How roller coaster designers use math in their careers?

Basic mathematical subjects such as calculus help determine the height needed to allow the car to get up the next hill, the maximum speed, and the angles of ascent and descent. These calculations also help make sure that the roller coaster is safe.



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Vector calculus is a powerful tool for those in the business of ride design and creation. Calculus methods allow us to determine the maximum height attainable by a roller coaster before the track is even built.

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Programs such as AutoCAD are used to draft, adjust, and detail designs in accordance with ride standards. 3D CAD software, such as CATIA, SolidWorks, or AutoDesk Inventor, allow designers to have every step in the roller coaster design process contained within one computer program, including: 3D modeling.

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The roller coaster uses a control system that includes Programmable Logic Controllers (PLC) that synch up using a wireless network to control the seven trains operating on the track.

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A roller coaster demonstrates kinetic energy and potential energy. A marble at the top of the track has potential energy. When the marble rolls down the track, the potential energy is transformed into kinetic energy. Real roller coasters use a motor to pull cars up a hill at the beginning of the ride.

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In roller coasters, the two forms of energy that are most important are gravitational potential energy and kinetic energy. Gravitational potential energy is the energy that an object has because of its height and is equal to the object's mass multiplied by its height multiplied by the gravitational constant (PE = mgh).

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10 Things You Never Knew About Roller Coasters
  • If all countries were as cold as Russia, roller coasters may not exist. ...
  • The world's fastest roller coaster is very fast. ...
  • The U.S.'s first roller coaster was very slow. ...
  • There's a roller coaster still in use that's over 100 years old.


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A roller coaster does not have an engine to generate energy. The climb up the first hill is accomplished by a lift or cable that pulls the train up. This builds up a supply of potential energy that will be used to go down the hill as the train is pulled by gravity.

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There are two types of electromagnetic propulsion used on roller coasters: linear induction motors (LIM) and linear synchronous motors (LSM). Wicked has horizontal and vertical LSM powered launches. Linear Induction Motors use multiple sets of high powered electromagnets secured to the track.

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Roller coasters are designed to run on two basic scientific principles: 1) gravity and 2) the transfer of energy. On Earth, gravity is the force that pulls objects toward the ground. The transfer of energy is what causes objects at rest to move and objects in motion to slow or stop.

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Potential and Kinetic Energy It helps the car's weight maintain momentum as it flies down the track. Other forces try to diminish that energy, such as friction and air resistance, but engineers design coasters to be resilient against these factors.

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Gravity, inertia, g-forces, and centripetal acceleration give riders constantly changing forces which create certain sensations as the coaster travels around the track.

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One of the most widely-known roller coaster engineers is Werner Stengel, who is recognized for his significant contributions to the advancement of coaster design.

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