## Shawl Math

Posted onI had a phone call with a potential employer the other day and I found myself trying to explain one of the ways that I use my mathematical and forecasting skills in a situation where someone else might not recognize the opportunity. They make perfect sense in my head, but sound a little bit rambling when I try to explain them. Putting these instances in writing, with examples and diagrams, can only help. The example that came up on the phone was from my time with Mochimochi Land, and I’ll cover that in a future post. Today, I’ll stick to something more current.

I recently started knitting the Nurmilintu shawl out of some beautiful gradient yarn. The wedge shaped shawl alternates between solid garter stitch and panels of lace. When I finished the first garter section, I still had quite a bit of yarn left. In general, that’s a good thing, as it’s better to have too much yarn than not enough. In this case, however, failing to use all of the yarn would mean not using what I considered to be the prettiest color at the end of the gradient. So, last night, after finishing the first section, I stopped, weighed my yarn, and made adjustments using a Google spreadsheet. (I miss Microsoft Excel, but can’t justify the expense.)

The first step was to count the stitches in the shawl. It starts with a cast-on of four stitches. On odd rows, there’s an increase at the beginning of the row and a decrease at the end. The stitch count doesn’t change. On even rows, there’s only the increase at the end of the row and the stitch count increases by one. So, every pair of rows, the stitch count increases by one. The instructions are to repeat these rows until there are 79 stitches. 75 repeats (150 rows) will accomplish this. Using the geometric formula for the area of a trapezoid, the total number of stitches is:

(150 rows) * (4 stitches + 79 stitches) / 2 = 6,225

Making the same calculations for each section, I ended up with a total of 20,720 stitches. So, the first section of the shawl represents 30% of the stitches. Weighing what was left of my 100g skein of yarn, I found that it was only 25% used up.

My first thought was to add an additional section, as suggested by the pattern. I was able to try this out on paper. Each garter section after the first is 36 rows long (+18 stitches) and each lace section is 18 rows (+9 stitches). This would increase the total to 29,225 stitches and that would mean that I was only 21% through the pattern with 25% of my yarn gone. So, not an option. Instead, it made sense to increase each section.

If my first section (6,225 stitches) took 25g of yarn, then 100g of yarn should get me 24,900 stitches. I set my calculations up in a spreadsheet, multiplying each row length by the same factor and then adjusting that number to get close to 24,900.

- First of all, I added two more rows at the end to account for binding off the stitches. Three might make more sense, as it’s important to bind off a lace project very loosely.
- Secondly, while the garter sections can be any length, the lace sections need to follow a chart. This limits them to a repeat of six rows.

If I needed these calculations to be more robust – for example if this blog post results in a lot of knitters asking me to make custom pattern adjustments – I would set this up with a bit of code and/or formulas. As I only needed this answer once, the sheet is set up to require a little trial and error on my part to get to the optimal number. Once I knew that the adjustment would be small, I hard-coded the number of lace rows at 18 and then recalculated the adjustment for the garter rows only. When I was happy with the closeness of my number, I replaced the calculated row counts with the next-lowest even integer.

It’s also important to remember that knitting is pretty variable in practice and the amount of yarn I’m using can vary. For this reason, I tried to keep the estimated stitch total well under 24,900. I also calculated how much yarn should be left in the skein at the end of each garter section. That way, I can check and adjust my estimates as the project continues, and I’ll be more likely to succeed in using all of the blue yarn without running out.