Roller coasters gain potential energy from lift hills to complete their circuits through a transfer of gravitational potential energy to kinetic energy via conservation of energy. Launch coasters use hydraulic or electromagnetic systems to accelerate trains from zero to high speeds without lifts. When designing coasters, circular motion equations involving velocity, radius, and period are considered for safety regarding elements like loops. The first loop-the-loop element was introduced in 1975 due to its smoother g-force profile compared to a basic circular loop. Track design must account for varying loop radii to prevent uncomfortable bumps.

1. The Physics of Roller Coasters By Joshua Coyston

4. 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.

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

7. V stands for Velocity

8. r is the radius of the circle.

10. X is A-B = 23 – 8.625 = 14.375

11. Y, by chance, is also 14.375

12. Z =(X2+Y2) = [(14.375)2 + (14.375)2] = 20.329A=23m Z m So, d=20.329m  r=10.165m. Given that T5s: X m Y m V=(2*10.165)/5 V=12.8 m/s or 28.6 mph (3sf) B m

13. 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.

14. The Curious Case of Saw’s Differing Radii Red Line – How the track is. Green line – How the should be to prevent a ‘bump’.

15. Thanks for listening…