Slide Rule for the Modern Day
Introduction: Slide Rule for the Modern Day
Ah the noble slide rule.
Once an staple of the engineer's tool belt, this form of handheld analog calculator seems to have been forgotten by all but a few. Lurking in the shadows hides a fascinating, elegant piece of technology, a tool able to perform a surprisingly large variety of calculations, all the while exemplifying all the elements of good design.
Even if the slide rule became "obsolete" in the 70s as electronic calculators took their place, I knew that I had to build one myself. Getting a hold of a slide rule is not an issue since you can buy them cheaply on ebay, but I knew I wanted to build one anyway to:
1. Learn about what makes good design by totally immersing myself in one example of it
2. Challenge myself to recreate an older technology with a modern approach
3. Throw myself into a marathon of different manufacturing techniques to force myself to finally learn how to use new tools that might be helpful later in life
So stick around, learn about the slide rule, and even if you won't build one, there might be plenty of methods and ideas you might be able to apply in your own work!
Step 1: Brief Context on the Slide Rule
As mentioned before, the slide rule is a calculator. 51
By using various scales, a sliding central piece, and a cursor (the outermost sliding piece with a vertical red line), the user can multiply, divide, find cubes, cube roots, squares, square roots, sines, cosines, tangents, reciprocals, logarithms and exponents! Not bad for a couple of sliding sticks.
In the 1900s, companies like Keuffel & Esser, Post, Pickett, and Dietzgen produced many models of slide rules, some of which you can pick up and play with at flea marks and ebay for as little as $5-10. For context, check out the pic above comparing my own slide rule and one made by the Post company in Japan some time in the mid 20th century.
Back in the 1600's, <PERSON> publicized the concept of logarithms and their weird but useful properties. You might remember from the high school precalc days that the logarithm function can convert products into sums, and vise versa.
Shortly after <PERSON>'s publication, people noticed that we could exploit that special property and use two parallel rulers to multiply and divide. Above, you can find a diagram I made in TikZ showing how one might go about generating one of the scales, the "C" and "D" scales.
Step 2: The Generating Function
Eventually, new scales were developed that could perform all the other operations I mentioned earlier, each one using a specific function (based on the base ten log, of course). I've compiled the "generating functions" I used in my slide rule into a table above in case you're curious.
The general strategy for coming up with new scales is:
* Plot numbers at the value returned by the generating function
* Realize that two numbers placed across from each other represent setting their returned values equal to each other
* Sliding the central piece represents adding or subtracting values
* Certain equalities between generating functions reduce to useful operations
Above, I sketched out an example that illustrates the concept. Because the C scale has generating function log(x), and the A scale has generation function 1/2 log(x), we use the facts we know to conclude that these two scales in combination have a useful property: we can use them to find squares and square roots.
The mathematical background for all the other scales is complicated (but interesting), but to save you from my endless blabbering about why slide rule math is so great, I'll restrain myself!
Step 3: Slide Rule Design
The slide rule design has a lot going for it in terms of "good" design:
* Simple & elegant construction of few parts
* Smooth slide and cursor slide action is pleasing to use
* Accurate to around ± 0.2%, enough for applications as involved as some skyscrapers and space expeditions
+ If you pay attention, in the iconic Apollo 13 movie you can see slide rules at Mission control AND in the spacecraft itself!
* Teaches user to master concepts of [the infamous] sig figs and orders of magnitude
* Will still work even in the inevitable heat death of the universe since it requires no power
Take time to acquaint yourself and get friendly with all the components of the device, using the anatomy diagram above
Step 4: Tools and Techniques
One of the major goals of this project was to recreate an older technology using modern techniques that would not have been accessible back then. 855