#1216 What are the physics of roller coasters?

What are the physics of roller coasters? Designers of roller coasters have to pay a lot of attention to physics because they need the roller coaster cars to move, they need them to stay on the tracks, and they need them to go fast enough to be thrilling but not so fast that they kill the customers.

The first important part of a roller coaster is to get it to move. Roller coasters don’t have engines, so the force has to be supplied from somewhere else. Typically, roller coaster cars have four wheels that are connected to a metal track. Roller coasters can be made of wood or metal, but in either case, the track is made of metal tubing. The roller coaster has no way of powering itself, so all of the force necessary has to come from the track itself. The most common way of giving the roller coaster cars energy is to tow them to the top of a very tall tower where the ride will begin. As the car is pulled up the tower, it develops potential energy. Potential energy is calculated by multiplying the weight of the roller coaster car by the acceleration due to gravity (which is always 9.8 m/s on Earth) and the height of the hill. A heavier roller coaster car will have more potential energy than a lighter one, and a roller coaster car on a higher hill will have more potential energy than one on a lower hill. The designers of the roller coaster have to work this out because they need enough potential energy for the roller coaster car to make it all the way around the track.

When the roller coaster car is at the top of the starting hill, it is released and the potential energy gets converted into kinetic energy, which powers the roller coaster and dictates the speed it will reach. Each time the roller coaster car hits a hill, it will start to lose kinetic energy and develop potential energy. Once it gets to the top of the smaller hills, its potential energy will be converted into kinetic energy and it will start to move again. Unless there is another pully somewhere on the course, the starting hill must be high enough to give the roller coaster car enough energy to get around the whole course. The roller coaster car will constantly lose energy from wind resistance and friction with the rails, which all needs to be taken into account. A perfect roller coaster will bleed off all of the kinetic energy, so there is almost none left when it gets back to the station.

The second thing the designers need to pay attention to is how to keep the cars on the tracks. Newton’s first law of motion states that an object in motion stays in motion. This can be seen by looking at the Voyager Probes. There are no forces acting on them, so they continue to move in a straight line. With a roller coaster, the kinetic energy driving the roller coaster car forward will make the car want to keep going in a straight line. When it comes to a bend, the connection with the track has to be strong enough to overcome that energy going forwards. To make sure roller coaster cars grip the tracks very well, they don’t have single wheels, but they have sets of wheels that grip the track from the top, bottom, and side at the same time.

The third thing that the designers need to be aware of are the limitations of the human body. Roller coasters could be built much higher, and they could be designed to go much faster, around corners that are much sharper, but then all of the riders would die, and that kind of defeats the object of the roller coaster. Designers want to give the riders a thrill, but not to kill them. Our bodies are not very strong and we can only sustain a certain amount of g force. G force is a measure of acceleration and it explains how much force is acting on something. It is calibrated in units of g, which stands for gravity. 1 g is the normal gravity of Earth and is what we all experience all of the time. If you are on a roller coaster and it accelerates very quickly, you will be exposed to more force and possibly 2 or 3 g, depending on how quickly it accelerates. 3 g means you are experiencing three times the force of Earth’s gravity, so a 70 kg person would feel 210 kg. On a roller coaster, you are exposed to these forces when they accelerate, when they brake, when they go up, when they go down, and when they turn left or right. The faster you are going and the sharper the change of direction, the more g force you will feel. And this is what limits roller coasters. Our bodies have evolved to live and pump blood under 1 g. If the force is increased to 2 g or more, we find it harder to pump blood. For a few seconds, it is ok, but for longer periods of time it can be uncomfortable and even fatal. With training, people can withstand up to 10 g, but not for very long. If a roller coaster has g force that is too high, people will be uncomfortable and may even get injured. Designers have to work out exactly how much g force to create to give a feeling of thrill, but not to injure. There are a lot of physics that need to be considered. And this is what I learned today.

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Sources

https://en.wikipedia.org/wiki/Physics_of_roller_coasters

https://science.howstuffworks.com/engineering/structural/roller-coaster3.htm

https://en.wikipedia.org/wiki/Potential_energy