The Physics Behind the Thrills

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The Physics Behind the Thrills

• Danny Messinger
• PH2010
• Fall 2007

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A Brief History

• Russian Ice Slides
• Montagnes Russes
• Switchback Railway
• Scenic Railway
• Modern Roller Coaster

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A Few Powerful Ideas
A few basic laws and ideas are used to provide
riders with a safe and thrilling experience

• Acceleration, Jerk and Snap
• Conservation of Energy
• Weightlessness
• Centripetal Acceleration
• Clothoid Loops

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Acceleration, Jerk and Snap

• Acceleration - first derivative of velocity
• Positive and negative G-Forces
• Typical range from 4G to -1G
• Jerk - second derivative of velocity
• Rate of change of acceleration
• Riders need time to changes and adjust muscle
  tension
• Snap - third derivative of velocity

A roller coaster designer must have a
comprehensive knowledge of kinematics in order to
guarantee an exciting (and safe) ride
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All About Energy

• Potential Energy
• The energy of position
• U mgh
• As the train climbs the lift hill, it is building
• potential energy

• Kinetic Energy
• The energy of motion
• K 1/2mv2
• As the train travels down a hill, its velocity
• increases which increases its kinetic energy

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Conservation of Energy

• Ideally, the law of conservation of energy
  provides a good model for roller coasters
• Esystem K U
• Realistically, the law of conservation only
  provides a basic tool for analyzing roller
  coasters

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Friction

• Friction is what eventually brings your ride to
  an end
• Dissipative force
• Esystem Emechanical Ethermal
• ?Esystem 0

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Weightlessness

• Parabolic hills cause the sensation of
  weightlessness
• Riders are experiencing freefall due to this
  trajectory

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Centripetal Acceleration
ac v2 / r

• Points toward center of circular path
• Felt by riders as a force pushing them into their
  seats
• Centrifugal force is actually the riders
  inertia trying to keep them continuing in a
  straight path
• Higher velocity higher ac
• Smaller radius higher ac

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Feeling Loopy
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The Clothoid Loop

• The characteristic upside-down teardrop shape
  is found on all modern coasters
• Minimizes forces on riders and allows a higher
  entry speed
• Early circular loops pulled over 13 Gs
• Modern clothoid loops pull only 3-4 Gs
• Circular loops would result in high jerk - a
  dangerous problem

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Linear Induction Motors

• A linear induction motor provides an alternative
  to the traditional chain lift
• Powered through alternating current
• Space-saving alternative to lift hill
• Exciting launch sensation

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Bibliography

• Coasterimage www.coasterimage.com
• Knight, Randall Physics for Scientists and
  Engineers 2004 182 - 200
• Roller Coaster Database www.rcdb.com
• Roller Coaster Physics http//ffden-2.phys.uaf.ed
  u/211_fall2002.web.dir/
• Ultimate Roller Coaster Roller Coaster History
  http//www.ultimaterollercoaster.com/coasters/hist
  ory/
• Wikipedia Roller Coasters http//en.wikipedia.or
  g/wiki/Roller_coasters

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Any Questions?