Jul 15, 2012

The Math

This is the calculation I used to get a 2% depth of shade on my 1100g of fibre using 15g of dye powder dissolved in 1L of water.

If we consider the dye company's instructions for 1% depth of shade using:

10g dye powder : 1L water
1000mL dyestock : 1000g of fibre

I could have used the same dyestock and doubled the volume of dyestock for the same weight of fibre. However, I used 1.5 times as much dye powder in my stock, so I have a stronger stock. Not quite enough to give me a 2% depth of shade (it would give me 1.5% using the same ratio of stock to fibre), so I have to calculate how much dyestock, given my stock strength, I need for the same 1000g of fibre.

1.5 x 4 = 6 / 3 = 2

I bolded those bits so we can see that I can also do 3/2 x 4/3. That gives us 12/6, which we all know as 2.

Right. So I need 4/3 (or 1 and 1/3) as much dyestock to get a 2% depth of shade on 1000g of fibre.

1000mL x 4/3 = 1333mL

Then we'll add in my 100g of fibre (I have 1100g total), so I'll take a tenth of 1333 and find it's about 133. I'll add them together, giving me 1466mL of dyestock required for 1100g of fibre.

You'll recall that I'm also going to be mixing colours to get the perfect doodoo brown, so once I figure out those ratios, I'll know exactly how much I need to mix up to get 1466mL. Then, for each 100g skein of yarn I'm dyeing, I'll need 133mL of dyestock. If I put more than one skein in the pot, I'll multiple 133 by however many skeins I'm using and then I should get dye exhaustion.

Also going into the pot are:

  • 220g salt
  • 55mL acetic acid (each adjusted for 1100g of fibre)
Look how that works out, will you? Divide those numbers by 11 (one for each skein), and you get:
  • 20g salt
  • 5mL acetic acid
Nice and even. I'll be using half the amount at the beginning, then I'll add the other half of the salt after 20 minutes of cooking and the rest of the acid after 40 total minutes. I'll leave it on to cook for close to an hour, then pull it off and let it cool in the pot so it doesn't felt. It'll continue to take up dye if there's any left to take up after an hour.

I think we're set. Let's go make the perfect brown ... and do some laundry so I have something to wear this week.

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