More Enhanced Hanson Knots

[Dennis Pence]

In a previous discussion about the Hanson Knot, some enhancements were proposed near the end of the discussion.
    Hanson loop knot   https://forum.igkt.net/index.php?topic=7278.0

I was motivated by how Ashley moved to enhance the Overhand Noose [#1114] by moving to a Figure Eight Noose [#1116], then by moving to what could be called a Figure Nine Noose [#1118}, and finally by moving to what could be called a Figure Eleven Noose (Ichabod Knot) [#1123].  I explored what you can get by replacing the Overhand part of any knot in the Hanson Family with a Figure Eight or a Figure Nine part.

The original Hanson Loop is not very secure under "ring loading."  In fact, if you have trouble untying a Hanson Loop, try "ring loading" the loop because this tends to loosen the Overhand part.  The following two diagrams show how I found it best to replace the Overhand part with a Figure Eight and a Figure Nine.  Both hold better for moderate "ring loading". 

[Dennis Pence]

Each of these enhancements can also be make to the Hanson Inverse Loop (which is so popular on the Internet).  First, here is the connection between the Hanson Loop and the Hanson Inverse Loop.  The Hanson Loop starts with a Crossing Turn (first diagram, this was Alden Hanson's notation for this part).  Then you finish with the Overhand part (second diagram, how a right-handed person might tie this).  The third diagram is the mirror-image Hanson Loop (as a left-handed person might tie it). The only change with the next diagram is to switch the standing part and the free end, giving the Hanson Inverse Loop as a right-handed person might tie it.  Finally in the last diagram we show how the Hanson Inverse Loop starts with an Overhand Knot.

We then do this with our two enhancements.

[Dennis Pence]

Most are not familiar with a Reversed Figure Nine which is how you need to begin with the last inverse above.  You begin with a regular Figure Nine [ABoK #521, which Ashley calls an Intermediate Stopper].  Without untying, you "flip" the knot to get the Reversed Figure Nine Stopper Knot.

[Dennis Pence]

If you do not intend to have any ring loading, here is a variation for the Figure Nine version.  For larger, stiffer rope, I like to tie this Hanson Figure Nine Loop B with the free end.

With smaller, more flexible cord, you can use the method that Ashley suggests for his Figure Nine Noose [ABoK #1118].  Tucking in this fashion a second time gives something similar to the Ichabod Knot [ABoK #1123].

You can do the same tucking with the inverse, but I don't understand why you would want all of this extra wrapping with the part coming from the standing part rather than with the part near the free end.

[Dennis Pence]

The suggestion from Heinz Prohaska (he claimed prior credit for what we call a Hanson Bend and he called a Ram Head Knot) was to replace the single Overhand part with a Double Overhand part (his Double Ram Head). {See the March 2006 issue of Knotting Matters.}  When he tied this bend, he put both wraps of the Double Overhand part inside the Crossing part.  Based upon what we saw from the Figure Nine enhancement and the Ichabod enhancement, we can suggest variations using a Double or Triple part where only the first wrap goes through the Crossing Turn.

[agent_smith]

Hello Dennis,

With respect to your "reply 1":

You use the word mirror to describe what I see as a transposition.
In my view, the term 'mirror/mirror image' implies opposite chirality (like holding a knot up to a plane mirror and the reflected image is of opposite chirality).

I suggest that the term "transposition" may be more appropriate.

The S.Part is transposed with the tail segment.

[Dennis Pence]

Hi, Mark,

Sorry to disagree, but I think that the diagrams I have labeled Mirror or Mirror Image do change the chirality (without changing the standing part and the tail/free end) compared to the diagram to the left. (I used my drawing program to get this mirror image.)  Then the next diagram does change the standing part and the free end (what you call a transposition) from the mirror image.  I was trying to show the relationship between the original, primary Hanson Loop Knot in the patent document and what most people now call the "Hanson Knot" which appeared second in the patent document and is really a mirror-transposition of the original.  Alden Hanson thought of all knots with the same structure as being equivalent, and he even included bends.  What he was really patenting was a knot structure or family rather than a particular knot.

Mathematicians think of x as the input for a function named f and think of f(x) as the output.  The inverse function f^-1, if there is one, takes you back or switches the input and the output.  Knot tyers often think of the standing part as the input for the knot and the free end as the output because you usually do most of the tying with the free end.  Thus, they think of the inverse knot as having the same structure but the standing part and the free end have been switched.  We do not usually think of the mirror image as a different knot, but the transposition (switching the standing part and the free end) definitely gives a different knot.  I like using the term "inverse" but if you prefer the term "transposition" I am OK with that.

[agent_smith]

Without a specific image - its hard to agree or disagree about anything.

I've attached an image to illustrate exactly what I mean by "transposition".
With words alone, it is hard to achieve a clear and definitive exchange of ideas.
The attached photo below perfectly encapsulates what I was trying to explain in my previous post.

