The basics of how roller coasters work is by taking the coaster up to the top of a very tall hill and let it roll down. By taking the coaster to the top of a hill, it increases the coasters potential energy. This allows the coaster to gain velocity and increase acceleration as it rolls down the hill from all the potential energy converting to kinetic energy. This gives the thrill of the high speeds that that every one loves. If the potential energy is great enough, then designers can include many different features to the ride such as loops and corkscrews, not just smaller hills.

             Potential energy is calculated by multiplying the mass of an object by the acceleration of gravity and the height from the zero line, usually the earths surface.  There is also elastic potential energy that considers the energy formed from compressing or stretching things like a spring or rubber bands. This is calculated by multiplying the spring constant of the material by the squared deformation distance of the material from the original position, then halving it.

             Kinetic energy is calculated by halving the mass and squared velocity of the object.

            Finding all components at certain points on the track like the velocity needed to make a loop, the speed that allows the coaster to make a banked turn without causing to high g-forces from centripetal forces, and other losses of energy through the the track like friction are very necessary. This allows engineers to find the total energy needed to allow the coaster to complete the track. By using the conservation of energy equation which states that the initial and final energy must be equal, they can work backwards from the end of the track to the beginning. Since they have an idea of how the coaster should act through out the ride, they can determine the best layout of the track. This also is important in the thrill area where they make it so that in loops or tops of hills, one can get the coaster to have a velocity so that it continues forward but the normal forces between you and the cart are zero, giving the feeling of weightlessness. Anyone who has ridden a roller coaster lives to feel the sensation.

            Aside from dropping a cart from the top of a hill to gain potential energy, some coaster designs use spring and slingshot combination to launch a coaster at high speeds. This is usually used on short coasters that aim for the high-speed factor to thrill the riders, or for those that are in small confined areas where a large hill would not work. This works by using the potential energy of elasticity to increase the energy of the cart where a spring is either pulled or compressed to launch an object.