How knots weaken rope

Practically every loop, hitch, or bend has a lower breaking strength than the rope it was tied in. This is because, with the rope under tension, the geometry of the knot usually forces the standing part to kink where it enters the knot.

For illustration, imagine you have joined two ropes by putting their running ends together and wrapping both in an overhand knot. I know you would never do that, but it's been known to happen. Here's a close-up of the scene of the crime:

  
   |   \________/   |
    \              /
     \____________/
______/    /\    \______
          /  \   
_________/    \________

The outside of the curve is longer than the inside. So when the rope is under tension, only the outside part of the curve is bearing the load. Effectively, the weight-bearing part is not as thick as elsewhere on the rope. Therefore the rope will tear here at much lower loads than what it would take to snap a straight section.

When I got my Pioneering merit badge, many moons ago, there was a chart in the booklet that listed the strength reduction factors for the standard knots they taught. The numbers listed were all integer multiples of 5%, which struck me as a little too neat to be real. I probably learned those numbers at the time. Since then, I have reclaimed those brain cells to memorize some knots that don't weaken their ropes so badly—knots whose running ends enter and exit more or less straight in line:

• the alpine butterfly loop
• the figure eight on a bight (and the figure eight bend, tied with the same re-tracing technique)
• the rigger's bend

A moment with Google reveals many actual measurements of the strength reduction factors, for those who want to know them.