"B" is a transposition of "A" (and vice versa).
They are not 'mirrors' of each other.

Also, just in case  of any possible misinterpretations, I am not accusing or implying anything (we live in a strange era where people get offended by anything).
In other words, I am merely positing what I see as a "transposition".
That is, I am introducing the term "transposition" - to describe what is going on with knots A and B - and I am unaware if that term has been used before?

And this ties in nicely with the relationship between bends and eye knots.
To derive 8 possible eye knots from a 'parent bend': 4 will be derived from the principal linkages, and the remaining 4 will have undergone a transposition.

[Dennis Pence]

I agree.  The transposition doesn't always give a dramatically different knot, but in the case of the Figure Eight Eye Knot, the two have slightly different difficulties of untying.  In my limited tests, the one below on the left (where the standing part is "inside" at the bottom of the knot) took about 17 seconds to untie while the one below on the right (where the standing part is "outside" at the bottom) took about 30 seconds to untie.  I did similar tests with a Figure Nine Eye Knot and found that the "inside" version took about 23 seconds and the "outside" version took about 34 seconds.  {My big complaint with the Figure Nines was how long it took to correctly tie them and how difficult it was to get the wrappings to be entirely smooth.  When you failed to do this perfectly, it could take over a minute to untie them.  Thus, the standard line that the Figure Nine Eye Knot is easier to untie (see NetKnots.com) is definitely false.  But an optimally-tied Figure Nine Eye can easily beat a poorly-tied Figure Eight Eye.}

[alanleeknots]

          Hi Mark
                     Very often when I create a knot, regardless if it is a good or bad knot.
                      I apply a load to the tail and check on it a lot of times.
                       I find some good maneuvering ideas that enrich my knot-tying skills.
                        Or sometimes even find A very nice knot with no effort.
                     Thanks for introducing the term "transposition". I like it.  alanleeknots

[agent_smith]

Thanks Alan.
I had been thinking about Either End Loading (EEL), chirality, and loading profiles for a while.
My work with the relationship of 'bends' and 'eye knots' led me to the idea of 'transposition'.
And then I noticed Dennis's posts and the 'Hanson' knot.

Here is the original patent for the 'Hanson' knot.
Link: https://tcscouts.org/roundtable/inventing/US4711476.pdf

Dennis - I note the spelling is Hanson (not Handson).

I must admit that I was dubious and sceptical as to how 'art' could be patented (it is a "US' patent and anything is possible in the USA!).
I did not think a 'knot' could be patented - and indeed, in some countries it is not possible.
Rather - 'Copyright laws' normally protect works of art.

I also have to be honest and say that I don't really care much for the 'Hanson' knot.
I note in the patent that the descriptions of the geometry use non technical novel descriptors and fail to mention
the use of a 'Crossing hitch' which is one of the key elements to prevent jamming.

Chirality is not specifically mentioned although there is a reference to a 'mirror image' - so Hanson was
likely thinking about including mirror reflected versions of his knot just to cover all the possibilities in his patent.

[Dennis Pence]

Mark,

Thanks for the spelling correction.  I sometimes type too fast! (I have corrected it.)

The original patent is also available at the US government site (uspto.gov) where you can do a search for the patent no. 4711476.

If you do a search there, you find that Alden W. Hanson applied for many patents.  I have a letter (written after his death, promoting the knot to Michigan scout councils) that seems to indicate that he was somehow associated with Dow Chemical Co. in Midland, Michigan.  Thus, he was very familiar with the patent process.  I don't think he was serious about restricting access to the knot as much as he wanted to publicize the knot and scouting.  (Apparently, he was an adult scout leader.)  Notice that he labelled the parts of the knot with the 12 points of the Scout Law.  The letter says that he donated the patent to the Boy Scouts of America.

I have a copy of the 1989 printing of the booklet "Knots and how to tie them" published by the Boy Scouts of America, where some of the patent diagrams have been printed.  More recent editions and printings still have these.  Oddly, they printed Figs. 9, 10, and 1 first, and named this the Hanson Knot.  Then they printed Fig. 5 (rotated 180 deg, mislabeling the standing part and the working end), Figs. 6, 7, 8 (rotated 180 deg), and 3 next, naming this the Handon Knot (Variation).  I think it is much easier to tie the variation (which is my preferred version) using the method Alden Hanson gives in Figs. 20 and 21.  The scout booklet's way of presenting the variation (particularly the rotations) makes it very hard tie the knot.

You can consider the Hanson work in Figs. 28-34 (where he used the points of the Scout Law to label the parts) as in the spirit of your work connecting "eye knots" and "bends" although he was not as complete there (and the bend and tie-ins are not completely clear).  Of course he was moving from his various eye knots to bends, and you, Mark, like to go the other way.

I consider the publications in IGKT Knotting Matters (2004, 2005, 2006) related to the knot to include the early effort to enhance the knot by Heinz Prohaska.