Although roller coasters have changed quite a bit since the ride first became popular, the basic design principles remain the same. Whether the ride consists of an old wooden track with a few hills and turns, or a modern steel track with a variety of corkscrews and loops, all roller coasters rely on the conservation of energy.
The law of conservation of energy states that within a closed system, energy can change form, but it cannot be created or destroyed. In other words, the total amount of energy remains constant. On a roller coaster, energy changes from potential to kinetic energy and back again many times over the course of a ride.
Kinetic energy is energy that an object has as a result of its motion. All moving objects possess kinetic energy, which is determined by the mass and speed of the object. Potential energy is the energy an object has as a result of its position. Potential energy is stored energy that has not yet been released. Gravitational potential energy is potential energy that results from an object's position in a gravitational field, and is equal to the object's weight multiplied by its height. For example, a book placed on a shelf possesses gravitational potential energy because of Earth's gravity. If the book were moved to a higher shelf, it would gain potential energy.
For most roller coasters, the gravitational potential energy of the cars at the peak of the first hill determines the total amount of energy that is available for the rest of the ride. Traditionally, the coaster cars are pulled up the first hill by a chain; as the cars climb, they gain potential energy. At the top of the hill, the cars have a great deal of gravitational potential energy, equal to the cars' weight multiplied by the height of the hill. When the cars are released from the chain and begin coasting down the hill, potential energy transforms into kinetic energy until they reach the bottom of the hill. As the cars ascend the next hill, some kinetic energy is transformed back into potential energy. Then, when the cars descend this hill, potential energy is again changed to kinetic energy. This conversion between potential and kinetic energy continues throughout the ride.
In reality, the conversion between potential and kinetic energy (both are forms of mechanical energy) is not perfect. The force of friction acts on the moving cars, decreasing the total amount of mechanical energy in the system. The mechanical energy is not lost, however. It is transformed into thermal energy, which can be detected as an increase in the temperature of the roller coaster's track and car wheels. Because of friction between the coaster cars and the track (not to mention air resistance as the cars move forward at great speed), the amount of mechanical energy available decreases throughout the ride, and that is why the first hill of a roller coaster must always be the tallest.