The Wonder of Physics
How do designers get the most out of a roller coaster ride?
Several formulas are used to determine speed, how safe it would be to enter a corkscrew without the cart falling off the rails, and, most importantly, just how high could that loop-de-loop be?
One of the first things to consider, is the cart's velocity and acceleration. The formula for velocity is as follows:
v = d/t
Where v is the velocity, d is the distance traveled, and t is the time.
Other things that could have a factor, is the height of the hill and/or the presence of friction, depending on the design of the roller coaster.
Now, how does a designer determine forces on a loop?
The first thing to realize is that there is no such thing as Centrifugal force! What a rider is really experiencing is Centripetal force, which pulls the individual towards the center of the loop. This can cause what's often called a "g-force." Formulas for determining this force are as follows:
a = v^2/R
g’s = a/9.81
Where a = the acceleration of the centripetal force, v is the velocity, R is the radius of the loop, and 9.81 represents earth's gravity.
Some other important things to note, is that roller coasters demonstrate Sir Isacc Newton's first and second laws quite well. Newton's first law states that an object at rest, will remain in rest, just as an object in motion will remain in motion. His second law states that the acceleration of an object is directly proportional to the force acting on it and it is inversely proportional to its mass.
For more indepth information, visit: How Rollercoasters Work.