The Energy Cost of a Roller Coaster Ride

Access to Mountain Bike Park can be very expensive - the admission fee for the day is $ 100. [1] And then an interesting question is how much does it cost to get on the roller coaster? Or, more specifically, how much is the energy cost per ride? Does this account for the majority of the ticket price?

With some simple calculations, you can get an overview of energy costs. Let's take an example of a roller coaster, Goliath, from Hexagon America (Gurnee, IL). Goliath has a mountain of chain elevators that can reach the height of roller coasters and passengers up to 180 feet (55 meters). The position energy of the mountain can be obtained by the formula.

Where m is the mass, g is the gravitational acceleration (9.8 m / s 2), and h is 55 m. Since we are interested in the potential energy of each passenger we set it to be the weight of a typical person plus the weight of a roller coaster train divided by the number of passengers to 70 kg. As an estimate of the weight of each train we use twice the weight (140 kg) of that person. In the calculation of potential energy, it becomes as follows.

Since the roller coaster train stops at the end of the journey due to friction and drag (orbit, brake, air etc.), all of this energy is exhausted, in other words, this is the total per capita energy cost per capita . If we assume it is much smaller than the energy required by a chain crane, we ignore the energy required to run operator controls, brakes and other safety mechanisms

0.4 cents per person per way. However, for friction and other reasons, you can see that the elevator system is not 100% effective. You can recalculate with different efficiency. In other words, the efficiency is 5%. This will result in $ 3.8 x 10 -3 / 0.05 = 0.075 dollars, or 5 cents per run. (For some calculations, more than the number shown is used.)

Even with an efficiency of 5%, 5 cents per Goliath is negligible compared to the $ 100 ticket. This suggests that energy costs may not be a driving force for price; perhaps maintenance and inspection, initial design and construction, land cost or other factors really drive the cost of the roller coaster park one day I will.

© Jonathan Timcheck. The author guarantees that the work is the author's own work. In addition, Stanford University does not provide information other than typesetting and reference guides. The author permits the reproduction, distribution and display of this work in an unmodified form. This is because it is used only for non-commercial purposes. All other rights including commercial rights belong to the author.

[1] H. Martin, "Ticket prices for Universal Studios, Disneyland, and other theme parks are on the rise", Los Angeles Times, March 6, 2017

[2] D. Moran, "Six Flags Great America's Goliath wins three Guinness World Records" Chicago Tribune, May 3

Riding a roller coaster is an exciting experience with rich physical features. Part of the roller coaster physics is work and energy physics. Cycling usually begins with the chain and motor (or other mechanical device) lifting up the train to the top of the mountain with force on the train of the car. When the car is lifted to the top of the mountain, gravity begins again and the rest of the vehicle is an experience of energy conversion. At the top of the mountain, the car has plenty of potential energy. Potential Energy - Vertical Position Energy - It depends on the mass of the object and the height of the object. The great potential energy of a car is due to the fact that they rise from the ground. When a car falls into the first drop, they lose most of their potential energy that is consistent with their height loss. Then the car gains kinetic energy

Access to Mountain Bike Park can be very expensive - the admission fee for the day is $ 100. An interesting question is how much does it cost to get on a roller coaster? Or, more specifically, how much is the energy cost per ride? Does this account for the majority of the ticket price? With some simple calculations, you can get an overview of energy costs. Let's take an example of a roller coaster, Goliath, from Hexagon America (Gurnee, IL). Goliath has a roller coaster and mountain chain lift that can reach the height of the passengers. The position energy of the mountain can be obtained by the formula.