Mathematicians Have Developed an Equation for the Perfect Climbing Rope

Ropes are a rock climber’s lifeline, but they’re not perfect. They can protect climbers from fatal falls, for example, but they don’t do much to stop the adventurers from jerking uncomfortably after a sharp drop, or from crashing painfully into the side of a cliff face after plummeting several feet. Fortunately for rock climbers, a group of mathematicians at the University of Utah have developed a formula for the perfect theoretical climbing rope.

As Gizmodo explains, the perfect rope currently only exists on paper: Researchers believe it would theoretically be possible to make, but only once the right materials are identified. As they write in a study published in the Journal of Sports Engineering and Technology, the perfect rope wouldn’t just break a climber's fall—it would also brake it. That is, the rope would decelerate a climber’s fall in much the same way cars decelerate when you softly step on the brakes.

Researchers believe shape-memory materials could be used to develop such a climbing rope. Right now, shape-memory materials are used in a wide variety of products, including eyeglass frames, underwire bras, and even golf clubs. These materials “remember” their shape and return to it after being stretched or deformed—a quality that could be used to make ropes that absorb more energy and exert a braking force for falling climbers.

"With a normal rope, you're going to experience increasing force the longer you fall, whereas with an ideal rope you'd still fall suddenly until the rope tightens, but once it begins to tighten, it would exert a constant force on the climber," researcher Graeme Milton explains. "So it would like constant braking rather than a sudden jerk."

Unfortunately, shape-memory materials are both too heavy and too expensive to be used in a revolutionary new climbing rope. But the study’s authors hope that more research into materials could help make their ideal rope a reality. "We don't want to make too bold a claim," Milton notes. "We are giving the climbing industry a new avenue to explore."

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