Cardigan math

I have 630 grams of BFL Aran to knit my brioche rib sweater. According to the pattern, it ought to take 750 grams of yarn. However, I am not using the recommended yarn or gauge. How close will I be, and if I won't make it, how much more yarn should I dye?

I have finished the back, which weighs exactly 180 grams.


Calculating from the pattern, I can figure the relative proportions of the back, fronts and sleeves.

Back: 7281
Fronts: 9082
Sleeves: 13518

total = 29881

means that back is 24% of garment and I would need 750 grams

Now if I make sleeves more narrow, reduce cuffs, make collar more narrow, I get it down to

Back: 7281
Fronts: 7970
Sleeves: 10536

total = 25787

means that the back is 28% and I need 637 grams. Sigh, so close.

Cardigan in progress

Wool2Dye4.com sells some nice yarns, including a BFL Aran that is just wonderful. However, it is not common for indie dyers to dye and sell this yarn. When they do, it is often hand-dyed in small batches in bright variegated colors.

It's not hard to understand why. While many folks will purchase hand dyed yarn over the internet, they usually want it for a one-skein project, like socks or a hat. There's too much risk in purchasing enough for a sweater. And cost. Hand dyeing is labor intensive so the cost of a sweater's worth of hand dyed yarn would be quite dear.

Why would indie dyers create sweater sized dyelots? That's another issue. I doubt there's much of a market. There's a lot of capital invested in dyeing a large enough dye lot of Aran yarn for a sweater. Most of the BFL Aran that gets purchased from indie dyers goes into knitting wool soakers. For those not in the know, that's diaper covers. They are awfully cute and seem practical but what a use for a premium yarn!




So I figured I would dye this yarn and make a sweater.




I had in mind a brioche rib cardigan, although I really didn't know how to knit one. I just love the brioche stitch and thought the yarn would work well. I figured the internet was my friend in figuring out the How.

Well, I found the gold mind! Brioche stitch heaven. Nancy Marchant has created one of the clearest and most useful sites on the internet. And a pattern for a simple brioche cardigan as well! Frankly, given all the information she provides for free, anyone who understands sweater construction could figure out that sweater on their own, but it was only five bucks, it would save some math and damn! She deserves the money just for the information on her website!





Of course there's something I hadn't considered. Brioche takes more yarn than stockinette. I am not sure I dyed enough for the sweater. Lots of back of the pattern calculations estimating square inches to knit and square inches per gram of what I have knit --- I may be really, really close.

I did take careful notes on the dyes used, I can probably dye another skein or two close enough to work -- maybe alternating rows on the sleeves, but I'll finish the back and do more calculations before deciding if I need to do that.

Teaching the kid to fly

Last weekend my husband took a brief vacation and left the kid behind. Sure, we've been away from him before overnight. He's been to sleepovers and sleep away camp. When he was younger we even occasionally left him with a sitter and went away for an anniversary or birthday weekend. But this felt different.

This time we told our 14 year old that we wanted to go camping without him and he needed to call a friend and get himself invited over to spend the night. And he did. Friday he rode his bike to school with his pannier packed with pajamas and toothbrush, because his sleepover friend commuted by bike. He would bike home the next morning (from Phinney Ridge! Crossing Aurora by himself!) then leave to spend the day with another friend. He could then come home, make himself dinner and keep himself occupied (that's what the internet and video games are for, right?) until we got home Saturday evening. We had the cell phone and alerted several neighbors who were happy to be available in case he needed assistance. And we were off. Did I worry? Of course! Independence is a long and gradual process, a process we have to encourage, even if it's scary. (More scary for me than the kid, actually.)



We went to the Columbia National Wildlife Refuge in the Channeled Scablands. Eastern Washington has the wildest geologic history I can imagine. No recent natural event has come close to the forces that have shaped that landscape. First, the earth opened and lava flooded the land, hundreds of miles covered fifty feet thick. Over about a million years, this happened over and over again. Enough lava in total to cover the entire continental US 39 feet deep. Then, some time elapsed and the world went into an ice age. Eastern Washington was not covered by the continental ice shelf, but Northeast of there, a finger of the continental glacier formed a dam in the mountains of Montana, creating a massive lake behind. The dam failed in a cataclysmic flood where all the water drained from Montana through Eastern Washington to the Columbia River and to the sea. Took less than a week and estimates say that the flow was more than the combined flow of all rivers in the world combined. This happened again and again, perhaps once every 50 years for a couple thousand years. The flooding tore up the land, eroding the basalt layers into a complex of channels and potholes. Giant ripple marks that are only recognizable as such from airplanes. Gravel bars the size of small mountain ranges.



The Columbia National Wildlife Refuge was formed because the Potholes Reservoir dam created by The Project in the 1940s raised the water table nearby. So the desert south of the reservoir now held water in the potholes and the lowest parts of the channels, water that attracts and aids wildlife of all sorts.



We hiked in the refuge and in the neighboring Drumheller Channels. Although we didn't time our hikes to optimize wildlife viewing --- the crepuscular hours are ideal for that --- we did see quite a variety. Birds, bugs, frogs, even a couple coyotes, but fortunately no snakes.

Saturday's hike we were treated to the sound of ravens making a fuss. We stopped and observed an adult pair and a juvenile pair up on the edge of a mesa. The adult pair each flew off the mesa, around the corner and perched back up top aways off. Then they called and called. Eventually the juveniles followed, but instead of flying out and around, they took the shorter path across the top, flying inexpertly no more than a few feet off the ground. Well, the parents did not sound too pleased about that and cawed up a storm.

