Step 4Aspect Ratios
Technically, it is the inner diameter of your ring divided by the diameter of the wire.
Practically, "it tells you how fat the donut is."
The smaller the AR, the fatter your ring.
For the sake of simplicity, you can take your mandrel size as the inner diameter of your rings. You can look up the diameter of your wire, just make sure both diameters are in the same units.
AR becomes important when you want to have the optimal ring size for your project. Weaves have a range of ARs that will work, but there's a much narrower range for what looks best. Some ARs simply will not work for some weaves, and AR may even alter the weave you're making (Spiral will turn into Jens Pinds with a small AR).
I very rarely bother with actual AR measurements, but the concept is very important when selecting rings (don't pick fat rings for Full-Persian 6-in-1, I will laugh at you).
Take a look at the three Byzantine samples.
The inner diameter of the rings is the same: 3/16", but the wire diameter increases towards the right. Note how the weave looks really wimpy with the large AR (the skinnier rings), and looks the best with a smaller AR. (But any smaller than that final set, the rings won't fit in the weave!)
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