The math and physics of knitting

  

https://www.sciencenews.org/article/how-one-physicist-unraveling-mathematics-knitting

I know this wanders around a bit, but the bottom line is in the last paragraph.

 I would put good knitting up; not just with Knot Theory, but with advanced multidimensional  Manifold Theory.  Instead of a thousand page mathematical proof, the competent knitter produces a better and more useful object, likely a garment.

 

Moreover, folks doing knot theory/manifold theory, deal with continuous sets of numbers, while knitters deal with quantum stitches, that have sizes and locations that depend on a large number of variables. Quantum physics is more difficult than knot theory.

 

Mathematical knots and manifolds have abstract forms, such that a line has zero width and a plane has zero thickness. Yarns on the other hand  have real thickness which may not be constant during use, and yarns may change its length in use.  Some yarns material stretch in use and some shrink in the wash, or when you dry your wool socks too close to the campfire  : (   Some yarns (hemp, cotton) get shorter as they absorb water and many yarns get heavier as they absorb moisture, which changes their fit and drape.  And, some yarns tend to untwist and fall apart when they get wet.

 

Then, there is the nature of the yarn. Twist holds yarn together.  More twist, and the yarn is more durable, more elastic, and more stable. However, put a lot of twist in a thick yarn ply and you get “barbed wire”. Yarns designed to be durable have more and finer plies (with high twist), that are then plied together or plied and cabled  (plied yarns twisted together).  Twist is very expensive – mills competing on cost put less twist in their yarns. (And try to disguise their motive by bragging about how fluffy and soft their yarns are.)

 

Wool has scales that tend to lock the fibers together giving the fabric great durability. “Washable” wool yarns have the scales chemically removed, and have less durability.  Nylon is cheap, slippery, and strong. Wool does not grab on to nylon and nylon does not hold wool, so the addition of nylon reduces the durability of wool fabrics – the wool abrades off and you are left with a net of  nylon fibers, so you assume that nylon must add to the durability of the (sock).  No, it is a cheap filler that facilitates wear, so that you buy more socks.

 

All of that is theory before we get into practicality. I have 2 men’s sock patterns, one by a London fashion editor (Mary Thomas), and the other from a yarn mill (Briggs & Little) that caters to people knitting serviceable objects for people working in the cold. The patterns differ by 4 stitches in the heel. The slightly wider heel in the pattern from B&L  is MUCH, much more durable than the narrower heel from Mary Thomas. Small changes in a knitting pattern can result in large differences in the object’s serviceability and durability.

 

The use of different yarns can affect durability and comfort the as much as the stitch pattern.

Yarns with low twist plies tend to be soft and weak. They produce fabrics that are not particularly warm. They are for fashion. Fashion is not expected to endure. If one wants a sweater that is very warm and durable, knit it from a yarn built up from fine plies. If you want a sweater for a dramatic sportive look to wear in a centrally heated pub use a softer spun, more bulky yarn. The real sailor’s sweater will be too warm to wear in a (heated) pub.  (A weatherproof sweater can be designed to vent when the wearer is warm and not vent when the wearer’s skin is cold. These designs only work with weatherproof fabrics. Such venting can reduce the need to layer garments.)

 

 On the other hand, the less dramatic stitch-work in the real seaman’s sweater will be more effective padding when you are storm tossed against spars and rails at sea (or in the “slot” on SF Bay). And, the real fisherman’s sweater will be “weatherproof”.  You can wear it in the rain, and it will be warm and it will feel warm and comfortable. (If vented, the venting may allow a cold stream of water to run down your back.)  In heavy or wind blown rain, you may feel the rain, but such storms do not last long, and when the deluge diminishes to an ordinary rain, then within 15 minutes, you will feel warm and comfortable. Likewise a “garage sale” fall while skiing may allow snow under the sweater, but once the snow has been scraped out, a few minutes later the sweater is comfortable.   That is; a thin layer of fabric next to the skin has dried, and the garment again is warm and comfortable.

