I've been dyeing yarn again, and I've been thinking about how to use my weird ugly yarn, in a project by itself. Online warp calculators give you yarn requirements based on how many items you want to make assuming you have access to an infinite amount of yarn, but what I want to know how is many napkins or dishtowels I can make with a extremely limited amount of yarn.
I spent an evening working out an equation, so here it is, be warned, though I haven't tested it in real life, though I ran the numbers back through a warp calculator, and it seems to work out. It also doesn't take shrinkage, draw in, or take up into account, but, then, neither do I. I like my dishtowels to measure around 21.5" x 30" on the loom and my napkins to be around 18" square. And then I live with whatever they shrink down to.
Alright! Here we go:
If you want to use the same yarn for warp and weft in a balanced weave (epi = ppi)**
Max Warp Length in yards = 1/2[(loom waste in yards) + (weight of yarn in oz) * (yards per lb for the yarn)/(width of warp in reed)*(epi)*(16 oz)]
If you want to just make a warp and use a different yarn for weft, the equation is easier:
Max Warp Length in yards = (weight of yarn in oz) * (yards per lb for the yarn)/[(width of warp in reed)*(epi)*(16 oz)]
If you don't know where to look up your yards/lb for a yarn Handwoven has a chart you can use, which also suggests setts.
As an example, I have this hideous yarn I dyed last summer:
It's a 4/2 cotton, and according to the Master Yarn Chart, it's 1680 yd/lb, and its sett for plain weave is 15 epi. I've weighed it, and it's 6.54 oz. I want to make dishtowels, so my width in reed is 21.5.
Max warp= 1/2 [0.5 yd loom waste + (6.54 oz x 1680 yds)/(21.5 in x 15 epi x 16 oz)] = 1.3 yards
if I want the warp to also be used as the weft, which I think would be pretty hard to look at, and also would only make one 30" towel.
If I want to use a different weft, I can go with:
Max warp = (6.54 oz x 1680 yds)/(21.5 in x 15 epi x 16 oz) = 2.129 yards
This is almost enough to make two 30" towels and I could squeeze out a few more yards by adding stripes to the warp, perhaps by adding two 1.5 inch stripes as borders, I could calculate this by using a width in reed number of 18.5. This gives me a warp of 2.47 yards, which I'm much more confident will give me the yarn I need to make two towels.
** if your planned epi and ppi are different numbers, you'd need a different equation.
