Aerospace Engineering Issue I Mechanical Engineering Physics Sports & Recreation Volume I

Roller Coasters

About the Author: Jeff Wurfel, Mark Garciano

Mark Garciano was a junior majoring in Computer Science. Jeff Wurfel had an acting stint as a character in the play "Foot Talk" that he both wrote and assistant directed. His heroes are Carl Sagan, Optimus Prime, and Derek Jeter. He plans on "buying the Clippers and turning that franchise around."

Millions of people ride roller coasters every year and have turned the roller coaster business into a billion dollar industry. Usually, while the passengers are whizzing around on the hills of the coaster they aren’t thinking about the designers that made the rides possible or the laws of physics that coasters are based on. Roller coasters have a long history that dates back to the 1700’s and come in many different forms. The evolution of the roller coaster has made them unbelievably fast and monstrously huge. The best is yet to come as technological advances continually raise the bar for speed, size, and most importantly – safety.


There are three types of people in this world: those who love roller coasters, those who like roller coasters, and those who get nauseous when they look at one. A roller coaster gives its riders an experience that nature never intended humans to have. Passengers can go faster than most people can in cars, sometimes upside down, all on a track that is smaller than a highway lane and higher than most office buildings (Fig. 1). These marvels of human ingenuity make the daredevils crave more and at the same time make the faint of heart woozy. Despite the fact that roller coasters are a significant engineering development, most people know little about them besides the fact that you require a certain minimum height to ride them. Roller coasters have come a long way since their invention. To allow them to be massive and yet go fast, engineers must come up with foolproof designs with the intent of always going a step further in giving the people what they want, bigger and faster.

WillMcC/Wikimedia Common
Figure 1: Roller coasters such as this one, found in Wild Adventures, Georgia, USA, draw crowds of thrill-seekers every summer.

From Ice Slides to Modern Coasters

Roller coasters have a long history dating back to eighteenth century Russia. Their roots come from Russian Ice slides, which were slides made of ice found at most fairs. Riders used wooden or ice carts to make it down these perilous rides. A French businessman attempted to bring this idea to France but the climate would not permit it, and he was left with a “slurpee slide” (a slide with most of the ice having melted). He modified his design by using waxed wood with a wooden cart on rollers. Early models were extremely dangerous with accidents occurring frequently. However, the interesting thing was that the more accidents that happened the more people were drawn to the rides.
In America, coal miners were using a small-scale railway system called the Mauch Chunk Railway to transfer coal back and forth. At first the only occupants of the Mauch Chunk Railway were the coal and mules to haul the carts back up. Soon, people got the ingenuous idea that one could use these systems as recreational rides for people. Thrill seekers started paying $1 to ride up to the top of hill from where they were released and sent back down with just gravity as the power. These rides were going faster than 100 miles an hour on 40 mile long tracks, faster and longer than any modern version and almost as safe. In 1870 the coal miners started using steam engines and underground tunnels leaving the Mauch Chunk Railway to the tourists. Eventually a hotel and restaurant were built on the top of the mountain so that people could relax and get a meal before their ride down [1].
The first true coaster came in 1890 with Marcus Thompson’s invention of the switchback railway, in which passengers would climb a flight of stairs to ride wooden carts down a series of bumps. Once at the end, the passengers walked up another flight of stairs and the cart was switched onto a track that was going in the opposite direction. It wasn’t long until a version was built that did not require the switching of tracks. In the early part of the twentieth century many different coaster ideas were being put into use, most of which died out for safety reasons or general disinterest by the public; leap-the-gap coasters, Virginia Reels (in which people rode rotating carts), and Ticklers were some of these. In 1959 Disneyland opened Matterhorn Mountain, the first roller coaster made out of steel. Since then many new features have been added to roller coasters including a safe loop-the-loop and various stand up models [1].
The newest incarnation of coasters resemble something that the original inventors would never have dreamed of. Modern roller coasters are usually at least 100 feet high with the tallest one, Superman’s Escape (at Six Flags Magic Mountain), towering at close to 40 stories. A typical coaster track is anywhere from half a mile to a mile long. When it’s time for the heart-pounding drop the slope can take on an angle of 60 degrees, much steeper than anything found on the open road. Most have a top speed of around 50 miles an hour but just recently the 100 mph speed barrier was broken by the very same Superman Escape ride at Six Flags. The Superman Escape ride is able to achieve such a high speed because it is the tallest coaster and features the steepest slope, close to a 90-degree angle. The thrill of the steep drop is due to a force called a G-force, which is directly related to the gravitational force. At 50 miles an hour the riders will experience a G-Force of four, which means they experience a force four times the force of gravity. The G-force is directly related to the height of the coaster and causes the coaster to go faster. Getting the coasters to go higher and faster while keeping them safe for passengers takes special designing. This is where the engineering companies come in; they design thrilling, yet safe roller coasters and allow people to enjoy them [2].

