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).

  • Increase section uses 40% of total yardage
  • Decrease section uses 60% of total yardage (!)

The most important takeaway from this article:

Start decreasing before you used up 40% of your yardage available, otherwise you will run out of yarn before finishing!

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

Kite Shawl Calculations: Increase Section

Let’s have a look at the shawl geometry for the increase section first. Only the right half of the shawl is shown in the picture below (the left side is symmetrical). The letters W and H stand for total width and height; the letter h symbolizes the height after a certain number of rows worked.

Kite shawl calculations: Basic geometry of the increase section

The basic increase rate is one stitch every two rows, creating – together with the chevron shaping – a total increase angle of 15°. Our example uses h = 50 rows, and knowing our increase rate (one every second row) we have a total number of 26 stitches, assuming we start with one single stitch.

As we’re working on the chevron not straight upwards, these 26 stitches represent the width at the edge shown in pink below.

Kite shawl calculations: Basic geometry of the increase section

But this width is not what we want to know – we want to know the total width, W. To calculate W, we need to dig out our trigonometry knowledge first.

We know the width at the pink line (p = 26 stitches) and we know the triangle between the pink line and the two sides called W is perpendicular. And as the two sides are of equal length (W), we know the other two angles are 45°.

We can now calculate W by the formula sin(45°) = W/p, hence W = p*sin(45°). The sine of 45° equals 1/sqrt(2) which is approximately 0.707.

So we achieve the formula W = 0.707*p.

If we put aside gauge calculations for a moment and just use the number of stitches and rows as rough numbers, we now know that our shawl measures h=50, p = 26, and thus W = 18.4.

The area A of the green triangle can be calculated by subtracting the white triangle (side length=W) from the triangle formed by H (H= h + W) and W:

A = (W*H)/2 – (W*W)/2 = (18.4*(50+18.4))/2 – (18.4*18.4)/2 = 629.3 – 169.3 = 460.

(If you need a unit, it would be “stitches squared” – yes, I know it’s very theoretical. But before we start taking gauge into account too, this will do for the moment.)

Kite Shawl Calculations: Decrease Section

The same principles for calculation as outlined previously apply for calculating the right side of the decrease section. We assume that our decrease section is of the same height as the increase one, making a total of 100 rows. A schematic is shown below.

Kite shawl calculations: Basic geometry of the decrease section

 

Right Side (Yellow)

The area of the right side of the increase section is then (adding the two triangles of the large one separated by the dashed line, and having now 51 total stitches on the right side),

W*W + (p2*51)/2 = 18.4*18.4 + (26*51)/2 = 1001.6 (again, the unit is stitches square).

Left Side (Pink)

The area on the left side is simply given by W*W = 339 (stitches square).

Percentages

Let’s now calculate percentages.

Our total area is 339 + 1001 + 2*460  = 2260 stitches square (numbers rounded), thus

Increase section: 2*460/2260 = 40%

Decrease section: (1001 + 339)/2260 =  60%

You see that if you’re starting to decrease after you have used up 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.
  • Repeat the last two rows until you have 7 sts total.
  • 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 used less than 40% of your yardage available.

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 st between CSS and the left edge of the knitting.
  • Bind off all sts.

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!

Julia <3

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6 thoughts on “The Fade Mathematics: Kite Shawl Calculations

  • September 11, 2017 at 7:33 pm
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    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

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