# The Maths Behind The Perfect Climbing Rope

Rock and mountain climbers rely on strong, yet elastic ropes to keep them safe should they happen to fall. Now mathematicians at the University of Utah have come up with an equation to design an ideal climbing rope — one that would be safer and more durable. They described this perfect rope, and a promising class of materials that might be used to make it, in a recent paper in the Journal of Sports Engineering and Technology. Mathematician Trevor Dick shows some slick climbing moves in Parley's Canyon near Salt Lake City. (Image: Justin Boyer/University of Utah)

Climbing ropes are designed with a bit of stretch in them — the better to absorb some of the impact during a fall — although the ropes will gradually lose their elasticity over time. They're usually made of nylon fibre, twisted at the core to give the ropes their strength. But "with a normal rope, you're going to experience increasing force the longer you fall," co-author Graeme Milton said in a statement. That means a harder jerk when a falling climber hits the end of the rope, depending on how far he or she has fallen.

An ideal rope, like the one envisioned by Milton and his co-authors, would slow down climbers as they fall by applying a constant deceleration force, thereby bringing the climber to a gradual stop rather than hitting the end of the rope with sudden jerk. It's the same concept as applying the brakes evenly when decelerating in a car over a short fixed distance to avoid giving yourself whiplash. As Milton explained, "The ideal climbing rope would decelerate a falling climber in the same way that on an aircraft carrier, the braking cable and its hydraulics slow down and stop a jet within a short distance."