Some Notes on Spinning and Weaving Math.

So, to make a tunic for my measurements, I need about 1.8 meters of fabric 90 centimeters wide. With this, and some facts about the thread, I can calculate how much I need to spin.

How much thread by weight

Realistically, fabric requires hundreds to thousands of meters of thread to make. This is unwieldy to measure by length as I don’t have several kilometers to lay it out (Also, handspun thread has a problem with unspinning if not handled carefully). This makes measuring all of the length impractical, but I can easily measure it by weight.

So first, I need some base weights:

With these variables we can calculate the weight of the Cop (Wc) and use that to calculate our total length of thread (Tl)

So, The spindle is made of 2 pairs of chopsticks, a single chopstick, and 2 elastic bands. This material weighs approximately 15 grams. Thus, Ws=15g 3.2 meters of thread weighs approximately 1 gram. I wove a swatch of fabric 4x5cm with this fabric using approximately 3.2 meters of thread. This swatch weighs 1 gram. The weight of the spindle with a cop of yarn on it weighs 56g. Thus, Wtot=56g With this we can calculate the Weight of the Cop as 56g-15g=41g. Thus, Wc=41g. Using this weight, we can calculate our total length of yarn by multiplying Wc by Wm or 41*3.2 giving us a value of 131.2 which we have, in our reckoning, converted to meters.

Thus, from the math above we can work out that we have 131.2 meters of thread with 41g of fur spun. Accommodating for rounding error, I think it is probably closer to 130 meters.

How much thread do we need for a Tunic

In order to work out the amount of thread needed for a tunic, we need to work out how much warp we need, and then we can double that because of the associative and commutative properties of Multiplication.[1] For the warp we need to prepare 2 meters. This allows us 20 centimeters (.2 meters) of extraspace for the head weave to attach to the loom, and some extra for cutoff and preparation. This means we have a length requirement of 200 centimeters per thread. In order we need to work out the number of threads we need for our weave width we need to work out our ends per inch. We can do this two ways:

  1. Weave a small swatch at least 2 cm wide and count the threads
  2. Wrap the thread around a 2 cm measuring stick and count the thread loops to fill the gap

I have done both!

My woven swatch has approximately 15 ends per 2 cm, and my wrap test (tightly wrapped) gives me 16 ends per 2 cm. Together, the numbers agree that I am looking at between 7.5 (which we must round up to 8) and 8 ends per cm. Multiplying this by our width of 90 cm we get 720 threads to make our warp. Multiplying this by our required 200 cm length, we arrive at 148000 cm of thread. Converting this into a much less scary and more manageable number of meters, we divide by 100 and get 1480 meters of thread to make our warp. The calculation for the weft is done the same way, allowing us to double the number to give us our total required thread:

2960 Meters of thread, or 3000 Meters of thread incorporating some safe rounding error correction and accommodating for breaks, tears, knots, and other things we will have to fix in the weaving process.

How long will this take

It has taken me approximately 3 hours of spinning to come to 130 meters of thread. I am not a fast spinner, but I am also not the slowest. This means I will need to spin somewhere around 60 hours of time to weave this tunic, or somewhere between 20 and 80 days of just spinning when I feel like it. I could probably speed up the calendar time if I dedicated a few hours of free time a day to this.

However, I don’t think my time is the limiting factor. In one session of grooming, my doggo yields around 70-80 grams of fur. If the above equations hold, that is about 300 meters per grooming session. Which means that it will take at least 10 weeks of grooming to get the fur I need.

I either need more dogs, or some other fiber to cut this with…

A thought on Fur growth

I think we are at the tail end of a big shed for Atlas, meaning he is starting a slump of fur production. I might start tracking his fur production to see what times of year he is the most fuzzy.

Footnote

[1] To calculate Warp length you need the variables for Width of Material in Centimeters(W), Ends per Centimeter(EPcm), and Length of Total Weave including cutoff(L). The equation is W*EPcm*L. To Calculate Weft Length you use those same variables in the form L*EPcm*W. Thus, both answers are identical and the total length for a woven material can be calculated as W*L*EPcm or roughly the Ends per Centimeter of the area of the weave in Centimeters squared.