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Calculating Rings Per Coverage
Article © MAIL User: Chainmailbasket_com
Chain:
rings per cm = rings per inch / 2.54
Sheet:
rings per square cm = rings per square inch (RPI²) / 6.4516
Dimensional:
rings per cubic cm = rings per cubic inch (RPI³) / 16.387064
Rings per coverage information is valuable in project planning. It is nice to know roughly how many rings will be going into a project: a chain for a necklace or bracelet, perhaps, or a sheet weave being used to make a shirt or other clothing item, for example. All you need to do is figure out how much total material will be required for an application, and then use the rings per coverage data for a specific weave using specific ring sizes to get an idea of what you're facing. Rings per volume are far less commonly used, as there are very few true dimensional weaves, and their uses are much more limited.
You'll notice that I take my measurements starting at the 10" gradient. The reason for this is that the tape measure I'm using is kind of worn out and ratty near the end. I always take measurements with the weave stretched out fully. With sheet weaves, the weave must only be stretched out one way. For example, I'll stretch European 4 in 1 horizontally for the rings per length measurement, and keep it stretched out that way when measuring for rings per width.
Despite the samples being measured in this article being rather small, it's a good idea to use as large a sample as possible. The larger the sample, the more accurate the resulting data will be.
Chain Weaves (Rings Per Length)
Chain weaves are the most straightforward to collect this information for. All you have to do is measure a length of the chain and count how many rings are in that length, then use division to find the rings per unit. Two examples are presented:
Full Persian 6 in 1
Ring size:
wire: .048" (18 SWG / 1.2mm) stainless steel
mandrel: 1/4" (6.35mm)
ID: .278"
AR of 5.8
This sample is 3" long. In this example, I've used two larger rings to pull the weave to its tightest form (without pulling any rings apart), while I make the measurement. There are four rings per unit in FP6-1, and there are 12 units in this sample, making it 48 rings long.
48 / 3"
=16 RPI
There are 16 rings per inch for this weave at this ring size.
Quint Reinforced Inverted Round (C2)
Ring sizes:
wire: .063/2" (16 SWG / 1.6mm) stainless steel
mandrels: 7/16" (11.1mm), and .602" (15.3mm)
IDs: .494", and .687"
AR of 7.8, and AR of 11
In the picture, the sample appears to be about 3 5/8" long, but stretched out, it's closer to 3 11/16". The chain is 10 units long, and there are seven rings per unit (five angled rings and two "captives"). (10 * 7) = 70 rings total.
70 / 3 11/16"
= 70 / 3.6875
=18.98 RPI
The rings per inch for this weave at this ring size is 18.98.
I keep this data in a spreadsheet which automatically calculates these values with the same formula. These two samples are presented. Column J uses the formula "=I2/H2" for the Full Persian entry on the second line, and the same formula is used all the way down to calculate rings per inch. AR (which is optional) is calculated the same way using ID (inner diameter) divided by WD (wire diameter):
Sheet Weaves (Rings Per Area)
Sheet weaves are expanded in two directions. Therefore there are two measurements to take and the product of them provides us the rings per area. In the case of the examples shown, rings per square inch is calculated.
Straightforward Sheet Weaves
Sheet weaves like European 4 in 1, 6 in 1, 8 in 1, etc., Dragonscale, and even Half Persian 3 Sheet 6 in 1 are easy to measure, as they contain straightforward rows and columns.
European 4 in 1
Ring size:
wire: .063" stainless steel
mandrel: 5/16" (7.94mm)
ID: .346"
AR of 5.5
This sample is from a chainmail shirt that I made. It is important to measure from the start of the first ring, to the end of the last ring (which is tucked underneath in this case). There are 14 rings in a just over 5 7/8" length. It's close to 1/128" above than this, so I'll use 5 113/128".
14 / 5 113/128"
= 14 / 5.8828125
=2.3798141 RPI
Just like we did with the length measurement, it's important measuring the width to start where the first ring begins and end where the last ring ends. Also remember to count the rows leaning in both directions. In this example, approximately 3 11/32" worth of weave width comprises 13 columns. The curve of the tape measure makes it difficult to judge this from the picture, but I can vouch for it.