 

Such fabrics require wool fibers to be densely packed (e.g., ~spacing between wool fibers less than 40 microns). This slows air flow through the fabric and stops most liquid water.  If we think of a knitting needle as a lever for moving loops of yarn,  and  calculate the leverage available, and the muscles available to provide power; then, hand held needles (cable needles or single point needle or DPN)  have very limited leverage (e.g., 1:3) and are driven the small muscles of the hand via the fragile tendons of the wrist. However, if one end of the working needle is supported, than the available leverage is much higher (1:10).  In the picture of Elisabetta Matsumoto knitting, her working needle is supported by a knitting belt (not visible) and the work is driven by her shoulder muscles.  A knitting belt is the fastest proven technique for hand knitting.

 

The Fair Isle stitch pattern she is knitting has a second strand of yarn carried behind the fabric, which greatly increases warmth of the fabric, which advantage is offset by less stretch.  Traditional Shetland Fair Isle knitting was done with rather fine 2-ply yarns, and the fabrics were warm, light weight, very low bulk, and  well suited for the climate.  A similar knitting technique was used for “weaving” vests which produces a similarly warm fabric/weight with slightly more stretch.

 

The invention of the square rigged ship, some where in the vicinity of the Channel Islands circa 1,000 AD, demanded some way to keep active sailors warm above deck, even in foul weather.  Hence, what we know today as “fisherman’s sweaters”.  Production of such sweaters require the use of knitting sheaths to support the working needle. Knitting sheaths give the knitter more leverage, and allow tighter knitting.

 

Many of the traditional fisherman’s designs make use of the different properties of different stitch patterns used next to one another, to improve the over all characteristics of the object. For example basket stitch used between bands of purling to make a sweater that well suited to rowing or hauling a line.  It is also fast and easy to knit, so it was very popular and was known as “Lizard Lattice”. When such combinations are considered, there are a very large number of useful knitting stiches.

 

Such hand knit sweaters, kept Shackleton’s men warm in their year (1914 -1917) on the Antarctic ice.  And, they have enough stretch to allow sailors to preform acrobatic work. Objects hand knit with a knitting sheath can be truly “weatherproof”. The last large group of people to knit using knitting sheaths were men on British destroyers in the Pacific during WWII. They knit to pass the time while on battle stations. They hated that knitting because someone was about to try and kill them. They  loved it because, if they were still knitting, nobody was actually shooting at them.

 

In the period 2005 -2010, several of the old British mills producing the dense yarns used for the traditional fisherman’s sweater had failures of their 100-year old spinning equipment and they stopped producing such yarns.  When I started hand spinning such yarns, I was told it was impossible and had never been done.  In fact, such yarns had been spun in the past, and they can be seen in any museum with a good textile collection.

 

The standard text on modern knitting techniques is (The Principles of Knitting) , and the author teaches the history of knitting sheaths, but does not know how to use knitting sheaths. 

 

I think that from 1,000 AD, until ~ 1840 AD thousands of bright eyed, nimble fingered knitters somewhere between the Shetlands and Lisbon were doing what Elisabetta Matsumoto and her advisors would consider graduate level, university physics. Those knitters could run their hands over a departing fisherman, and when the fisherman returned, he would have a fisherman’s sweater well suited to his duties on board, the climate where his ship fished, durable enough to last a fishing season; and that sweater was knit to fit.  These are a set of skills we have lost.  Elisabetta Matsumoto does not even know that weatherproof wool fabrics can be knit.

Good sock yarn

 I like good socks.  Good socks require good yarn. I do not like the commercial yarns that I see in retail yarn shops or fiber festivals.  Thus, often I spin my own sock yarn.

However, sometimes I buy 2-ply/ 5,600 ypp weaving warp, and ply (cable) it up into sock yarn.

Weaving warp in various grist is often available very inexpensively as "mill ends".  

For the last 10 years, this has been my source of "commercial" sock yarn. I buy 2-ply warp, and cable it up into sock yarn.  Today, I think this is the easy approach to a Sheringham gansey. A Sheringham is enough knitting effort, that you may as well use a very good yarn. 

Mostly, I get such yarn from :   http://www.mitzis-yarn-weaving-knitting.com/

(I am her customer - no other relationship.)

Better yarn

 I started spinning circa 2006, because the venders that sold me the "gansey" yarns that I loved were closing. It took me years to get/make the spinning equipment that I needed, and more years to learn how to use it. I assure you that having the right spinning gear is half the battle. 

