23 March 2018

More Yarn Management for Center-Out Circles

In yesterday's post, I wrote about how to create a gradient with evenly-spaced rings. Today's post is related. It still involves center-out circles and geometry.

Let's say you want to make a center-out circle. You have a pile of yarn that is all the same color, so you aren't concerned with rings or gradients or color effects. You just want to know how big a circle you can make with that pile of yarn. Is there a quick way to find out without playing yarn chicken?

The area of a circle = π r2

If we draw concentric rings, we can think about how much yarn is in each ring as compared to the whole project.

Recall our math:
  π 12 =    1π
  π 22 =    4π
  π 32 =    9π
  π 42 =   16π
  π 52 =   25π
  π 62 =   36π
  π 72 =   49π
  π 82 =   64π
  π 92 =   81π
π 102 = 100π

Another way of thinking about this is a circle that is twice the diameter of another will have four times the area. A circle that is three times the diameter of another will have nine times the area.

What does this mean for yarn usage and project planning?

Start by weighing the yarn. Then begin knitting (or crocheting) the center-out circle.
When you have used 1/100th of the yarn, stop and measure the circle. If continued, you should be able to knit (or crochet) a circle 10 times larger than the current one. You should be able to work 10 times the number of rounds. As with gauge swatches, making measurements over small areas can introduce larger errors. But, you can keep checking your work.

At 1/100th multiply diameter by 10.
At   1/81st multiply diameter by  9.
At   1/64th multiply diameter by  8.
At   1/49th multiply diameter by  7.
At   1/36th multiply diameter by  6.
At   1/25th multiple diameter by  5.
At   1/16th multiply diameter by  4.
At     1/9th multiply diameter by  3.
At     1/4th multiply diameter by  2.

(For those of you who want decimals, the progression for multiplying yarn weight on your calculator 1/100th = 0.01, 1/81st = 0.012345679, 1/64th = 0.015625, 1/49th = 0.020408, 1/36th = 0.02777778, 1/25th = 0.04, 1/16th = 0.0625, 1/9th = 0.11111111, 1/4th = 0.25.)

In the diagram above, the pink circle is one unit across, the blue circle is two units, and the green circle is three units. That means if you were knitting those circles and it took 1 skein to make the pink circle, it would take 4 skeins to knit a whole circle the size of the blue one or 9 skeins to make a whole circle the size of the green one.

The reality is that unless I were working with a very large quantity of yarn, I wouldn't trust my reading at the 1/100th mark. But I might trust my reading at the 1/9th mark. And I'd certainly trust the 1/4th mark. So you should be able to get an idea whether or not that shawl will really be the size you want — or whether you have enough yarn to knit all 300 rounds in the shawl pattern — without having to do a lot of knitting and then face the heartache of losing at yarn chicken.

And as with the concentric circles I discussed yesterday, this method also works with center-out squares, neck-down triangles, and half-circles.

22 March 2018

Planning a Gradient Yarn

Today I'm writing a little about geometry. Specifically, I want to show you what the r2 term really does to your yarn usage when you knit (or crochet) a center-out project.

If you have ever worked a center-out circle — or a center-out square, or even a neck-down triangular shawl — you may have noticed the project starts off quickly. Those first few rounds or rows just fly off the needles. And then the sprint turns into a run. And the run turns into a jog. And the jog turns into a crawl. And at the end, you find yourself spending an entire evening or more just binding off.

If you look at a circle, you can see that each round gets longer. The plodding tempo makes sense without getting into the math specifics. But what I want you to think about today is, "What does this mean for yarn usage?"

Let's say you want to knit a center out circle with ten individual skeins of yarn, each a slightly different color along a gradient but all the same yardage. What will happen to your stripes?

What happens is the stripes become narrower and narrower. (For those of you interested, there is a square root involved in radius/diameter progression. The numbers go 1, 1.4142, 1.732, 2, 2.236, 2.4494, 2.64575, 2.828427, 3, 3.162 as you track through the square roots of whole numbers.) If you keep knitting far enough, the gradient will "break," meaning it becomes so narrow that eventually a new color can't even complete one full round. For most people, this is not the effect envisioned.

Below is an example of the effect most people want.

The center circle is one unit in radius. The next circle out is three units radius. Then 5, 7, 9, 11, 13, 15, 17 and 19. The center circle and all the rings are the same width, just like a target bullseye. What does this mean for yarn usage?

The area of a circle = π r2

So the area of the center white circle is π 12 = 1π.
The next circle is π32 = 9π. But we want the area of the yellow-orange ring, not the area of a whole circle. That means we have to subtract the white center circle from the yellow-orange circle.
9π − 1π = 8π.
So if you used 1 meter of yarn to work the white center circle, you will need 8 meters of yellow-orange yarn to work the first ring. If you used 3 meters of yarn to work the white circle, you will need 24 meters (3 × 8 = 24) to work the yellow-orange ring.

What happens if we extrapolate the math for the whole figure?
  π 12 =    1π
  π 32 =    9π         9π   −   1π =  8π
  π 52 =   25π      25π   −   9π = 16π
  π 72 =   49π      49π  −  25π = 24π
  π 92 =   81π      81π  −  49π = 32π
π 112 = 121π    121π −   81π = 40π
π 132 = 169π    169π − 121π = 48π
π 152 = 225π    225π − 169π = 56π
π 172 = 289π    289π − 225π = 64π
π 192 = 361π    361π − 289π = 72π

Interestingly, this same proportion works for squares, triangles, and half circles.

