Loops -The first looping coasters were circular tracks and they were very dangerous.

For the sake of simplicity, let's assume that the car's speed remains the same as it travels around the loop. At the top of all loops, it is desirable to have 1G of force to hold people into their seats. Thus, 2G's are required to have 1 G in a weightless environment. Here is why:

(2G of rotation - 1G of gravity = 1G of centrifugal force)

 

At the bottom of the loop you'd experience 3G's

(2G of rotation + 1G of gravity = 3G of centrifugal force)

In reality, trains are faster at the bottom of loops and slower at the top. Designers of loops realized that the speed at the top was slowed due to friction, air resistance, etc... Therefore these designers increased the height of the drop and made the train go even faster. This was okay at the top, but at the bottom of the loop, riders would sometimes experience up to 10G's. Many complained of whiplash injuries or broken necks. A broken neck could ruin your day.

It wasn't until the 1970's when Anton Schwarzkopf, working with Werner Stengel, that the Clothoid loop (pronounced 'clockoid') was fully developed. What they did is decrease the radius of the loop at the top, where the train would be going slow, and then increase it's radius as the track came down the other side. In this way the curve at the bottom isn't sharp enough to hurt people. Yet at the top, the radius is tight enough to keep riders pressed into their seats at all times. The first successful vertical loop opened at Six Flags Magic Mountain in 1976 on a coaster appropriately named Revolution. Now, one year before, in 1975, Arrow opened the Corkscrew at Knott's Berry Farm, but this element was a helix placed on it's side, called a Corkscrew, and inverted riders twice.

 

Centripetal Force = The push or pull on a moving object toward the center of its curved path.