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The Physics Behind the Thrills

The Physics Behind the Thrills. Danny Messinger PH2010 Fall 2007. A Brief History. Russian Ice Slides Montagnes Russes Switchback Railway Scenic Railway Modern Roller Coaster . A Few Powerful Ideas.

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The Physics Behind the Thrills

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  1. The Physics Behind the Thrills Danny Messinger PH2010 Fall 2007

  2. A Brief History • Russian Ice Slides • Montagnes Russes • Switchback Railway • Scenic Railway • Modern Roller Coaster

  3. 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

  4. 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

  5. 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 All About Energy…

  6. 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

  7. Friction Friction is what eventually brings your ride to an end • Dissipative force Esystem = Emechanical + Ethermal ∆Esystem = 0

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

  9. 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 rider’s inertia trying to keep them continuing in a straight path • Higher velocity higher ac • Smaller radius higher ac

  10. Feeling Loopy

  11. 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 G’s • Circular loops would result in high jerk - a dangerous problem

  12. 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

  13. 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.edu/211_fall2002.web.dir/ • Ultimate Roller Coaster; Roller Coaster History; http://www.ultimaterollercoaster.com/coasters/history/ • Wikipedia; Roller Coasters; http://en.wikipedia.org/wiki/Roller_coasters

  14. Any Questions?

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