Knitting for Engineers II - Proportionality

In an earlier post, I started giving some tips on how to break away from a pattern and adapting it to your own needs. Once you have the schematics of each piece of your garment with the proper measurements and your gauge, you are ready to go. After that, it's all a question of proportionality.

The simplest illustration of the method is my skirt/poncho.

The original gauge (given in the pattern) is:
16 sts = 4''
20 rows = 4''

My gauge (from swatching) is:
20 sts = 4"
30 rows = 4"

Knitting patterns tell you to adapt your needle size to match the gauge. This is a lot of work as you work by trial and error to get the right swatch, and is limited as you can only go one needle size or so up or down. Going too small will result in a very tight weave, uncomfortable to work with and stiff. Going too large will result in a loose weave, a garment that won't be as warm and won't hold its shape.

I very rarely adapt my needle size to obtain the gauge. Instead, I adapt the pattern to my gauge. That is fairly easy to do, and by the same token, I can adapt the size.

This skirt/poncho is a simple pattern. We begin by casting on the proper number of stitches to get the waist measurement desired and then do regular increases. The task at hand is:
1) Figure out the original waist measurement
2) Change the number of stitches we cast on to obtain the waist measurement we want
3) Adjust the increases according to the differing gauges.

1. Figuring out the original waist measurement

This is apparently given in the pattern: 24'' for the smallest.
We can check from the gauge and number of stitches to cast on. We are told to cast on 108 stitches. According to the gauge, that is 108/16 * 4'' = 27''. So we learn something here: the gauge is for the stretched measurements. 27'' is the actual waist measurement.

2. Adapting to the measurements we want

The measurements I needed were smaller than that. I went with 25'', stretched measurements. Now we use my gauge to figure out how many stitches I had to cast on:
number of stitches to cast on = 25/4 * 20 = 132 stitches (to make it an even number)

Here I cheated by noting that this was close to the number of stitches for the Medium size and went with that (126 stitches). For a more involved pattern, this would have allowed me to use the prescribed numbers of stitches for the medium size, instead of having to figure it out on my own from the measurements and the gauge. In the end, I am glad I went a little smaller. The skirt (would I wear it as such) is just snug enough around the waist.

You noticed by now that this is not very precise. Normally, you would want to be more precise (stick to the 132 stitches found), but this is a pattern that is forgiving, given the highly elastic waist ribbing, and the fact that the garment doesn't follow the body snugly otherwise.

Now you may wonder: "How did going for a size smaller than XS result in having to follow the directions for Medium?". If you have experience knitting or are just good with numbers, you will notice that my gauge requires more stitches to make 4'' than the original one. The yarns and needles I used are smaller than what the pattern called for.

3. Adjusting the increases

This is the harder part, as it makes use of both aspects of the gauge (stitches and rows). But the basic idea is simple. We have 1) a starting circumference,  2) a finishing circumference, and 3) the height over which we want to achieve the change in circumference. For simplicity, let's look at the original pattern, instructions for XS. The instructions for the decreases are the same for all sizes. Here,
1) The starting circumference is 108 stitches
2) The ending circumference is 292 stitches
3) This all happens over the course of 46 x 2 rows (1 increase, plus 45 more, every other round)

For clarity, I will use the longer line of logic (there is a quicker way, but it's also more obscure). We are going to figure out the starting and ending circumference in inches from the gauge given in the pattern (the original gauge) and then figure out how many stitches this translates to in our gauge.

The starting circumference is 108/16 * 4'' = 27 '' (we did that one before)
The ending circumference is 292/16 * 4'' = 73 ''
The height over this is all happening is (92 rows)/(20 rows) * 4 '' = 18 "

We transfer that into our gauge:

Starting circumference = 27''/4'' * 20 = 135 sts (again, we are assuming the XS size)
Ending circumference = 73''/4'' * 20 = 365 sts
Number of rows over which to increase = 18''/4'' * 30 = 135 rows

So we need to increase (365 - 135) = 230 stitches over 135 rows. This translates to 230/4 = 57.5 increase rows (4 increases per increase row). That means 1 increase row every 230/57.5 = 4 rows.

To make the skirt shorter, I simply stopped when it was "long enough". A couple rows of ribbing, fringes and done.