Walk the line. Mathematicians have calculated a "sweet spot" for rope balancing that depends on the rope's sag.

Steffen A. Frost

How to Become an Expert Tightrope Walker

Life is a constant balancing act, especially if you're a tightrope walker. The best athletes make treading a circus high wire or a low-hanging slackline look effortless, but they're actually juggling complex challenges of perception and motor control. Now researchers have constructed a mathematical explanation of how such nimble acrobats remain upright. Their calculations point to a theoretical "sweet spot," or optimal conditions for a person to balance on a line with minimal effort. Such a model may help scientists better understand how the brain and body work together to pull off difficult tasks.

The study originated from a thought experiment, as researchers at Harvard University pondered the ultimate balancing challenge. Keeping steady on a stationary plank or beam is hard enough, but a rope adds the destabilizing element of motion. A rope not only sways but also moves in response to a person's movement, forcing the walker to constantly change position. In this shaky feedback loop, "small errors can be amplified very easily," says study author L. Mahadevan, an applied mathematician and scientist.

The researchers created a simple model of a person on a rope with forces, masses, angles, and velocities to describe how the rope and person respond to each other. They also considered the sensory systems that alert us when our bodies start to teeter, including our eyes, the organs of our inner ear, and orientation information from our ankles and knees. In their calculations, they suggest that rapid information about falling provided by the inner ear is sufficient to help a rope walker maintain his or her balance.

The team also discovered that a key feature affecting balance is the rope's sag. A tight rope with little sag makes quicker vibrations, whereas a loose rope with a lot of sag makes larger back-and-forth swings. Between these two challenging extremes exists a "sweet spot"—an optimal sag of about 3 feet where balancing is easiest, the researchers report online today in the Journal of the Royal Society Interface.

The sag of a rope changes as a person walks along it, and it is greatest when the person is halfway across. A rope walker who finds the sweet spot can balance more easily because there, "all your sensory control information can be easily tuned to the dynamics of the rope," says study author Paolo Paoletti, an applied mathematician.. "The time that you need to react coincides with the time that the rope makes one swing."

Expert balancers have discovered this optimal sag through repeated practice, the researchers say: A handbook for learning slacklining instructs beginners to set their ropes to sag 3 or 4 feet in the middle. "The mathematical model essentially converts this intuitive notion into a quantitative description," Mahadevan says. "It makes predictions that are testable."

The paper addresses the important role of the physical environment in maintaining balance, in addition to the traditional focus on the nervous system, says John Milton, a computational neuroscientist at Claremont McKenna College in Claremont, California, who was not involved in the work. "This interplay is the nice thing about this paper." However, he says, the study's real contribution will happen once its predictions are tested with experiments. "The jury is out whether when someone is balancing on a slackline, does the nervous system actually go for the optimal solution?"

The study's authors are trying to answer that question in collaboration with Francisco Valero-Cuevas, a motor neuroscientist at the University of Southern California in Los Angeles. By outfitting expert slackline walkers at Santa Monica Beach with wireless devices that measure movement and stability, the researchers are testing whether stability changes along the length of the slackline as the model suggests.

Valero-Cuevas says the complexity of slackline walking appeals to him because "high performance behaviors are more likely tied to evolutionary fitness, like jumping from rock to rock or maintaining balance on a branch." He adds that studying how people learn and perform complicated tasks reveals the strategies and limitations of the brain and the body in demanding situations. This can provide insight into impairment and rehabilitation, he says. "What to us is very simple to do, like taking a step, to someone who has had a stroke can be just as challenging as learning to slackline."