Why is a clothiod lope used in roller coasters designs?

Answer 1

Circular loops require greater entry speeds to complete the loop and the greater entry speeds subject passengers to greater centripetal acceleration through the lower half of the loop (greater g-forces). If the radius is reduced at the top of the loop, the centripetal acceleration is increased sufficiently to keep the passengers and the train from slowing too much as they move through the loop. A large radius is kept through the bottom half of the loop, thereby reducing the centripetal acceleration and the g-forces acting on the passengers. Hence, a clothiod Loop. The "Flip-Flap" Railway in 1888 is an example of why circular loops are no longer used in roller coaster designs. The "Flip-Flap" railway subjected passengers to 12G's, 6G's over the maximum g-force modern Roller Coasters subject their passengers. The high g-forces sustained in a circular loop often resulted in injuries to the neck and back.