Knitting Math by KimB

Knitting is a popular activity. Knitting requires physical, mental and artistic abilities all at the same time. Using colored yarns and various methods of looping the yarn in rows along a sticks of various dimensions and shapes, knitters create clothes, blankets, tapestries, toys and lots of other items. The famous Weasley Jumper(Sweater) being a common holiday gift in the Harry Potter series as an example.

For the most part, knitters concern themselves with the number of stitches and where to make a loop change. They use repeating patterns to create cables and designs. What they don't consider is Physics.

Well, the Physicists are taking notes and it turns out knitting is pretty darn complex. They love it.¹

There are several interesting areas:


Strechiness

Elasticity or Stretchiness. Yarn by itself is not very elastic but when knitted into a sweater or socks it is very elastic and can stretch as much as double the individual lengths. The type and way the loops are formed creates stretchiness.

Material Properties. The end product displays properties beyond that of the base material used. Taking a one dimensional shape (yarn) and turning it into a multidimensional object (sweater). The sweater has many times the strength of the individual yarns or loops.



Smocking Variations²

An embroidery technique called "smocking", used before elastic was developed, gathers fabrics in a way that it can be stretched.² By using various knots, smocking creates a bending energy that translated into stretchiness. A smocked cuff can expand and then contract. A gathered/smocked cuff shirt is almost a required costume for any production of Hamlet.

Knitted knots are interlocking slip knots looped back and forth. A knot pulled to the front is a "knit stitch" and a knot pulled to the back is a "purl stitch". Combining front and back knots creates the pattern and linking them in different ways creates 3D shapes.

Each stitch or pattern yields a different amount of elasticity. Not only does it expand but it returns to the original shape. The amount of "give" depends on how many stitches are linked or crossed over the neighboring loops. Physicists are working out the math that goes into how a single thread of yarn becomes a bendable knitted item and how much stretchiness it will display. Once they sort it all out, they can use predictive modeling for new materials and new applications for knitted items.

Analyzing Weasley Sweaters is just the start.

Knitting Slip Knot

References

1. https://arstechnica.com/science/2019/03/physicists-are-decoding-math-y-secrets-of-knitting-to-make-bespoke-materials/
2. https://en.wikipedia.org/wiki/Smocking
   
   

   Smocking Stitches
   A	Cable stitch
   B	Stem stitch
   C	Outline stitch
   D	Cable flowerette
   E	Wave stitch
   F	Honeycomb stitch
   G	Surface honeycomb stitch
   H	Trellis stitch
   I	Vandyke stitch
   J	Bullion stitch