Magazine article Science News

Chaos for Fun and Profit

Magazine article Science News

Chaos for Fun and Profit

Article excerpt

Much of the fun of an amusement-park ride arises from its stomach-churning, mind-tingling unpredictability. The Tilt-A-Whirl, for example, spins its passengers in one direction, then another, sometimes hesitating between forays and sometimes swinging them abruptly from one motion to another. The rider never knows exactly what will come next.

Yet these complicated, surprising motions result from a remarkably simple geometry. A passenger rides in one of seven cars, each mounted near the edge of its own circular platform but free to pivot about the center. These platforms, in turn, move at a constant speed along an undulating circular track consisting of three identical hills separated by valleys, which tilt the platforms in different directions. The movements of the platforms are perfectly regular, but the cars independently whirl around in an irregular manner.

Intrigued by the possibility that the motion of the Tilt-A-Whirl cars may represent an example of chaotic behavior, Richard L. Kautz of the National Institute of Standards and Technology in Boulder, Colo. and Bret M. Huggard of Northern Arizona University in Flagstaff worked out a mathematical equation to describe the forces acting on each car. Solving this equation to determine how a car would move, they obtained results that closely mimicked the Tilt-A-Whirl's actual behavior. The researchers describe their results in the January AMERICAN JOURNAL OF PHYSICS.

The mathematical model developed by Kautz and Huggard suggests that when the platforms travel at very low speeds along the track, the cars complete one backward revolution as their platforms go over each hill. …

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