Circular Slide Rule

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Introduction: Circular Slide Rule

After seeing Phil B's Making Your Own Slide Rule, I went on a huge slide rule kick. I did a lot of research on them, and when I did, I discovered that there are circular variations. One of the nice things about circular slide rules is that you'll never run into the "run the cursor off the end of the slide rule" problems, since there is no "end" to a circular slide rule. Plus, circles are nice. Ok! Let's get slidin'!

Step 1: Design the Slide Rule

The first thing you'll need to do is design the rule. There are places on the internet that have templates for circular rules, but I wanted to design my own. It turned out that in the process, I learned a lot about how slide rules worked. Anyways, I wrote a C code to produce a .svg file of the front and back faces, along with the interior pieces that hold the rule together while letting it slide around. The code is below, and the result is in "slide_stator.svg". The cursor is in "cursor.svg". I designed these files so that the rule could be cut out of acrylic with a laser cutter. I don't have my own laser cutter, so I had the guys over at ponoko.com do the cutting for me.

Anyways, some notes on the design:

On one side (let's call this "side 1"):
  * A log scale (inner)
  * A C/D scale (sliding)
  * A sine scale, in radians (outer)

On the other side (side 2):
  * A K scale (inner)
  * An A/B scale (sliding)
  * A cosine scale, in radians (outer)

UPDATE: At someone else's suggestion, I'm also attaching .pdf versions of the templates, so people can just use card stock. Note that when you look at the files, the lines are very very thin. This is because the Ponoko folks need to have the templates in a certain format.

Step 2: Tools and Materials

For the assembly, you won't need much:

 * Tweezers
 * White acrylic paint
 * Superglue
 * Lubricating oil
 * A steady hand

Step 3: Prepare Pieces

After getting my pieces in the mail, I had to unpeel all the protective backing from all the pieces. I went with 3mm black acrylic for the slide, and 3mm clear acrylic for the cursor. You might want to use the tweezers to peel the small pieces. After unpeeling everything, take note of which side is which. They're marked in the pictures (side 1 has the C/D scale, side 2 has the A/B scale). Also, note the blank circular pieces. These are the pieces that get sandwiched between the two faces of the rule, allowing it to slide.

Step 4: Paint the Numbers and Tics

(I actually did this part after I assembled the slide, but you'll definitely want to do this BEFORE assembly.)

The scoring marks weren't bright enough to be able to see the tic marks and numbers easily, so I decided to use white acrylic paint to  make them stand out. Luckily, you don't need to hand paint each individual line: just glob a whole bunch of paint over the tics and numbers, and then wipe off the excess with paper towels or rags. Do the same for the cursor pieces with the fancy-pants design on them. The acrylic is so smooth that the paint doesn't stick to the un-scored parts, and only stays in the grooves. Awesome!

Step 5: Assemble the Slide

Ok, here's where you're going to need the steady hand. It's really important that everytihng gets positioned just about perfectly here, otherwise the slide won't be able to slide, and/or you won't be able to read the scales on side 2 correctly.

First, take the larger of the sandwich pieces, and carefully superglue it to the outer ring of side 2 (the one with the A/B scale). It's very important that the rings are flush ALL the way around. Then take the inner ring of side 2, and superglue it to the inner ring of  the sandwich pieces, making sure the interior is flush.

Now you'll superglue the inner ring of side 1 to the other side of the inner sandwich ring. However, you need to make sure that the two sides are properly aligned. Take a sheet of paper and draw a straight line with a ruler across it. Fold down this line, and tape it to the inner ring of side 2, making sure to bisect it with the marked line. Now, find the side of the bisected circle that has the index on both the A/B scale, AND the K scale. This will be where two 1's line up. Put a little arrow on the guideline here, so you know which way the index should go on the other side. Now flip the whole thing over, unfolding the paper at the same time.

Use the guideline to superglue the inner ring of side 1 in the correct position. Make sure the 1 (the index) points towards the little arrow, and also that the interior circle is flush all the way around. Did you get it? Phew! But wait, there's more!

Do the same process of creating a guideline on the outer ring of side 2. Place the inner rings (all three that are now glued together) in the middle of the face down outer rings, making sure that side 2 FACES DOWN. Now, take the outer ring of side one, and superglue it to the outer sandwich ring ONLY. Since it's superglue, you only need a tiny bit; if you use too much here, there's a chance that it will seep out onto the inner rings, which would make it so it doesn't slide at all. Bottom line: use superglue sparingly here.

