Why Climbers Never Let the Rope Make a Wide V
Hang a weight from two ropes and widen the angle between them: the pull on each rope grows — past 120°, each rope carries more than the whole weight. Measure it, then prove it.
Where this idea comes from
Start here — these are the sources that inspired this exploration.
Introduction
Climbers anchor themselves to two bolts with slings that meet in a V, and they obsess over the angle at the bottom. Below 60° each sling carries comfortably less than the climber's weight; past 120° each sling carries more than all of it — and one infamous rigging mistake, the 'American Death Triangle', makes things worse still. You can measure the whole effect with string, two luggage scales and a school bag, then explain it by splitting each rope's pull into components. The same geometry decides how picture wire, washing lines and slacklines are rigged.
Guiding Questions
- Rig it: a weight hung from two strings over two anchor points, a luggage scale in each string. Record the readings as you widen the V. What pattern do you see?
- Split each string's pull into horizontal and vertical parts. Use the balance of forces to predict the tension at any angle — does your formula match the scales?
- Find the angle at which each rope holds exactly the full weight, and explain to a non-mathematician why widening the V keeps making things worse.
- Climbing sites warn about the 'death triangle' rigging. Model it, compare it with the ordinary V, and quantify exactly how much worse it is.
- The same V shows up in washing lines, picture wire and slacklines. Choose one, change something about the setup, and investigate when it gets dangerous.