How do you even measure such a thing and why would you bother? Machinist Tom Lipton shows how and then explains why it might be useful to know the thickness of various colors and types of ink.
Different colors have different thicknesses? That's right—red, blue, and black Sharpie lines are not equally thick.
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In the video below Lipton uses a Johansson Mikrokator to measure the thickness of various lines. A mikrokator is like a dial indicator only far more precise. By way of comparison, the scale on the cheap dial indicator I use to align woodworking machines is graduated in thousandths of an inch; Lipton's mikrokator is graduated in millionths.
The process of measuring is as follows. Lipton starts by zeroing out the plunger of the mikrokator against a gauge block of known thickness. He removes the block, draws a series of lines on it, and then places it back under the plunger. The added thickness created by the lines of Sharpie ink cause the plunger to sit slightly higher, a distance that registers on the scale of the mikrokator.
If the scale reads zero with just the block and 132 millionths after the block has been inked then we know the ink is 132 millionths of an inch thick. Lipton performed this test multiple times with different types and colors of ink and came up with the average thickness of various lines. He also tested Dykem Layout Fluid, a pigment machinists use to color the surface of metal prior to scribing marks on it (to make the marks easier to see).
Lipton compiled the data into a table that can be seen near the end of the video (8:20). So why would it matter that black Sharpie lines are 118 millionths of an inch thick and red Sharpie lines are 160 millionths of an inch thick? Well, if a machinist knew he needed to increase the height of a fixture by approximately 160 millionths of an inch he could draw a series of red Sharpie lines on the bottom of it. Or some other color or type of ink for a different distance.
It may seem crazy to think in terms of such small increments of distance but this is the level of precision required for certain machining operations.
The notion of using lines of ink as "shims" does not feel foreign to me. I've never measured it but as a carpenter and woodworker, I know that layers of paint have a certain thickness. If I'm making fine adjustments to the fit of a door I might shim out a hinge by sticking one or more layers of duct or masking tape to the back of it. What Lipton talks about doing with ink is just a more precise way of doing what a carpenter does with tape.