Skip to Content
Uncategorized

Designing The Perfectly Smooth Roller Coaster Ride

Mathematicians have derived the shape of a roller coaster that gives a perfectly smooth ride

One of the challenges that roller coaster designers face is controlling the forces their passengers experience as they take the ride.

The forces in a vertical plane are simple to state. They are the sum of the gravitational force pulling down and any centrifugal force that depends on radius of curvature and acts normally to the track.

The easiest track to design is circular but this causes a problem, “In practice this leads to unpleasantly large time variation of the normal force,” say Arne Nordmark and Hanno Essat the KTH Royal Institute of Technology in Stockholm. So designers are forced to rely on other more complex shapes, such as the clothoid.

So a reasonable question to ask is what shape should the tracks be to deliver a constant smooth normal force to a passenger taking the ride. Such a roller coaster would offer the perfect smooth ride.

(A curious feature of Nordmark and Essat’s analysis of this problem is that they say it is related mathematically to Kepler’s problem of planetary motion. Who’d have guessed.)

The answer, say the Swedes, is the shapes in the picture above. These do not yet appear to have a name–Nordmark and Essat call them Case 1 trajectories. Readers of the arXiv Blog will surely have better ideas. Suggestions in the comments section please.

Ref: arxiv.org/abs/1007.1394: The Comfortable Roller Coaster – On The Shape Of Tracks With Constant Normal Force

Keep Reading

Most Popular

Here’s how a Twitter engineer says it will break in the coming weeks

One insider says the company’s current staffing isn’t able to sustain the platform.

Technology that lets us “speak” to our dead relatives has arrived. Are we ready?

Digital clones of the people we love could forever change how we grieve.

How to befriend a crow

I watched a bunch of crows on TikTok and now I'm trying to connect with some local birds.

Starlink signals can be reverse-engineered to work like GPS—whether SpaceX likes it or not

Elon said no thanks to using his mega-constellation for navigation. Researchers went ahead anyway.

Stay connected

Illustration by Rose Wong

Get the latest updates from
MIT Technology Review

Discover special offers, top stories, upcoming events, and more.

Thank you for submitting your email!

Explore more newsletters

It looks like something went wrong.

We’re having trouble saving your preferences. Try refreshing this page and updating them one more time. If you continue to get this message, reach out to us at customer-service@technologyreview.com with a list of newsletters you’d like to receive.