Eximius Diu slide rule, v1

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Eximius Diu 6 - version 1, May 2012 (now superseded)

I've built an improved Eximius Diu 6, but have retained the web page of the old one here for comparison.

Eximius Diu 6 - version 1, May 2012

Spiral slide rules are more compact than linear and cylindrical ones for very long scales. They have the added advantage that the inner turns of the slide rule are shorter than the outer turns. If we arrange the scale so that the numbers increase from inner to outer, and the inner spiral turn is one tenth the diameter of the outer, then the accuracy will be the same at the beginning and end of the spiral. The accuracy is about the same (slightly better) within the interior of the spiral.

I wrote a computer program to generate an image of the spiral, add markers and text at the correct logarithmic locations along the spiral, and add some colors etc. Ignoring the irony that it took a computer to generate the slide rule (though it's quite possible to generate the slide rule manually as it would have been done in the old days), the result is a usable slide rule that is accurate to 6 decimal places across its whole range. You need to be very careful to get that last digit of accuracy.

The slide rule was printed at 600 dpi on A0 paper, then trimmed and laminated. The spiral diameter is 750 mm (29.5"), with 135 spiral turns giving a scale length of 175 m (574 ft). Due to the nature of spiral slide rule scales, this is equivalent to a linear slide rule of length 318 m (1043 ft). In other words, a linear or straight slide rule would need to be 318 m long in order to have the same 6 digits minimum accuracy at all points: Linear slide rules are 10 times more accurate at the low end near 1 than at the top end near 10, whereas a spiral slide rule can compromise by making the accuracy more constant from end to end.

For a more detailed explanation of slide rule accuracy see... Slide rule accuracy

Two additional sheets of clear plastic film were cut to the diameter of the spiral, scored with a pin to make a very thin marker line from the centre to the edge, and pinned over the laminated printout to become the equivalent of the two cursors.

Using the Eximius Diu slide rule

There are three layers to the slide rule: the printed and laminated image, and two overlaid transparent layers. Each transparent layer has a very fine line etched from the centre to the outside of the spiral. A pin is pushed through the three layers so that the etched line in each transparent layer can be rotated independently. If this had ever been made as a commercial unit it would have to be made more robust, but the pin does a fine job fine of demonstrating the principle.

The Eximius Diu 6 slide rule laid out on a table. The spiral is 750mm diameter (about 30"), printed on paper and laminated. Above that are two transparent circular layers called Cursor A and Cursor B. All three are pinned through their centers so that the two cursor layers can be independently rotated. Each of the two cursor layers has a thin line from the centre to the outside. See the clothes peg at the bottom, used to hold either the two cursor layers, or all three layers, in position.

Click the image for a larger view.


The three layers centred with the pin, so that the two etched lines can be rotated. Call the first transparent layer "Cursor A" and the top one "Cursor B". I used another two layers of blank laminate - they weren't quite as transparent as I'd hoped, so some of the images are a little cloudy.

Click the image for a larger view. You will see the pin sticking up, and the two very thin and somewhat faint cursor lines - Cursor A heading up towards 1 (pointing at about 1 o'clock in the image), and Cursor B at about 5 o'clock.

Doing a calculation - let's try 1.23456 * 4.56789. The correct answer to 6 decimal places is 5.63933. First align Cursor A so that its etched line goes through 10 (it will also go through 1 and the centre).

Keeping Cursor A fixed over 10, rotate Cursor B to pass through the first multiplicand (1.23456).

Fix Cursors A and B together (e.g. using pegs or clips) so that we can rotate them together around the slide rule without changing their position relative to each other. We need to preserve the angle between the two etched lines.

Rotate Cursors A and B together until Cursor A's line goes through the second multiplicand (4.56789)

Now Cursor B's line will pass through the solution, we just need to find which turn of the spiral is the correct one.






The simplest way to find the spiral loop that the answer lies on is to take a regular slide rule and calculate the approximate answer. You could do it by counting rings, but it's easier with the regular slide rule. The pic shows a Faber Castell 52/82 calculating 1.234* 4.57 to be about 5.64, so we know the answer is around there.

Back to the Eximius Diu 6, we can easily see which is the correct loop of the spiral to use, and we can (very carefully) estimate the result to be about 5.63932. Click the image to enlarge it to see the red arrow. The correct answer is 5.63933, so we were pretty close here, and within the 6 decimal places accuracy.

Some low res images

The slide rule is a bit big to show here at its full resolution (at 600 dpi and 18,000 x 18,000 pixels the png file size is 28MB). Meanwhile here are a few lower resolution images, starting with the whole slide rule, diameter 750 mm. Click on the image to see it at about actual size, but with the resolution reduced to 120 dpi.

About actual size, resolution reduced to 120 dpi. Use the scroll bars to scroll the image...

Eximius Diu 6

Zoomed in the area around 10..

Zoomed in the area around 1..

Make your own Eximius Diu 6 v1..   (note that this is an older version)

Download a high resolution (600 dpi) PDF file that you can print and laminate. Print it on A0 or similar size paper, sized so that the diameter of the spiral is 750 mm (about 30"). Then laminate it. Then make two additional transparent layers, cut them to a circular shape just large enough to cover the whole slide rule spiral. Mark both transparent layers with a very fine line from the centre to the periphery (I used a pin to scratch along a steel rule, then a non-permanent marker along the scratch, then wipe the excess leaving a very fine black line in the scratch). Pin the three layers carefully through the exact center, and you're ready to go. As an alternative to a pin, you might also consider using a CD/DVD case similar to that show by Ying Hum here. Let me know if you find a better way of doing the cursor.

Download EximiusDiu6-v1-D750mm-T135-L175m-600dpi.pdf (22 MB). Please note this pdf is copyright. It can be downloaded and printed freely for any use. Please give acknowledgement if distributing it.  If you make one of these, I'd be interested to know - just drop a note in the guest book. Dave Hoyer, Dec 2012.

Update, Aug 2013. I've made up a new version that will be more practical to use. This includes a different color layout to help guide the eye to the numbers being sought, a circular slide rule around the outer edge for the initial estimate, and more practical acrylic cursors. See EximiusDiu6 v2

Copyright © 2013, Dave Hoyer.