The aspect ratio (or AR) is a way of describing how thick/thin a ring is. This is desperately important to chainmaillers because not all weaves use the same size rings. Let me repeat that, since it’s really important… Not all weaves use the same size rings. Here are a couple weave examples to show you why that statement is quite so important. I’ll use Full Persian and Birdcage for these examples because Full Persian likes a very thin ring and Birdcage likes a very thick ring.
Our two rings. On the left is a “hula-hoop” ring. Its inner diameter is large compared to its wire thickness. On the right is a “chunky-monkey” ring. Its roughly the same overall size, but much sturdier.
Full Persian weave made with both rings. It works really nicely with the hula-hoops, but we run out of room almost immediately with the chunky-monkeys. Full Persian requires each ring to pass through six other rings, and the path that they follow is pretty complex. Hula-hoops are great for that sort of weave, but chunky-monkeys are too crowded.
Birdcage (AKA Byzantine) weave made with both rings. While it is possible to make the weave with both types of ring, the chunky-monkeys look a lot better. Birdcage prefers rings that will take up enough space to make the pattern hold steady. Chunky-monkeys are great for that sort of weave, but hula-hoops look messy.
Now that I’ve convinced you that each weave has its own idea of “perfect” ring size, we need a way to say whether a particular ring is like a hula-hoop, like a chunky-monkey, or somewhere in between. The aspect ratio (AR) of a ring is a single number that describes the thickness/thinness of that ring size.
aspect ratio = inner diameter ÷ wire diameter
For the example rings that I used, the AR of the hula-hoop is 5.17 and the AR of the chunky-monkey is 3.41. The higher the AR, the thinner the ring. It doesn’t matter what the overall size of the ring is, what’s important is the comparison of ring diameter to wire diameter. The AR will be the same for a perfect Birdcage ring no matter whether that ring is a couple millimeters wide or a couple inches wide.
You can use that relationship to figure out any of the pieces if you know the other two. You can dust off your high school algebra, or you can just use this “cheat triangle.” If you stick your thumb over the thing you need to know, whatever is left visible tells you how to find it. (My thanks to Jim for this wonderful adaptation of the Ohm’s Law Triangle. The idea is entirely his.)
So what does all this mean to you? Since each chainmail weave has an ideal AR, you can now take some of the guesswork out of what size rings to make/buy. Let’s look at a few examples…
You know the weave and the wire size, but you don’t know the inner diameter.
ID = WD x AR
You’re making Birdcage (ideal AR of 3.5) and you’re using 18ga wire (0.040″). You don’t know what would be the best inner diameter for your rings. Multiply the wire diameter by the aspect ratio. 0.040″ x 3.5 = 0.14″ which is very close to 9/64″.
You know the weave and the inner diameter, but you don’t know the wire size.
WD = ID ÷ AR
You’re making Full Persian (AR of 5.25) and you want the rings to be 3/16″ (which equals 0.1875″). Divide the inner diameter by the aspect ratio. 0.1875″ ÷ 5.25 = 0.0357″ which is 19ga (or really, really close anyway).
You just found some mystery rings. What should you make with them?
AR = ID ÷ WD
When you measure your rings, you find that the wire is 1.3mm thick and the outer diameter is 7mm. Subtract two wire thicknesses to determine that the inner diameter of these mystery rings is 4.4mm. (Yes, you can measure the inner diameter directly, but I find it easier and more accurate to do a little subtraction.) Divide the inner diameter by the wire diameter. 4.4mm ÷ 1.3mm = 3.38, which is a reasonable size for Birdcage, European 4-in-1, and Turkish Round.
Aspect ratio is a profoundly useful concept. There are so many weaves out there (more every day!) and being able to figure out for yourself what rings to use is really helpful.
If you browse the family portraits for various weaves, you can see the aspect ratio in action. All the sample chains are made with rings of the same AR, even though the overall size of the chain varies dramatically with gauge.
If you’d like some hands-on experimenting, I recommend one of the AR samplers – 22ga through 10ga rings with the same aspect ratio.
And finally, the lazy method! I encourage you to calculate at least a few aspect ratio manually, to help the concept stick in your memory, but after that… I use an Excel spreadsheet to answer Aspect Ratio questions. (Life is too short for repeated trips to the calculator!) Please download a copy for your own use and amusement: spiderchain_AR.xlsx (last updated October 23, 2015)
If you want a quick reference, you can tap/click for a larger version of the picture on the right. It’s just a screenshot of the “proper” spreadsheet, complete with color flagged European 4-in-1 sizes. This grid will be miserable to browse on a phone, but it’s better than nothing at all! *grin*
The aspect ratio is a wonderfully useful concept. I hope this explanation helps you understand how to use it!