Coasters-101: Vertical Loops
There is something quite remarkable about being able to defy gravity and part of the charm of roller coasters is that they let you do exactly that. The vertical loop is one of the most common yet thrilling elements found in steel roller coasters. Very few feelings can match the excitement of dangling upside down at a great height without falling out!
Early roller coaster loops, including the first one, a 13-footer built in 1846 in Paris, were simple circles. The circular shape of the loops lead to a huge difference in g-forces at the bottom of the loop compared to the top. To make it all the way around without being pulled off at the top by gravity, coaster cars hit the circle hard and fast, shoving rider’s heads into their chests as they changed direction with a sudden snap that occasionally broke bones.
Vertical loops were finally made safe and comfortable in 1975 by Werner Stengel (of Stengel Engineering). He ditched the perfect circle and designed a loop with a radius of curvature that decreases as the vehicles are turned upside down. Stengel realized coaster trains are faster at the bottom of loops and slower at the top, just like when they traverse an airtime hill. The shape of a loop determines how much force is felt by the passengers at different locations along the loop. Centrifugal force is the force that points out from the center, while centripetal force is the force that keeps the object in its circular path (gravity for an orbiting satellite, for example). Centripetal force is the same force that prevents water from falling out of a bucket that is swung upside-down on a string.
Werner Stengel created a safe and smooth vertical loop by gradually decreasing the radius of the track using an Euler spiral or clothoid (or klothoide and pronounced ‘clockoid’) configuration. Clothoids are frequently used in railways, road building, and highway exits. While the upper part of the vertical loop is a half circle, the lower part has a completely different shape, that of a “Cornu spiral”, where the radius of curvature increases as you get closer to the ground. The clothoid shape leads to a slower onset of lower forces on the body by keeping the g forces at the top of the loop close to those of the bottom, leading to a much safer and enjoyable ride for passengers (and no broken bones)!
The first roller coaster with a modern (clothioid) loop was Revolution at Six Flags Magic Mountain in 1976.
To learn more about how coasters are designed check out Coasters 101: An Engineer’s Guide to Roller Coaster Design.