If you did everything correctly, you should be able to slide the inner rings freely. Mine were a little sticky, but after the oil (next step), they were moving pretty smoothly.

Step 6: Assemble the Cursor

Before assembling the cursor, you'll want to oil the slide. I used stone sharpening oil since it was the only thing I had on hand, but it ended up working very nicely. I'm pretty sure you could use any oil lubricant, as long as it doesn't affect acrylic.

Anyways, take the three innermost circular pieces left over from the slide pieces, and superglue them in a stack directly over the circle pattern on one of the cursor pieces. If everything is still lined up correctly, you should be able to push the three stacked pieces through the middle of the slide pieces. CAREFULLY glue the three clear endcap pieces onto the end of the cursor as shown in the picture.

Finally, superglue the final cursor piece onto the top of the three-circle-stack and the endcaps. Woot! It's done!

Step 7: Use It!

So as not to leave you hanging, here's a few examples of what this slide can do. Suppose you want to calculate 2.08 * 4.30:

 * Position the inner index of the C/D scale on 2.08 of the outer C/D scale.
 * Move the cursor to 4.30 on the inner C/D scale.
 * The answer is on the cursor on the outer C/D scale. In this case, it looks to be about 8.94.

To calculate sines, you use the cursor and the sine scale. For example, if you wanted to know sin(0.89):

 * Place the cursor on 0.89 on the sine scale.
 * Read the answer on the outer C/D scale. In this case, it looks to be about 0.777.

Now, if you've been paying attention, you'll notice that the scales on side 2 go counterclockwise, whereas the scales on side 1 go clockwise. This is so that reading a number on side 1 corresponds to an answer on side 2. To calculate squares and cubes, you need to use the second side. For example, to find 9^2 and 9^3:

 * Align the indices on the C/D scale (line up the 1's).
 * Place the cursor on 9 on the C/D scale.
 * Flip the rule over. 9^2 is on the A/B scale, and 9^3 is on the K scale.

Ok! I hope you've enjoyed this! I had a lot of fun making this one. As always, comments and constructive criticism are welcome.

P.S. - If you didn't catch my *cough cough* note back in step 1, I'm entering this into the Epilog challenge. I can only assume that if you've read this far, you're at least mildly interested in this, which warrants a vote in my book. So please vote for me! Thanks!

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    63 Comments

    Very cool design! Going to give the acrylic version a try! We have a workshop coming up next spring and I would love to make these as little gifts for everyone!!

    that's awesome! I'll try to make it for sure!

    I have a circular slide rule from the '50s or '60s that allows woodworking calculations using fractions; i.e., 3¼" x 6. It also has some inch to metric tables, etc. The other side is pretty much what one'd find on a standard slide rule.

    2 replies

    Would you be willing to post a pic of the wood working rule? I collect slide rules, and don't think I've ever seen one like you describe.

    Here you go. On the first side, the DS (Drill Size) and DT (Double Thread) scales are used with the L scale. As you can see, the A and the L scales have, on their upper portions, a decimal scale. The lower portion of each, called Af and Lf respectively, have a fractional scale.

    The back side has the normal scales for computing angles via sines and tangents, but also has a simple fractional to decimal chart around the inner scale.

    What's nice is you can do your normal math and get fractional results, which can come in handy for woodworking.

    IMG_0085.jpgIMG_0086_2.jpgIMG_0087.jpg

    This is fantastic! I really like the stand you made for it as well. Thank you so much for sharing!

    Cool design, fun to make -

    Changed the layout up a little bit to capture the pointer (recessed center wheel) and added lasercut cardboard inserts to lift the rotating arms and keep them from dragging (hidden inside, works great though).

    Used a Epilog Helix 45

    sliderule2.jpgsliderule1.jpg

    Hi! Its a long time after this is posted. However, when I try to buy/upload the files to ponoko.com, I get this error "Your design contains open shapes with fill colors applied"(upload) or if I buy it, the second file automatically disappears. What should I do for this?

    1 reply

    I solved that by contacting the ponoko people, and they might have updated your file to the new accepted format too. However, looking at the price they charge, I decide that I may print them myself...But the PDFs are not in their actual size, how do I generate the precise size of PDFs from that SVG? Thanks!(Sorry, but I have not used inkscape a lot before)

    this is great but.... the SVG files have the parts shown in different scales as far as I can see the the PDFs certainly do. Can you post them at the same scale?
    Thanks :)

    2 replies

    Update: I just determined that Instructables resizes .pdfs to letter size when you download them... Bummer.

