Sphere Research's Slide Rule Universe, Build your own slide rules!

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Sphere Research Corporation
3394 Sunnyside Rd.
West Kelowna, BC, Canada V1Z 2V4
Phone: +1 (250) 769-1834

A great source for test equipment, repairs, calibrations, useful metrology information, and of course, SLIDE RULES!

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Welcome to the slide rule universe...CLICK to hear Robby

At this site, you can:

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BUILD a slide rule from scratch, now UPDATED with Log Log rules

UNDERSTAND HOW + WHY a slide works, a full explanation

Build Your Own Slide Rule!

Thanks to some very public-spirited slide rule experts (one in the UK, one in Canada), we now can provide some computerized tools that will allow you to build several different types of slide rules.

The fist section shows how to make a simple rule, and suggestions for all the mechanical steps. The second section has scales for very advanced rules, and you can follow the same general methods to create a full blown multi-function log log rule for your use. It is also possible to use adhesive laser-jet film for the scales, and then seal them with another layer. This sandwich can then be applied to a more rugged body material to make a very tough and durable rule.

No matter what method you use, we hope you will enjoy these projects, and get a bit more insight into how slide rules work.

Project #1, Build a Simple 4-scale Straight Slide Rule

Thanks to the efforts of Linux guru

Brian Ronald in the UK, you can build your own working slide rule with the aid of a postscript compatible laser printer and some careful construction technique. The sample below is made by this nifty technique, and works great, a perfect project for school classes or the mathematically curious. Just use your mechanical skills, a bit of imagination, and follow the simple steps below.

Project Ruler

1. Print out either the

Postscript .PS file, or the

Adobe Acrobat .PDF file to generate the scales on a sheet of paper. The better the resolution of your laser printer, the more accurate scale placement will be. The rule is a 4 scale ABCD design, capable of multiplication, division, squares and square roots. The logarithmically spaced intervals of the scales allow added distances to multiply, substracted distances to divide. It is a very simple mechanical computer that only hints at the very advanced math that is behind its operation.

2. Laminate the scales to thick card stock with contact cement, or double sided tape. You can make the top surface tougher by covering it with a clear adhesive film. Using a very clean straight edge, slice the scales apart from the slide. The cuts must be parallel to allow the slide to work.

3. You can make several different body and slide styles, depending on how you make the build-up of the layers. You will need a solid back, or end braces, to hold the assembly together. build up a suitable body and slide with more layers, so you can allow a gap and edge for the slide to keep it in place. Once the body and slide are working, you can make a cursor.

4. The cursor has a solid back, and a film front (make a line on laser film overhead sheets). The edges are made of the same card stock, or anything else handy. be sure the cursor is aligned square at the left and right hand indexes, this requires clean and square edges on both the body and cursor.

If all has gone well, the rule will work just as expected. If not, well, at least you have some appreciation for how sophisticated this simple little device really is! Imagine making one hundreds of years ago, without that convenient laser printer....

Want to make something really incredible for your class? Print any of these projects to laserjet compatible FILM transparancies, and make a PROJECTION rule for demonstrations. Wahoo, now that is a handy teaching item...

E-Mail Us ! Send us PICS if you or your class make some, we'll be happy to add your efforts to this page!

Project #2, Build an Advanced Log Log Straight Slide Rule

Thanks to the efforts of Canadian

John Savard in Alberta, you can build some fairly spectacular rules with unique scale arrangements to help teach how a rule works, and for better computing flexibility. Once again, just use your computer to print the files, some mechanical skills, some variation of the assembly procedure above, and John's great scale layouts.

John has provided two interesting designs, each in PDF format, so you can use them with any printer. Needless to say, the better the printer and its resolution, the better and more accurate the scales will look on the finished rule. Each file has all images required. Just CLICK on the rule image below to get the required PDF.

The Model A design: (single sided body, double sided slide)
The Body/Slide Image

CLICK to Download the PDF

The Slide Reverse Image

CLICK to Download the PDF

The Model B, 50 inch scale design: (single sided body, double sided slide)
The Body/Slide Image

CLICK to Download the PDF

The Slide Reverse Image

CLICK to Download the PDF

The horizontal cut marks on the edges of the images show where to slice the physical rule to split the body from the slide. Ideally, a shear or similar tool is needed, to insure clean, parallel edges, or the rule will not work.

