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A roller coaster is an elevated railway (as in an amusement park) constructed with sharp curves and steep inclines on which cars roll (Merriam-Webster). Some of the goals of the designers are: using physics to increase the thrill of the ride, e.g., by increasing ‘airtime’ to safe levels, making the ride more comfortable by reducing lateral force acting on the rider and minimizing energy loss by friction for efficient rides. A roller coaster is a perfect example of physics at work as each track and train is as a result of careful analysis, calculation, evaluation and cross-examining. This essay explains how roller coaster structures integrate the laws of physics in the manufacture, and it unravels how the train moves since it has no engine.

## Laws of Physics in Relation to Their Design

Currently, there are mainly two types of roller coasters: wooden roller coasters and steel roller coasters. In the design of a roller coaster, the height of the first incline must be calculated to give the cars enough energy to propel them all the way through the ride and back to the station. The acceleration in the drop must not be too high, as it may cause whiplash.

In wooden roller coasters, resistance from wind and friction is put into consideration, as this may cause valleying. The lateral and vertical forces that the loaded cars exert on the track must be calculated at every point to ensure that the support structure is adequate (‘How Products Are Made’).

“The load wheels employ a cast aluminum hub with a thin tire made from polyurethane” (Bradley and Parent, 2003). Engineers must combine these requirements for the load wheel: low rolling resistance, high load endurance, smooth ride and low maintenance cost (Coaster101, 2011).

## Laws of Physics in Relation to Their Action

### The Start and First Drop

When the ride starts, an electric winch winds the train to the top of the first hill. This takes about 50 seconds. In some other rides, the train is launched from the start by a hydraulic system. It works by using a cable that is attached to a catch-car which connects to the bottom of the train and a winch that winds the cable when it is turned by a motor. In the hydraulic accumulator, the hydraulic fluid and nitrogen gas are separated by a piston. Since it’s incompressible, the hydraulic fluid is pumped into the accumulator compressing the nitrogen gas. When the pressure is high enough, a valve is opened and the hydraulic fluid rushes out, powers some motors which turn the winch, hence pulling the cable and accelerating the train at speeds of above 150km/h (Green, Aranda and Gordon, 2016). In the electric winch train, an anti-rollback device prevents the train from moving backwards in case the chain pulling it breaks. The train consequently builds up potential energy. At the peak of the hill, the potential energy is at its maximum and kinetic energy at its minimum. It then moves downwards in free fall, and this is called ‘airtime’. The downward movement is due to gravity applying a constant force on the train. “The coaster track serves to channel this force – they control the way the coaster car falls” (Harris and Threewitt, 2019). Newton’s first law of motion, which states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force, takes place here. In the next hills, the energy would constantly change from kinetic to potential. During this period of free fall, the riders experience a feeling of weightlessness since the force of gravity acting on their bodies is less than 9.81N/kg. This is negative G-force and it contributes to airtime as inertia force tends to keep the riders at the crest of the hill, hence, they momentarily, slightly rise from their seats at this point. At the bottom of the first hill, the kinetic energy is maximum and the potential energy minimum. Riders experience positive G-force (a force greater than 9.81N/kg) hence pushed to their seats.

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### The Second Drop or Loops

The coaster then rises another hill obeying Newton’s first law of motion. The second hill is usually lower compared to the first since the train’s acceleration is lower. Riders here have a second ‘airtime’ experience. Some roller coasters may have a second hill while others have loops shaped like a tear-drop. “They do not use circular loops any more since they require greater entry speeds to complete it. This subjects passengers to greater centripetal acceleration through the lower half, therefore greater G’s” (Ffden-2.phys.uaf.edu, n.d.). This could cause injuries or breaking of the neck.

The clothoid loop is much safer and subjects the train and riders to less stress as the distance is shorter at the top, hence a smaller radius and an increased centripetal acceleration to keep the riders and the train in the loop at a safer velocity. The increased radius at the bottom reduces the centripetal acceleration acting on the riders.

For the designers, their nightmare is keeping the G-force at safe levels and at the same time giving a rider the thrill he or she wants. The designers have to calculate the force felt by the rider, which should be below 5 times the normal gravitational pull. The normal centripetal acceleration formula would be used. Two forces are exerted on the rider as he or she enters the loop, i.e., weight and reaction force. Therefore, as he enters the loop, the reaction force must overcome the pull of gravity and provide centripetal force. At the top of the loop, the gravitational force does not need to be overcome since it contributes to the centripetal force.

