Simple Top Rope Problem

"Top Roping" is a type of climbing in which the climber stays below the anchor at all times. Here is an example photo:

https://www.vdiffclimbing.com/basic-top-rope/

I am going to do some simple math for the forces in a top rope, in order to show the degree with which forces can increase if anchors are in the incorrect locations. In the above drawing, the anchors are 30 degrees apart, considered the maximum safely allowable by many. If the force downwards is me hanging, this is what occurs:

  • m=75kg
  • g=9.806
  • F=mg=735.45
  • T=735.45/2=367.725 (divided between the two strands of rope).
  • 2sy=735.45      so     sy=367.725,      therefore  s=367.725/cos(30)=424.6=A

                So our total Newtons per anchor increased by almost 100 N just by having a slightly wide anchor!so our 2s_y=735.45 so s_y=367.725, therefore s=367.725/cos(30)=424.6=A