Wednesday, January 9, 2013

New Dimensions in Slide Rule Technology

The other day I posted that there is a new record that has been set with the development of the Eximius Diu 6 slide rule by David Hoyer. Please see my post on this subject.

In thinking about this slide rule I realized that it is a member of a class of slide rules that doesn't get much attention.  Let me be more specific.
We are all familiar with the linear slide rule.  This is a slide rule like the K&E Deci-Lon. Here the scales are linear and can be moved relative to each other with the aid of a cursor to keep track of specific points on the scales and to transfer a reading from one scale to another.
Also, we are all familiar with the circular slide rule. This would be slide rules like the Gilson Midget Circular Slide rule. Here there are typically two indicators that you can set the distance between and then move them to another position on the slide rule without changing the angle between them.
Finally, there are the cylindrical slide rules Like the K&E 4012 Thacher slide rule.  Here, in effect, the scales are wound in a helical fashion around a cylinder.  This was done to get a longer scale in a smaller space, increasing accuracy. Interestingly, Prefessor Fuller and his cylindrical slide rule call his slide rule "spiral"

What David Hoyer has done with his Eximius Diu 6 slide rule design is to put a spiral scale on a flat surface, somewhat like a circular slide rule, but, unlike the circular slide rule, there is more than one revolution (or turn) that the scale transverses.  Another way of looking at this is that the circular slide rule is the degenerate case of the spiral slide rule where the scale only traverses one revolution.

The way to use the spiral slide rule is very similar to the circular slide rule with two indicators to mark the difference indicating an angle between two numbers.  But, unlike the circular slide rule where there is no ambiguity as to where the resultant number (solution of the multiplication or division) is located, this is not the case with the spiral slide rule.
Specifically, there are multiple possible results where the indicator crosses a scale and the user must select one.  The only way to determine which of these crossings is the correct one as suggested by Hoyer is to use a more conventional slide rule, either linear or circular, to approximate the solution, and then find the place where the indicator crosses the scale "near" the approximation. While some might say that this is begging the question of why use the spiral slide rule, the answer, of course, is accuracy.  The Eximius Diu 6 pulls in a full 6 places of accuracy over its entire scale.

But, there is something unkosher about using this method to find the solution to an arithmetic computation on any slide rule. If you are going to use another device to get the solution, you may as well use an electronic calculator in the first place and get a precision of much greater than 6 places of accuracy.

So, the question I pose is whether there is some sort of mechanism in the way of arms, etc. that would allow the Eximius Diu 6 the throne for which it is intended?   Can we construct it in such a fashion that we do not have to go out to some auxiliary device to pull the answer out of the hat, so to speak?

Please comment below if you have a solution to this problem.

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