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Roller Coaster Inversions
A roller coaster inversion is a roller coaster element in which the track turns riders upside-down and then returns them to an upright position. Early forms of inversions were circular in nature and date back to 1848 on the Centrifugal railway in Paris. These vertical loops produced massive g-force that was often dangerous to riders. As a result, the element eventually became non-existent with the last rides to feature the looping inversions being dismantled during the Great Depression. In 1975, designers from Arrow Development created the Roller coaster element#Corkscrew, corkscrew, reviving interest in the inversion during the modern age of steel roller coasters. Elements have since evolved from simple corkscrews and vertical loops to more complex inversions such as Immelmann loops and cobra rolls. The Smiler at Alton Towers holds the world record for the number of inversions on a roller coaster with 14. History Prototypes (1848–1903) The first inversion in roller coaste ...
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Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ...
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Corkscrew (roller Coaster Element)
Roller coasters are widely known for their drops, inversions, airtime, and other intense ride elements that contribute to the ride. They are also made up of a variety of features and components responsible for the mechanical operation and safety of the ride. Some are very common and appear on every roller coaster in some form, while others are unique to certain makes and models. Amusement parks often compete to build the tallest, fastest, and longest roller coasters to attract thrill seekers and boost park attendance. As coaster design evolved with the aid of computer-simulated models, newer innovations produced more intense thrills while improving overall quality and durability. Common elements Banked turn A banked turn is when the track twists from the horizontal plane into the vertical plane, tipping the train to the side in the direction of the turn. Banking is used to minimize the lateral G-forces on the riders to make the turn more comfortable. When a banked turn continu ...
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Steel Roller Coaster
A steel roller coaster is a type of roller coaster classified by its steel Railway track, track, which consists of long steel tubes that are run in pairs, supported by larger steel columns or beams. Trains running along the track typically rely on wheels made of polyurethane or nylon to keep each train car anchored to the track. The introduction of tubular steel drastically changed roller coaster innovation, allowing for greater speeds, higher drops, and more intense elements such as Roller coaster inversion, inversions. Arrow Dynamics is credited with inventing tubular steel track and introducing the first modern steel coaster with the opening of Matterhorn Bobsleds at Disneyland in 1959. Older steel-tracked coasters existed previously in a simpler form, such as Little Dipper (Memphis Kiddie Park), Little Dipper at Memphis Kiddie Park in Brooklyn, Ohio, which is the oldest operating steel coaster in North America. The oldest in the world is Montaña Suiza at Parque de Atraccione ...
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Arrow Dynamics
Arrow Dynamics was an American manufacturing and engineering company that specialized in designing and building amusement park rides, especially roller coasters. Based in Clearfield, Utah, the company was the successor to Arrow Development (1946–1981) and Arrow Huss (1981–1986), which were responsible for several influential advancements in the amusement and theme park industries. Among the most significant was tubular steel track, which provided a smoother ride than the railroad style rails commonly used prior to the 1960s on wooden roller coasters. The Matterhorn Bobsleds at Disneyland, built in 1959, was Arrow's first roller coaster project. In 1975, Arrow Development introduced the first corkscrew style track Corkscrew, at Knott's Berry Farm that sent riders through a series of corkscrews. Arrow created several other "firsts" over the years, introducing the first suspended roller coaster in almost a century, The Bat, in 1981, and the first " hypercoaster", Magnum ...
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Corkscrew (Cedar Point)
Corkscrew is a steel roller coaster located at Cedar Point in Sandusky, Ohio, Sandusky, Ohio, United States. Built by Arrow Dynamics, Arrow Development and designed by Ron Toomer, it opened to the public on May 15, 1976. The coaster features Arrow's first vertical loop and was built during the same time period as The New Revolution (roller coaster), The New Revolution at Six Flags Magic Mountain, Magic Mountain. Revolution, which opened seven days prior, is credited as the first modern-day coaster to feature a vertical loop, while Corkscrew is credited as the first roller coaster in the world with three inversions. History Corkscrew was originally announced in 1975 as The Great Lake Erie Roller, a name designed to tie in with the nearby Lake Erie, the action of rolling, and "roller coaster". The name was partly based on Great American Scream Machine (Six Flags Over Georgia), The Great American Scream Machine at Six Flags Over Georgia. The coaster would be manufactured by Arrow ...
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Clothoid
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.Levien, Raph"The Euler spiral: a mathematical history."Rapp. tech (2008). The behavior of Fresnel integrals can be illustrated by an Euler spiral, a connection first made by Marie Alfred Cornu in 1874. Euler's spiral is a type of superspiral that has the property of a monotonic curvature function. The Euler spiral has applications to diffraction computations. They are also widely used in railway and highway engineering to design transition curves between straight and curved sections of railways or roads. A similar application is also found in photonic integrated circuits. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral: *Its curvature begins with zero at t ...
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Loop The Loop (Coney Island)
Loop the Loop was a dual-tracked steel roller coaster that operated on Coney Island in Brooklyn, New York, from 1901 to 1910. The coaster was one of the first looping roller coasters in North America. History Loop the Loop was the second looping roller coaster ever to be built on Coney Island and was one of a handful of early looping roller coasters built in the United States in the late 1800s and early 1900s. It was designed by Edward Green and manufactured by Edwin Prescott. The coaster was operated independently, and was not part of one of the cohesive amusement parks which existed on Coney Island. The coaster was built at the corner of West 10th and Surf Avenue on Coney Island, near the current location of the famous Coney Island Cyclone and at the location of the former Switchback Railway. The Loop the Loop lasted from 1901 to 1910 but was a relative commercial failure because of the low rider volume. This low rider volume was partly a function of the small cars on the c ...
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United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 contiguous states border Canada to the north and Mexico to the south, with the semi-exclave of Alaska in the northwest and the archipelago of Hawaii in the Pacific Ocean. The United States asserts sovereignty over five Territories of the United States, major island territories and United States Minor Outlying Islands, various uninhabited islands in Oceania and the Caribbean. It is a megadiverse country, with the world's List of countries and dependencies by area, third-largest land area and List of countries and dependencies by population, third-largest population, exceeding 340 million. Its three Metropolitan statistical areas by population, largest metropolitan areas are New York metropolitan area, New York, Greater Los Angeles, Los Angel ...
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Brooklyn
Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelve original counties established under English rule in 1683 in what was then the Province of New York. As of the 2020 United States census, the population stood at 2,736,074, making it the most populous of the five boroughs of New York City, and the most populous Administrative divisions of New York (state)#County, county in the state.Table 2: Population, Land Area, and Population Density by County, New York State - 2020
New York State Department of Health. Accessed January 2, 2024.

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Coney Island
Coney Island is a neighborhood and entertainment area in the southwestern section of the New York City borough of Brooklyn. The neighborhood is bounded by Brighton Beach to its east, Lower New York Bay to the south and west, and Gravesend to the north and includes the subsection of Sea Gate on its west. More broadly, the Coney Island peninsula consists of Coney Island proper, Brighton Beach, and Manhattan Beach. This was formerly the westernmost of the Outer Barrier islands on the southern shore of Long Island, but in the early 20th century it became connected to the rest of Long Island by land fill. The origin of Coney Island's name is disputed, but the area was originally part of the colonial town of Gravesend. By the mid-19th century it had become a seaside resort, and by the late 19th century, amusement parks had also been built at the location. The attractions reached a historical peak during the first half of the 20th century. However, they declined in popularity aft ...
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