# Gordian knots?

1. Feb 9, 2017

### john101

Hi.

I've been searching for some description of the following. Something that will explain it and perhaps even some maths about it.

Take a rod or a stick and tie a string around its middle.

Hang it so the string is unwound, still.

Start turning the rod so the string twists around.

Keep twisting.

If at any time you let the rod go the string unwinds again to rest.

Keep twisting and you can see the string twists to a point where it suddenly creates a knot.

If you at that point let the rod go it only unwinds to the knot but no further.

If you keep twisting it forms knot after knot until the whole string is a row of knots that wont unwind.

If you keep twisting a third set of knots pop into existence.

It seems the thickness of the string, the length of the string, the weight of the rod are factors that determing things.

Is this something that anyone anywhere has looked at and have words to describe it and perhaps even something that can predict and generally explain it.

Last edited: Feb 9, 2017
2. Feb 9, 2017

### john101

It seems it's only possible to get a third set of knots. Probably depends on thickness of string.

Reminds me of the trick re folding a sheet of paper more than nine times. Mythbusters tried that one in a hangar using a roller and forklift. From memory they set a record.

3. Feb 9, 2017

### collinsmark

Would it be possible to post a video or even a diagram of what you trying to describe? I don't understand what you mean.

4. Feb 9, 2017

### john101

Yes.

The string is fixed at the top and the rod is spun around and the string twists and at some point creates a knot that is difficult to unwind...etc.

5. Feb 9, 2017

### collinsmark

Okay, I think I understand now.

The "knots" you describe are not really knots, so to speak. They are just loops that form on the string.

This is not my field of expertise, but I'm sure somebody else here might be able to help better. The mechanical engineering sub-forum might be the best place to look.

In the mean time, I believe this might be explained in terms of stresses on the string. As the string is twisted it gains torsional stresses. Each loop that forms in the string effectively reduces the torsional stress. If the string was rigid, these loops would introduce bending stress, and in that case, it would be the result of the string attempting to balance torsional and bending stresses. In the case of a normal string though, bending stresses are negligible, and the loops merely shorten the effective length of the string (increasing the potential energy of the rod by raising it up) -- still, however, each loop reduces the torsional stress of the string.

So why don't the loops always vanish when the rod is released? I'm guessing friction.

Again though, this isn't my area of expertise and someone in the mechanical engineering subforum that knows more about stresses could probably help better.

6. Feb 9, 2017

### john101

Hmmm.. makes sense. It seems the 'knotting' momentarily reduces tension in the string. That it doesn't unwind becuse of friction makes sense.

Then it looks to me that that tension is stored in the unwound loop.

When watching the formation of a loop they all seem form in the same way. As the knots form the 'string' becomes stiffer. And the rod rises and becomes harder to turn until the next knot forms.

7. Feb 9, 2017

### Staff: Mentor

Here's something related to this phenomena

http://www.livescience.com/43536-yarn-muscles-100x-stronger-human-muscles.html

A researcher twists and coils fish line to make a muscle that reacts to heat.

It also may be related to supercoiling but I couldn't find an example of a rubber band or string doing this although as a kid we would wind up model plane powered by rubberbands and watch the coil up when they couldn't twist anymore and that was essential to adding more flight time.

8. Feb 10, 2017