How Roller Coasters Are Affected by Math

Samantha Robinson
Math105

Math and Roller Coasters

It’s not something that most people think about when they’re standing in line for an hour waiting for two minutes of thrill, but math has a lot to do with building a roller coaster. The engineer needs to know how long and how high the ride needs to be before it can begin to be put together. These measurements have to be precise because the first drop has to give it enough speed to carry it through all the features of the ride. They would also have to take into consideration whether it will be made out of wood or steel because a wood coaster can not be as high as a steel one. The weight of the cars plays a part in the structure since it can’t be too heavy or this will interfere with the speed. It will also cause it to fall down the steep sloop it travels to get to the first drop. To name a few, geometry, algebra and trigonometry are used when a roller coaster is being designed. There are various types of rides and they all have to be built differently.
The corkscrew is shaped like a twisted spiral. Geometry definitely plays a big part in the creation of this ride because the track rails have to be equal so the wheels can stay in sync. When a launch coaster is being put together the engineer needs to calculate the amount of stress that can be put on the launching gear. This again, is where the weight of the cars comes in. If the launching device can’t move the cars because they’re too heavy, the gear may break which could cause people to be hurt and the park could lose money during the duration of the repair. Geometry is the one that we notice the most because it’s involved in the dives, loops, twists and turns as well as going upside down. All of these features are based on triangles, angles, cylinders, circles among other shapes. One example is the loop de loop feature which makes the ride move in a circle. The builder has to make sure that the g-forces on the ride, which is responsible for the feelings that you get when the ride takes a sudden drop or goes through a loop, are consistent for the entire time it’s moving in a circular motion.
When the ride is at the top of the track, it has the most potential energy, which is the energy of a vertical position. This is based on how big on how high the ride is. Once the cars drop, they obtain kinetic energy. As it goes on, the ride goes through different heights. There are a few formulas used when a coaster is being created. Some of them are KEinitial + PEinitial + Wexternal = KEfinal + PEfinal
This goes through the relationship between mechanical energy and external forces. KE=0.5 *mass* (speed) ^2 and PE = mass *g* height is used to calculate the kinetic and potential energy which all plays a part in the height and the speed. Speed of course is the reason why the rides are loved so much. The fastest speed is when the ride makes its initial drop. This is measured in feet and is determined by the vertical difference between from the top of the biggest drop to the bottom. Physics is also a type of math that can be found in the creations of roller coasters. All three Newton’s Laws are used when a roller coaster is developed. A formula used often is F = ma, where F is force, m is mass, and a is acceleration. The amount of breaks needed is determined by how big the coaster is. The distance between the breaks have to be exactly right to prevent the ride from going off track or not stopping at the base of the ride. This will also keep it from stopping in the middle of the ride. As previously stated, steel coasters and wood coasters have to be built differently. Steel roller coasters use a lot of triangle shapes, and they normally hold the record for the highest and fastest rides. As of 2005, the fastest roller coaster is the Kingda Ka which is located in Japan. Speed peaks at 128 mph. Hypersonic XLC held the record for the steepest angle which was 90 degrees. I’m not sure but I think the Griffon at Busch Gardens has that beat! The length also plays a part in how high you have to make the drops and what degree of angle to make it. If the ride is too long for the row of cars to keep a speed that keeps going, than the engineer has to make the launch more forceful or the drop has to be higher and steeper. If the drop is too short the engineer has to add breaks on the track to slow the train down to maintain proper speed and stop when it’s supposed to. The person the controls the whole ride, of course play a big part and this also deals with math. They would need to time the distance between each set of cars exactly and know when to send them off because if there is more than one set running and the operator sends the off too soon due to a lack of judgment, they could hit each other. Most importantly, a person would need to know how much it would cost to put a ride together, because there’s nothing worse than having to stop a project that you worked so hard to put together and there’s not enough funds to complete it. These are just a few ways that math is related to putting a roller coaster together.
As I’ve explained, it takes a lot of hard work, a vivid imagination and of course good math skills to put together something that so many look forward to trying out at amusement parks. I myself definitely enjoy the adrenaline rush and the speed that roller coasters give. It would be nice to know that more of our youth would be interested in something that challenging but fun. I can’t wait to find out what the next thrilling ridge will be!