A rollercoaster has no engine or power source of its own, for most of the ride, the car is moved by gravity and momentum. A catapult launch can be used to set the coaster car in motion or chains and a motor to drag it up a hill. The car is gradually stopped by friction, using clamps at the end of the tracks. Once the coaster rolls over the first hill, gravity takes over and all the built-up potential energy transforms into kinetic energy. As the train goes along the track, it loses energy to friction and air resistance. Gravity applies a constant downward force on the rollercoaster cars.
As Newton’s first law of motion states that an object in motion tends to stay in motion, the coaster car will maintain a forward velocity even when it is moving up the track, opposite the force of gravity. When the rollercoaster ascends one of the smaller hills that follows the initial lift hill, its kinetic energy changes back to potential energy. In this way, the course of the track is constantly converting energy from kinetic to potential and back again.
This fluctuation in acceleration is what makes rollercoasters so much fun. In most rollercoasters, the hills decrease in height as you move along the track. This is necessary because the total energy reservoir built up in the lift hill is gradually lost to friction between the train and the track, as well as between the train and the air. At its most basic level, this is all a rollercoaster is; a machine that uses gravity and inertia to send a train along a winding track.
G forces are important concepts when it comes to understanding coaster physics. Gravity isn't a G force, but G forces are measured in terms of what you feel when you are sitting still in the earth's gravitational field. When in this state, you are in a 1-G environment.
On Earth, at 1-G, gravity pulls one down towards the ground. But the force noticed isn't actually this downward pull; it's the upward pressure of the ground underneath. The ground stops your descent to the centre of the planet. It pushes up on your feet, which push up on the bones in your legs, which push up on your rib cage and so on. This is the feeling of weight. At every point on a rollercoaster ride, gravity is pulling you straight down to the Earth’s centre. However, this is also happening when you are falling, and experiencing less than 1 G. Therefore the rollercoaster seat also accounts for G force which pushes back up on you. If there wasn't such a force, you'd fall through the seat. When sitting still, the seat must exert the same amount of force as the earth, directed oppositely, to keep you sitting still.
The other force acting on you is acceleration. When riding in a coaster car that is travelling at a constant speed, the downward force of gravity is felt. When a coaster car is speeding up, the actual force acting on you is the seat pushing your body forward. But, because of your body's inertia that is separate from that of the coaster car, you feel a force in front of you, pushing you into the seat. You always feel the push of acceleration coming from the opposite direction of the actual force accelerating you. This force feels exactly the same as the force of gravity that pulls you toward the Earth. These G-forces are a measure of acceleration forces, where 1 G is equal to the force of acceleration due to gravity near the Earth's surface (9.8 m/s2, or 32 ft/s2).
A rollercoaster constantly changes its acceleration and its position to the ground, making the forces of gravity and acceleration interact in many interesting ways on your body.
At the top of a hill inertia may carry you up, while the coaster car has already started to follow the track down, you would briefly undergo free fall. Galileo was the first to recognise the connection of falling bodies; if a body starts from complete rest, it falls straight down, accelerating as it falls, however if it starts with some horizontal motion, the path it takes will be a parabola which points downwards. When plummeting down a steep hill, gravity pulls you down while the acceleration force seems to be pulling you up. At a certain rate of acceleration, these opposite forces balance each other out, making you feel a sensation of weightlessness lifting up out of the seat for an instant. In free fall the seat isn't supporting you at all and exerts no force on you, therefore you would be experiencing 0 Gs. If this situation is prolonged, you will eventually hit the safety bar, which will then exert a downward force, to keep you in the seat. Since G forces are measured positively when the train exerts an upward force on you, they are measured negatively when the force is downward.
‘Free-fall’ has a strange effect on your body because it is composed of many loosely connected parts. When your body is accelerated, each part of your body is accelerated individually. Normally, all the parts of your body are pushing on each other because of the constant force of gravity. But in the ‘free-fall’ state there is hardly any net force acting on you. This is what gives that unique sinking feeling in your stomach. The same thing happens when descending in an elevator at high speed as mentioned earlier as an example of Newton’s first law of motion.
Most of the time, a rollercoaster represents constrained fall, Galileo's inclined planes represents this; it provides partial support for an object falling down it, preventing it from falling as fast as it ordinarily would. The basic rule of falling down an inclined plane is that the falling body will accelerate faster the steeper the plane is. This principle applies to rollercoasters, even though the track on drops is usually not straight, like an inclined plane. The steeper a drop, the faster the train accelerates down it. When going down this incline, the seat only partially supports you as it doesn't completely balance the force of gravity and you experience between 0 and 1 G.
