# Laser-Engraving Hairlines: When A Line Isn’t A Line

When is a line not a line? When it’s a series of tiny dots, of course!

That’s the technique [Ed Nisley] used to create a super-fine, colored hairline in a piece of clear plastic — all part of his project to re-create a classic Tektronix analog calculator from the 1960s, but more on that in a moment.

[Ed] tried a variety of methods and techniques, including laser engraving a solid line, and milling a line with an extremely tiny v-tool. Results were serviceable, but what really did the trick was a series of tiny laser-etched craters filled in with a red marker. That resulted in what appears — to the naked eye — as an extremely fine hairline. But when magnified, as shown here, one can see it is really a series of small craters. The color comes from coloring in the line with a red marker, then wiping the excess off with some alcohol. The remaining pigment sitting in the craters gives just the right amount of color.

This is all part of [Ed]’s efforts to re-create the Tektronix Circuit Computer, a circular slide rule capable of calculating all kinds of useful electrical engineering-related things. And if you find yourself looking to design and build your own circular slide rule from scratch? We have you covered.

# Genaille’s Rods: When Paint Sticks Do Math

What is a hacker, if not somebody who comes up with solutions that other just don’t see? All the pieces may be in place, but it takes that one special person to view the pieces as greater than the sum of their parts. As [Chris Staecker] explains in the video below the break, Henri Genaille was one such person.

When French mathematician Edouard Lucas (himself well known for calculating the longest prime number found by hand) posed a mathematical problem at the French Academy, a French railway engineer named Henri Genaille developed the rods we’re discussing now.

Genaille’s Rods are designed to perform multiplication. But rather than require computation by the user, the rods would simply need to be laid out in the correct order. The solution could readily be found by just following the lines in the correct pattern. This might sound a lot like cheating, and that’s exactly what it is. No manual math needed to be done. Genaille also created rods for doing long division, which we’re sure were every bit as enthralling as the multiplication rods. Demonstrations of both are included in the video below.

While Genaille’s Rods have gone the way of the slide rule, we can’t help but wonder how many engineers and scientists carried around a set of marked up wooden sticks in their pocket protector.

If designing and building manual mathematical machines is something that you think really adds up to a good time, check out this post on how to design and build your own circular slide rule!

# Rubber Band “Slide Rule” Doesn’t Slide, But Rotates

Around here we mostly enjoy slide rules. We even have our own collections including some cylindrical and circular ones. But [Mathologer] discusses a recent Reddit post that explains a circular slide rule-like device using a wheel and a stretchable rubber band. While it probably would be difficult to build the actual device using a rubber band, it can do wonders for your understanding of logarithms which still show up in our lives when, for example, you are calculating decibels. [Dimitri] did simulate the rubber band for you in software.

The idea is that a perfect rubber band has numbers from 0 to 10 evenly marked on it. As you rotate a wheel attached at the 10 mark, the rubber band stretches more and more. So the 10 and the 9 have relatively little space between them, but the 1 and the 2 are much further apart. The wheel’s circumference is set so that the 1 will exactly overlay the 10. What this means is that each spot on the wheel can represent any number that differs only by a decimal point. So you could have 3 mean 0.03, 300, or — of course — 3. Of course, you don’t need to build the wheel with a rubber band — you could just mark the wheel like a regular circular slide rule.

# Circuit VR: The Wheatstone Bridge Analog Computer

We are always impressed with something so simple can actually be so complex. For example, what would you think goes into an analog computer? Of course, a “real” analog computer has opamps that can do logarithms, square roots, multiply, and divide. But would it surprise you that you can make an analog device like a slide rule using a Wheatstone bridge — essentially two voltage dividers. You don’t even need any active devices at all. It is an old idea and one that used to show up in electronic magazines now and again. I’ll show you how they work and simulate the device so you don’t have to build it unless you just want to.

A voltage divider is one of the easiest circuits in the world to analyze. Consider two resistors Ra and Rb in series. Voltage comes in at the top of Ra and the bottom of Rb is grounded. The node connecting Ra and Rb — let’s call it Z — is what we’ll consider the output.

