Trust the Numbers!

Not every successful machine knitter is a genius, but for me, machine knitting is a much more intellectual process than hand knitting is. It requires very careful calculations before starting a project because there’s no way to try on a work-in-progress while it’s hanging on the needles of the machine, and it isn’t possible to assess the true size of the pieces of the knitting while they are being made because the weights that are attached to the knitting to maintain tension distort the size of the fabric. The true size of the garment isn’t evident until it is assembled and blocked. In fact, the very process of moving the carriage from one end of the machine to the other requires close attention to many details all at the same time. As quickly as you can move the carriage and knit a row, twice as quickly a disaster can happen if the yarn isn’t in its proper place or the wrong lever has been moved or any of the other hundreds of moving parts aren’t where they ought to be. I have learned that machine knitting isn’t the thing to do if I’m distracted or tired, and I wouldn’t recommend it for anyone with memory issues.

For months I had been promising my husband a machine-knit raglan pullover using many narrow stripes of my plant-dyed yarn, but in April, when I was hoping to knit it, I was very sick with the flu, which not only made me physically weak but also too stupid for machine knitting. It took six weeks to regain the bandwidth for the math and the situational awareness required for machine knitting. In mid-May, I finally felt strong enough to wrap my brain around learning how to machine-knit a husband-sized raglan, which was a shape I had never machine-knit before. First I measured a sweater I had hand-knitted for him a few years ago, one that he likes and wears a lot. The 51-inch circumference was good. I was going to have to work the garment in pieces, so each piece was going to be 25.5 inches wide. The body and sleeves of that sweater were a bit too short, so I added several inches to my calculations, bringing the sleeve and body length from hem to underarm to 17.5 inches. The depth of the yoke was also good, so I used that number, 10.5 inches. The biggest problem with the fit of the sweater I was using as a template was that it rode up badly at the back, and needed short rows at the back to compensate for the fact that my husband’s back is at least an inch and a half longer from shoulder to armpit than it is down his chest between those two points. I had to decide how many short rows would be needed, where to put them, and how to reconcile the length discrepancy between front and back.

Having knitted very often with the yarn base I used for plant dyeing (Wollmeise lace), I already knew the gauge I would get from the tension I was planning to knit at: 15 stitches over two inches, 21 rows over two inches, at tension 7.0. Then I plugged my numbers into Elizabeth Zimmermann’s “EPS” (Elizabeth’s Percentage System), which is a set of equations that provide numbers for standard, classic garments, in proportions that work well on many kinds of bodies, including my husband’s, without modification. I’ve been using EPS as my go-to for years in my hand knitting (with modifications), so it wasn’t hard to adapt the system to machine knitting. EPS assumes knitting in the round, and my machine knitting is done is in flat pieces, so the resulting numbers are divided in half where appropriate, plus two stitches for the selvedge, one at either end. In order to get started on the knitting, I needed to know how many stitches to cast on, how many rows to knit to get to the armpits, and how many stitches to put on waste yarn for the armhole shaping. First I multiplied the chest measurement times stitch gauge to get what Elizabeth called the “key number”, 51 x 7.5 = 382.5, which I rounded up to 384 in order to cast on 192 stitches. Then I multiplied the garment length from hem to armpit by the row gauge, 17.5 inches x 10.5 = 183.75, rounded up to 186 to accommodate 10 rows of folded hem and a number of rows that was evenly divisible by four, for the 4-row stripes. According to EPS, the number of stitches at the armpits that need to be put on waste yarn is .8% of the key number at each armpit, 384 x .08 = 30.72. By the time I got to that point in the knitting, I decided to modify that number slightly.

