The (the­o­ret­i­cally) per­fect climb­ing rope.

Climb­ing ropes have come a long way since the days of stiff hemp cord. A mod­ern dy­namic ny­lon rope will catch a fall­ing climber softly, ab­sorb the force with­out plac­ing large loads on the rest of the sys­tem, and last a long time. It’s been decades since the mod­ern kern­man­tle (core plus sheath) rope hit the mar­ket, and the gen­eral de­sign hasn’t changed much since. But could it be im­proved? What would make a rope per­fect? A new study by a team from the Uni­ver­sity of Utah at­tempts to an­swer those ques­tions, and it sug­gests that there is hope for softer catches in the fu­ture.

The study, pub­lished in The Jour­nal of Sports En­gi­neer­ing and Tech­nol­ogy, iden­ti­fied the most im­por­tant fea­tures of an ideal climb­ing rope and proved on pa­per that such a rope could ex­ist. The team de­ter­mined the ideal rope to be one that catches a climber while ap­ply­ing the small­est peak load over a pe­riod of time and ab­sorbs nearly all the en­ergy from a fall. Th­ese two fea­tures alone mean that a rope could pro­vide the per­fect catch with­out any adverse ef­fects on the climber or sys­tem.

The idea arose from Justin Boyer, a mas­ters stu­dent in Dr. Graeme Mil­ton’s math­e­mat­i­cal mod­el­ing class. Mil­ton has a PhD in physics from Cor­nell Uni­ver­sity, as well as time spent work­ing at NYU’s pres­ti­gious Courant In­sti­tute of Math­e­mat­i­cal Sci­ences. Mil­ton cur­rently works as a dis­tin­guished professor of math­e­mat­ics at the Uni­ver­sity of Utah in Salt Lake City, where he moved in 1994 to be closer to hik­ing, ski­ing, moun­tain biking, and canyoneer­ing. Though Mil­ton doesn’t climb, Boyer and grad­u­ate as­sis­tant Trevor Dick are climbers, and they were able to pro­vide climb­ing knowl­edge when ques­tions arose. The team was joined by Davit Haru­tyun­yan who worked out the math­e­mat­i­cal proof that the “ideal rope” could ex­ist.

The study fo­cused on the math­e­mat­i­cal side of the ideal rope, show­ing that the most im­por­tant be­hav­iors—small­est peak load and max en­ergy ab­sorp­tion—ac­tu­ally fit to­gether. On pa­per, the re­search looks like a se­ries of com­plex equa­tions that are in­de­ci­pher­able to the layper­son. For a sim­pler ex­pla­na­tion, Mil­ton com­pares the ideal rope be­hav­ior to brak­ing in a car.

“If you brake right at the very end, you’re maybe go­ing to get whiplash,” he says. “But if you ap­ply con­stant brak­ing over time, you’ll avoid that.” In other words, once the rope be­gins catch­ing a fall­ing climber, she would ex­pe­ri­ence a con­sis­tent brak­ing force un­til the rope reached its fully stretched length, then the rope would slowly re­tract to its nor­mal length, in­stead of bounc­ing back up.

While no ma­te­rial cur­rently ex­ists that can achieve the team’s ideal prop­er­ties, they see po­ten­tial in shape-mem­ory ma­te­ri­als, which are used to make a va­ri­ety of prod­ucts, from artery stents to golf clubs to heli­copter blades. The study cited many po­ten­tial ben­e­fits, rang­ing from shorter rope elon­ga­tion and fall dis­tances to de­creased max­i­mum load on the climber and all other parts of an an­chor/be­lay sys­tem. A rope made from shape-mem­ory wires could ap­ply a con­stant brak­ing force up to 8% elon­ga­tion, and only stretch be­tween the climber and the top cara­biner. In com­par­i­son, the ropes we use to­day will stretch up to 15% across the en­tire length from be­layer to climber. The shape-mem­ory rope could brake over a much shorter dis­tance while achiev­ing the same peak forces on a climber, mak­ing ledge falls less likely.

Per­haps one of the big­gest ben­e­fits is the dura­bil­ity of th­ese new ma­te­ri­als. Mod­ern ropes shrink, be­come stiffer, and pro­vide harder catches over time, but cur­rent shape-mem­ory wires can un­dergo mil­lions of de­for­ma­tions be­fore they are sus­cep­ti­ble to fail­ure.

Of course, this is all the­o­ret­i­cal. While shape-mem­ory ma­te­ri­als that meet some of the team’s re­quire­ments ex­ist, none are suit­able for climb­ing ap­pli­ca­tions. The ma­te­rial that would cre­ate the math­e­mat­i­cally ideal climb­ing rope doesn’t ex­ist yet, and cur­rent ma­te­ri­als are pro­hib­i­tively ex­pen­sive. For ex­am­ple, wire made from niti­nol, a shape-mem­ory ma­te­rial com­prised of nickel and ti­ta­nium al­loy, costs $500 per me­ter. Shape-mem­ory ma­te­ri­als may also have other draw­backs, such as poor kno­ta­bil­ity, high weight, and tem­per­a­ture-de­pen­dent prop­er­ties. One so­lu­tion may be to com­bine shape-mem­ory ma­te­ri­als with cur­rent rope ma­te­ri­als.

Mil­ton hasn’t taken the team’s re­search to any out­door gear man­u­fac­tur­ers since pub­lish­ing the pa­per, but the au­thors hope it draws in­ter­est from ma­te­rial de­vel­op­ers. An op­ti­mal climb­ing rope could have other in­dus­trial ap­pli­ca­tions that would war­rant the re­search and in­vest­ment needed to de­velop it. For ex­am­ple, the study sug­gests it could be used as a tether for drop­ping cargo out of a heli­copter with­out a parachute.

“The ma­te­ri­als you re­ally want with th­ese char­ac­ter­is­tics don’t ex­ist yet,” he says. “But if you put some­thing out say­ing, ‘ This is re­ally what we’d like,’ then there could be ma­te­rial providers that de­velop it.”

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