The Physics of Roller Coasters

By Joshua Coyston

How roller coasters completetheir circuits

•‘Gravity’ is said to be the reason why roller coasters complete their circuits, but this isn’t technically true.

A lift hill moves the car / train up, increasing the gravitational potential energy (GPE). The car then gains kinetic energy as it loses gravitational potential energy. This conservation of energy explains why a standard roller coaster can never go higher than the height of its lift.

Launch Roller Coasters•Launch roller coasters are very different though; they have no form of lift to gain energy.

•Some roller coasters use LIM/LSM launch systems, which is where the train is propelled by electromagnets. This creates a very quick acceleration.

•Hydraulic systems are most commonly used for launch roller coasters, as they provide a constant acceleration during the entire launch. They usually require 8 pumps of approx. 500 horsepower to launch.

Hydraulic Motor

Circular Motion•When roller coasters are being designed, safety is of upmost importance. When looking at aspects such as vertical loops and such, circular motion is most commonly taken into account.

•V stands for Velocity•r is the radius of the circle.•T is the period of oscillation in the circle.

Circular Motion in Action

A=23m

X m

Y m

Z m

•B is 3/8 of A. B = (23* 3/8) = 8.625•X is A-B = 23 – 8.625 = 14.375 •Y, by chance, is also 14.375•Z =(X2+Y2) = [(14.375)2 + (14.375)2] = 20.329

B m

So, d=20.329m r=10.165m.Given that T5s:

V=(2*10.165)/5V=12.8 m/s or 28.6 mph (3sf)

The Clothoid Loop

The Clothoid Loop, commonly known as ‘The loop-the-loop’ or a ‘Vertical Loop’, was first used on a roller coaster in 1975 and was designed by Werner Stengel. The main reason for this is because the circular loop causes much higher G-Forces on the body.

The Curious Case of Saw’s Differing Radii

Red Line – How the track is.Green line – How the should be to prevent a ‘bump’.

Thanks for listening…