Vol. 38, No. 18

1-21-2009
By:

Ask the Expert, 1/22/09

What is the formula to figure out if a roller coaster can go upside down without falling off the track?
When a roller coaster car becomes inverted, such as when it enters a vertical loop and reaches the top of the loop, it will stay on the track if its speed is greater than Critical Velocity (which is equal to the square root of [g x R], where g is gravitational acceleration of 9.8 meters per second² and R is the radius of the loop in meters).

The centrifugal forces on the coaster at the top of the loop oppose the downward force of gravity and try to keep the car on the track. If the speed of the car is greater than the Critical Velocity, the car will not crash and burn. But if the speed of the car is less than the Critical Velocity, it will literally drop to the ground.

Anybody who designed a coaster after Isaac Newton invented his Laws of Motion could have easily solved this problem. Newton developed his laws in the late 1600s, so anybody who took freshman physics would understand that problem. We actually teach roller coaster physics in our First-Year Engineering Program and have the students build functional models. And you’ll see them build vertical loops that sometimes won’t work. This is the reason.

How much leeway do roller coaster designers give to their car speed?
If you’re riding on a coaster with a loop, you better have a lot of faith the designer gave it enough speed. They will typically use a wide margin of safety, exceeding the Critical Velocity by 50 percent or more.

Coaster conditions change with temperature and weather. Coasters will run differently on different days. If it’s colder, it might run slower. Roller coaster designers understand these things and they measure the different critical speed points on different days. The weight or mass of the car doesn’t matter nor do the weight of the occupants.

When you go to King’s Island, they’ll tell you they build a lot of margin of safety into their coaster design. You don’t want to get close to the critical speed. It’s just like commercial airplanes. They’re built to survive certain types of stresses on the wing structure such as wind shear, gusty winds, dives and pullouts, where lots of G-forces are greater than the maximum credible operating condition would be.

There are built-in safety margins, and I’m sure the coaster designers do that.

Is the same formula needed for roller coasters that hang from the rail?
No, they have a double set of wheels that lock on to both sides of the track and keep them hanging from the track. For a standard coaster, it’s the curvature of the loop that keeps the cars forced against the track.
If you had a coaster that went through a half circle but then tried to run straight ahead upside down for a while, it would fall right down. With hanging coasters locking themselves to the track, they won’t drop or fall and really add to the thrill effects.

Have a question for an expert? Send it in an e-mail to oncampus@osu.edu.

onCampus Home