Thousands of years of trial and error have led to humans lacing their shoes in the strongest way possible, Monash University mathematician Dr. Burkard Polster has found. But we haven't adopted the best way of tying laces into knots - many of us still use knots that are more likely to come undone. Dr. Polster, a Logan Research Fellow in Monash University's School of Mathematical Sciences, has used mathematical formulae to identify the strongest and most efficient ways of lacing shoes. His research is published today in the international journal "Nature".
"Given a single lace and a row of eyelets down each side of a shoe I wanted to find out the best ways of lacing shoes in a reasonable manner, that is, a manner in which the shoelace visits all eyelets and every eyelet actually contributes towards pulling the two sides of the shoe together" Dr. Polster says.
So what is the strongest method of lacing? "The number of ways in which you can lace your shoes is astronomical but the two most popular methods have historically been to use criss-cross or straight lacing" says Dr. Polster. "Mathematically speaking, these are also the strongest methods. Thousands of years of trial and error have led humans to the best approach". "But the most efficient method of lacing, that is, the one that uses the least amount of lace is a rarely used type of lacing known as bowtie lacing".
Figure A - Criss-cross lacing, one of the two strongest lacings
Figure B - Straight lacing, the other strongest lacing
Figure C - Bowtie lacing, the lacing that uses the least amount of lace
And once the lacing is done, what is the strongest way to tie shoelaces? "Ignoring the loops people make when tying their laces, you find that most people place one half knot on top of another. This results in either a notoriously unstable granny knot or a very stable reef knot, depending on whether the two half-knots have the same or opposite orientation" Dr. Polster says. "In fact, most of us seem to tie granny knots which frequently come undone. If you are a granny-knot person, you can turn yourself into a reef-knot person by simply changing the orientation of one of the half-knots".
Run The Planet thanks the Monash University website (www.monash.edu.au) for the permission to reprint the article "A knotty problem - What's the best way to lace our shoes?" by Dr. Burkard Polster.