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Aspect Ratio
Article © MAIL User: Vacacita

Aspect Ratio

A common question when learning a new weave is "What size ring should I use for this?" The best way to find an answer is to understand the concept of aspect ratio. This value, something of a magic number, serves as the mediator between weave and ring size. If you know the right AR for a weave, you can determine an appropriate ring size. If you know the AR of the rings you have, you can find out what weave you can make with them.
So what is AR? Mathematically speaking, it is the ratio of the inner diameter of a ring to the diameter of the wire it is made of.
Image: vacaardiagram.gif
You can think of ID as the hole in a donut, and WD as the thickness of the donut itself. (Mmmm... donuts.) These lengths can be measured with calipers, or you can use reference charts to estimate them. Both measurements must use the same units (inches, millimeters, etc.) so that the units will cancel properly. Note that you can't plug in the gauge for the WD; it has to be the actual length measurement with appropriate units.
Okay, so now that the number-crunching stuff is out of the way, what does this actually mean? Compare these two rings:

Image: vacaarfat.gifImage: vacaarthin.gif
thick wire
small hole
small AR
thin wire
big hole
large AR

Imagine trying to weave a chain with each of these ring sizes. If the AR is too small, you won't be able to fit the rings into the weave. If the AR is too big, the weave will be floppy and may not hold its shape. That's why finding the right AR is so important.
Here's how changing the ID or wire gauge affects AR. These are sterling silver rings; gauges are in AWG.
Image: vacaarringex.jpg
For rings with the same wire gauge, making the ID smaller decreases the AR. With the same ID, going to a thinner wire gauge increases the AR.

AR in Action

AR determines how loose or tight a weave will be. Each weave has an optimal AR, or range of possible ARs, and maillers generally establish their own preferences. To produce a stable, attractive weave, use rings with an AR close to the recommended value.
Consider these three sterling silver Byzantine chains, each woven with a slightly different ring size:
Image: vacaarbyz.jpg
The top two ring sizes have similar ARs, and the weave is nice and snug. The results are similar even though the IDs and wire gauges are different. The third chain uses rings with a much higher AR; the ID is bigger than in the first chain, and the wire is thinner than in the second chain. The weave is very loose - it has a lot of open space and is much less stable. The arrow shows where one unit of the Byzantine has flipped back on itself, which doesn't happen with the other chains.

In the ring comparison photo, the first, third, and fifth rings have similar ARs, so those ring sizes will probably work for the same weaves. (I use these sizes for Full Persian 6-1 and Half Persian 4-1.) Likewise, the second and fourth rings have similar ARs and can be used for the same weaves (such as the Byzantine in the photo above).

Within the range of possible ARs, there is some room for personal preference. Increasing the AR by increasing the inner diameter or using a thinner wire will make the chain looser and easier to weave. Decreasing the AR slightly will tighten the weave, but it may be harder to work. Take this into consideration when you see recommended sizes.

Math Made Easy
Fortunately, you can use ARs without having to go through lots of calculations. Some very thoughtful maillers have created reference charts that will do most of the work for you:

Zlosk's Aspect Ratio Table - This table tells you the preferred AR for several weaves. Zlosk also has a FAQ page about aspect ratios here.

Venom's Pit has several handy AR-related charts. The "Weave Ratio Chart" is similar to Zlosk's table; the "ID/SWG Ratio Chart" is similar to Sushi's chart, but gives IDs in millimeters as well as inches (and WDs in inches, mm, and SWG gauges); and the "Recommended Ring Size Chart" gives specific sizes for weaves in SWG and fractions of inches.

The Fudge Factor: Springback
Unfortunately, the AR you calculate or get from a chart isn't always the exact AR of the rings you have, unless you're starting with actual measured values. This is because most metals have a certain amount of springback: if you wind a wire around a mandrel, it "springs back" instead of staying tight against the mandrel. (The same thing happens when you open or close a ring.) The result is that the inner diameter of the rings is slightly larger than the diameter of the mandrel, increasing the AR. The degree of springback depends on several factors, including the metal used, the temper of the wire (dead soft, half hard, etc.), and the speed at which the wire is wound.
This means that you have to be careful comparing ring sizes in different materials. For example, I made some box chain with bright aluminum in 20g (AWG) 1/8" rings, and then tried it with sterling silver in the same size from the same manufacturer. The silver chain was too tight and the weave was distorted. I realized later that the aluminum has more springback, so the actual AR is slightly bigger than the actual AR of the silver rings even though they were both made with a 1/8" mandrel. In general, silver tends to have less springback than steel or aluminum, depending on temper.

Experience is generally the best way to sort out exactly what size will work best in what metals, but estimated AR is a good guide. Some ring sellers recommend certain sizes for certain weaves, and you may learn from other maillers' preferences.

Quick Tips
* For the same wire gauge, smaller ID = smaller AR; larger ID = larger AR.
* For the same ID, thicker wire = smaller AR; thinner wire = larger AR.
* Smaller AR = tighter weave; larger AR = looser weave.
* Smaller AR = stronger ring.
* Pay attention to whether your wire gauge is AWG or SWG; 16g AWG 1/4" rings have a different AR than 16g SWG 1/4" rings.
* If you have a preferred size for a weave, use the AR for that size to find another ring size that will work:
AR x new wire diameter = new ring ID
new ring ID / AR = new wire diameter

* Because of springback, rings made with a harder wire will generally have a slightly higher AR than rings made with a softer wire (when the wire thickness and mandrel are the same).

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