# How to Calculate Coloring Ink Consumption?

Coloring ink is used to color natural fibers. Colored fibers are required to effectively identify fibers in a group of fibers called bundle that are encapsulated in loose tube. Natural optical fibers have a cylindrical profile. Coloring is a thin coating of UV curable coloring ink over the surface of Natural optical fibers. Though very thin, this coating has a thickness and therefore the diameter over the color coated fiber is more than that of the natural optical fiber. Structurally, if we take out the natural optical fiber from colored optical fiber, the Color coating over natural optical fiber can be considered as a hollow cylinder.

Color coating thickness is typically in the range of 3 to 5 micrometers. More thickness is not preferred both performance wise and cost wise. CLt    = Colored fiber thickness
CLid   = Natural optical fiber outer diameter (Colored fiber inner diameter)
CLod  = Colored fiber outer diameter

The unit mass of a hollow cylinder structure is given by the following formula:
M = V x Md
where M = Mass or weight of the material in kg, V is the Volume of the material in mm3, Md is the Material density or specific gravity in g/cc (cm3). Volume of this hollow cylinder is given by the following formula: where, Vcl is the volume of hollow cylindrical structure, Clod is the outer diameter of colored fiber in mm, CLid is the outer diameter of natural fiber (before coloring) in mm., l is the unit length in mm.

Example:
Colored optical fiber diameter = 260 μm = 0.26 mm, Natural optical fiber diameter = 250 μm = 0.25 mm
Coloring ink density = 1.13 g/cc
Putting these values in the above formula: which means, we need 4.526 grams of coloring ink to color 1 km of Natural optical fiber.

The above values should be multiplied with stranding factor to get the weight of coloring ink required in one kilometer cable. Stranding process induce excess tube and fiber length in the finished cable.

For example, assuming that in 24 fiber cable, where all the fibers are colored using the following color codes, the calculation is shown below;
Fiber Colors : Blue, Orange, Green, Brown, Grey, White
Tube Colors: Blue, Orange, Green, Brown
In one tube, there are 6 colored fibers. Such 4 tubes along with 2 fillers are stranded around a strength member. Then the quantity of coloring ink required for each color can be derived from the following formula:

TWcf = M x Sx Tx Fn

where TWcf is the Total weight of coloring ink, M is the weight of coloring ink, Sf is the stranding factor, Tn is the number of tubes, Fn is the number of fibers per tube. Suppose, for a given design with a certain central strength member diameter and loose tube diameter, the stranding factor is 1.015, then
TWcf = 0.004526 x 1.015 x 4 x 6 = 0.1103 kg

The above results shows that we need a total of 110.3 grams of coloring ink. Unit consumption for each color will then be We consider the Excess fiber length in the tube after stranding process is zero. The reasons are explained in the stranding process.  #### Author: Thomas Mathew

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