The Physics Book by Clifford A. Pickover

Author:Clifford A. Pickover
Language: eng
Format: epub
Publisher: Sterling
Published: 2011-10-31T16:00:00+00:00

Max Planck, 1878.

SEE ALSO Big Bang (13.7 Billion B.C.), Photoelectric Effect (1905).

Molten glowing lava is an approximation of blackbody radiation, and the temperature of the lava can be estimated from the color.

Clothoid Loop

1901

Edwin C. Prescott (1841–1931)

The next time you see a vertical loop in a roller coaster track—aside from wondering why people would allow themselves to be turned upside down and careened through insane curves—notice that the loop is not circular, but instead has an inverted teardrop shape. Mathematically speaking, the loop is called a clothoid, which is a section of a cornu spiral. The curve is employed in such loops for safety reasons.

On traditional roller coasters, the potential energy provided by gravity is often introduced in a large initial climb that is converted to kinetic energy as the roller coaster begins to plummet. Circular loops would require that the cars enter the loop with a greater entry speed than cars in a clothoid in order to complete the loop. The larger entry speed required by a circular loop would subject riders to greater centripetal acceleration through the lower half of the loop and dangerous g-forces (where 1 g is the g-force acting on a stationary object resting on the Earth’s surface).

For example, if you were to superimpose a clothoid curve on a circle (see diagram), the top of the clothoid loop is lower than the top of the circle. Because a roller coaster car converts its kinetic energy to potential energy as it rolls around the top of the loop, the decreased height of the clothoid can be reached at lower speeds and decreased g-force. Also, the short arc at the top of the clothoid allows the car to spend less time at a location where the car is both upside-down and traveling slowly.

One of the earliest uses of the teardrop shape was observed in 1901, when inventor Edwin Prescott built the Loop-the-Loop at Coney Island, New York. Prescott was largely self-taught in mechanics. His 1898 version of the “centrifugal railway” called for a circular loop, but the sudden centripetal acceleration placed too much strain on the riders’ bodies when the cars rounded the loop at high speed. Prescott patented the teardrop-like design in 1901.

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