The Fade Mathematics: Kite Shawl Calculations

Yesterday I wrote about the construction of kite shawls and I promise you two things: The formula for kite shawl calculations, and a pattern template for them. Here we go!

This article contains a bit of math. If you feel intimidated no worries, you’ll find a simple pattern template using a percentage system at the end of this article!

For the impatient, here are the key facts about this shawl shape (an extensive overview of kite shawls can be found in yesterday’s article The Secrets of Kite Shawls):

  • Percentages of yardage for each section vary.
  • Percentages depend on the ratio of rows in the increase vs. straight section.
  • For regular kites this ratio is 2:1.
  • You can knit kites without a straight section.

The most important takeaway from this article:

If you work the regular kite start decreasing before you have only 46% of your yardage available, otherwise you will run out of yarn before finishing. In other words: the decrease section uses almost half of your yardage!

Details can be found below, as well as a pattern template at the very end.

Kite Shawl Calculations

Increase Section

Let m be the number of rows in the increase section and assume starting with one stitch only. Our total increase rate for each half is one stitch every other row, so after m rows we have m/2 stitches on each side.

The area covered by the increase section therefor is m*m/2.

Straight Section

Let n be the number of rows in the straight section. Regular kite shawls have n = m/2 rows in their straight section. The area covered by the straight section is m/2*n (left side) and m/2*n + n*n/2 (right side).

If you omit the straight section, which is totally possible, this area obviously equals zero.

Decrease Section

The number of rows in the decrease section is determined by m as we decrease all stitches we created during the increase section. We decrease one stitch every other row on the left half thus the number of rows we need equals m.

On the left half we have an area of (m*m/2)/2, on the right side the area equals (n+m)/2*(m/2) + (m/2 * m/4)/2.

Section Percentages

The percentage of each section is calculated by summing up all section areas to get the total area. Let the total area be A and the areas for each section be a1, a2 and a3 (a1 = increase, a2 = straight, a3 = decrease).

The increase section uses a1/A * 100% of the total yardage, the straight section a2/A *100% and the decrease section a3/A *100%.

These percentages strongly depend of the ratio m/n (for n not zero).

For n=m/2 the percentages are

  • 24% (increase section)
  • 30% (straight section)
  • 46% (decrease section)

You see that if you’re starting to decrease after you have used up a bit more than a half of your yarn available you will run out of yarn before finishing.

Kite Shawl Pattern Template

Setup

  • CO 5 sts and knit one row.
  • Next Row: K1, YO, k to last st, YO, k1.
  • Next Row: Knit.
  • Next Row: K1, YO, k1, cdd, k1, YO, k1.
  • Next Row: K1, YO, k to last st, YO, k1.
  • Next Row: K1, YO, k2, cdd, k2, YO, k1.
  • Next Row: K1, YO, k to last st, YO, k1.

You can see the center spine stitch now (the position  of the cdd on each RS row). This stitch is called CSS from now on, and is used as your main orientation landmark.

Increase Section

  • Next Row: K1, YO, k to 1 st before CSS, cdd, k to last st, YO, k1.
  • Next Row: K1, YO, k to CSS, purl CSS, k to last st, YO, k1.
  • Repeat the last two rows until you have worked m rows.*

*Please see above for an explanation what m and n stand for. The abbreviation “st” means “stitch”.

Straight Section

  • Next Row: K1, YO, k to 1 st before CSS, cdd, k to last st, YO, k1.
  • Next Row: K1, k to CSS, purl CSS, k to last st, YO, k1.
  • Repeat the last two rows until you have worked n rows.

Decrease Section

  • Next Row: K1, YO, k to 1 st before CSS, cdd, k to last st, k1.
  • Next Row: K1, k to CSS, purl CSS, k to last st, YO, k1.
  • Repeat the last two rows until you have only one stitch between CSS and the left edge of the knitting.
  • Bind off all stitches

 

I really hope this article helps you understanding the principles of kite shawl calculations a bit better, and hopefully it prevents you from running out of yarn knitting kite shawls in the future (like I did two – yes, two! times).

Let me know if you still have any questions about kite shawls by leaving a comment below!

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23 thoughts on “The Fade Mathematics: Kite Shawl Calculations

  • September 11, 2017 at 7:33 pm
    Permalink

    Sorry, but in german: ich finde deine Design- und Constructionsposts unglaublich großartig! Hilft mir so sehr dabei, eigene Idee umzusetzen. Ganz herzlichen Dank für all deine wunderbaren Informationen!
    Liebe Grüße, Cora

    Reply
    • September 11, 2017 at 8:14 pm
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      Gern geschehen – my pleasure! 🙂

      Reply
  • September 11, 2017 at 11:32 pm
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    hi, I love the shawl pictured. Is there a designer credit or pattern link?

    Reply
    • September 12, 2017 at 2:31 pm
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      Michelle, this shawl is one of the Plant Anatomy patterns. It’s my design and not yet published but will go live within the next days. I’ll post an article and notify my mailing list as soon as it’s available!

