Amusement Park Math

Summer is heading quickly our way and this is the season most people head off to enjoy amusement parks of all sorts.  Some such as Disneyland, Knott's Berry Farm and Seven Flags over Texas, while others are strictly local or are part of a carnival wandering from town to town.

Each one of these parks provide a wonderful opportunity to explore all sorts of amusement parks, rides, etc to see where the math is.

If you've ever been to Disneyland, you've had to weight in lines but the company has taken great pains to make the wait much easier.  It is what I call the mathematics of handling large groups of people so the ride itself is not slowed down but is actually an application of queing theory.

For instance, on many rides such as Tom Sawyer's Island Rafts, each raft can take a set number of people so park employees designed the waiting area so the correct number of people were grouped. When the raft arrived at the loading area after discharging the previous trip, it could be quickly loaded with the preset group.  As soon as the raft took off, another group was assembled for the next raft.  The groupings made the loading and discharging smooth. In other rides, the waiting line may be wide but there is a U-turn at the end which naturally funnels people into a narrow line making loading the ride so much easier.

Another use of mathematics is to figure out how to move say 500 people out of a theater after a show while moving another 500 people into the theater.  I classify theater as the building housing a show or  a ride that uses a closed room that functions as a space ship.  The closed area does not move so they have to move people in one side and out the other.

Most amusement parks use data mining to predict the movement of people through the park.  In addition, it helps the company determine the pricing for the facility.  Will they offer a daily rate, a package of several days with special activities or without.  Many rides are classified as simulator rides where a specific experience is simulated for people such as the Star Wars ride.

Then there are the various rides, many of which get a pull up to the top of the first hill and then released so that the energy powering the ride is provided through the curves and hills of the ride.  If things are too steep, the cars won't get up the hill, if they aren't steep enough, the ride will poop out soon.

One site such as this one.  It takes students step by step through the process of designing a roller coaster beginning with the first hill, its height and slope, the height of the second hill, a loop,  and at the very end, the site gives you a rating on the safety and fun rating. The site explains why your choices may not be safe.

Let me know what you think, I'd love to hear.  Have a great day.