Here's how the inventor describes his challenge:
...vertical curves on pleasure railway structures have been limited on account of centrifugal force, the curves being` confined within limits which will permit gravity to overcome centrifugal force sufficiently to keep the cars on the rails and the passengers in their seats. More abrupt vertical curves will be more sensational as it will give the passengers the feeling of being lifted off their seats as the cars take the incline.
It seems like the only way to provide for user safety is to reduce the acceleration on the curve and the thrill, which would be a typical trade-off. As with many other breakthrough inventions, Miller found a solution that allowed a roller-coaster designer to escape the trade-off: the car would stay on a sharp vertical curve, held on the rails with three pairs of wheels: two vertical and one horizontal.
Before the Miller's solution, the force of gravity was not strong enough to hold the car in place when it accelerated along sharp curves, either vertical or horizontal. After the new side and bottom rollers were introduced, the car would stay on rails, compensating for centrifugal acceleration. Today, many roller-coasters use the 90 year-old solution to give the riders as much fun as they can bear.
tags: invention, trade-off, solution, problem