Coaster Physics
(c) 1997 Brian George

Here you go fellow brains. This is all words, and lots of 'em too, no pictures. So enjoy!

To start off, the most important factor in roller coaster physics, is gravity. Like they say, "what goes up, must come down". Gravity, for those who don’t know (who doesn’t), is the attraction that pulls a smaller body downward to a larger body, with the larger body on earth being the earth itself. Applying gravity to roller coasters, no hills on the ride can be taller than the lift hill, the initial hill.
As the train descends from the top of the lift hill, it begins to accelerate, or in other words, it picks up speed. The speed of the roller coaster depends on the height of the lift hill, the angle of the first drop and the distance traveled on the first drop. The longer the train has to descend on the first drop, the more time gravity has an effect on the acceleration. Acceleration due to gravity is a constant number, 9.8 meters per second squared (9.8m/s2)
Another essential in roller coaster physics is energy, and the two types of energy are potential energy (PE) and kinetic energy (KE). PE relies on the height of the roller coaster. The higher the lift hill, the more PE it will have (the more PE is stored), therefore the ride will be faster. To determine the PE, there is a very simple equation, and that is: mgh. In English, that’s telling you to take the mass of the train plus its riders (m), multiply that by the acceleration due to gravity (g), and then multiply that by the height of the lift hill (h). Note: To find the mass of the train plus its riders, just estimate the weight the riders add, but it would be safe to ask about the train. As the train descends down the drop, the force of gravity converts the PE into KE. The equation to find the KE is: ½mv2 (2 means squared) Which means take one half of the train’s mass plus the rider’s mass (m), and multiply it to the velocity (v) squared. The transfer of PE and KE continues all throughout the ride as the train ascends and descends the many hills.
There are also forces that interact when riding roller coasters. Two of the main forces the riders will experience are G-forces and inertia. Inertia is simply the force that keeps the rider going, therefore, inertia is constant regardless of the speed or direction of the coaster. However, G-forces aren’t as simple to explain. Naturally, when sitting, you experience 1 G, and that is derived by taking your body weight and multiplying it by 1. 1 G is what everybody feels on earth. In roller coasters, the only time you feel 1 G is in the loading station and on the chain lift. Everywhere else, the rider’s body weight will be varying. In the dips, or troughs of the track, the rider’s body forces itself into the seat, which is experiencing a positive G-force. In other words, the rider’s body weight will appear to increase. It is inertia that presses the rider into the track. For example, if a rider weighs 100 pounds, and he/she experiences 4 G’s in a particular dip, he/she will apparently weigh 400 pounds (100 X 4). The exact opposite occurs at the crests of the roller coaster. This is where the rider will experience a negative G-force, resulting in the apparent decrease of body weight. At times, the rider will near weightlessness. Once again, inertia is the culprit. Inertia pushes the rider out of the cars, thus decreasing body weight. For example, a 100 pound rider experiencing 2 G’s at the crest of a hill, will weigh apparently 50 pounds (100/2).
A third force dealt with in coasters is centrifugal force. Centrifugal force pushes objects in a circular motion outward. Centrifugal, or "center fleeing", is experienced in a vertical loop and also in turnarounds. An easy way to grasp this concept is when the train turns left, the riders get forced to the right.
To understand the possibilities and dangers of G-forces a little bit better, it is worthy to note that Air Force pilots can only endure 11 G’s before they blackout. Prior to 1976, roller coaster designers were struggling to create a successful looping design. In the early 1900’s, the first attempted loops resulted in G-forces nearing 12. Many riders would return to the station with sore, or snapped necks. In 1976, many designers realized that a clothoid loop would result in a much more comfortable ride. A clothoid loop looks like an upside-down teardrop. By using this type of loop, with radii of varying lengths, the centrifugal force is reduced. Whereas in a loop of one separate radii, similar to those of the early 1900’s, the train would require too much speed to complete it, therefore heavily increasing the G-force.
Finally, when the coaster comes to a complete stop, PE and KE is equal to zero, and the G-force is back to normal, 1.
And believe it or not, I got a D in Physics this semester! Wassup with that?!

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