But at least I now knew how many stitches to cast on and how many rows to knit before I had to do anything that required thinking, so I cast on for a 10-row folded hem, since I don’t like ribbing. Now I could do the fun and easy part, selecting colors. I did the hem in a natural-like commercially dyed Wollmeise colorway, because I have a lot of it and my plant-dyed colors are in much smaller quantities. Then I dug into my big bag of little cakes of plant-dyes and started knitting stripes of blues, blue-greens, greens, browns, pink tans, purplish tans, orangish tans, yellows, and browns. When I first started knitting this project, I hadn’t yet decided whether the striping would be random or on a repeating rota, but pretty early into it I decided that life would be easier and the result would probably be more pleasing to the eye if I used a rota and matched the stripes at all the seams. On the other hand, lots of related colors are more interesting than fewer colors, so my rota ended up at 22 colors, which I arranged in an ordered circle on the bed behind my seat at the knitting machine and carefully replaced when I was done using each one in order to preserve the rota.

My 22-color striping rota of yarn I dyed with weeds and kitchen waste

When I finished row 186, I had to stop in order to do some serious thinking about the numbers for the raglan, where to place the additional rows in the back to keep the sweater from riding up when my husband wore it, and how to reconcile the difference in length between front and back when the sleeves joined those two pieces.

To start off, I plugged my numbers into Elizabeth’s formula to get a theoretical number for the widest part of the sleeve, since that number would be very important to figuring the depth and slope of the raglan. EPS says that the sleeve at its widest is 33% of key number, that is, 384 x .33 = 126.72. According to EPS, I would put 8% of key number, 30.72 sleeve stitches, onto waste yarn, leaving me with 96 sleeve stitches to decrease at a rate of a stitch at either end every other row, after first knitting without decreases for an inch, 10.5 rows. So if I added 96 and 10.5, I would get 106.5 rows, which, divided by my row gauge of 10.5 rows to the inch, would come to 10.14 inches of yoke depth, pretty close to the 10.5 inches of yoke depth on the template sweater, and when I measured my husband’s body, it looked OK. This gave me a starting point from which I could adjust my numbers to get where I wanted to go, but I wasn’t there yet. I wanted to end the raglan shaping at the end of a 4-row stripe. So I increased the sleeve width to 134 stitches, decreased the stitches on waste yarn to 28, and decided to start the raglan decreasing on row 2 of the third 4-row stripe, i.e. on row 10. Of the 192 stitches on the machine, 28 stitches (14 stitches at either end), were put onto waste yarn, which I did for all parts of the sweater, back, front, sleeves. Next I decided that 28 4-row stripes, 112 rows, would be a good depth for the raglan on the front side, the side that wasn’t getting the extra rows. As for the extra rows, I decided that 14 extra rows would probably be enough, and decided to place them at the end of stripes 1, 5, 9, 13, 17, 21, and 25.

Now I had a plan that would enable me to finish the back, and the numbers were quite close to the numbers a strict adherence to EPS would have given me, although I had played with the formula a bit to get the raglan to end where I wanted it to end, by adding several stitches to the width of the sleeve and subtracting a couple of stitches from the number of stitches placed on waste yarn. One can also adjust the number of rows at the beginning of the raglan that aren’t decreased, beyond the inch that EPS instructs, more if the body and arms are narrow and the depth of the yoke needs to be longer, or the decreases could start immediately if the sleeves and body are rather wider and the yoke depth doesn’t need to be so long. The lovely thing about EPS is how easy the numbers are to calculate. At a rate of decrease of two stitches every two rows, the number of stitches to be decreased is same as the number of rows where the decreases occur. Add in the number of undecreased rows at the start of the raglan, and you know ahead of time the depth of your raglan yoke.

However, if one is up for a little bit more math, the slope of the raglan can be calculated so that you get the width you want for the sleeves and body and the exact yoke depth you want, while achieving a smooth distribution of decreases even when the numbers don’t divide into each other evenly. It’s called the Magic Formula, and it has been around for a long time, although I didn’t discover it until a machine knitter on Facebook named Julie Magson provided an explanation for it in simple, non-mathematical terms. She gave me permission to copy her file directly into this blog post, but I don’t know how to make it copy coherently into the word processing structure WordPress provides, so I will put the idea into my own terms.