      Reply
  • September 16, 2017 at 9:18 pm
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    It was only with the help of a tutor that I passed geometry and had to take basic algebra 3 times! However, I love reading articles by those who live and breathe the math and can apply it to their knitting. Since I never made it to advanced math, I appreciate the written instructions! I love the diagrams. I appreciate how you have dissected shawl shapes and explained their basic patterns.

    Reply
    • September 16, 2017 at 9:26 pm
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      Thank you!

      Reply
  • October 8, 2017 at 4:44 pm
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    Brilliant article – thank you so much! I work at a LYS, and have designed a multi-color boomerang bias shawl pattern for our shop, after figuring out the simple maths for it. Given the popularity of these “kite” shawls (I didn’t even know this type of asymmetrical triangle had a name!), I’ve been wanting to make another for the shop, and while I’d figured out the maths for the symmetrical part of it, the yarn usage is something I’d have not figured out. So, your article is very timely, as I’ve been sitting down drawing up schematics for various ways to incorporate my own design ideas into this shawl style, based around yarns we carry at our shop.

    I do great with the simple math and geometry when it comes to knitting, but the trig part that you described above I would not have been able to ever figure out (barely got through trig in college), since I’ve forgotten the little bit about it I did manage to learn.

    I found your site via a Pinterest link, and am so glad I did. Will look forward to subscribing!

    Happy knitting,

    -Sonya

    Reply
    • October 10, 2017 at 8:07 am
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      Glad the article is of help! 🙂

      Reply
  • Pingback:Das war wohl nix und nochmal Schnee | Lavendelhexe

  • May 3, 2018 at 10:24 am
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    First of all, thank you so much for all the information you share on your blog, especially the series on shawl design, because that is what I needed just now. I am now in my shawl stage because they are so easy and satisfying to knit up!

    I just wanted to let you know that the ratio 40-60% for the kite shawl did not work for me. I carefully weighed my yarn, stopped increasing on the left side a little before reaching 40%, and when I was attaching the last ball of yarn I realized I would not be able to finish it, I would need at least another 82 grams of yarn, almost a whole extra ball. So taking this amount into account, the ratio turns out to be 33%. If I want to finish the shawl – meaning to knit until there is no stitch left to the left of the center spine – I have to stop increasing on the left side when I reach 30% of my proposed yardage.

    Reply
    • May 6, 2018 at 9:01 pm
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      Thanks for your comment! I’ll have another look (the ratio in question worked well for me when I wrote the article, but I haven’t knitted or designed another kite shawl since) and get back to you.

      Reply
  • September 28, 2018 at 8:48 pm
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    Hi,

    I’m trying to do a kite shawl but I don’t get the math in the decrease section…

    The right row is: K1, YO, k to 1 st before CSS, cdd, k to last st, k1.
    There is 1 st increase and 2 stitches decrease, we finish the right side row with 1 stitch decrease.

    Then the wrong side row is: K1, k to CSS, purl CSS, k to last st, YO, k1.
    The YO counts as an increase.

    At the end of both rows the stitch count is back to normal.
    There is no decrease…

    Is there something I’m missing ??

    Thanks for the help 🙂

    Reply
    • October 12, 2018 at 8:27 pm
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      You are in fact not really decreasing stitches, but the CSS shifts so it ‘looks’ like a decrease. It’s a bit hard to explain. It seems like you’re knitting sideways. Hope this helps!

      Reply
      • January 28, 2019 at 11:43 pm
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        I am so glad you explained this because I couldn’t figure out the decrease that is not decreasing. Why do you make the stitch in the center a purl stitch?

        Reply
  • Pingback:Constructing The Fade: The Secrets of Kite Shawls - knitting.today

  • February 4, 2019 at 5:44 pm
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    Thank you for this article! I’ve been looking at kite shawls and trying to figure out how they are constructed without having one in hand or having made one. You have saved me a bunch of work.

    Reply
    • February 6, 2019 at 8:49 pm
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      My pleasure 🙂

      Reply
  • February 7, 2019 at 3:43 pm
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    Awesome article. Thank you so much for the formula and template pattern!

    Reply
    • February 7, 2019 at 7:50 pm
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      My pleasure! 🙂

      Reply
  • February 8, 2019 at 8:56 pm
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    Thank you for posting this explanation. I had to put all distractions aside, and it took me a while, but I got it. I stand in awe of you.

    I do have a question regarding your sample “Kite Shawl Pattern Template” though.
    Directions read as follows for the “Setup” (with my st count in parentheses) :
    CO 5 sts and knit one row. (5 sts)
    Next Row: K1, YO, k to last st, YO, k1. (7 sts)
    Next Row: Knit. (7 sts)
    Repeat the last two rows until you have 7 sts total. (already have 7 sts)
    Do I just do the obvious and simply skip the last line of directions? Thank you!

    Reply
    • February 10, 2019 at 6:32 pm
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      Thanks for your comment! The post has been updated according to your suggestions.

      Reply
    • February 18, 2019 at 4:53 pm
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      If CSS and CDD are the same thing why are both used in the same line. that is confusing to me. CDD is center double decrease, what is CSS?

      Reply
      • February 18, 2019 at 7:36 pm
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        It’s not: “css” means center spine stitch, “cdd” means central double decrease.

        Reply

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