The “Granny Knot”

Do your shoelaces sit crooked? Do you retie your shoes several times a day? These are both signs of a Granny Knot. Learn the “one simple trick” for keeping your shoes neatly and securely tied.

UC Berkeley Study

Front page of UC Berkeley research paper

In April 2017, a research paper by UC Berkeley titled The roles of impact and inertia in the failure of a shoelace knot was published by The Royal Society A., Mathematical, Physical and Engineering Sciences.

Even prior to the official launch date of the paper, I was being asked for comment by news services from all over the world. I even participated in two BBC Radio interviews.

At the time of the interviews, the full research paper was still under embargo. All that I had to work with was the limited information in the paper's abstract. Only when the official embargo was lifted (about a day later) was I able to read the actual research paper.

The following is my detailed analysis – and criticisms – of this research.

Study Methods

The researchers' initial observations were that a shoelace knot – particularly one tied with a weak Granny Knot – often came undone fairly quickly while walking. However, that same knot didn't fail if the person either sat on a desk and swung their foot backwards and forwards a similar number of times without ground contact or if they stomped their foot on the ground a similar number of times without any swinging.

This suggested that the interplay of both swinging and stomping forces experienced while running or walking was required for a shoelace knot to untie itself.

High-Speed Video

Using a high-speed video camera, a person's granny-knotted shoes were filmed while running on a treadmill to observe the mechanics of what actually happened when the knot came undone. This confirmed that the “whipping” of the loops and free ends of the shoelace helped to pull the knot loose.

Controlled Experiment

A test rig was constructed, comprising a pendulum arm with a test knot attached. This arm was repeatedly pulled away from vertical and allowed to swing back to vertical and bump against a “wall”. This was calibrated to bump at about the same g-force as a foot striking the ground while walking (approx. 7 × gravity).

Testing involved repeatedly bumping for a 15 minute period – or until knot failure – and measuring the amount that the ends had slipped from their initial length.

Initially I wondered why their setup was oriented to bump against a wall instead of against the ground. The reason was not stated in the paper, but I'm guessing that this orientation allowed the loops and loose ends to hang downwards, simulating how those of a forwards-moving foot would be orientated ahead of the knot.

End Masses

In order to “magnify” the inertial effect of the free ends, masses were added to the ends. Testing with progressively greater masses from 1 gram to 3 grams produced progressively greater rates of slippage, and in turn, more rapid / frequent knot failure.

Finally, the knot was tested in various orientations: with the whole knot oriented at either the front of the pendulum or to the side of the pendulum, and with the loops and loose ends oriented either horizontally (“across the shoe”) or vertically (“along the shoe”).

Study Results

I won't go into the results in detail, as these can be found in full in the published paper. In general, their results quite convincingly corroborated previous “Granny Knot” tests as well as backing up my own advice that excessively long shoelaces are more likely to come untied because the loops and loose ends “flop around” more.

Their other finding – that the directions of both impact and swing influence the untying – is the subject of one of my criticisms, as detailed further below.

Criticisms of Published Results

What's interesting to me is some of the things that they didn't include in their paper:

No results were published for the number of “weak” knots (ie. “Granny Knots”) that failed completely without end masses attached. For the “strong” knots with no end masses, there was negligible slippage and zero total failures. It's possible that “Granny Knots” performed equally well (ie. zero failures). It's thus also possible that the testers resorted to adding end masses when their original test setup failed to give measurable results.
No images were published of the templates used to guide the tying of the knots. My own website shows three different techniques that produce the identical “standard” shoelace bow, while differences in the way the loops and ends are pulled or twisted during tightening further influence the finished shape and integrity of the knot.
No clear images were published of the knots before, during or after testing. The testing used black shoelaces, which are very difficult to observe, photograph or film. The usual shadows where shoelace segments overlap are lost in the dark, making it much harder to visualize those overlaps. The few images and videos that were published using those black shoelaces made it more of a challenge to interpret, verify or critique the experiments and results.

Criticisms of Testing Methodology

I have several criticisms of the testing methodology, including lack of scientific discipline, missing important contributing factors, or missing the whole point that “Granny Knots” are the chief cause of shoelace knots coming undone for the average person under normal circumstances (ie. without heavy attachments on the ends of their shoelaces).

Here's my four main criticisms:

Criticism #1

Incorrect Mounting of “Weak” Knots

The only published photo of the “weak” knot was one showing the two different orientations (horizontal bow vs vertical bow), part of which I've reproduced at right (vertical bow). As mentioned above, the black shoelaces lacked sufficient contrast to check the construction and placement of the knot. I've therefore Photoshopped the image to enhance the crossovers in the very centre of the knot.

Initially I was puzzled, as the image did not match any “Granny Knot” with which I was familiar. It took a fair bit of experimentation to discover what was wrong: their knot had been flipped from the usual orientation and mounted on the test rig inside-out.

Compare UC Berkeley's “weak” knot photo (above) against my four test photos (below), which depict either left-over-right or right-over-left “Granny Knot” oriented normally or inside-out (flipped vertically). The photos have been subtly colored to highlight those parts of the knots that are on the outside.

