Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Overhand knot efficiency

  1. Oct 1, 2011 #1
    Given a flexible, inelastic and incompressible string of radius R, how much at most would it shorten from tying an overhand knot in it?
  2. jcsd
  3. Oct 10, 2011 #2
    The following is not the answer to the question you asked, but try this for starters:

    The http://en.wikipedia.org/wiki/Overhand_knot" [Broken].

    http://en.wikipedia.org/wiki/Ropelength" [Broken] 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.
    Last edited by a moderator: May 5, 2017
  4. Oct 10, 2011 #3
    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?
  5. Oct 11, 2011 #4
    Wiki, Loren, just follow the links in my post.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook