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Trigonometry Uses in Roller Coasters

Making a roller coaster exciting means including as many long, steep drops as possible. But making a roller coaster safe involves understanding the speeds, forces and loads that it will generate as the cars whiz round the track. Trigonometry is a key tool for calculating these factors and making the roller coaster as safe and thrilling as possible.

Calculating Required Energy
- Roller coasters are generally driven by the energy acquired by winching the roller coaster to the top of a slope and releasing it. Trigonometry functions allow designers to work out the angle and the of length of the slopes that the height and position of the peaks will generate. This in turn allows them to calculate the force the cars will acquire from a drop and calculate whether this will be too much or too little to drive the cars around the circuit at the required speed.
Optimising Thrill
- The thrill of a roller coaster is a function of the length and steepness of its drops. However, roller coasters are required to conform to certain limits on factors such as height, G-forces generated and steepness of turns. By using vertical and horizontal lengths to determine the diagonal length, trigonometry allows designers to see how steep and long its descents will be from a given height and over a given distance. This allows them to alter the height and length of a descent exactly to produce the maximum permissible thrill.
Constructing Supports
- You may have noticed that the lattice of supports under traditional roller coasters comprises triangles. This is because triangles are extremely strong shapes that cannot be reshaped without changing the length of the sides. This means the material, rather than the joints, takes the strain when loads are placed on it. Designers must then use trigonometry to calculate the volume of materials required to support a given track design.
Calculating Vibration
- Trigonometry can be used to calculate the angles and lengths of triangles in actual, physical shapes, but it is also essential for mathematically analyzing waves. When a wave is drawn on a graph it is shown as a wiggly line of regular-size peaks and troughs. Trigonometry can be used to look at the distance between these peaks and troughs and make calculations with regard to frequency, amplitude and wavelength. Understanding the vibration caused by roller coasters using this form of analysis is essential to constructing safe rides. Excessive vibration in certain wavelengths can cause materials to fatigue and collapse.

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