That was the coolest thing we saw until lunchtime we were sitting in the shade under a cliff and noticed that a coyote was watching us from across the channel. Just standing on the edge of the opposite mesa and staring. He looked just like a large dog, but with the binoculars we could see the distinctive fur patterns and scrabbier body of a wild coyote.

That was the coolest thing until we were walking back in the bottom of a channel when we suddenly saw a huge bird flying away from us along the top of the mesa to our right. It stopped and looked back and had the unmistakable face of an owl! I've never seen an owl in the wild and what is it doing out in the day?

Right then another huge bird flew in front of us from the right cliff to the taller left cliff. We stopped and got out the binoculars and saw that the bird on the right was a juvenile, still fluffy and downy while the bird now on the left was an adult Great Horned Owl. Parent number two soon made its presence known and was also above us on the higher cliffs on our left. Unlike the ravens, these birds were not ignoring us and getting on with their teaching. We were being watched. Franz also got the impression that if we kept walking the trajectory we were going, we'd be pretty close to the fledgling and perhaps attacked by the parents. So after watching through the binoculars for a while, we continued on, passing much closer to the left side than the right. After we were through, I looked back and saw that the juvenile was now down in the channel, practicing flying maneuvers near the ground.

Our fledgling? Well, he managed just fine without us.

More fun with mathematics (and knitting)

Just about anyone with a school-aged child is aware of the controversies in mathematics education. As a former math teacher and the parent of a ninth grader, I follow it pretty closely. The other day I read an article from a fellow arguing that algebra ought to be an elective in high school, that not many people ever have to use algebra in real life, so why make everyone suffer through it. He was especially critical of word problems and claims that there are no real life word problems that anyone would ever want or need to solve.

I guess he only knits rectangles.

I get lots of blog hits from folks looking for shawl calculation help. Many people knitting a triangular shawl from the top down want to know how many pattern repeats they can finish before they run out of yarn. I gave a method (using algebra) in this post and a follow-up in this post.



I recently started Ene's Scarf, my first triangular scarf/shawl knit from the bottom up. Meaning: cast on a terrific number of stitches, then decrease regularly until they are almost all gone, bind them off and block out to triangular shape.

Again, this isn't really a triangle, but a trapezoid. Cast on 375 stitches, decrease two stitches per row until you are left with 19 stitches, then do a bind-off that grafts them together.

This time, I know I have enough yarn. (Elsebeth Lavold's Silky Wool. Purchased to make Cozy from knitty.com, frogged for a variety of reasons.) All I really want to know is when I have reached the halfway point for the psychological assurance. However, if I were worried about having enough yarn, I would use the same calculations --- but factoring in the extra yarn used in the cast-on row more carefully.

First: Draw a picture and determine what I know and what I want to know.




For Ene's Scarf:

C = cast on = 375 stitches
B = end (not exactly bind-off, but close enough) = 19 stitches
H = number of rows = 179

note that if one really does decrease two stitches per row, the numbers are a teeny bit off -- one would end up with 17 stitches. That's because in this pattern, there are a few rows that don't follow the rules completely, but the difference is negligible for my needs.

Total number of stitches = Area of trapezoid = 1/2(C+B)*H = 35,263

I know that I will have knit half the scarf when I reach row h with r stitches where the area of the top trapezoid with base r is exactly half the area of the whole trapezoid.

I have two unknowns, h and r. Fortunately, I can solve for r in terms of h, so I will end up having an equation with one unknown and I can solve it.

h = rows left to finish
r = number of stitches in the row where there are h rows left.

So r = 19 + 2h

Area of top trapezoid is 1/2(19 + r) * h = 1/2(19 + 19 + 2h)h = 19h + h²


So we have to solve for h where

19h + h² = 1/2(35,263) = 17,631.5

h² + 19h - 17,631.5 = 0 is a quadratic equation, easily solved by the Pythagorean Theorem.

Do you want to see the calculations? I thought not. But I'll show you anyway. There are two real solutions to this equation, but we are only interested in the positive solution. Therefore, we only care about

(-19 + (19² - 4 * (-17,631.5))^.5) / 2 = 124 (more or less)

I will be halfway done when I have 124 rows left. 179 rows total, means I will be halfway done when I have finished 55 rows.

Blueberry Shawl

I've been having trouble deciding whether to knit a new sweater using stash yarn or purchasing more Cascade 220 to remake Forecast. And if I do reknit Forecast, what color? (I could always choose to finish a work in progress, but that's never as fun as starting something new!) So I went browsing at A New Yarn which has a decent selection of C220, but not the color of the Japan sweater. They do have a different yarn in the most gorgeous blue (Sapphire in this link, I believe). That would make a wonderful sweater, but it would cost more than twice as much as a C220 version. And infinitely more than knitting a sweater from stash.

So instead I wandered around and looked at the odds and ends. A New Yarn is a non-profit yarn store that raises money for a Women's shelter. They stock some good basic yarns but also take donations. So you never know what odd balls of Rowan or Malabrigo will be scattered around. I found a skein of Shetland in a tweedy blue-purple. It has a really old looking label and the colorway is Blueberry --- not one I can find currently for sale.


It is probably not a coincidence that I chose a blue-purple colorway. Not exactly the same as the Japan Sweater, but pretty close.

In one week it became a Flower Basket Shawl. I chose this pattern because I wanted something I knew would be easy to do without stitch markers since I have kinda lost mine all over the house. I knew the pattern would be easy to memorize and I knew it would be easy to add pattern repeats to maximize using the available yarn.

US 7 addi lace needles
9 pattern repeats
86 grams, 340-350 yards used
blocks to 63 inch wingspan 24 inches deep (could have been blocked deeper with less wingspan as well)