With the right gear, I can sit down with a bin of wool, and quickly spin the yarn needed for a good British Seaman's sweater. Those knitting yarns were based on 5,600 yards per pound worsted spun singles as a 5-ply. Or, I can spin 6,000 ypp singles and make a 1,200 ypp like most modern "gansey" yarns such as Frangipani. Or, I can ply up those 5,600 ypp singles as 4-ply to make a nice yarn at 1,260 ypp.

I do not need fancy wool.  After much comparison and testing, I think buying raw fleece and scouring it, oiling it, and combing it myself produces the best fiber for hand spinning. Much of the commercial fiber is treated to reduce crimp.  However, the Heinz-57 wool sold by the Woolery, can produce an excellent produce if I wash it, oil it, and comb it.   It really can be spun into fine lace yarn, and it makes good yarns for socks, hats, sweaters, and whatever.  I have spun a thousands yards of "good" singles in ~5,6000 ypp range from it right as it comes out of the bag.  It does not spin as nicely as fiber I process from the raw fleece, 

Key to this is that: Mostly, I spin worsted.  One of our famous spinning teacher tells how when she was a girl, there were 2 ways to spin. There was worsted, and the wrong way.  Woolen, semi-woolen, and semi-worsted were not acceptable. The the famous teacher goes on to tell how wonderful it was to learn all the other spinning techniques.

I accepted her wisdom, and learned all of the different spinning techniques.  I used those techniques to spin different kinds of yarns, and I knit the resulting yarns. I used the resulting objects. And, I relentlessly moved toward spinning worsted.

There are 4 reasons:

1) Speed of Spinning: A double drive spinning wheel with differential rotation speed between the spinning bobbin and the flier, allows spinning worsted as fast as it can be drafted. And worsted can be drafted as fast as the wheel can insert twist. A  double drive spinning wheel with differential rotation speed between the spinning bobbin and the flier can insert twist much faster than any other kind of  wheel or spindle. Worsted needs less twist than woolen or the "semis" and thus over all can be spun faster.  On my modified Ashford Traditional, I can spin a hank (560 yards) of 5,600ypp worsted single in Alden's golden hour of 48 minutes. In 5 hours by the clock, I can spin the 5-hanks of worsted single needed to ply into 500-yards of real gansey yarn.  Woolen spun yarns need 30% more twist, so it takes  me 6.5 hours by the clock to spin woolen singles of the same grist.

2) Durability: Twist holds yarn together. Twist a fine single, and you have a strong, elastic thread.  Put the same twist into a thicker single, and you have barbed wire. Put the twist necessary to make the thicker single a competent yarn, and there is not enough twist to make the object as durable as one fabricated from fine singles (plied together). Yes, spinning high twist yarns and plying them together is a lot of effort, but not as much effort as spinning twice and knitting twice because the object was not durable.

3) Drape of the Fabric: Woolen spun yarns do not lend themselves to fabrics with graceful drape. Woolen fabrics tend to hang.  

4) Warmth:  Fabrics from woolen spun yarns tend to have more bulk and less warmth. Many, including famous spinning instructors, confuse bulk with warmth.  Woolen objects that have been tightly woven or knit, then fulled (related to felting) can provided great warmth, but fulling takes away much of the elasticity, and comfort of the fabric.  If you want elasticity and wearing comfort, and warmth, use a worsted spun thread to make the  fabric.  

 

 

Here is a photo of a sock in progress, being knit at a gauge of 12 spi x 20 rpi:

The needles are 12” US 000; the yarn is 6-ply (cabled 3 x 2) 1680 ypp, with light ply  twist so it is very  splitty, but gives great fill.  There is lots of twist in the yarn plies so it does not need nylon. This yarn is a bit more durable than the 4-ply Behive that was traditional for Sheringham ganseys, but the Behive produces a softer fabric on these needles. (Mills put nylon in socks, because nylon is cheaper than wool and the extra twist that makes wool more durable.)

 

Note the blunt needles. These make the knitting motions much smaller; and thus, much faster. However, knitting this tight, if I drop a stitch, I need a crochet hook (that green thing) to fix it. This is not knitting I can do in a dark movie theater.

 

This is one of my favorite fabrics. It is NOT “weatherproof” but is very warm, light, elastic, with a lot of  cushion.

The knitting sheath for this project is on the left. It is not a traditional design, but with adapters, it works for any size or length of needle, and thus allows many different knitting techniques.

 

 My knitting diary is  on the right.

 This is the second sock of  the pair, but the first sock was not handy to photograph.