First, put away the calculator and do the arithmetic the way they taught you in 4th grade, on pencil and paper, because the calculator’s decimals won’t give you the information you need. The summary is, you’re dividing the number of decrease rows by the number of stitches you want to get rid of and then you multiply those two numbers together and subtract the sum from the number of rows to get the remainder. Since there’s a remainder, which isn’t a whole number, add 1 to the number you got as the answer to your division sum to make it a whole number. The remainder and the rounded-up number are the number of decreases and rows-apart for the number of stitchers that couldn’t be evenly divided. Then subtract the remainder from the number of stitches that need to be decreased. That number and the evenly divided number you got from the first calculation is the number of stitches you’re decreasing and how far apart they are. This set of calculations makes better sense when you do it for yourself, so I did it for myself using the numbers for my husband’s sweater: 52 decreases over 112 rows.

Here’s my math. I divided 112 rows by 52 decreases. That gave me 2 with a remainder of 8, after subtracting 104 (52 x 2) from 112. Then I subtracted 8 from 52 and got 44. This means that if I had decided to make my raglan slope using the Magic Formula, I would have decreased 8 stitches every 3 rows for 24 rows and then a stitch at either end of every other row for 44 rows.

Now that I had the rest of my numbers, I could get back to the machine and knit the raglan shaping on the back, which would have 14 extra rows in seven stripes spaced every four stripes. I had my 22-color rota arranged in a circle on the bed, and I needed some kind of memory aid to make sure that I did the extra rows in the right color, in the right place, without disrupting the rota. I found a plastic lid lying around, so I put it on the yarn cake for the first stripe like a little hat, and when I picked up that color to knit it, I counted four cakes ahead and put the hat on the fourth cake and repeated that action every time I reached a 6-row stripe. As the back of the sweater grew, so did my anxiety that the knitting looked enormous, and my husband is not an enormous guy. I know that you can’t judge the size of a piece of machine knitting by the way it looks when it’s hanging from the needles because the needles are farther apart than the stitches will be when it’s off the needles, and the fabric is stretched way out of shape by the weights needed to maintain stitch tension. I knew that, but I was still worried that the resulting sweater would go down to my husband’s knees and the sleeves would drag on the ground. But my gauge was accurate and I had double- and triple-checked my calculations. Trust the numbers and tell that nervous voice in your head to shut up!

The front of the sweater got 4-row stripes all the way, while the back had seven 6-row stripes to provide the 14 extra rows to prevent it from riding up on my husband’s body. I decided that the simplest and most anatomically correct way to reconcile the difference was to place the short row turns on the shoulders at needle 0 of the sleeves, that is, the midline of the knitting. That way I didn’t have to do any clever math to figure the placement of the turns, and the curve in my husband’s back that was necessitating the extra rows extended to the area covered by the top of the sleeves. I found out later that machine knitters usually put the short rows near the edge stitches on the back, and I will do that when I start knitting sweaters with set-in sleeves, but I don’t think that would have been the best solution for a raglan.

Close-up of short rows on the midline of the shoulder cap. Short side left, long side right

It had been six months since I had last done short rows, and I wasn’t sure I could do it without making some stupid mistake that would cause everything to fall off the needles and onto my feet. So I put in a lifeline, which I’d never done before, and sure enough, I needed that lifeline. I think I forgot to close the door to the yarn feeder because I was distracted by doing everything else right. That happens in machine knitting, or at least it happens in my machine knitting. I followed my rota accurately, did my memory aid with the “hat” on the yarn cakes for the short-row stripes, and when I got to the last set of decreases, I decided not to do them because I was a little worried that the neck opening would be too small for my husband’s big melon of a head to get through.

I continued to worry that my numbers were going to betray me and I was going to end up with an unwearable waste of pretty yarn, so as soon as I had pieces that could be seamed, I hung the side stitches of the front and back onto the needles and did the side seams so that I could check length and width on his body. What a relief, I hadn’t knitted him a dress. I also seamed the first sleeve as soon as I could and saw that it was generously sized but the numbers had not betrayed me. As Ronald Reagan said, trust but verify, and my numbers had checked out in real life.

