TITLE: Knot security (When to trust your life with a knot)
QUESTION [37 upvotes]: This question is related to a a question about self-tightening knots.  
I am supervising a senior thesis and my student is interested in knots.  My student is also a rock climber and has an interesting idea for a project, but I am not sure how reasonable it is.  She wants to look at the mathematics of knot security.  As a climber, she may tie a single rope to a closed loop or tie two pieces of rope together.  There are some knots you should trust your life with and others you should avoid while hanging from a cliff.  She wants to understand what properties of a knot make it secure.  I like the idea, but I have no idea what kind of model we would use.  The only articles I could find were about knot security for surgeons tying sutures and were based on experimental evidence only.
Does anyone know any mathematical references for studying physical knots and knot security?

REPLY [5 votes]: Louis Kauffman's masterful book "Knots and Physics" has some thoughts on it. Especially the introductory chapter, and then later a small chapter called "The Theory of Hitches". Worth a reading IMO..