A new way to tie an old knot

The tying diagram Ashley gives for ABOK #2217 has a 4-fold axis of symmetry:

Tying a knot according to a diagram like this is quite time consuming. One must redraw the diagram by photocopying to the size needed. And in tying the knot, one pins the rope to the diagram. This is a pain because the rope moves around, the pins come out, etc. And the pins can damage the appearance of the rope.

In this post I give an alternative method of tying this knot, and several others like it, that is easier to set up, is much faster for each knot, and uses cheaper materials. Rather than an expensive cork board, we will use a 2×2 and build the knot as if it were a sort of Turk’s Head knot, on a cylindrical of square form.

First, to show that this method of tying the knot gives an identical knot, observe that the following diagram gives the same pattern of numbers as the Ashley diagram:

These drawings are how one converts a path in a 2-manifold into an over/under knot. This knot has 40 crossings (or 41, as the bitter end is hidden). Following the path of the rope, every other crossing will be an “under.” Beginning with the start point, label the under crossings in sequence. Along the way, you will also visit all the “over” crossings. If there is already a number there, then great, at that point in making the knot you will be laying rope on top of rope. But if there is no number yet there, then the “under” rope is not yet placed. This means that when you do get around to that crossing, you will have to dig under the “over” rope that is already there. Mark these crossings with a circle.

The result is an Ashley tying diagram. To tie the knot with this diagram, pin it out on a cork board. Lay rope along the diagram. Whenever you meet a crossing marked with a circle, there should already be a rope there and you need to go under it. This is quite a pain.

Turk’s heads are cylindrical knots. Most Boy Scouts know how to tie small Turk’s Heads in the hand. Larger Turk’s heads are tied on a cylinder. Suppose one wishes to tie a Turk’s head with 8 bights. One finds 16 nails and a wood cylinder of appropriate size. One marks two rings on the cylinder and puts the nails on these rings in equally spaced intervals. One chooses an offset for the left to right and right to left movement. Starting at the left side at nail 0, you go to a right nail and then back to a left nail with the offsets one has chosen. To tie the Turk’s Head with a single line, one must return to nail #1, 3, 5, or 7 as these are relatively prime to 8. The offset on the right side is typically chosen to be close to half the total offset for left to right and back. The crossing diagram is trivial in that the rings on the cylinder alternate between left over rigth and right over left. So there is no need to deal with a tying diagram. In addition, one runs the cord freely from side to side and so there is no need to pin the cord.

The above cylindrical diagram for ABOK #2217 means that it possible to tie this beautiful knot using the Turk’s Head’s method.

Materials: 50 feet of 5/32″ cord. 1 1/2″ diameter wood ball. 6 inches of wood 2×2. 16 screws or nails, 5/8″ long. 15 feet of thin wire or thread to be used as a guide. [Metric: 10 meters of 4mm cord. 40mm wood ball. 20cm of wood 5cmx5cm. 16 screws or nails, 15mm long. 5 meters of thin wire or thread to be used as a guide.]

No need to be exact, just get the nails or screws into the square wood piece approximately as follows:

Next we tie the guide wire to the wood. We’re going to label the four rings of screws, from the left in the picture, “outer left”, “inner left”, “inner right”, and “outer right.” Tie one end of the guide to an outer left screw. We’re going to wind it diagonally around the wood, back and forth. The rule for winding is fairly simple, but it is different when you are going from left to right versus when you’re going from right to left.

Starting on the right, from an outer screw go two sides to an outer screw; And from an inner screw go one side to an inner screw. Starting on the left, from an outer screw go two sides to an inner screw; And from an inner screw go two sides to an outer screw:

OL -> OR + 2,
IL -> IR + 1,
IR -> OL + 2,
OR -> IL + 2.

Eventually, after visiting all 16 screws, you should get back to where you started and your form will look something like this:

As with any Turk’s Head, different rings will be either left over right, or right over left. You need to mark this on the form. I used a black magic market to mark the places where left would go over right. (The unmarked crossings will have right over left.) The result looks something like this:

Now tie the cord to a screw on the left side of your wood. Wind the cord along the guide wire, bringing it under itself where needed to be compatible with the marked crossings. This doesn’t take very long at all. Early on your knot will look like this:

And eventually, following the guide wire and going over or under as needed, you return to where you started:

Lift a few bights off of the nails and remove the knot from the form:

The knot is now done with 1-ply, but it is too loose to be pretty. So pull out some of the excess cord, bringing the knot to a more spherical shape:

Before you get it too small, put the wooden ball inside. Pull more cord out of the knot, leaving it loosely around the wood ball. Then tighten it up a little, but still leaving it pretty loose:

Now we double the knot. Note that the beginning and ending points of the knot are next to each other. That means you can lead the working end back into the knot, following alongside the other end. To do this you will have to go over and under where the other lead does this. After a few minutes your knot should progess like this:



In doing this, you may find it useful to have a large crochet needle.

When you get back to the origin, take one last extra dive so that the two ends of the rope come out separated by one crossing. This makes it look more symmetric (and is shown in the Ashley drawing as crossing number 41):

For the dimensions suggested, you should have enough room to add a 3rd ply. Our photos are for a smaller ball with room only for two plies. So add another ply according as you think appropriate.

Finally, it’s time to tighten up the knot. When you’re done, the knot should be quite hard as the rope will be pulled tight. To tighten up the knot, work out the excess line the same way you’ve done it before. Uh, did I forget to mention how this is done? Ok. You move a loop of excess cord through the knot starting at one end and working the loop through to the other end. By the time you get from one end to the other, you will have tightened up each individual part of the knot. Here’s a drawing showing a loop partway worked through the knot:

I suppose I should also mention that it is important to eliminate twists in the knot as you pull excess material through it by moving a loop. Twists could become kinks if you leave them in. And try to avoid tearing up the material while you’re doing this. The finished 2-ply knot: