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# The Mathematics of Roller Coasters

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## Varshaa Thorali

on 3 June 2014

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#### Transcript of The Mathematics of Roller Coasters

the slope allows us to accurately determine the speeds that will be generated at various points along the track
speed increases as slope decreases (-), speed decreases as slope increases (+)

Equation
y=AcosB(x-C)+D
can be sin as well
A: amplitude
B: width
C: left/right
D: up/down
piecewise functions because most roller coasters are not a perfect cos/sin equations
contains loops, straight paths, hills, twists, turns
Loops
Centripetal Force
Newton's Laws of Motion
Centrifugal Force
The Mathematics of Roller Coasters
Varshaa Thorali, Jenna Kim, Kevin Lin, Kevin Liu
The Ride!

Bibliography
Per 4
Slope & Speed
Galileo Galilei
Velocity
Velocity is speed with direction and on a roller coaster, the velocity changes each time the direction is changed
The coaster must also have a minimum velocity or critical velocity at the top of the loop to make it through the loop.

THE Physics of it
The initial ascent is to give the roller coaster a reservoir of potential energy. Throughout the ride, the ride will only have the certain amount of potential energy given from the beginning and all it does is convert potential energy into kinetic energy.

The gravity and height of the cars is what gives the roller coaster potential energy to change into kinetic energy

Experiment with a simple roller coaster “Roller Coaster simulator”
Marble could take any path until it reaches the same height it starts from assuming no friction
With friction, it will keep rolling until it reaches the stop height

Acceleration
Climbs
forced into seat
Peaks
(airtime)
lighter weight
Drops
weightlessness

Velocity Does Not Matter
Loops
heaviest at bottom, weightless at top
rapidly changing forces

Banking
reduced lateral G force

Equations
The wheels also determine a lot of things for the roller coaster. Some wheels guide the coaster, other wheels control sideways movement, and the final set of wheels keep the coaster on the track even when inverted.
"Amusement Park Physics." Amusement Park Physics. Web. <http://www.physicsclassroom.com/class/circles/u6l2b.cfm>
Berkowitz, Bonnie, and Laura Stanton, Published: July 1, 2013. "Why Roller Coasters Make Us Scream." Washington Post. The Washington Post. Web. <http://www.washingtonpost.com/wp-srv/special/health/why-roller-coasters-make-us-scream/>
"Calculus Behind Roller Coasters." Prezi.com. Web. <http://prezi.com/shtrkmrdbwex/calculus-behind-roller-coasters/>
"Design of a Thrilling Roller Coaster - Introduction to the Project." Homepage. Web. <http://www.maa.org/publications/periodicals/loci/joma/design-of-a-thrilling-roller-coaster-introduction-to-the-project>
Hollis, Elwyn, Department Of Mathematics, Armstrong Atlantic State University, and Ga 31419 Savannah. Mathematica(l) Roller Coasters. Web. <http://www.math.armstrong.edu/faculty/hollis/vita/Coasters.pdf>
"Math Apprentice - Real World Math." Math Apprentice - Real World Math. Web. <http://www.mathplayground.com/MathApprentice/roller_coaster_engineer.html>
"Roller Coasters." Roller Coasters. Web. <http://www.datagenetics.com/blog/march42014/index.html?utm_medium=App.net&utm_source=PourOver>
"The Physics of a Coaster." The Physics of a Coaster. Web. <http://www.coasterforce.com/coasters/technical-info/physics-of-a-coaster>
Wayne, Tony. Roller Coaster Physics Part 1A. Web. <http://vip.vast.org/BOOK/PDFFILES/PART1A.PDF>

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