Math in the real world: Roller coasters

This is another post in a series I’m doing on math in the real world.

When my son and I were on the roller coaster, I was again in awe about how quickly even a small roller coaster like this travels, and how it doesn’t drive right off the tracks.

Roller coasters have to be constructed fairly carefully, and follow some mathematical rules in their construction. They need to first be concerned about how to make the roller coaster safe. They need to calculate exactly how fast it will travel through the loops and turns, and how much of an angle they will need to prevent the roller coaster from taking a dive during those turns. They need to watch out that they don’t cause the participants of the roller coaster to pass out during a turn as they experience additional forces on their bodies!

The various costs associated with a roller coaster need to be calculated as well. There’s the cost to build, maintain, and operate the roller coaster. There’s an additional cost to pay for insurance for the roller coaster, which means an actuary needs to examine the probability of a problem occurring for any given roller coaster. The operator of the roller coaster needs to determine, given the cost to operate the roller coaster, etc… what they should charge to make a return on their investment, and attempt to maximize their profits.

While you could use a roller coaster simulator to explore some of this math, it’s a lot more fun to experience it in person…