World's smoothest roller coaster ride: Swedish mathematicians draw the perfect loop

July 16, 2010 By Devin Powell, Inside Science News Service
Credit: Ann-Marie Pendrill, University of Gothenburg

At the age of 74, retired roller coaster designer Werner Stengel still spends his days riding the latest loop-de-loops.

"Trying to explain the thrill of a roller coaster to someone who has never ridden one is like trying to explain color to a blind person -- you just have to experience it for yourself," said Stengel, who in 1975 created the first modern roller coaster loop, built for Six Flags' Magic Mountain in California.

But for summer vacationers who are tired of having their heads jerked around by the , Swedish mathematicians have published new designs for what could be the smoothest, most comfortable way to flip head over feet.

Using the same equations that describe how the planets orbit the sun, Hanno Essén of Sweden's Royal Institute of Technology in Stockholm drew a series of potential roller coaster loops that have one thing in common -- the force that riders would feel pushing their stomachs down into their seats stays exactly the same all the way around the loop.

Riders would get the visual experience of a loop without any whiplash.

"If you were in a car without windows and the track were perfectly smooth, you would not know that you were in a roller coaster," said Essén. "You'd just be pressed to the seat by a constant force."

This force, the centripetal force, is the same one that prevents water from falling out of a bucket swung upside-down on a string. The shape of a loop determines how much of it we feel at different spots on the loop.

Early roller coaster loops -- including the first one, a 13-footer built in 1846 in Paris -- were simple circles. To make it all the way around without being pulled off at the top by gravity, coaster cars hit the circle hard and fast, shoving riders' heads into their chests as they changed direction with a sudden snap that occasionally broke their collarbones.

In the 1970s, Stengel talked to NASA to figure out how much force rider could safely tolerate. He created the modern standard: 6 G's, which makes a rider feel six times heavier than normal.

To improve safety, Stengel ditched the circle. He designed a new loop that pinched at the top, a shape borrowed from exit ramps on German highways. This clothoid curve -- which tapers from a gentler arc at the bottom to a tight curve at the top -- is standard in today's amusement parks, where loops are now up to 200 feet tall. It eases riders into a loop with a force of 3-4 G's at the bottom that gradually lessens on the side of the loop to, often, a feeling of weightlessness at the top.

The new Swedish design, which to the naked eye looks similar to a clothoid loop, would in theory smooth out these changes in force into one constant force, said Stengel. But he doubted that it could achieve this uniformity if actually built.

That's because roller coasters aren't as simple as a dot moving around a curve. They jostle on imperfect tracks and are slowed down by friction and wind resistance.

Even if the force could be kept constant, the riding experience would depend on where you sit. Passengers in the front and end cars feel greater G forces than those the middle cars at the coaster's center of gravity.

Different parts of a rider's body would also feel different forces, according to Ann-Marie Pendrill, who studies roller coasters at the University of Gothenburg in Sweden.

"Your head would feel a little lighter than your bottom," she said, explaining that the head is closer to the center of the loop, where the centripetal force is smaller.

For now, the new design will remain an academic exercise -- which, to veteran thrill seeker Stengel, is just as well.

"It sounds a bit boring to ride," he said. "Part of the fun of a is being pushed around with changing forces."

Explore further: Low Risk of Traumatic Brain Injury from Roller Coaster Rides, Researcher Says

Related Stories

Study: Roller coasters linked to common ear injury

April 30, 2010

The sharp turns, ups and downs, and high speeds of today's roller coasters bring a lot of thrills, but if you're not careful, the ride could also cause damage to your ears, say physicians at Henry Ford Hospital in Detroit.

Astronauts to Ride Rails in Emergency

October 4, 2007

As NASA revamps Launch Complex 39B to host the new Orion spacecraft and Ares I rocket of the Constellation Program, engineers are preparing to install a new kind of departure system to evacuate astronauts.

NASA and Zero-G Agree on Regular Shuttle Runway Use

April 4, 2006

NASA and Zero Gravity Corp. of Fort Lauderdale, Fla., announced today the company -- known as ZERO-G -- will begin to regularly use the space shuttle's runway and landing facility at NASA's Kennedy Space Center, Fla. This ...

Simple twists of fate

September 30, 2008

A novel Brandeis University study this week in PLoS Biology reports on some of the molecular gymnastics performed by a protein involved in regulating DNA transcription. Using state-of-the art tools, researchers observed the ...

Recommended for you

Two new planets discovered using artificial intelligence

March 26, 2019

Astronomers at The University of Texas at Austin, in partnership with Google, have used artificial intelligence (AI) to uncover two more hidden planets in the Kepler space telescope archive. The technique shows promise for ...

Infertility's roots in DNA packaging

March 26, 2019

Pathological infertility is a condition affecting roughly 7 percent of human males, and among those afflicted, 10 to 15 percent are thought to have a genetic cause. However, pinpointing the precise genes responsible for the ...

Facebook is free, but should it count toward GDP anyway?

March 26, 2019

For several decades, gross domestic product (GDP), a sum of the value of purchased goods, has been a ubiquitous yardstick of economic activity. More recently, some observers have suggested that GDP falls short because it ...

Droughts could hit aging power plants hard

March 26, 2019

Older power plants with once-through cooling systems generate about a third of all U.S. electricity, but their future generating capacity will be undercut by droughts and rising water temperatures linked to climate change. ...


Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Jul 16, 2010
Passengers in the front and end cars feel greater G forces than those the middle cars at the coaster's center of gravity.
?? They trace the same path.
not rated yet Jul 17, 2010
the speed of the coaster slows as it goes through the loop so those at the front are most way round when the main mass hits the slow point at the top of the loop.
I would imagine...

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.