Safer than a Car

Safety has always been an issue with coasters. High speeds and great heights have always made parents apprehensive about allowing their children to go on the rides. Computer design systems have made roller coasters safer by making the designs much more predictable and reliable. After the roller coasters are tested and simulated on the computer, they are built and extensively tested again before they are put into use. Even after they have been made available for the public, theme parks perform routine check-ups on the rides to ensure their safety and they have no qualms about shutting down a ride for repair. Many of us know the disappointment of going to an amusement park and discovering that one of our favorite rides is out of commission for repair. The check-ups ensure not only a secure ride but also one that will last for a long time. In fact most of the roller coasters put into use in the fifties are still in use today, including Matterhorn Mountain [1], [3].
One of the comforting things about the roller coaster experience is that a coaster ride is safer than a normal car trip. The biggest of all safety features in roller coasters is the removal of the possibility of human error. Unlike cars, a roller coaster is controlled by a computer; hence, it is impossible for it to make a bad decision. Also, there is only one cart so there is no chance of miscommunication and dangerous interaction between two vehicles, the leading cause for car accidents. The track that the carts glide on provides a clearly defined path for the ride to follow, so even if the riders don’t know what’s coming next the designers do. The ability for the cart to be attached to the track, as well as the harnesses that keep the riders in, has provided the designers the ability to design amazing rides that feature corkscrews and loop-the-loops [3]. Loop-the-loops and other features rely in part on centrifugal force.

Roller Coaster Physics

First, let us discuss the energy of roller coasters and the science of how roller coaster trains move. Due to its motion, the coaster train possesses energy called kinetic energy. It is numerically equal to half the product of the train’s mass and velocity. With faster speeds, the kinetic energy of the train will increase. The equation for kinetic energy is:
KE = (1/2)*mass*velocity^​2   [1]

The other type of energy is gravitational potential energy, which can be considered as energy in the train on account of its height above the earth. In other words, if the train is at a large height, it has a larger tendency to move downwards. Hence, its potential energy will be greater. The equation for potential energy is:

PE = mass*gravity*height  [2]

Consider lifting a roller coaster up a hill. Energy is exerted (by a chain lift) in order to lift the train up the slope, creating energy that becomes available as potential energy. Then, when the coaster drops down the slope, the potential energy is converted to kinetic energy. The higher the train is lifted the more potential energy is created, and the farther down the train falls the more potential energy is converted into kinetic energy. Thus the train will pick up more speed as it falls. The haul up the lift hill is the only source of energy a roller coaster will have, operating solely on the energy created by the chain lift. At different areas of the track there are different levels of potential and kinetic energy. For example, at the top of a hill, the train will have high potential energy and only a little kinetic energy. Thus, it moves slowly at this point. While the train is at dips, it is moving at its fastest, and it will have high kinetic energy and low potential energy.

If we ignore friction, it is very simple to determine the speed of the train. Because the sum of potential and kinetic energies is a constant, ET (total energy) = KE + PE, the speed of the train only depends wholly on its distance below the ride’s highest point.

G Forces

An important concept in understanding roller coaster physics is the idea of G forces. G force is the term used when measuring the gravitational force you feel when you are in the earth’s gravitational field. The force you feel while sitting still is called one G, while the force you feel while in falling motion is a force less than one G [4]. When on an incline such as the slope of a roller coaster, you still experience the G force, but in a constrained fashion because of the track, the train, and your seat. Instead of a straight free fall you experience a fall according to the slope of the track and accelerate as the train moves downwards.
Then, you experience a G force from zero to one. G forces can also be described as weight. In one G, a scale will register your ordinary weight. In zero G (during a perfectly vertical free fall, for instance), you would feel weightless [4]. Roller coasters can exert G forces greater than one. This occurs generally when the train is at the bottom of drops. Due to the force of the seat preventing you from falling and the track turning the train back upwards, you feel a force greater than if you were sitting still. Banking a turn is a way to convert lateral Gs (force directed horizontally) into positive Gs (G force more than zero). As the train goes into a turn of a track that is tilted, the train will tilt as well so that the floor of the train will exert forces on the rider rather than the side of the train, turning some of the G forces into positive Gs.

Development of Loops

The first looping coasters had circular loops. But dangerous G forces caused injuries such as whiplash and broken necks. Hence, Anton Schwarzkopf and Werner Stengel developed the Clothoid loop with the intent of providing a smoother ride. They decreased the radius of the loop at the top and increased the radius at the bottom. This resulted in a smooth, wide curve at the bottom and a narrow curve at the top. In earlier models, the rider could feel up to 10 Gs in circular loops but with the creation of the Clothoid loop the force dropped to 3 Gs [4].


Modern roller coasters have an interesting history. First there were ice slides, and then unsafe roller slides and coal trains that gave birth to the wooden roller coasters of yesteryear. Now we have electromagnetic motor-powered steel and fiberglass coasters designed by computers. Roller coasters will continue to develop with the rest of the world. They will continue to go faster and higher with more tricks. With new materials being developed and new safety programs being made, there will undoubtedly be even better roller coasters to get thrills from (or be sick over).


    • [1] David Bowers. History of Roller Coasters. 2000. Internet: http://www.cinternet​.net/~bowersda/histo​ry.htm, 3 March 2000.
    • [2] Six Flags Theme Park. 2011. Internet: http://www.sixflags.​com, 3 March 2000.
    • [3] S&S Worldwide. 2000. Internet: http://www.arrowdyna​, 3 March 2000.
    • [4] Jim Wiese. Roller Coaster Science. John Wiley Sons & Inc: 1994.

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