Some helpful comments from John on his interesting designs:

In addition to designing these slide rules to be useful as practical instruments of calculation, given present circumstances, I have placed particular emphasis on making it easy for people unfamiliar with the slide rule to learn to use it in a gentle step-by-step manner.

1) The simplest and most obvious way to multiply two numbers on a slide rule is by using the A and B scales. That kind of multiplication makes it obvious that two logarithms are being added, since the operation being performed is clearly the addition of two distances: first, the distance from the index to the first number on the A scale, then the distance from the index on the B scale (placed under the first number on the A scale) to the number on the B scale (over which one finds the product on the A scale). One rule provides an A scale and a B scale which slide against each other, and another has two K scales, which can be used in exactly the same way.

2) The way multiplication is ordinarily performed on a slide rule is with the C and D scales. By seeing how the A and B scales repeat themselves, understanding why the procedure works, an essential step in being able to remember it, is made easier.

3) The log-log scales on a slide rule, which are used to raise numbers to powers, span a considerable distance. Since this kind of scale can be intimidating, the model A rule includes the LL scale, which works in conjunction with the K scale instead of the C or D scale. This kind of log-log scale was actually used on some of the earliest slide rules with log-log scales.

4) The CI scale, which can be thought of as showing reciprocals, can also be used to perform multiplication in conjunction with the D scale. On both rules, it is possible to slide the CI scale against the D scale when the slider is in its reverse position. Some people prefer to use a slide rule this way. When division is performed on these scales, as with multiplication on a regular C and D scale, there are now two possible operations to perform, but in this case, one can tell which one is needed before the fact, based on whether the dividend is greater than the divisor, instead of after the fact, based on whether the product is greater than 10.

5) Multiplying using the CI and D scales illustrates the principle needed to go on to the next step: multiplying using just one scale on the slider, in combination with the cursor and the index points on the body of the rule (taken from scales not otherwise used).

Let us imagine we are using C and DI scales on a slide rule to multiply (instead of CI and D scales). To multiply 3 by 2, bring the 3 on the C scale over the 2 on the DI scale, and then the index of the C scale points to the product on the DI scale. And, because the two scales are the same scale, only reversed, the index of the DI scale also points to the product on the C scale.

With a single scale on the slider, acting like the C scale, one first has to find the backwards distance to the first number to be multiplied, as the DI scale would have given that distance to you. This can be done by moving the first number to be multiplied to the index on the body of the rule, and then moving the cursor to where the index on the slider now is.

Having the cursor where it would have been if one had a scale acting as the DI scale, one now moves the second number to be multiplied on the slider to the cursor. The product, on the slider, is now over the index on the body of the rule.

Having the cursor where it would have been if one had a scale acting as the DI scale, one now moves the second number to be multiplied on the slider to the cursor. The product, on the slider, is now over the index on the body of the rule.

This is the method needed to take advantage of the M1 through M5 scales, which provide a 50-inch scale for high-precision multiplication, without having to have a second copy of these scales on the slide rule.

My first slide rule was a Mannheim from Engineering Instruments Ltd. of Peru, Indiana, but I received, also as a Christmas present, a better one while still in Junior High, a Ricoh No. 121. While at University, I bought myself a Sterling Decimal Trig Log-Log, but wound up sticking with the Ricoh until I could afford a pocket calculator. And I used several of those on my way to earning a Master's degree in Nuclear Physics.

John Savard

Here's an excellent example of John Savard's design built by Luis from Spain, with some notes on how it was done:

CLICK for Bigger PIC!

Hi!
First of all, congratulations for your web page! I'm Luis, from Spain. I was looking at the "Build Your Own Slide Rule!" page and I made my own Log Log rule (see photos). It has been done by printing the Log Log design on photo paper. I noticed I needed to plastify it...and I did an "experiment" - I glued that photo on a transparency plastic paper with Loctite, Super Glue... and it was just perfect! I did it only at the printed side. As you can see slide rule body is done with cheap-thin wood. Finally I took a CD case, cut it and put as rule's glass, painting a thin line with a ball pen and protecting it with cellophane... and the work was done :) Email Luis HERE. Hope you will like it! ;) regards, Luis

MORE PROJECTS ADDED December 14 , 2003:

Here's another slide rule from John that illustrates full Log Log operation, in a single sided rule.