13 / 3 11/32"
=13 / 3.34375
=3.8878505 RPI
Taking the RPI length and multiplying it by the RPI width gives us rings per square inch:
2.3789141 * 3.8878505
=9.25 RPI²
Half Persian 3 Sheet 6 in 1
Ring size:
wire: .062" bright aluminum
mandrel: 9/32" (7.14mm)
ID: .308"
AR of 5.0
You might be thinking that finding rings per area is more difficult for this weave because it expands as a rhombus. This doesn't matter too much, as each row of the same number of rings, like in the example shown is the same length. This sample is 7 rings long and measures 1 13/16".
7 / 1 13/16"
=7 / 1.8125
=3.862069 RPI
Also, every row added adds the same to the width as the last, as with any straightforward sheet weave. This sample is 9 columns wide and measures 1 1/4".
9 / 1 1/4"
=9 / 1.25
=7.2 RPI
The product of RPI length and RPI width offers the rings per square inch:
3.862069 * 7.2
=27.81 RPI²
This data can be put in a spreadsheet, but it will require a few columns more than the one used for chain weaves. Formulas are used to calculate rings per inch for the length, RPI for the width, and a third one, the product of the two, for rings per square inch:
Less Straightforward Sheet Weaves
When a sheet weave doesn't contain the simplistic row x column structure, it becomes more difficult to derive rings per area data. Ones that come to mind include Japanese 4 in 1, and Staggered Captive Inverted Round Sheet.
Staggered Quad Captive Inverted Round Sheet (C1)
Ring size:
wire: .048" stainless steel
mandrels: 17/64" (6.75mm), and 11/32" (8.73mm)
IDs: .303", and .397"
AR of 6.3, and AR of 8.3
There still are rows and columns, like with straightforward sheet weaves, however, each row is not made up of rows of single rings. So this weave must be divided into repeatable "units". Regarding length, we count the number of units long this weave is. This example is 12 units long and measures 2 7/8".
12 / 2 7/8"
=12 / 2.875
=4.173913 RPI
The picture is sligthly misleading, but this sample does measure 2 1/16"
When you look at the structure of this weave, you will note that it is chains of Quad Captive Inverted Round separated by rows of connector rings. Concerning the width, it is important to observe the number of rings in a full unit. With this weave, there are four captives surrounding one cage ring, plus one connector ring. This makes up one full, repeatable unit. Six (6) rings per unit times the number of units in the width of the sample (6 * 3 = 18) comprise a width of 2 1/16".
=18 / 2 1/16"
=18 / 2.0625
= 8.727272727 RPI
Multiplying RPI length and RPI width yields the rings per square inch:
4.173913 * 8.727272727
=36.43 RPI²
This data is appended to the sheet weave rings per square inch spreadsheet:
Japanese 4 in 1
Looking at this weave, you'll notice that each row is not the same. One row contains vertical and horizontal rings, while the next contains half the number of rings, which are all verticals. Almost the same principle needs to be applied as with the previous example to figure out rings per area. The difference lies in the fact that the total number of repeatable units must be counted for both the length and width of this weave. However, one value used must be the total number of repeatable units, and the other must be the product of the number of repeatable units and the number of rings per repeatable unit, which is three in this case (one horizontal and two verticals). The example shown above is five repeatable segments long. Five repeatable segments of three rings each in width makes it 15 rings wide (3 * 5 = 15). The sample contains 75 rings (5 * 15).
Confusing? A little bit.
Difficult Sheet Weaves
Hexagonal webs and other hexagonally-expanding weaves, such as Voodoo Hexagonal, Japanese 12 in 2, Captive Orbital Hex Cage, Japanese Dragonscale, as well as other sheet weaves that don't expand in a rectangular and/or parallelogrammatical fashion add even more to the challenge of extracting rings per area data. For this reason, I will not attempt to do this or try to explain how in this article. I will just say that it can be done...
Dimensional Weaves (Rings Per Volume)
It is possible to collect rings per length, rings per width, and rings per height for dimensional weaves, multiply the three, and receive the number of rings per volume (cubic inches, e.g.). This can be done with any of the dimensional weaves like Japanese 4 in 1 Cube, Japanese 8 in 2, and Byzantine Web Square Cube. This information would be far less beneficial than chain and sheet data to most maillers, as dimensional weaves are generally only used in sculptural, and other less common applications. I won't provide any examples, but using the information and techniques described above, it can be done.
Also Noteworthy
With technological advances in the art of maille, via mathematical formulas, it is not unreasonable to suggest that only one set of data need to be taken for any (most) given weave type(s). If one were able to concoct a formula to calculate the rings per coverage data as it was scaled up or down to different ring sizes, then they could start with one basic dataset. With the use of mathematics, almost anything is possible.
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=647