LOOPS & SCREWS
The designer of a looping roller coaster must ensure that the running wheels of the cars remain firmly in contact with the track at the top of the loop so:
Loops and Screws
In designing early metal coasters, engineers had to learn as they went along. The first 360-degree loop-the-loops, for example, were designed as perfect circles, which turned out to be aesthetically pleasing but physically bad. The relatively gentle curve made the coaster lose speed at the top of its climb, lowering the centripetal force and causing upside-down riders to drop out of their seats. While this feature helped reduce annoying lines at ticket booths, it proved unpopular with fussy park patrons. Eventually loop-the-loops were designed into a sort of teardrop shape called a clothoid loop which sharpens the upper portion of the curve, keeping both speed and centripetal force high.
Other such design refinements involve the corkscrew, which is typically built to resemble a sort of stretched spring lying on its side, with the cars riding around and around on the spring's interior. When the design was first tried, engineers discovered that the large number of turns and the track friction led to a loss of momentum and slow-moving coaster. The answer was to lift one end of the corkscrew a bit, so that while the train spirals, it also heads slightly downhill.
Basic Physics
When our coaster car is rounding the loop it is really trying to move in a straight line but is being forced to continue to move in a circular path by the rigid track. This creates the desired force in the form of pressure between the track and the wheels of the coaster car.
In a practical coaster the designer will ensure that the coaster cars running wheels remain firmly pushing towards the track and that the riders are firmly seated so it is reasonable to increase the centripetal acceleration at the loop top to 2G. The riders then experience a 1G force equivalent to normal body weight and have a more comfortable ride.
At the bottom of the loop, the riders are therefore subjected to an acceleration greater than the normal 1G and will feel heavier than normal. In fact, due to the dynamics of 'looping the loop' the entry speed of the cars into the loop must be significantly higher than at the top resulting in an acceleration of several g's and therefore a proportionaly high 'G force'.
Although there are amusement devices which create high accelerations for very brief periods, high positive centripetal forces of 7G or greater would be unpleasant for many people. High positive G's may cause a blackout if sustained for more than a few seconds due to blood draining from the head towards the lower body and a consequent loss of oxygen from the brain.
A common method of lowering the maximum G forces is to change the loop profile from circular to teardrop. This shape has a much larger radius at the bottom than at the top. The top section is usually a circular arc while the bottom section will be an arc of larger radius or, more commonly, a 'clothoid' arc which has a smoothly changing radius.
Banked Turns
Assuming high g's don't reduce you to a flapjack with shoes, and low g's don't launch you into an adjacent zip code, you still have to concern yourself with horizontal motion that phenomenon you experience on a bus when a sharp turn crushes you against the muttering man in the aluminum-foil hat sitting just to your left. The two biggest things that determine horizontal motion are speed and radius of turn. When the train comes out of the station, you're going less than 10 miles per hour, so your turn can have a radius as little as 30 feet. At 60 miles per hour, that radius has to grow to about 115 feet to keep horizontal motion down. Even the widest turn, however, can still get you a little cozy with your seat mate. To eliminate this remaining bumping and not incidentally to help keep the car on the track, the turns are banked.
On very low speed turns, tracks are banked perhaps three or four degrees. On high-speed turns with the widest radii, the bank is up to 65 degrees. The whole purpose of this is to make the force of the turn move down through the rider and into the seat. Bank any further than 65 degrees, of course, and you run the risk of having something else pass through the rider and wind up on the seat.