What’s the tallest loop-the-loop roller coaster that we could ever build and ride safely?

Amusement park physics taken to the next level.

Rock Bottom
Published in
18 min readFeb 26, 2016


Roller coasters have been the feature attractions of amusement parks for as long as they have been around. The thrill of being hurtled along a track of sharp dips and turns in a speeding car is unmatched by any everyday sensation. But one innovation in particular elevated the thrill of thrill rides to a completely different level — the vertical loop.

The first vertical loop, or “loop-the-loop” roller coaster was constructed in 1845 in Paris.

Vertical loop roller coaster in Paris, 1845

Hey, I know the image is pretty grainy, but I can see enough to know that it would take a lot to get me on that thing. Luckily for us, though, modern-day loop-the-loop coasters have come a long way in the past 170 years, using steel instead of wooden frames and changing the shape of the loop slightly to protect riders from potentially harmful accelerations.

And as they’ve become more safe, they’ve also become much bigger. Currently the title for the world’s tallest belongs to Six Flags’s “Full Throttle,” which features an immense loop of radius 25 meters!

“Full Throttle” roller coaster in Valencia, California

That’s pretty impressive, but what if we wanted to build the tallest possible loop-the-loop roller coaster that we could ever safely ride on? Sound like an impossible task? Read on and I’ll show you that with a bit of physics and a few simple calculations, this question is completely within our reach — and also a lot more interesting than you may think. But before we begin, let’s be scientific about this and define some things a little more precisely.

1. The Question

What is the radius of the tallest vertical loop roller coaster that we could ever build and ride safely on planet Earth? (It will soon become clear why the additional details are necessary.)

2. Implications



Blake Bullwinkel
Rock Bottom

I like to write about math, science, machine learning, and other stuff.