What is the maximum shortening of a string after tying an overhand knot?

[Loren Booda]

Given a flexible, inelastic and incompressible string of radius R, how much at most would it shorten from tying an overhand knot in it?

 

[sneutron]

The following is not the answer to the question you asked, but try this for starters:

The http://en.wikipedia.org/wiki/Overhand_knot" .

http://en.wikipedia.org/wiki/Ropelength" is expressed as a ratio to thickness and depends heavily (for simple knots) on crossing number (3 for trefoil).

The absolute minimum length/thickness for any type of knot was shown to be 15.66, and for the trefoil specifically the answer is 16.372.

 

[Loren Booda]

These are great lines, sneutron! Where did you get them?

Could projections of a knot's perpendicular surfaces (while the linear string rotates) give any insight?

 

[sneutron]

Wiki, Loren, just follow the links in my post.