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.

Slide Rules Were The Original Personal Computers

Unless you are above a certain age, the only time you may have seen a slide rule (or a slip stick, as we sometimes called them) is in the movies. You might have missed it, but slide rules show up in Titanic, This Island Earth, and Apollo 13. If you are a fan of the original Star Trek, Mr. Spock was seen using Jeppesen CSG-1 and B-1 slide rules in several episodes. But there was a time that it was common to see an engineer with a stick hanging from his belt, instead of a calculator or a cell phone. A Pickett brand slide rule flew to the moon with the astronauts and a K&E made the atomic bomb possible.

Slide rules are a neat piece of math and history. They aren’t prone to destruction by EMP in the upcoming apocalypse (which may or may not include zombies). Like a lot of things in life, when it comes to slide rules bigger is definitely better, but before I tell you about the 5 foot slide rule in my collection, let’s talk about slide rules in general.
Continue reading “Slide Rules Were The Original Personal Computers”

Bil Herd: Computing With Analog

When I was young the first “computer” I ever owned was an analog computer built from a kit. It had a sloped plastic case which had three knobs with large numerical scales around them and a small center-null meter. To operate it I would dial in two numbers as indicated by the scales and then adjust the “answer” by rotating the third dial until the little meter centered. Underneath there was a small handful of components wired on a terminal strip including two or three transistors.

In thinking back about that relic from the early 1970’s there was a moment when I assumed they may have been using the transistors as logarithmic amplifiers meaning that it was able to multiply electronically. After a few minutes of thought I came to the conclusion that it was probably much simpler and was most likely a Wheatstone Bridge. That doesn’t mean it couldn’t multiply, it was probably the printed scales that were logarithmic, much like a slide rule.

Did someone just ask what a slide rule was? Let me explain further for anyone under 50. If you watch the video footage or movies about the Apollo Space Program you won’t see any anyone carrying a hand calculator, they didn’t exist yet. Yet the navigation guys in the first row of Mission Control known aptly as “the trench”, could quickly calculate a position or vector to within a couple of decimal places, and they did it using sliding piece of bamboo or aluminum with numbers printed on them.

Papercraft Dial Is The Slide-ruler Of Current Limiting Resistors

This paper dial makes selecting current limiting resistors a snap. [Giorgos Lazaridis] came up with the tool, which he describes in detail in the Worklog tab of his writeup. If you want one of your own he also posted a PDF which you can print, cut, and tack together.

At this point we can calculate resistor values for LED circuits without looking at reference material. But it wasn’t always like that. This wheel will be a fantastic tool for those just starting out in hobby electronics who are trying to grasp the theory behind lighting up a simple project. The outer wheel references the source voltage, with the inner being a gauge of forward voltage across the LED(s). Line those two values up and you can read the optimal resistor value in the window seen to the right. But wait, there’s more! As you can see in the video after the break the opposite face of the dial also includes a window which will tell you the power dissipation so that you may choose a properly rated resistor. Slick!