Getting there!
Only have to attach the sleeves. All the “knitting” is done, and I am waiting for the sleeves to dry, so I am about to cast on my knitmas gift! Yayness! Can’t wait to see how this jumper looks on Friday at the shoot. The weather looks absolutely woeful, so I’ve had to wrack my brains for an indoor location.

p.s. If you’re a regular reader, you’ll know of my penchant for etymology. I just had to look up rack v. wrack. Quite interestingly, either is useable wrt brains and nerves… Rack is edited so more often, but I prefer wrack myself in this context.
Xe

Still working on armholes and armscyes and caps and ellipse perimeters. Was very happy to discover Ramanujan’s approximation for the perimeter of an ellipse:

And this great page from My Measuring Tape on drafting different styles of sleeves is easily adaptable to knitted wares.

I have been slowly working my way down through Knitty’s Knitted Sleeve editorial from ’05, and I’m now around about the point where I realise I really have to get the armscye sorted before going ahead with designing the sleeve cap :)

I have the bodice armscye mostly sorted now, but I’ve been looking for some kind of indication as to what slope to use for the curve of the cast off (working up) at the armhole. If it’s too slow to decrease, the armscye will be triangular, and if it’s too quick, it’ll be square. What’s the happy, curvy, medium? I found a physical armscye curve online, having read this article on pattern drafting on Your Wardrobe Unlocked.

So, if the physical object exists, there must be a software equivalent, right? (my design’s totally digital) Or even just an equation… but can I find one? Nay, I say unto thee, my google searching skillz extends not to such a hit.

Still workin’ on it.

Boy is design hard.

But I absolutely looooove it!!!!!

Ooh, update! I’ve discovered from this UTube video by munnikusum, that a good place for the curve to end (just before the vertical rise to the shoulder) is halfway up that shoulder line.

Last night I popped up a formula for calculating the stitches on a particular row in the cap of a set-in sleeve. And I kind of just left it there, with no explanation. My excuse is my eyelids were sticking to my eyeballs from lack of sleep.

So, now let’s not talk about knitting or maths at all and go on to glass production.

Way back when, if you wanted a pane of glass, you got a glass blower to spin a disc of molten glass. The disc would be cut to shape when it cooled and every pane would have a pontil mark from the glassblower’s pipe. (circa mid 1700’s)

In 1953, the Pilkington brothers developed the float-glass method for making flat glass.

In between, if you wanted flat glass without a pontil mark, your blower would blow up a cylinder, knock off the ends and cut the still malleable glass up one of the sides. He then opened and flattened the cylinder into a rectangle. It never went completely flat, which is why some old glass looks “wavy”.

Sleeves at their most basic are cylinders. If you knit one flat, you make a rectangle just like the glass cylinders above. Now, scale it up just a teensy bit, and a sleeve can probably be better approximated by a truncated cone intersecting a plane. Unless you’re making a cap sleeve, the armhole is also a closed curve. Hence, it’s an ellipse. Just needs a bit of chopping up to get it flat.

A set-in sleeve on a pattern schematic looks like the below. (Actually, usually they’re a bit wider, proportionally speaking).

Now, the equation I came up with last night is pretty much the same as the one I gave for knitting a circle. If you use it in the same way, you will knit an ellipse. Here’s that ellipse one again:

This reads “the number of stitches on row n is a (measured in stitches) by the root of (1 minus (the row number by the gauge over b (measured in stitches)) squared)”

a is half the width of the ellipse and b is half the height.

gauge is sts/10cm over rows/10cm

This will give you the stitches for a quarter of the ellipse (i.e. the curve in the positive x & y quadrant on the cartesian plane), you need to double it to get the stitch count for an entire row and mirror it to get the corresponding bottom half of the ellipse (where y<0).

However!

We want to do set-in sleeves. We’re not actually knitting an ellipse, we’re knitting the cylinder from which an ellipse has been cut, i.e. the negative space of the ellipse.

So the sleeve circumference at its widest point (usually, unless you’re doing a bishop or bell, more on that to come!!!) is usually at the bicep (check out this knitty winter ’04 feature). Call this circumference cAssuming a sleeve which is the same width as the armhole at the intersection (i.e. straight, not a puffy sleeve with extra material), then a is c/4. b is half the depth of the armhole. Very important note: these are the measurements of the fabric, not the model.

Assuming bottom-up construction, the sleeve width just as you are about to start decreasing for the sleeve cap is c. Set n = 1 and increase by 1 for each row. The rowcount decreases at a rate of to the midpoint of the set-in curve, when . Then, the rowcount continues to decrease, and the simplest way to calculate it thereafter is to just reset n=1 and use

So that’s my convoluted THEORY. Need to knit it up and see if it works! I’ll update again when I do.