zlosk.com: Chain Mail - Opacity Equations and Table

Chain Mail - Opacity Equations and Table

Section of 4-in-1 maille

The picture above shows a section of 4-in-1 maille. A glossary of the terms I'm using is listed below.

opaque link area: the gray area of the links inside the yellow square
total link area: the whole yellow square
opacity: the ratio of opaque link area to total link area, expressed as a percentage
gap area: the orange section in the middle
max gap: The approximate length of a side of the gap area. Since the links are pulled as far apart as they can, I am assuming the the gap length is at its maximum. The gap area roughly forms a square turned 45°, and the area of a square is length x length, I took the square root of the gap area to get the max gap.

Opacity / Max Gap Table

Size	Opacity	MaxGap
16Gu 3/16"	88.0%	.06" x .06"
14Gu 1/4"	85.9%	.09" x .09"
18Gu 3/16"	71.8%	.10" x .10"
16Gu 1/4"	71.0%	.13" x .13"
14Gu 5/16"	72.5%	.16" x .16"
18Gu 1/4"	54.2%	.17" x .17"
12Gu 3/8"	78.5%	.17" x .17"
16Gu 5/16"	56.8%	.21" x .21"
18Gu 5/16"	44.7%	.23" x .23"
14Gu 3/8"	59.5%	.24" x .24"
12Gu 7/16"	68.5%	.25" x .25"
16Gu 3/8"	48.2%	.27" x .27"
14Gu 7/16"	52.3%	.30" x .30"
12Gu 1/2"	58.7%	.32" x .32"
14Gu 1/2"	46.6%	.37" x .37"
12Gu 3/4"	42.1%	.57" x .57"

Here is the code used to generate the opacity table. It is written in VBA for Excel:


Function Opacity4in1a(WireDia As Double, RingID As Double) As Double

  Pi = 4 * Atn(1)

  R1 = RingID / Sqr(2)

  r2 = RingID / 2 + WireDia

  

  If R1 / r2 < 1 Then

    theta = Application.WorksheetFunction.Acos(R1 / r2)

    alpha = (Pi / 2#) - 2# * theta

    Pyth1 = Sqr(r2 ^ 2 - R1 ^ 2)

    OpenArea = R1 ^ 2 - 0.5 * alpha * r2 ^ 2 - R1 * Pyth1

    OpenArea = 8 * OpenArea

  Else

    a = RingID / 2

    

    OpenArea = Pi / 4 * a ^ 2

    

    b = a + WireDia

    d = RingID

    g = 0.5 / d * (d ^ 2 - a ^ 2 + b ^ 2)

    e = Sqr(b ^ 2 - g ^ 2)

    

    c = 2 * e 'chord length

    r = a

    h = r - 0.5 * Sqr(4 * r ^ 2 - c ^ 2)

    phi = 2 * Application.WorksheetFunction.Asin(c / (2 * r))

    l = r * phi

    area = 0.5 * (r * l - c * (r - h))

    OpenArea = OpenArea - area

    

    r = b

    h = r - 0.5 * Sqr(4 * r ^ 2 - c ^ 2)

    phi = 2 * Application.WorksheetFunction.Asin(c / (2 * r))

    l = r * phi

    area = 0.5 * (r * l - c * (r - h))

    OpenArea = OpenArea - area

    

    OpenArea = 8 * OpenArea

  End If

  

  ClosedArea = 2 * RingID ^ 2

  Opacity4in1a = 1 - OpenArea / ClosedArea

End Function

Here is the code used to generate the opacity table. It is written in VBA for Excel. A lot of the code is the same as the opacity code.


Function MaxGap(WireDia As Double, RingID As Double) As Double

  Pi = 4 * Atn(1)

  R1 = RingID / Sqr(2)

  r2 = RingID / 2 + WireDia

  

  If R1 / r2 < 1 Then

    theta = Application.WorksheetFunction.Acos(R1 / r2)

    alpha = (Pi / 2#) - 2# * theta

    Pyth1 = Sqr(r2 ^ 2 - R1 ^ 2)

    OpenArea = R1 ^ 2 - 0.5 * alpha * r2 ^ 2 - R1 * Pyth1

    MaxGap = 4 * OpenArea

  Else

    a = RingID / 2

    

    OpenArea = Pi / 4 * a ^ 2

    

    b = a + WireDia

    d = RingID

    g = 0.5 / d * (d ^ 2 - a ^ 2 + b ^ 2)

    e = Sqr(b ^ 2 - g ^ 2)

    

    c = 2 * e 'chord length

    r = a

    h = r - 0.5 * Sqr(4 * r ^ 2 - c ^ 2)

    phi = 2 * Application.WorksheetFunction.Asin(c / (2 * r))

    l = r * phi

    area = 0.5 * (r * l - c * (r - h))

    OpenArea = OpenArea - area

    

    r = b

    h = r - 0.5 * Sqr(4 * r ^ 2 - c ^ 2)

    phi = 2 * Application.WorksheetFunction.Asin(c / (2 * r))

    l = r * phi

    area = 0.5 * (r * l - c * (r - h))

    OpenArea = OpenArea - area

    

    MaxGap = 4 * OpenArea

  End If

  

End Function

Questions or comments? Email me at mailler@zlosk.com.

This page last updated on January 6, 2005.