*Clothoid Loop*

Roller coasters today employ clothoid loops rather than the circular loops of earlier roller coasters.  This is because circular loops require greater entry speeds to complete the loop.  The greater entry speeds subject passengers to greater centripetal acceleration through the lower half of the loop, therefore greater G’s.  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’s acting on the passengers.