tag:blogger.com,1999:blog-4004592252895499792.post2372967825905738980..comments2021-05-17T07:59:43.426-07:00Comments on eScienceCommons: The math of rock climbingeScienceCommonshttp://www.blogger.com/profile/07669694248203452186noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4004592252895499792.post-48586413941755746842010-09-03T14:20:17.202-07:002010-09-03T14:20:17.202-07:00A really interesting exercise to do is to calculat...A really interesting exercise to do is to calculate the KiloNewtons of force on a piece of gear in a given fall. For example, how much much force is held by your first piece of gear if you are a 190# climber who is 7 feet above your first piece, which is placed 9 feet above the ground. <br /> The results are very surprising, and are non-intuitive to climbers who think the first piece doesn't have to be "that good" because it is closer to the ground than pieces higher up. <br /> I built a spreadsheet which takes 4 variables;<br />climber weight, rope stretch percentage, rope length, and fall length. That spreadsheet changed the way I climb trad. ;-)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4004592252895499792.post-91517469314894882872010-08-02T10:54:08.741-07:002010-08-02T10:54:08.741-07:00Climbers know that fall factor is important -- it ...Climbers know that fall factor is important -- it determines how much impact a falling climber feels when the rope comes tight. But most don't know the reason why. You can find a good explanation in the article<br /><br />"Taking a whipper---The fall-factor concept in rock climbing" by Dan Curtis, The College Mathematics Journal, vol. 36, no. 2 (March 2005), pages 135-140.<br /><br />The explanation amounts to solving a differential equation, and he walks you through it. One semester of college calculus (in the language of the AP exams, Calculus AB) should give you enough background to read Curtis's article.<br /><br />By the way, in case it wasn't clear from the video, the fall factor is always between 0 (best) and 2 (worst or most unpleasant).Skip Garibaldihttp://www.mathcs.emory.edu/~skip/noreply@blogger.com