|Ivars Peterson's MathTrek|
May 1, 2000
The unpredictable motion of the Tilt-A-Whirl's cars occurs when the ride's seven platforms travel at a speed of about 6.5 revolutions per minute along the undulating, circular track (see Tilt-A-Whirl Chaos (I), April 24, 2000).
At such a platform velocity, even slight changes in starting position lead to radically different sequences of car movements. It becomes virtually impossible to predict several seconds ahead of time what a car will do next. Such a sensitive dependence on initial conditions is a hallmark property of chaos.
Interestingly, Tilt-A-Whirl fanatics know by experience that they can actually take advantage of this sensitivity. They can affect the motion of a car by throwing their weight from side to side at crucial moments, turning cycles with little or no action into thrilling whirls.
"Thus, it would seem that aficionados of the Tilt-A-Whirl have known for some time that chaotic systems can be controlled using small perturbations," says Bret M. Huggard of Northern Arizona University and Richard L. Kautz of the National Institute of Standards and Technology.
It turns out that Tilt-A-Whirl operators can also take advantage of this sensitivity.
Shortly after the publication of The Jungles of Randomness, where I described the Tilt-A-Whirl model developed by Huggard and Kautz, I received a message from software development engineer Dave Boll of Colorado. He described his experience one summer running a Tilt-A-Whirl, "which is easily the most entertaining carnival ride to operate."
Why? The operator can actually orchestrate the movement of individual cars. A single lever controls the ride's speed, so an operator can slightly retard or accelerate the ring of platforms at any moment. By applying just the right amount of velocity change at exactly the right time, it's possible to spin a particular car. For example, if a car is currently not spinning, is about to go uphill, and is positioned toward the inside, accelerating the platform will send the car into a very fast spin.
That's what makes the ride so attractive to operate, Doll says.
Of course, any adjustment in speed affects all cars. What happens to particular cars depends on its current spin, its position with respect to the ride's hills and valleys, whether the car is on the inside or outside of its platform, and the velocity change applied by the operator. Very fast spins occur in the same direction as the platform is rotating, and slower spins are in the opposite direction.
Superior spins also provide a bonus for the alert operator. Such whirling inevitably shakes loose coins out of the pockets of passengers--"tips" that can be gathered up after a ride is over and the riders have stepped away!
"There is an art to giving good rides," Doll remarks. "A good operator can sustain a spin on any car, in any direction. After some practice, it is possible to control two cars at once."
"What I usually did was to focus on one particular car, and if I could get another to spin with it, I would try to time it so that both cars maintained their spins as long as possible," he adds.
Scientists and engineers have only in the last decade or so begun to apply the same principle to the control of chaos in electronic circuits and lasers and to the management of chaos in the heart and the brain. The goal is to stabilize and suppress chaos in some cases and to maintain and enhance it in other situations.
In fact, the sensitivity to initial conditions that characterizes chaos can offer considerable advantages, allowing systems designers greater flexibility in their choices of materials and architectures and making possible multipurpose systems that adapt quickly to changing needs. Just as gearing allows you to operate a heavy truck with a few fingers on the steering wheel, chaotic dynamics offers a similar ease of control in a variety of situations.
The most intriguing possibilities for control involve biological systems. Research teams have already managed to stabilize the irregular heartbeats of a mass of heart cells and to turn on or off seemingly random patterns in the electrical activity of neurons.
Such successes suggest that biological systems may use chaos and the richness of chaotic dynamics to adjust their behavior on the fly. Multipurpose flexibility is essential to higher life-forms, and chaos may be a necessary ingredient in the regulation of the brain. Controlled chaos in the brains juggling of electrical signals, for example, may play a role in the human ability to produce strings of different speech sounds quickly enough to carry on an intelligible conversation.
Copyright 2000 by Ivars Peterson
Ditto, W.L., and L. Pecora. 1993. Mastering chaos. Scientific American (August):78.
Kautz, R.L., and B.M. Huggard. 1994. Chaos at the amusement park: Dynamics of the Tilt-A-Whirl. American Journal of Physics 62(January):59.
Ott, E., and M. Spano. 1995. Controlling chaos. Physics Today (May):34.
Peterson, I. 1998. The Jungles of Randomness: A Mathematical Safari. New York: Wiley.
______. 1994. Chaos for fun and profit. Science News 145(Feb. 26):143.
______. 1991. Ribbon of chaos. Science News 139(Jan. 26):60.
Peterson, I., and N. Henderson. 2000. Math Trek: Adventures in the MathZone. New York: Wiley.
The Sellner Manufacturing Company, which makes the Tilt-A-Whirl, has a Web site http://www.whirlin.com/.
To learn more about the mathematics underlying chaos you can try The Chaos Hypertextbook at http://hypertextbook.com/chaos/ or visit the University of Marylands Chaos Group Web site at http://www.chaos.umd.edu/.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.