currently operating at three Six Flags amusement parks in the United States, those being Six Flags Over Georgia, Six Flags Great Adventure and Six Flags Great America. Each of these steel coasters were designed and built by Swiss manufacturer Bolliger & Mabillard and opened in 2002 and 2003. Since 2003, Six Flags has installed Superman: Ultimate Flight in three of their parks. Themed to the popular comic book character, Superman: Ultimate Flight has been installedSuperman: Ultimate Flight simulates flying by positioning its passengers parallel to the track, supported by harnesses and facing the ground through most of the ride. In the station, riders board the train sitting down. After the train is locked and checked, the trains are raised into the flying position. After the ride, the seats are lowered back into the sitting position for the next round of riders.

Twisted Colossus

Twisted Colossus is a steel roller coaster located at Six Flags Magic Mountain in Santa Clarita, California. Originally designed and built by International Amusement Devices, the roller coaster opened as Colossus, a dual-tracked roller coaster, on June 29, 1978. It was the tallest and fastest wooden roller coaster in the world and the first with two drops greater than 100 feet (30 m). Colossus became well known after appearances in film and television, including the box-office hit National Lampoon's Vacation and the made-for-TV movie Kiss Meets the Phantom of the Park.


Dæmonen is a floorless steel roller coaster at the Tivoli Gardens amusement park in Copenhagen, Denmark. Designed by Bolliger & Mabillard, it reaches a height of 28 metres (92 ft), is 564.0 metres (1,850.4 ft) long, and reaches a maximum speed of 77 kilometres per hour (48 mph). The roller coaster features a vertical loop, an Immelmann loop, and a zero-gravity roll. Dæmonen replaced Slangen, a family roller coaster, and officially opened on 16 April 2004. A record number of guests attended the park that year, but the public has since given the ride mixed reviews.

The Voyage (roller coaster)

The Voyage is a wooden roller coaster located at Holiday World & Splashin' Safari in Santa Claus, Indiana. Designed and built by The Gravity Group with the help of designers Mike Graham, Korey Kiepert, Larry Bill, Chad Miller, and former park President Will Koch, the roller coaster is themed to the famous voyage of the Mayflower by Pilgrims to North America in 1620. It opened to the public on May 6, 2006.

Hydra the Revenge

Hydra the Revenge is a steel Floorless Coaster at Dorney Park & Wildwater Kingdom in Allentown, Pennsylvania, United States. It is the only Floorless Coaster in Pennsylvania and was opened on May 7, 2005. Hydra was built on the site of the former wooden roller coaster Hercules, which was closed and demolished at the end of the park's 2003 season. Its name comes from the Greek Mythology story where Hercules battled the Hydra.

Orient Express (roller coaster)

Orient Express was a steel roller coaster located at Worlds of Fun in Kansas City, Missouri. Introduced in 1980, the ride was manufactured by Arrow Huss and designed by Ron Toomer. The red-orange track was in between the two entrances of the park. The station house is still visible, and contains the park's haunted attraction Lore of the Vampire and Club Blood. In 2004, the ride was replaced by Spinning Dragons, a Gerstlauer spinning roller coaster, which is still in operation as of 2020.

Zoomerang (Lake Compounce)

Zoomerang is the name of a boomerang steel roller coaster located at Lake Compounce in Bristol, Connecticut. Zoomerang is one of the forty-five functioning Vekoma boomerang style roller coasters in the world. They all feature a cobra roll and a loop, but the Lake Compounce Boomerang was the first boomerang to receive a Vekoma designed train. Early models used trains designed by Arrow Dynamics. In September 2007, due to paint deterioration, the ride was repainted with a new color scheme with purple tracks and teal supports.

Air time (rides)

In the context of amusement rides, air time, or airtime, refers to the time during which riders of a roller coaster or other ride experience either weightlessness or negative G-forces. With roller coasters, air time is usually achieved when the train travels over a hill at speed.

Roller coaster elements are the individual parts of roller coaster design and operation, such as a track, hill, loop, or turn. Variations in normal track movement that add thrill or excitement to the ride are often called "thrill elements".

Superman The Ride Steel rollercoaster

Superman The Ride is a steel roller coaster at Six Flags New England in Agawam, Massachusetts. Built by Swiss manufacturer Intamin, the hypercoaster opened to the public as Superman – Ride of Steel in 2000. It features a 208-foot (63 m) lift hill, a 221-foot (67 m) drop, and a maximum speed of 77 mph (124 km/h). In 2009, the park changed the name to Bizarro, named after a DC Comics character portrayed as the antithesis of Superman. In accordance with the theme change, the coaster's track and supports were repainted with a purple and dark blue color scheme, and other special effects were added. In 2016, the Six Flags reverted to the original theme, but instead of restoring the name, it was changed to Superman The Ride. A virtual reality feature was added the same year, which created an optional 3D experience for passengers, but was removed prior to the 2017 season.

History of the roller coaster

Roller coaster amusement rides have origins back to ice slides constructed in 18th-century Russia. Early technology featured sleds or wheeled carts that were sent down hills of snow reinforced by wooden supports. The technology evolved in the 19th century to feature railroad track using wheeled cars that were securely locked to the track. Newer innovations emerged in the early 20th century with side friction and underfriction technologies to allow for greater speeds and sharper turns. By the mid-to-late 20th century, these elements intensified with the introduction of steel roller coaster designs and the ability to invert riders.

Blue Fire

Blue Fire is a launched roller coaster at Europa-Park. The coaster opened in 2009 as part of a new Iceland-themed expansion to Europa-Park. As the first launched coaster built by MACK Rides, Blue Fire was the park's tenth roller coaster and the first to feature inversions. The ride's tagline is "Discover Pure Energy".

Wild Eagle

Wild Eagle is a steel Wing Coaster built by Bolliger & Mabillard at the Dollywood amusement park in Pigeon Forge, Tennessee. It is the first of its kind in the United States and opened to the media on March 23, 2012 before opening to the public on March 24, 2012. The roller coaster reaches a height of 210 feet (64 m) and reaches speeds of 61 miles per hour (98 km/h). In September 2012, the ride was voted as the best new ride of 2012 in Amusement Today's Golden Ticket Awards.


  1. Harris, Tom. "How Roller Coasters Work" . Retrieved 1 July 2010. At its most basic level, this is all a roller coaster is -- a machine that uses gravity and inertia to send a train along a winding track.