The closest match with similar looking crossings in the middle plus similar orientations of loops and ends is the right-over-left “Granny Knot” mounted inside-out (ie. the last photo).

Inside-out? How could this happen?

UC Berkeley's researchers used “A rigorous knot tying procedure and a template...”. An isolated shoelace was tied using a template to form an isolated “Granny Knot”. When completed, that granny-knotted shoelace was mounted onto the test rig.

Sadly, the rigor of the first step presumably wasn't carried through to the second step. The carefully-tied shoelace was not necessarily carefully-mounted.

Does the orientation matter?

Mounting a test knot with what is normally the outer, second knot (ie. the loops and loose ends) instead positioned on the inside and pressing against the yellow knot-mounting block would likely produce quite different results than those for a correctly mounted knot. That extra surface pressure would add holding friction to those parts of the knot that would otherwise be unrestricted and free to loosen naturally.

In that configuration, the test rig is no longer emulating the subject that it was designed to model. A real-world shoelace knot will never typically be flipped!

In addition, we have no way of knowing which of the test runs commenced with a knot mounted in a randomly-flipped orientation. Or maybe all were flipped?

Criticism #2

Rear-Impact vs Side-Impact Tests Flawed

During rear-impact testing, the ends – which are dangling downwards – partly land against the yellow knot-mounting block, altering and shortening their swing. In addition, the ends then collided with the lower part of the metal bar of the pendulum, sometimes arresting their swing and sometimes wrapping around that bar.

During side-impact testing, the ends would have suffered no such interference to their swing. Little wonder that the side-impact test – with its unrestricted end movement – resulted in greater slippage and knot failure using smaller end masses than the rear-impact test.

That said, I actually agree that the direction of impact could well have an effect. It just needs to be tested with fewer potentially interfering variables.

Criticism #3

Effects From Bottom of Knot Ignored

During each step in a typical shoe, the curvature of both the top of the foot and the shoe upper tend to flatten under load and are restored after push-off. Those curvature changes would in turn alter the angles of the shoelace segments entering the bottom of the knot, changing the knot's shape and friction profile.

However, in the test setup, the lace segments entering the bottom of the knot are kept straight, likely negating many of those important load+release effects. A setup that mimics the change in profile of the shoe upper during load+release could better explore those effects.

Criticism #4

Lack of Consultation

Multiple statements from the research paper and various press releases indicate the same lack of consultation:

We were able to show that the weak knot will always fail and the strong knot will fail at a certain timescale, but we still do not understand why there’s a fundamental mechanical difference between those two knots.

While the inferior performance of the weak version is well known in both common knot lore and surgical knot literature [1–4], we have yet to find a proposed structural characteristic to explain the inferior behaviour.

This is the first step toward understanding why certain knots are better than others, which no one has really done.

There are two ways to tie the common shoelace bow tie knot, and one is stronger than the other, but no one knows why.

Really? No one knows why? A quick Google or YouTube search for “Why shoelaces come undone” would have found plenty of information about “Granny Knots”.

They may have even discovered me – Professor Shoelace! The self-proclaimed world's shoelace expert. Inventor of several different shoelace knots. Whose website ranks #1 worldwide for shoelace-related queries.

Had they consulted me, I would have been happy to answer their questions, advise them in their research or peer-review their paper.

The fact is, I know exactly why a “weak” shoelace knot comes undone. Here's a brief paragraph that has been – in various forms – on my “Granny Knot” page since 2003 (fourteen years prior to the UC Berkeley study):

The difference is due to the adjacent contact points within the finished knot. In the balanced shoelace knot, tension on the bottom part of the knot (due to foot movement) will actually pull the adjacent top part of the knot tight. In the un-balanced “Granny Knot”, the adjacent contact points run in opposite directions, so the same tension on the bottom part of the knot will actually work the adjacent top part of the knot loose.

At the time of this UC Berkeley study, I'd long had one video on YouTube containing a close-up of the innards of a correctly tied shoelace knot, which I describe as “self-tightening”, versus a “Granny Knot” that “slips”.

I've since added a second video, which demonstrates the principles of adjacent contact points and shows exactly how an un-balanced “Granny Knot” simply pulls itself loose.

In closing, it's not that I'm peeved that they didn't ask my expert opinion – I really do believe that this constitutes a lack of consultation. Or maybe it's simply that scientific papers must only quote other published scientific papers – lending no credence to studies done by amateurs (such as “Professor Shoelace”).

Summary

This latest research by UC Berkeley was interesting to me. It delved deeper and probably with more scientific vigor than most previous research into why shoelaces come undone. The findings mostly bolstered previous findings and anecdotal evidence about “Granny Knots” and excessively long shoelaces.

That said, I feel that their testing was flawed in some areas, lacking in other areas, and that there was too much emphasis on the mechanics of untying rather than on the primary reason that so many people suffer from shoelaces that come undone – namely the “Granny Knot”.

When people read headlines such as: “Shoe-string theory: Science shows why shoelaces come untied”, or “Mystery of why shoelaces come undone unravelled by science”, they'd like to come away from the story having learned why it happens and – hopefully – how to fix it. An opportunity missed.