This one, inspired by the Yokota slide rule's scale arrangement, doesn't even require putting scales on the back slide of the slider, thus, construction is basically the same as the PostScript slide rule initially offered here as constructed by Brian Ronald.

This makes it more suitable for the most likely users of homemade slide rules, teachers wishing to introduce the idea of logarithms to their classes, as it minimizes the complications involved in the preliminary step of constructing the rules. Despite this, it is still a full-featured log-log decimal trig slide rule.

The Yokota-based Log Log design: (single sided body, single sided slide)
The Body/Slide Image

CLICK to Download the PDF

Circular Designs: (Single sided, two layers and cursor)

Here's a suite of 3 circular rules from John that use the same clear overlay (which makes both the rotating scales and the cursor), and 3 different white bodies. These variations offer a wide range of circular designs, in a large (8 inch diameter). Make the base images on white material, or adhesive white material, and then lmainate them to suitable card stock or other material. Make the clear layer on clear material, and cut the cursors out in any shape you prefer. All three items are then fastened in the center and secured with either a screw and nut or other fastener, and the rule is ready to use.

The scale identifiers (A, B, C, S, T, etc.) are added to every scale at the half interval marks (an unusual visual technique, but very effective). In this way, the scales are identifed no matter where the rule is positioned.

Body Image No. 1
D, A, T (Spiral), ST, S, CI, Sh (Spiral), Th, K, L

CLICK to Download the PDF

Here is the first of three templates for circular slide rule backgrounds. This one is for a general-purpose rule, except that hyperbolic functions are present, and log-log scales omitted. This is peculiar, but it is intended this rule will be used in conjunction with the one with two four-decade log-log scales, normal and reciprocal, as part of a set.

Body Image No. 2
D, A, M (Spiral), CI P, vP, rI, LL, L

CLICK to Download the PDF

This is the second of three possible backgrounds for the circular slide rule. This one features a logarithmic scale for multiplication that makes five turns around the rule. Unlike earlier versions of my circular slide rule, I put it far enough towards the outside that I could graduate it for a 20 inch rule instead of as for a 10 inch rule. Given the binary capability of the overlay design, it can indeed be used for accurate multiplication.

Body Image No. 3
D, A, LL+ (Spiral), LL- (Spiral), K, L

CLICK to Download the PDF

This is the third of three backgrounds for the circular slide rule. This one contains conventional log-log and inverse log-log scales. The log-log scales, but not the inverse log-log scales, are graduated for a 20" rule, except the last little bit.

Overlay/Cursor Image
C, B, K Scales

CLICK to Download the PDF

This file is the one that needs to be printed on clear plastic as the overlay for the family of three circular slide rules. Note the cursor line on the main disc, as well as the cursor templates (for which no border is given). This allows the rule to be used both in the simple fashion of a conventional slide rule for combinations involving one of the scales on the overlay, and as a "binary" type slide rule for any arbitrary pair of scales on the base as well.

Places to go in the Slide Rule Universe, people to see....

Click to visit!	Buy a slide rule from our extensive on line marketplace, with restored classics, amazing new in the box rules, and low cost first student rules. We have something for everybody, even a swap and sell area for visitors.
Click to visit!	Learn to operate and care for your slide rule with these on line manuals and directions. Learn what scales mean, how to use them and how to restore or keep your rule in good condition.
Click to visit!	Tour our extensive archives of slide rule manufacturers and models from all over the world. Find out who made what, and what became of them after they stopped making slide rules. See how slide rules survive today in the form of slide charts still made in the millions annually.
Click to visit!	Visit other slide rule places on the web with more slide rule data and information. From personal collections on line to (yes, it's really true) the international slide rule owners and collectors organization, the Oughtred Society.
Click to visit!	Nice things people have said about us in print and on TV, see the original articles. We always appreciate it!
Click to visit!	Visit our TEST EQUIPMENT site everything from Scopes, CRT's and DMM's to nixie tubes, HP and Tektronix spare parts. A little electronic something for everybody.
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