Roller coaster design
Roller coaster design is an engineering endeavor focused on creating thrilling amusement rides that subject riders to intense sensations through loops, turns, and drops. These rides exploit physical principles, particularly the conservation of energy, where potential energy at the highest points is converted into kinetic energy during descents. Historically, roller coasters can be traced back to ice slides in seventeenth-century Russia, evolving into the complex structures we see today, with the first modern designs emerging in the late 1800s.
Key design elements include the use of centripetal force to keep riders securely in their seats during twists and loops, as well as careful consideration of g-forces, which are the forces experienced by riders due to acceleration. Innovations in loop design have improved rider comfort, with modern loops using smoother shapes to minimize harsh forces. The dynamics of roller coasters are carefully calculated to ensure safety and maximize enjoyment, allowing for exhilarating experiences without compromising rider well-being. Amusement parks, like Ohio's Cedar Point, showcase the diversity and engineering marvels of roller coasters, with a record number of rides capturing the imagination of thrill-seekers.
Roller coaster design
Summary: Roller coasters are mathematically designed to provide safe and thrilling rides.
Roller coasters are entertainment rides designed to put the rider through loops, turns, and falls, inducing sudden gravitational forces. The rapid ascents and descents coupled with sharp turns create momentary sensations of weightlessness. One known precursor of roller coasters are seventeenth-century Russian ice slides, which sent riders down a tall, ice-covered incline of roughly 50 degrees. Modern roller coasters can be traced to the late 1800s. As of 2010, Ohio’s Cedar Point held the record for most roller coasters (17) in a single amusement park.
Conservation of Energy
The law of conservation of energy states that energy can neither be created nor destroyed, but can only be converted from one form to another. Roller coasters exploit this law by converting the potential energy gained by the car as it ascends to the top of a hill into kinetic energy as it descends and goes through the turns and loops. The potential energy of the car at the top of the loop is given by
E = m × g × h
where E is the total potential energy (joules), m is the total mass of the car (kg), g is the acceleration due to gravity (9.8 m/s2), and h is the height (m).
For example, consider a roller coaster car weighing 2200 pounds perched at the top of Cedar Point’s Top Thrill Dragster, which is about 426 feet high. The car, at this point, has accumulated 1000×9.8×130=1,274,000 joules or 1.2 megajoules of energy—the same amount of energy released by the explosion of a quarter kilogram of TNT. This potential energy is converted into kinetic energy as the car hurtles down the loops.
As the car expends potential energy, it is converted into kinetic energy, propelling it forward. In an ideal situation where there is no friction or air drag, the car would travel forever. However, because of friction and other resistive forces, the car decelerates and finally stops when it has expended all its potential energy.
Centripetal Force
Centripetal force is responsible for keeping the rider glued to the seat as the car executes turns and loops and even puts the rider upside down. Centripetal and centrifugal forces act on a body that is traveling on a curved path. Whereas centrifugal force is directed outwards, toward the center of curvature, centripetal force acts inward on the body.
G-Force and Loop Design
G-forces are non-gravitational forces, and can be measured using an accelerometer. Humans have the ability to sustain a few g’s (a few times the force of gravity), but deleterious effects are a function of duration, amount,
and location of the g-force. Many roller coasters accelerate briefly up to six g’s, depending on the shapes, angles, and inclines of loops, turns, and hills. Early roller coaster loops were circles. To overcome gravity, the cars entered the circle hard and fast, which pushed riders’ heads continually into their chests as the coaster changed direction. In the 1970s, coaster engineer Werner Stengel worked with National Aeronautics and Space Administration (NASA) scientists to determine how much force riders could safely tolerate. As a result of this and other mathematical investigations, he began to use somewhat smoother clothoid loops, which are based on Euler spirals, named for Leonhard Euler. In 2010, using the same equations that describe how planets orbit the sun, mathematician Hanno Essén drew a new and unique series of potential rollercoaster loops. Riders would get the thrilling visual experience of a loop without any of the typical jolting and shaking, because the force that riders would feel pushing them into their seats would stay exactly the same all the way around the loop.
Bibliography
Alcom, S. Theme Park Design: Behind The Scenes With An Engineer. Orlando, FL: Theme Perks Press, 2010.
Koll, Hilary, Steve Mills, and Korey Kiepert. Using Math to Design a Rollercoaster. New York: Gareth Stevens Publishing, 2006.
Mason, Paul. Roller Coaster!: Motion and Acceleration. Chicago: Heinemann-Raintree, 2007.
Rutherford, Scott. The American Rollercoaster. Norwalk, CT: MBI, 2000.