Starting to assemble the pieces of this men’s raglan pullover. Big sigh of relief that it’s the size it’s supposed to be, thanks to the magic of math!

When I was done with the machine-seaming of the second sleeve, the rest was finished by hand, with mattress-stitching for the raglans and a double-knitted neck band.

Detail of the double-knit neckband that I knitted by hand

Finally I could put the completed garment on my husband and rejoice in the triumph of achieving the fit my husband wanted, thanks to doing what my well-calculated numbers told me to do.

Husband modeling his comfy new sweater
Modeled close-up of short rows on shoulder cap. I may have missed the midline a couple of times. Oh well.
The view from the rear

I wanted to reinforce what I had learned about machine-knitting a raglan sweater, so I decided to make one for myself. I had some trendy speckled yarn by Haute Bohéme Fibers, a small local dyer that had a trunk show at my LYS, Lovelyarns, last winter, and a compatible skein from Neighborhood Fiber Company, Baltimore’s answer to Wollmeise, that would play nicely together. The hem, cuffs, and double-knitted neck band would be in a couple of Wollmeise Harmonista colorways. The plan was to make a scaled-down striped sweater in fewer colors and wider stripes by using EPS and the same method of reconciling the short rows on the shoulders at the midline of the sleeves, although there would be fewer short rows because I’m shorter and my back is straighter than my husband’s. There would also be a small amount of A-line shaping on the sides, seven stitches per side decreased over the course of 102 rows placed 20 rows above the hem and 30 rows below the armpit. I also decided I wanted some stitches left over at the neck after completing the raglan shaping, because I needed stitches for the seaming and some room to get my head through the neck. I did the calculations the way I did them for my husband’s sweater, using EPS, but I made a tactical error: I got cocky and just did the numbers on paper rather than counting everything out physically in a drawing or on the needles of the machine. If I fail to double-check my numbers in a physical way, I will (and did) make some erroneous logical assumption that will cause me to end up with a stitch or two more or less than I intended. I also miscounted the number of stitches I was putting on waste yarn at the armpits, and that threw off my calculations. Note to self: trust the numbers, but make sure you physically have the numbers you think you have.

When I bound off the last stitch from the machine, I heaved a heavy sigh of relief because I was now on the terra firma of hand work, which can have its delicate moments but spares me the sudden disasters out of nowhere that happen in machine knitting. But even as I sighed that sigh of relief, I began itching to cast on the next project. “Why would I be so relieved to be safely done with the machine knitting on one project while champing at the bit to start something new?” I asked Melissa, Lovelyarn’s owner, as I sat in the store with her, mattress-stitching the raglan yoke seams together and double-knitting the neck band by hand. “You just like scaring yourself,” she replied. Maybe I do. But I’m looking forward to the time when I know what I’m doing on the knitting machine to the point that the trepidation disappears and I can approach it with the same confidence that I have with hand knitting.

When I finished assembling my sweater, I had serious concerns about the fit. It blocked out to the measurements I had intended, and it got good reactions from people who saw me wearing it, but it still felt a bit constrictive and I was conscious of the outlines of fleshy protrusions. Since then it has grown on me. Literally– it seems to have relaxed and molded to my body in a more forgiving way, and I feel comfortable in it.

Showing off the decorative machine-knit seams in a histrionic pose

As for my husband and his sweater, every time he puts it on, it bunches up at the back of his neck and I have to yank it down. It looks fine once I’ve pulled it into place, but I think I probably should have put in more extra rows at the back, maybe 6 additional rows to bring it to 20 instead of 14. At least he usually puts it on with the front in front, unlike the original sweater I used as a template, which has now been replaced by his machine-knit, stripes-of-many-plant-dyed-colors, raglan sweater as his new favorite sweater.

Just the thing to wear for an evening bird-watching walk in northern Michigan

2 thoughts on “Trust the Numbers!

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