Formula Rossa in Abu Dhabi, UAE, travels at a speed of above 230km/h. These speeds would not allow it to negotiate corners easily, as the lateral force acting on the train would cause it to derail or make the ride uncomfortable. To fix this, the track is inclined inwards so that the some of the lateral force would be converted to positive or negative G (Palmer, n.d.). The train would then negotiate all curves easily without having to reduce its velocity. “The equation used to produce a perfectly banked curve is Tan(theta)=v^2/rg, where theta is the angle where no outside forces other than gravity are required to keep the car from sliding to the inside or outside of the curve” (Coaster101, 2010).

### The Final Part of the Ride

After all the twists, lifts and turns, the ride finally has to come to an end. After completing all the hills and turns, automatic brakes are applied. Originally, brakes that rely on friction were used. They would convert the kinetic energy to heat energy, hence stopping the train. The disadvantage was that they wore out easily. Today, metal fins on the train are passed through a magnetic field created by rows of permanent magnets (Green, Aranda and Gordon, 2016). Lenz’s law states that an induced electric current flows in a direction such that the current opposes the change that induced it (Encyclopedia Britannica, 1998). Therefore, passing the metal fins through the magnet would induce an eddy current that opposes the change, hence, the train will slow down because the kinetic energy is converted to heat by the eddy current (Green, Aranda and Gordon, 2016).

## Conclusion

As I conclude, I believe that the amount of physics used in the making of the roller coaster is still shallow and that more of it is untapped. The engineers should find a different material for making the load wheels other than polyurethane which lasts longer before wear. The eddy current used for stopping the train is brilliant and safer methods should be used to launch the track. Future research on the topic is encouraged so as to find solutions to some common roller coaster issues.

### References

1. Bradley, A. and Parent, K. (2003). Wheel Assembly for a Roller Coaster. US 6,598,919 B2.
2. Coaster101. (2010). Coasters101: Curves and Banking – Coaster101. [online] Available at: https://www.coaster101.com/2010/12/20/coasters101-curves-and-banking/ [Accessed 2 Feb. 2019].
3. Coaster101. (2011). Coasters-101: Wheel Design – Coaster101. [online] Available at: https://www.coaster101.com/2011/10/24/coasters-101-wheel-design/ [Accessed 3 Feb. 2019].
4. Encyclopedia Britannica. (1998). Lenz’s Law| Physics. [online] Available at: https://www.britannica.com/science/Lenzs-law [Accessed 2 Feb. 2019].
5. Ffden-2.phys.uaf.edu. (n.d.). Clothoid Loop. [online] Available at: http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/shawna_sastamoinen/clothoid_loop.htm [Accessed 2 Feb. 2019].
6. Green, H., Aranda, M. and Gordon, O. (2016). The Physics of Roller Coasters. Available at: https://www.youtube.com/watch?v=J8pJiV44hVM [Accessed 2 Feb. 2019].
7. Harris, T. and Threewitt, C. (2019). How Roller Coasters Work. [online] HowStuffWorks. Available at: https://science.howstuffworks.com/engineering/structural/roller-coaster3.htm [Accessed 2 Feb. 2019].
8. Madehow.com. (n.d.). How Roller Coaster Is Made – Material, History, Used, Parts, Components, Structure, Product, History, Raw Materials. [online] Available at: http://www.madehow.com/Volume-6/Roller-Coaster.html [Accessed 3 Feb. 2019].
9. Palmer, R. (n.d.). Roller Coaster Science: Thrills, Chills, and Physics| World Science Festival. [online] World Science Festival. Available at: https://www.worldsciencefestival.com/2015/06/roller-coaster-science-thrills-chills-physics/ [Accessed 2 Feb. 2019].
10. Physicsclassroom.com. (2015). Newton’s First Law. [online] Available at: http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law [Accessed 14 Apr. 2015].
11. Väisänen, A. (2018). Design of Roller Coasters. Postgraduate. Aalto University School of Engineering.
12. Wayne, T. (n.d.). Roller Coaster Design. [online] Mrwaynesclass.com. Available at: http://www.mrwaynesclass.com/ap/coaster/web/index04.html [Accessed 3 Feb. 2019].

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