When accelerating up a steep hill, the acceleration force and gravity are pulling in roughly the same direction, making you feel much heavier than normal. If you were to sit on scales during a rollercoaster ride, you would see your ‘weight’ change from point to point on the track; this would also be dependent on the fractional Gs experienced, as G forces can also be thought of in terms of weight. The scales would register your ordinary weight when you were sitting still, in 1 G. If you were in free fall, under 0 Gs, it would not register you as having any weight at all.
G forces greater than 1 can also be experienced at the bottom of drops. Here the seat not only prevents you from falling, it must also begin to divert your path upwards again, so it must exert a force greater than it would if you were sitting still. Thus, you experience greater than 1 G. In this case, you feel yourself being pushed down into the seat. What's really happening, though, is that the seat is pushing up on you.
On a rollercoaster, this full-body sensation is complemented by all sorts of visual cues such as the upside-down turns, dizzying heights and passing structures. Your body can't feel velocity at all; it can only feel change in velocity (acceleration).
Demonstrating Newton’s principle of inertia, a rollercoaster is affected by the force of gravity and supporting force of the track along its run. But if it’s travelling in a straight line, none of the forces will be directed towards either side and the riders will not experience any forces to either side either.
However if the train hits a curve, it will tend to want to go forward. The track has to exert a sideways force on the train to divert it from its path. The train, in turn, exerts a force on you. As you continue to try to go straight, you get pinned to the side of the car. Though you feel yourself being forced toward the outside of the curve; this effect is the centrifugal force. The force that is exerted on you is actually towards the inside; the centripetal force, because that is the direction in which you are turning.
As with forces directed vertically, lateral forces can be measured in terms of Gs. A 1-G lateral force would be equivalent to you lying on your side.
Several factors affect the strength of lateral G forces: the speed of the train and the tightness of the curve. The faster the train goes through the curve, the greater the force required to keep it on the track. Similarly, the tighter the curve, the more force is exerted on the train.
As you go around a loop, your inertia not only produces an exciting acceleration force, but it also keeps you in the seat when you are upside down. Centripetal forces cause motion along a curve or through a circle. This force pushes you in an inward direction. The varying forces in the loop put your body through the whole range of sensations in a matter of seconds. While these forces are shaking up all the parts of your body, your eyes see the entire world flip upside down.
When approaching the loop, your inertial velocity is straight ahead of you. As the train enters the loop, it has maximum kinetic energy and is moving at top speed. At the top of the loop, gravity has slowed the train down somewhat, so it has more potential energy and less kinetic energy and is moving at reduced speed. In the loop the intensity of the acceleration force is determined by the speed of the train and the angle of the turn. At the top of the loop, when you're completely upside down, gravity is pulling you out of your seat, toward the ground, but the stronger acceleration force is pushing you into your seat, toward the sky. Since the two forces pushing you in opposite directions are nearly equal, your body feels very light. Your own outward inertia creates a sort of false gravity that stays fixed at the bottom of the car even when you're upside down. You need a safety harness for security, but in top of the loop, you would stay in the car whether you had a harness or not. At the bottom of the loop you become heavy again as you are pushed inwards by centripetal forces resulting from the car seat.
Rollercoasters are quite safe from a physics standpoint, as the forces always conspire to keep the rider in the car. The designers calculate the forces on the coaster to make it feel dangerous, but really be quite safe. However, these calculations are done assuming the rider does nothing unusual. If one stood up in a sit-down coaster, the calculations would no longer apply; therefore negative Gs could be enough to eject you. On a curve, your centre of gravity may end up above the side of the car, resulting in the serious danger of being thrown out.
Rollercoasters are driven almost entirely by basic inertial, gravitational and centripetal forces, all manipulated in the service of a great ride. Amusement parks keep upping the ante, building faster and more complex rollercoasters, but the fundamental principles of physics revealed by Newton and Galileo at work still remain the same.
References
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David A Sandborg (1996) Physics of Rollercoasters. Canada. [Online] Available from: <> [Assessed 12th April 2010].
Harris, Tom. (August 2007) How Roller Coasters Work. HowStuffWorks.com. [Online] Available from: <> [Assessed 12th April 2010].
HowStuffWorks.com. (2003) Loop-the-Loops. [Online Illustration] Available from: <> [Assessed 12th April 2010].
The Encyclopaedia of Electrical Knowledge (2010) Technology - Rollercoasters. [Online] Available from: <http://www.electricalfacts.com/Neca/Technology/rollercoaster/lawsforces.shtml> [Assessed 10th April 2010].
The Physics Classroom (1996-2010) Newton's Laws. [Online] Available from: <> [Assessed 10th April 2010].
