Roller Coaster Designers Need Math

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Does your child love a theme park and hate a classroom? Do they leave a math test forgetting the issues they had with the assessment but get off an amusement-park ride and discuss the experience in detail? Do they have a wishlist of rollercoasters that they would love to visit? Do they have a dream ride that they think they could create?

Well if your child ticks any of these boxes and you need to entice them into doing their math homework, you can tell them that roller coaster designers need math.

In fact, math is necessary at every step of the way.

Right from the start the designer needs to know what the maximum velocity of the train should be so that it’s fun for the passengers, but also so that it’s not so fast that it veers off the track.

The track is tricky too with a huge amount of variables all controlled by someone with a head for math.

If the track is made from wood, then the rollercoaster cannot be as high as a roller coaster with a steel track – although it may be a bit cheaper to build. If the designer goes with the steel option, because let’s face it – higher is better, then they need to make a decision about whether to go for a launch coaster, or a classical “crank” coaster. These decisions are also deeply linked to math. For a car to be launched on a launch coaster it can’t be too heavy, the weight may break the launching gear or be too cumbersome to get through the ride. If a crank gear is used then a too-heavy car may force the chain to snap.

Then there is the actual shape of the coaster, the squiggly track that will determine just how hair-raising the experience will be. Your superstar designer will need to work out the height, speed and length of the ride as well as the amount of turns. As we said before, the slope and height of the first drop will set the pace for the rest of the ride especially if there are loops or bank turns throughout.

A lot of the best (if you define best as most terrifying) roller coasters have stomach-churning loops. To enter a loop from the bottom the train needs to go fast enough to propel itself up and through the coaster:

“The curving track creates a centripetal force, causing the cars to accelerate toward the center of the loop while momentum sweeps them forward. Loose objects like riders are pinned safely to their seats. The acceleration gives the ride its visceral thrill, but it also puts stress on the fragile human body—and the greater the velocity, the greater the centripetal acceleration,” explained a writer at Wired.

Some roller coasters were so extreme that the G-force caused their riders to lose consciousness. To solve this issue rollercoaster designers started using a tear-shaped loop called a clothoid, where the curve of the track is sharper at the top then it is at the bottom. This way most of the turn happens at the peak when the train of the coaster is at its slowest and the acceleration is the least.

The length of the roller coaster is also important. If the track is too long, a car may not be able to keep moving on it and may just pause mid-ride. If the track is too short, then the cars could come crashing through the train house. So breaks have to be placed strategically throughout the ride.

This should be enough math to keep your child going, but if it isn’t there are also operating costs, ride length and other details that would encourage a budding roller coaster designer to head back to their math classroom for more important lessons.




Marina Gomer is a journalist and mother of one.  She lives with her family in Sydney, Australia.