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# Aspect Ratio StudiesArticle © MAIL User: Blaise

The purpose of this article to to discuss the standardization of methods in the determination of valid aspect ratios for maille weaves, as determined by the formula AR = id / wd where AR = aspect ratio, id = inner ring diameter, and wd = wire diameter. It is based on discussions I have had with another M.A.I.L. board member, Drax, and is as much his intellectual child as mine (so you can blame him too if you don't like it :) ). It is only a preliminary attempt to codify a set of standards to which we can all subscribe for clearer communication on the topic.

In the recent past, many people have posted recommendations for aspect ratio requirements for certain weaves, even going as far as to post massive tables of these recommendations. While these are quite helpful, none have clearly documented the process by which they have obtained their numbers so that others can reproduce their results.

Outlined herein is one possible standardization scheme, posted for commentary and futher work, along with a small preliminary dataset I have developed.

Concepts:

In order to ensure that all AR discussions are on a level playing field, is is necessary to specify that there are actually two minimum aspect ratios for most weaves. The first minimum is the Absolute Minimum, which is the AR at which the weave becomes possible at all. It must be noted that weaves at their absolute minimum AR will usually 'lock up' after very few rings have been added, as the ratio is not sufficient for a continuous weave, so each added link is using up 'slack' in the weave, until there is no more room to continue the weave with another ring. The second minimum is the Practical Minimum. This is the minimum AR where a weave can be woven continuously to any desired length or area. Both minimums are important, as it would be easy to misadvise someone if an AR test did not take the difference into account, and sometimes it is beneficial to have a 'locked up' section in a design.

In order to accurately determine the inner diameter of a ring, it is necessary to recognize that regardless of whether hand or machine-made, no ring is a perfect circle, and no two rings are exactly the same size. Therefore, we must determine an Approximate Inner Diameter for every ring measured, determined by taking two measurements across the centerpoint of the ring, but on axes oriented 90° apart, and averaging the two measurements. This scheme relies on the approximation that a ring will have the characteristics of an ellipse, but should suffice for our purposes.

Method:

The suggested procedure is as follows:
1. Find an example of a weave which exhibits either of the two minimum AR characteristics, namely absolute minimum, or practical minimum. As yet, this process is trial and error, as it is unlikely that an experimenter will have access to an infinitely variable set of ring diameters and wire diameters.
2. Ensure that all rings for an experiment come from the same coil (or wire batch, if machine made), to ensure consistency.
3. Weave enough of the weave to be certain which of the two mimimums it represents (usually at least 10 rings, often more).
4. Hold aside five unwoven rings from the same batch, and close them in the same fashion as those in the weave sample.
5. For each ring, determine the wire diameter using as accurate a device as possible, usually a caliper capable of measuring in units of at most 1/100th of an inch (1/1000th is preferable), or the metric equivalent.
6. For each ring determine the approximate inner diameter, as outlined above, using the same measurement device as in the previous step
7. Average the wire diameters for the five test rings.
8. Average the a.i.d.'s of the five test rings.
9. Determine the AR using the formula: AR = id(average) / wd(average)

Procedural notes:

• When measuring wire and ring diameters, beware of tool marks, as they can cause dips in the wire which make significant differences. Try to choose measurement axes which do not intersect any tool marks.
• Where possible, use the same number of significant digits in all your calculations. My own calipers are too inaccurate to allow this, as they only resolve to 1/100ths of an inch, but it would produce the best results.
• Record the nominal guage or wire diameter, mandrel size(if used), and the material used, as it will allow others to reproduce results more easily.

Preliminary Tests:

 Weave Minimum AR Test Batch Nominal Data WD Axis1 Axis2 A.I.D. Avg. WD AVG. A.I.D. European 4 in 1 Absolute 3.3 18SWG, 1/8", nickel silver 0.043 0.043 0.043 0.043 0.043 0.142 0.142 0.142 0.140 0.142 0.142 0.142 0.142 0.142 0.138 0.142 0.142 0.142 0.141 0.140 0.043 0.141 European 4 in 1 Practical 3.7 16SWG, 3/16", copper 0.056 0.056 0.056 0.056 0.056 0.203 0.205 0.205 0.205 0.205 0.205 0.205 0.205 0.206 0.206 0.204 0.205 0.205 0.2055 0.2055 0.056 0.205 Full Persian 6 in 1 Absolute 5 18SWG, 3/16", nickel silver 0.043 0.043 0.043 0.043 0.043 0.213 0.215 0.215 0.212 0.213 0.215 0.212 0.212 0.217 0.213 0.214 0.2135 0.2135 0.2145 0.213 0.043 0.2137

Observations:

The measurements above are less than perfect. The calipers used resolve to 1/100", which is not ideal for our purposes, and significant digits were not universally observed. However, I believe the process itself is validated by the results. I await the comments from the membership...
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=197