How do you know a roller coaster is safe?

What makes a roller coaster ride exciting?

The folks at Newton's Apple wrote the following!

Overview

Isaac Newton never had a chance to ride a roller coaster. The first one was built 75 years after his death. But the principles involved in roller coasters are right up Sir Isaac's alley.

Newton's laws of motion describe how forces determine the motion of objects. Designers rely on the acceleration caused by those forces to make a roller coaster ride both thrilling and safe. The trick is knowing how to use the forces properly. If the forces are too great in one direction, for instance, they'll throw the car off the track. If an upward force is too large (giving you a feeling of heaviness), your heart cannot pump enough blood to your head and you faint. On the other hand, the lack of supporting forces can create feelings of incredible lightness. This can provide an electrifying ride that delivers you safely to the end.

Hypercoasters are about twice as tall as regular roller coasters. This larger scale adds new design challenges. Going down a 200-foot hill, a car has more time to accelerate and gains more speed. If while going at this fast speed the car experiences a sudden change in direction or speed, the car's acceleration changes. A big or sudden change in speed or direction can make a bigger acceleration. Since the force acting on the car (and you) is equal to its mass times its acceleration, the bigger the change in direction or speed and the less time that change takes, the greater the acceleration and the bigger the force you'll feel.

To keep these forces at safe levels, the designer has to stretch out the time and the distance it takes to navigate the curve at the bottom of the hill. This spreads the change out over time, decreasing the force you feel. The top of the next hill has to be high enough to slow the coaster down, or stretched out to a gentler or banked curve, so the car doesn't fly off the track.

Space is a problem. Coasters go forward two feet for every foot they climb. If the highest hill is 100 feet, it takes about 200 horizontal feet to get the car that high. If the highest hill is 200 feet, it takes 400 feet. Since land is expensive, the designers have to be creative about the use of space. A track shaped into a curve takes up less space than one left in a straight line.