I have been working on a few round flat pieces lately, baby blanket, doily, etc., and I started to think about how the increases are placed. I'm going to go through my thought process here.
1. If I cast on 6 sts and just keep knitting round after round after round, I will end up with a giant tube.
2. If I add increases, evenly spaced and every round or every few rounds, my piece will grow outwards and lie flat.
3. If I increase too little, my work will start to look like a bowl.
4. If I increase too much, my work will have ripples.
So, how do I know how much to increase and when? This is when my math teacher brain kicked in. It seems that there should be a way to figure this out with a formula. Here is my next round of thinking.
1. A lot of this type of knitting happens in sections, e.g. cast on 8 stitches and you end up working 8 sections.
2. The edge of one of these sections is the same as the radius of a circle. Think of a piece of pie; it is cut from the center of the pie to the outside of the circular pie plate. This cut is a radius.
3. Now, let's make a stitch a unit of measure. Follow my thinking here. A row is made up of several stitches side-by-side. The height of my work is the number of rows that I have made stacked on each other. Therefore, the number of rounds that I make is the number of stitches from the center of the piece to the outside edge or the radius. If I have a piece with 120 rounds then my radius is 120.
4. So, in a nice universe, 120 stitches should yield a circumference of 754 stitches ( C=2*Pi*r). However, knitted stitches do not have a 1 to 1 ratio. One stitch in height does not equal one stitch in length. Generally, you need 1.25 more stitches in height in order to match the length. This means that my circumference should be 80% of of the circumference stitches or about 603 stitches around.
Now dividing this by 8, for the 8 sections, I end up with about 75 stitches for each section at the end of my 120th rnd. I have gone from 1 to 75 stitches in 120 rnd; so, I have added in 74 stitches in 119 rounds or about .6218 stitches per rnd. Most patterns that I have looked at generally do their increases every other rnd. Following that idea, I would increase about 1.25 stitches every other round. Well, I can't increase .25 of a stitch. Of course this doesn't have to be super exact as the material will be forgiving. I could do one increase one time and two another as long as I end up in the ball park of around 75 stitches at the end.
Yeah!......Wait! In looking at different patterns, I'm finding that this is not consistent, meaning that the circumference stitches are not 80% of the radius stitches. What I have noticed is that none exceeds the 80%; however, several are much less than 80%. The majority seem to fall in the 55% to75% range with one or two as low as 43%.
I'm pretty sure that my math is correct and I can understand some deviation due to stitch types. However, this seems to be too much.
What am I missing here? It seems that there should be a straight forward mathematical calculation for figuring out the number of increases needed. Should I be looking at a range, that is, you can't do less than this percent for your increases and not more than 80%.