Area of a square =  a2, where a is the length of a side.
If you draw out the squares, you get the same effect, with the center square being 1 unit on a side, the next square is 3 units on a side, the next 5 units on a side, and so on.

A neck-down triangular shawl is just a square rotated 45° and cut in half. A half-circle shawl is just a circle cut in half. It is the same proportions, since the extra "½" just carries through all the calculations.

How does this affect planning for a project?

If you are purchasing skeins (or making up kits), you will need much larger quantities of yarn for colors farther out. If you are doing your own hand-dying, you can wind off appropriate amounts to produce the desired effect. If you wind 10 meters for the center, then wind 80, 160, 240, 320 and so on for each progressive ring. If you wind a more random amount — say 7 yards — then the progression is 56, 112, 168, 224. You just multiply your beginning amount by 8, 16, 24, 32, and so on.

If you have purchased a gradient yarn or kit, be aware of which type of project will best suit the yarn. If the color amounts are graduated in length, a center out circle, square, or neck-down triangle will work well. If the color amounts are the same, however, consider a scarf, blanket, socks, sweater in the round, or some other pattern where the rows or rounds are close to the same size throughout the project.

Tomorrow: more tips of planning center-out projects when you have a limited amount of yarn.

05 March 2018

Craft History at UGA

On Saturday, I traveled to the Georgia Museum of Art on the campus of the University of Georgia to tour "Crafting History: Textiles, Metals and Ceramics" at the University of Georgia. The tour led by curator Ashley Callahan was organized by Southeast Fiber Arts Alliance.

I hadn't given academic crafting much thought. The exhibit tells the history of craft instruction at UGA. If you attended the university or are familiar with craft history in Georgia, then I think you will enjoy the exhibit even more than I did. Teaching craft is often about innovation. Innovation comes from play. Expanding your skills within your craft often means learning and exploring new techniques. Students and instructors ask, "What if . . . ?" In a group environment, you can crowd-source the solution as different people explore different possibilities.

Wiley Devere Sanderson Jr. yardage, no date (1950s?), detail
Touring with a group also taps into group knowledge. For example, we looked at Wiley Devere Sanderson Jr.'s woven yardage. Suzi Gough, weaver and founder of SEFAA, remarked that the fabric looked like Bedford cord. Bedford cord is a textured weave structure that produces furrows running parallel to the warp. But when we got close to the fabric, we could see it was flat. I posit this may be an experiment in trompe l'oeil texture. The color is in the warp stripes. As best as I can tell, this fabric is tabby (plain) weave worked with a single-color weft (medium-dark green) — i.e. using only one shuttle. It could be executed on a 2-shft loom or rigid heddle. Easy! In the close up, notice the variety of carefully-chosen shades and tints of green. The orange-red color is almost a complementary color. The careful choice of color creates the illusion of texture without the work of a more complicate weave structure. Clever!

Glen Kaufman, Shaped Rug, circa 1976, detail of pile
Another piece utilizing color is Glen Kaufman's Shaped Rug from about 1976. Mr. Kaufman purposely disrupted the typically rectilinear form of the rug. You'll have to see the exhibit for yourself to see what I mean. In this detail, you can see the pile has been cut to different heights. And all the color is optically-mixed, since each color area has yarn of different colors. This rug really needs to be viewed in person, as the violet nearly glows. I would love to know the source of the yarn and dye, as it is still radiant 40 years later.

Edward S. Lambert, untitled, no date (1970s?), detail
Silk painting is a technique I have much admired by never tried. Edward S. Lambert's untitled piece has mandala-like geometric forms. The museum label mentions his interest in nature at the microscopic level. The fractal fringes of the shapes do seem derived from nature. The geometry provides an over-arcing organization, but the details seem chaotic and free. Once again, I'm showing you only a detail here of a larger piece. And as this is silk, the fabric is diaphanous, responding to even minuscule air movement.

Ken Bova, Welcome to the
Montana Grad Trap
, 1979
The exhibit includes ceramics and metalwork as well. There is a medallion and scepter set that for decades was used to inaugurate new presidents at UGA. The regal effect of these accoutrements reminds me of a modern take on Ingres' 1806 portrait of Napolean on his Throne. The bit of metalwork I want to show you here, however, is a ring — Welcome to the Montana Grad Trap by Ken Bova. The "publish or perish" system in academia means professors of craft need to exhibit their work. Metalwork faculty across several universities organized an exhibition of rings, which then traveled from campus to campus. This allowed them to pad out their curricula vitae by listing every venue. In other words, they very cleverly gamed the system. The ring case is well worth your time, as careful inspection will uncover wit and innovation. Rings make a great starting point for experimentation, as they are small and do not necessarily require a lot of time or material. In this way, they remind me of SEFAA's annual Square Foot Fiber Pin-Up Show. The ring case is full of the sort of play experimentation that results in breakthroughs. And it will challenge your idea of what a ring might be.

"Crafting History: Textiles, Metals and Ceramics" is on display through Sunday 29 April 2018. If you find yourself over towards Athens, give yourself an extra hour or two to explore this exhibit. The creativity and variety may inspire.