Sunday, March 18, 2012

Algebraic and Aesthetic questions



This is a 3-part question.

There are a total 210 grams yarn. It will be difficult-to-impossible to get more yarn that will match.
madelinetosh-purple

Madeline Tosh Merino Light in Clematis

The sweater consists of Back (B), Left Front (F1), Right Front (F2), two sleeves (S) and Ruffle (R’) which wraps all the way around the bottom, fronts, and collar. S and R’ both contain short row ruffles which should be the same depth.
As Pink as a Rosebud, updated and re-released by Susan Crawford

The body, consisting of B + F1 + F2, has used up 101 grams of yarn.

rosebud1


(A) Is there enough yarn to complete the project? What is the yarn deficit?

B = 98 caston + [56 rows even] + [cast off 8 each end twice for armhole] + [armhole dec to 78 over 4 rows] + [even 82r ]+ [cast off 12 each end 4 times for shoulders] + 30 bindoff
   = 98 + [98 * 56] + [(98 * 1) + (90 * 1)] + [(82+78)*4/2]  + [78 * 82] + [78 + 66 + 54 + 42] + 30
   =98 + 5488 + 98 + 90 + 320 + 6396+ 78 + 66 + 54 + 42 + 31
B = 12760 stitches

F = 30 caston + [inc to 42 over 12 rows] + [inc to 50 over 16rows] + [29 rows even] + b[indoff 8] + [19 rows even] + [decrease to 24 over 36 rows] + [31 rows even] + [bind off 12 + 1 row even + bind off 12]
   = 30 + [(30 + 42) * 12 / 2] + [(42 + 50) * 16 / 2] + [50*29] + [50 *1] + [42 * 19] + [(42 + 24) * 36 / 2] + [24 * 31] + [24 + 12 + 12]
    =30 + 432 + 736 + 1450 + 50 + 798+1188+ 744+ 24 + 12 + 12
F = 5476 stitches

TOTAL knitted stitches
= 2 F + 1 B
= 2(5476) + 1(12760)
= 23712 stitches knitted so far

Find exchange rate from stitches to milligrams (use milligrams instead of grams to make easier)
Y = stitches per mg of yarn = 23712st/101000mg = .23477 st/mg

Stitches still required if knit as pattern written = (2S + R’)

S = {[nonruffle part]} + [ruffle short rows]
   = {[Increase 16 to 43 st over 34 rows] + [32 rows even ]+ [decrease 43 to 16 st over 34 rows]} + [short rows 15 stitches wide of 2 rows every 2 regular rows]
   = {[(16 + 43) * 34/2] + [43 x 32] + [(43 + 16) * 34/2]} + [ 2*15 * (16 + 17 + 16)]
   = 1003 + 1376 + 1003 + 510 + 480 + 510
S = 4852

Ruffle R' requires 264 repeats of R
R’ = 264 R
 R = {nonruffle part} + {ruffle short rows}
    = {30*2} + {15 * 2}
    = 60 + 30 
R = 90
R’ = 264 * 90 = 23760

2S + R’ = (2*4852 + 23760)
33462 Stitches still required if knitted as written

mg yarn required = 33462/Y
= 33462 (1 mg/.23477 st) =
= 142,539 mg yarn still required if knitted as written

142,539 mg exceeds the remaining yarn of 109,000mg. There is not enough yarn to finish the project as written. The yarn deficit is 33.5 grams.


(B) How much do the short-row ruffles need to be shortened (in depth, not length) to be able to complete the project with the available yarn?

Ruffle depth = Z
Remaining stitches available = X = 109000mg (.23477st/1mg) = 25590 stitches remaining

S = [nonruffle part] + [ruffle short rows]
             = [Increase 1 + Z to 18 + Z st over 34 rows] + [16 + Z *32 rows even] + decrease 16 + Z to 18 + Z st over 34 rows] + short rows Z stitches wide of 2 rows every 2 regular rows
   = 34(1+Z+18+Z)/2 + 32(16+Z) + 34(1+Z+18+Z)/2
   = 34 + 64Z + 612 + 512 + 32Z + 34 + 64Z + 612
   = 160Z + 1804

R’ = 264 R
R = (15+Z)*2 + Z * 2
= 30+2Z +2Z
=4Z+30
R’ = 264 * Z = 264(4Z+30)
R’ = 1056Z + 7920

X = 2S + R’
            = 2(160Z + 1804) + 1056Z + 7920
            = 360Z + 3608 + 1056Z + 7920
            = 1416Z + 11528
25590 = 1416Z + 11528
14062 = 1416Z
Z = 9.93

This project could be completed with the remaining yarn if the ruffle is decreased to 9-10 stitches wide.

(C) Now for the hard part: Will this sweater look loserish if the ruffle is decreased by 30%, from 15 stitches to 10 stitches wide?

rosebud2
Even in a copy of a picture of a reprint of a copy of the original vintage pattern, the sweater looks nicer than the modern version. It probably has to do with the corset underneath. Hmm.

What should I do? Knit the ruffles shorter and block them out as much as possible? Put the project on hold and try to find more yarn? Stripe with a slightly different yarn? Something else?

Answers welcome!

PS: This is for all those people who said that algebra wasn't useful in real life, and also for all the people who say there is no art to knitting

5 comments:

betty said...

Being a left-brained person, I started to verify your calculations but decided that was not worth the effort. However, I did compare the numbers and they make sense in that the 2 F's used up less yarn than the B (which is the usual case), and each S requires less yarn than each F, which seems right for that sleeve.

The ruffle will take up 23760, whereas the B+2F+2S will use 33416, which means that is one big honking ruffle. In fact, it's a large part of the sweater.
That being said, I don't think you should make it narrower by 30% because it would change the look quite a bit. You might consider doing less short rows so that it doesn't ruffle as much, but that would change the look also.
I cannot tell the exact yarn color, but if it's a nice dark royal blue, I suggest using black for the ruffle. I think dark blue and black look nice together.

Rose Red said...

I have to admit my eyes glazed over in the math part (even though I am not adverse to maths when I need it!), but I wonder whether you would have enough yarn if you didn't do the sleeve ruffles at all? I think it's a lovely garment, but a tad too ruffly for my liking - I think a streamlined sleeve would complement the lovely ruffle around the body.

(I suspect the sleeve ruffles won't use 10,000 stitches, so maybe no sleeve ruffles and do smaller body ruffle? I do think it would look ok.)

Erin Kate said...

I'm afraid I'm no help with the math, but I can't wait to see how it looks!

Jenn said...

I didn't do your math..
But an idea, since the ruffles are the last parts you knit up, you can do the last few rows as a complementary or contrasting color. Or Simply do the entire neck ruffle as a different color.

Hope this helps..
Have fun!

Anonymous said...

I find the ruffles charming, & not necessarily frilly, so I'm not bothered by that aspect of the design. I actually like it just the way it is & think it would have an attractive drape (i.e., it wouldn't look like a sewn ruffle, just a decorative edge.) I find it a nicely balanced / proportioned garment. Therefore, I would try to keep the original design just as it was published in the 1930s.

That said: my feeling is that all the ruffles should be the same color and the same depth. So, if I were making this, I'd do all the ruffles in black. That would look intentional.

Silvana