    Thanks for the comment. I'm positive the .svg files are scaled correctly, my guess is your computer is resizing them to fit your screen. The .pdfs probably got rescaled when I exported from Inkscape, unfortunately. I've been trying to upload the actual Ponoko templates I used to have them laser cut, but the uploader isn't working correctly. :( I'm going to try using a diferent computer later to see if that works.

    thinking out loud here... is it possible to add a vernier to the sliderule? difficult I suspect but it would increase visual precision by an order of magnitude presuming the physical precision was sufficient. Might have to be non-linear too.

    I'm obviously going to have to break out my slide rule and find out...

    3 replies

    Allow me to quote from "Utilizing the Vernier Principle for Precise Readings of Slide Rule Setting" by Roger Wickenden, American Journal of Physics, Volume 16, Number 8, November 1948:

    "To use the slide rule as a vernier, one sets the right-hand index of the C scale directly over the 9 on the D scale; then for every ten divisions anywhere on the C scale there are 9 on the D scale. Thus the C scale becomes a vernier to read the D scale.........There is no reason why we must limit ourselves to tenths of a division. The slide rule vernier can be set to divide each division into five, eight, twelve, twenty, or indeed any convenient number of parts, according to which numbers on the C and D scales are originally lined up."


    Quick example. Put the cursor over the "pi" mark on the D scale. Move the C scale to the left until one full division on the upper C scale exactly matches the interval between the 3.1 mark and the "pi" mark on the D scale. The right index of the C scale lines up near to 4.2 on the D scale. These are the next two digits, so pi =3.142. It is more work, but it gives you an extra digit of precision, with care. My eyes aren't so good, but in the photo I made, you might even care to estimate with greater precision a value close to 3.1416.

    sliderulevernier.jpg

    There were vernier slide rules at one time; they were expensive and delicate, but indispensable if you needed better than 2-3 digits of precision in your calculations, but couldn't wait around to do long-form multiplication or division or look up trig functions in a table (which, at the 5 digit accuracy available from a vernier slide rule, was about a five pound book). FWIW, the men who designed and built the A-4 rocket (better known as the V-2, the world's first ballistic guided missile), calculated a number of its parameters with vernier slide rules; there were mechanical and electronic calculators around that were more accurate and about as fast, but they weren't even slightly portable (the smallest 5-digit mechanical calculator weighed, as I recall, around forty pounds, compared to two pounds or so for a 5 digit vernier slide rule).

    I think it'd be possible, but it looks like you'd have to have a vernier for each scale, unless you were really crafty. At the very least, you'd probably have to add another piece to the construction, which would complicate things. And they'd definitely have to be nonlinear, as all the scales are on a log scale. Interesting idea, though!

    Awesome! Loved this one!

    I'm looking for a slide rule that can be used in photography - one that you insert the flash number guide, the distance between the flash and the subject, and you read the aperture/speed/ISO (wow, there's a lot of variables on this one).

    There's a discussion about guide number slide rule here:
    http://photo.net/photography-lighting-equipment-techniques-forum/00UbPg

    Can you point me some guide where I can learn about the calculation of rules? Thanks!

    2 replies

    Thanks for the comment! I'm not a photographer, so I'm not quite sure what you're looking for. What I did find about guide numbers is this formula:

    GN = distance * f-stop

    but the wikipedia article says this only works for ISO 100. I couldn't find anything saying how the equation is modified for different ISOs. Anyways, if you're looking for something that does the above calculation, you can use any old slide rule: the C/D scale can do multiplication OR division, so if you wanted to calculate the f-stop from the GN and distance, you'd just do

    f-stop = GN/distance

    on the slide rule. Hope this helps!

    Hi!

    Thanks for your answer.

    I did some research on the topic, and found that when you increase the ISO, you must increase the f-stop. If your calculation points to f4 for ISO100 at a certain distance, you have to use f5.6 for ISO200, f8 for ISO400, f11 for ISO800, and so on (there's a sequence of f-stop and ISO).

    I also found a page full of "exposure calculators". Now I only need to get inspired and do the work...

    http://www.mathsinstruments.me.uk/page67.html