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.

Comments

[Mindmapper1]

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 :)

[drknotter]

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

[drknotter]

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.

[bulwynkl]

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...

[davelant]

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.

[ImageMaker]

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).

[drknotter]

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!

[cesarakg]

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!

[drknotter]

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!

[cesarakg]

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

[pheenix42]

Ooo, this is begging to be made from photo-etched brass! =D

[saxmaster765]

I just drooled a little.

[bertus52x11]

Great work!

[drknotter]

Thanks!

[the_burrito_master]

Does it mean I'm stupid if i don't see the point in this? What are you measuring exactly?

[Weldeon]

A slide rule was used before calculators. It did math.

[the_burrito_master]

After re reading the last step and paying more attention i saw that the * mark was used to multiply, haha.

[Erik van der Lelie]

Yoy make nic things, and you work with a lot of precicion, well done Greetings Erik

[tbgilbert]

OK, got the parts in and starting to assemble. After a dry run, i was thinking it may be worth the time to modify the design a bit, and add small index holes to align the rules and cursor. Hope to finish the 1st on this weekend.

[avatar_i]

I have a circular slide rule that was issued to pilots from WWI through the early 1960s' for navigation.
It attached to their thy so the pilot only needed one hand to use it.
I have been trying to find instructions on how to use it for about 25 years!
Can anyone help?
** Just saw the message from fazgard about pilot shops... ??? Pilot shops? **

[drknotter]

Without knowing the exact model, I couldn't really tell you much. However, if you're looking to learn how slide rules work in general, I'd go here. It's where I learned how slide rule's work, and how I eventually figured out how to design my own.

[avatar_i]

Thank you for the link, and the quick reply! I did not find that site on my own.

My traditional flat linear slide rule- which I still don't know how to work properly, is a Picket Microline 140. Your link will definitely help me there.

My circular slide rule which I would like to get to know correctly, is a Concise No. 300. It is just a bit over 12cm in diameter, or about 4 7/8".

This may sound stupid, but since the scales go round and round, I can't quite figure out how to apply anything from the  tradional rule to the round version.

[vincent7520]

excellent as a backup for my navigational calculator.
I have (never use now… ) a linear slide rule but will trade it for a circular one.
Very convincing.
You got my vote.

[tbgilbert]

Quick question, what dimensions did you use for your laser cut? I am guessing 3 x 181 x 181?
Fantastic project!! Plan on making several for my kids. You got my vote.

[drknotter]

Ponoko offers three sizes of acrylic for cutting: 181x181 (P1), 384x384 (P2), and 790x384 (P3). The cursor pieces were cut from clear 3mm P1, and the slide body was cut from black 3mm P2, since the pieces wouldn't fit in the P1 template.

I'd love to see pictures once you make them for your kids!

[tbgilbert]

Well, first one on order, same as yours. If that works out, I am going to try white with black markings. Man this brings back memories.

[drknotter]

Awesome! Post pictures when you've made it!

[Trelligan]

Please register this project on Ponoko, so we can order one directly. I'd really like to make this rule, but don't want to learn Ponoko by doing.

(5 stars anyway!)

[drknotter]

Thanks for the rating! I've added the designs to the Ponoko showroom. All you have to do is add the designs to your personal factory on Ponoko, and you can have them send you the pieces. Anyways, here's the link.

[sockless]

This is very similar to aviation computers (whiz wheels).
They have been around since before WWII and have all sorts of cool things built in to the scale for rates and unit conversion.

[Wazzupdoc]

Real nice job. The explanation was good too. I still have my circular slide rule! Works great and fits in a pocket in the cover of my "Common Logarithms" book.
What fun we had before TI-83's!

[Microbe]

Ahhhh...I had one of those when I was at school. I wish I still had it lying around, at least they never need to be rebooted.

[errolwahl]

this isgreat, i have been looking for circular slide years for the longest time, cool

[askjerry]

Just something to note... instead of painting the numbers and ticks, you can use laser sign plastic which is actually two colors fused together. You engrave through the first color to expose the second color. They are available in many combinations including some that look like wood with gold lettering, or metallic with black, blue, or red coloring. Generally they run between $12 to $15 for a 24x12 sheet. The two major manufacturers are Romark and IPI. You cand find these here:

Laser Bits - http://www.laserbits.com/index.php?main_page=index&cPath=76
(Apparently they are selling them in 3-packs now. $50)

Sign Warehouse - http://www.signwarehouse.com/c-ENIPI.html
-- Laserables 1/16 thick: http://www.signwarehouse.com/c-ENIPI-LAF.html
-- Heavy Metal 1/16 thick: http://www.signwarehouse.com/c-ENIPI-LY.html

Hope that helps!
Jerry
(I have an Epilog 35w laser)

[drknotter]

Thanks! Ponoko doesn't stock that kind of material, but if I ever get my own laser cutter, I'll definitely look into this.

[askjerry]

You can drop ship the material to them to cut it, or find someone else to do it. I should have my unit back online in a day or so... just need to reinstall the drivers on the new laptop. If you can't get them to do it contact me and I'll quote you a price.

Jerry

[dbennett]

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.

[pcairic]

and... THANK YOU FOR AN OUTSTANDING JOB!!!

of course!

[pcairic]

Aviation circular slide rules are still sold in any good pilot shop.
Look for E-6B, or Jeppesen CR-2, CR-3 and CR-5.

You can even order one from Japan. Check: http://www.concise.co.jp

[fazgard]

Outstanding and elegant.

Circular calculators have always piqued my interest, made quite a few out of cardboard for unique applications, but this really takes it to a new level ..

Very well done and good read.