Let’s say we have a 10 V battery feeding A and a perfect voltmeter that doesn’t load the circuit connected to Z. By Kirchoff’s current law we know the current through Ra and Rb must be the same. After all, there’s nowhere else for it to go. We also know the voltage drop across Ra plus the voltage drop across Rb must equal to 10 V. Kirchoff, conservation of energy, whatever you want to call it.  Let’s call these quantities I, Va, and Vb. Continue reading “Circuit VR: The Wheatstone Bridge Analog Computer”

# Design And Build Your Own Circular Slide Rule

You have to really like slide rules to build your own, including the necessary artwork. Apparently [Dylan Thinnes] is a big fan, based on this project he began working on a few months back. The result is a set of algorithms that automatically generates most of the scales that were common on slide rules back in the day. For example:

```K       Cubic scale, x^3
A,B     Squared scale, x^2
C,D     Basic scale, x
CI,DI   Inverted scale, 1/x
CF,DF   Folded scale, x*pi
LLn     Log-log scales, e^a*x
LL0n    Log-log scales, e^-a*x
L       Log scale, log10(x), linear
S       Sine and cosines scale, sin(x)
T       Tangent scale, tan(x)

```

If you’ve ever tried to manually draw an axis using a computer program — attempting to automatically set reasonable tick marks, grids, and labels — you can appreciate that this is a non-trivial problem. [Dylan] tackled things from the bottom up, developing several utility functions that work in concert to iteratively build up each scale. One advantage of this approach, he says, is that you can quite easily build almost any scale you want. We’re going to take his word on that, because the project is not easily accessible to the average programmer. As [Dylan] notes:

At the moment it’s still a library w/ no documentation, and written in a relatively obscure language called Haskell, so it’s really only for the particularly determined.

The project is published on his GitHub repository, and sample scales and demo program are available. Without knowledge of obscure languages and being only mildly determined, one can at least generate some sample scales — just downloading the Haskell environment, a few dependencies, and clone [Dylan]’s repository. The output is an SVG file which can be scaled to any desired size. In this follow-up Reddit post he discusses the fabrication techniques used for the acrylic circular slide rule shown in the lead photo.

It’s always been possible to make your own slide rules using pre-generated artwork — for example, the Slide Rule Museum website has a slew of various scales available in graphic format. But if you want to make a custom scale, or make one of that’s meters long, check out [Dylan]’s project and give it a whirl. For another take on making slide rules, check out this project that we covered last year.

# Homebrew Slide Rule Gets Back To Mathematical Basics

In the grand scheme of things, it really wasn’t all that long ago that a slide rule was part of an engineer’s every day equipment. Long before electronic calculators came along, a couple of sticks of wood inscribed with accurate scales was all it took to do everything from simple multiplication to logarithms and trig functions.

While finding a slide rule these days isn’t impossible, it’s still not exactly easy, and buying one off the shelf isn’t as fun or as instructive as building one yourself. [JavierL90]’s slide rule build started, ironically enough, on the computer, with a Python program designed to graphically plot the various scales needed for the fixed sections of the slide rules (the “stators”) and the moving bit (the “slide”).  His first throught was to laser-engrave the scales, but the route of printing them onto self-adhesive vinyl stock proved to be easier.

With the scale squared away, work turned to the mechanism itself. He chose walnut for the wood, aluminum for the brackets, and a 3D-printed frame holding a thin acrylic window for the sliding cursor. The woodworking is simple but well-done, as is the metalwork. We especially like the method used to create the cursor line — a simple line scored into the acrylic with a razor, which was then filled with red inks. The assembled slide rule is a thing of beauty, looking for all the world like a commercial model, especially when decked out with its custom faux leather carry case.

We have to admit that the use of a slide rule is a life skill that passed us by, but seeing this puts us in the mood for another try. We might have to start really, really simple and work up from there.

# Hands-On: Smarty Cat Is Junior’s First Slide Rule

You may remember that I collect slide rules. If you don’t, it probably doesn’t surprise you. I have a large number of what I think of as normal slide rules. I also have the less common circular and cylindrical slide rules. But I recently picked up a real oddity that I had to share: the Smarty Cat. It isn’t exactly a slide rule but it sort of is if you stretch the definition a bit.

## Real Slide Rules

A regular slide rule takes advantage of the fact that you can multiply and divide by adding logarithms. Imagine having two rulers marked in inches or centimeters — it doesn’t matter (see the adjoining image). Suppose you want to add 5 and 3. You count off 5 marks on one ruler and line it with up the zero inch mark on the other ruler. Now you count off 3 marks on the second ruler and that position on the first ruler will indicate the result. Here it lines up with the 8 mark, which is, of course, the correct answer.

That’s a simple addition. But if you can convert your numbers into logarithms, add the logarithms, and then back out to a regular number, you can multiply.