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    Re: 4-digit Circular Sliderules
    From: Hewitt Schlereth
    Date: 2015 Feb 22, 09:08 -0800
    Hanno, those of us who have used either a 10 or 20 inch slide rule or a standard circular one will appreciate the elegance of putting the 90 degree end of the scale on the outer rim. Great going.


    On Feb 21, 2015, at 9:21 PM, Hanno Ix <NoReply_HannoIx@fer3.com> wrote:


    I am thinking about a little manual, and that will take some time.
    I will be traveling - NEW ZEALAND, YAY! YAY! - to see the Southern sky and their Alps!

    A preliminary description here. For simplicity I start out with SCALE1.
    1. General lay-out.

    These are logarithmic slide rules ("SR") the principle of which you are familiar with, I think. Nevertheless, if only to establish lingo and to identify scales etc. lets recall the basics and describe the construction elements as we go along.

    General logarithmic SR's allow multiplication by adding two lengths, as in the straight SR's, or angles as in the rotational SR's. Division is done by subtraction of 2 lengths/angles. They are general purpose in the sense that the scales describe the logarithm of  the number range x = x1:dx: x2. There are special SR's, or scales, that describe some other function f(x) for x = x1:dx:x2 as for instance log[cos(x)]. I ignore them here, too.

    Mine are rotational SR's of the circular or spiral kind as opposed to circular SR's of the cylindrical kind - as in Bygrave, Fuller, etc. Again, we ignore here the latter as well as the straight SR's - same for "flat" cylindrical SR's.

    SR's for multiplication/division cover, in general, just 1 decade. It is up to the user to determine in which decade he wishes to calculate: 1:1:10, 10:1:100 or 100:1:1000, etc. He can transform the decade by imagining the period: 1.0:0.1:10.0 or 1.00:0.01:10.00, and so on. Periods are not printed.The technical difficulty in making / reading SR's increases with the "resolution", i.e. the visual separation of steps in the least significant digit, the one furthest to the right. 

    Normal engineering SR's allow to discern 1 step in the 901 steps from 1.00:0.01:10.00. Our SR's here are rare in that they clearly separate each single step out of the 9001 steps from 1.000:0.001:10.000.

    For a reason to described later my SCALE1 has on 2 scales:
    a 1.00:0.01:10.00 scale, and a 1.000:001:10.000 scale. The first is the B/W scale at the rim, the other is the 20-turn spiral emanating from near the center and ending just inside the B/W scale.

    SR's have pointers that indicate a number by resting over them. On circular
    SR's pointers are frequently thin lines scratched into some transparent material starting from the center, ending a the rime and pivoting around the center. My SR's employ 2 such pointers that can be moved around either individually or as a pair. These pointers indicate not unique numbers on the spirals, but 20 each, and so we need some method to identify which one of those 20 is meant.

    In come the colors. Ideally, we could identify a particular spiral with a particular color. However, it is difficult to find 20 colors that are clearly distinct visually from each other and the white background. We also need printing processes that print them truthfully - not a simple issue! I compromised by choosing a set of 10 colors repeated twice. This solves part of the problem. How to resolve the rest I'll describe in the usage chapter.

    Also, it proved advantageous for visual clarity to print the actual steps in B/W and the numbers in black. Only the baselines are printed in colors.

    There is another important detail. Colors identify also certain ranges of the B/W scale at the rim. Each such range at the rim corresponds to an entire spiral turn: they both make a pair of the same color, and so such a pair covers the same number range - spread over 360 degrees on the spiral and compressed to 18 degrees at the rim scale. I guess you get an inkling now, no?

    Let me end today's posting with the design of the scales themselves. In another email to follow soon I'll go into the usage and some examples. Please let me know until then if there are questions so far.

    OK, the scales: A regular ruler might cover 10 steps of some unit, and there is a thin marker that indicates the beginning and the end of a step.That makes 11 thin marks total on the ruler. If you'd do that for 9000 steps the markers would become very thin and therefore difficult to print and to see.

    My choice is different. Please look at the interval from 999 to 1000 at the outer end of the spiral. What you see is this: each entire interval, and not its limits, is indicated with marks: either a black mark or a white mark i.e. a space left white. This pattern proceeds in alternating fashion so that the even numbers 9900, 9902, 9004, 9006, 9008, 10000 become marked by  black spaces and the odd numbers in between by a white spaces.

    The result is that there are only 6 thick marks rather than 11 thin marks total which makes printing / reading substantiallly easier. In addition, I added a dot over each multiple of 5 so that there are just 2 marks between 2 dots. Now, locating a particular number is very easy - you might not even need to count!

    One more refinement: the numbers proceed from the center of the disk to the rim. Therefore the increasing diameters, or lengths, of the spirals compensate for the increasing density of the log scale from 1 to 10. That works out actually surprisingly well.

    Did you follow me so far?
    Got to go, soon more.


    There are 2 scales each running from 1 to 10 or 100 to 1000

    How to read the scale?

    On Sat, Feb 21, 2015 at 3:31 PM, Greg Rudzinski <NoReply_Rudzinski@fer3.com> wrote:


    These circular scales are very comfortable on the eye. How do they work ? Examples please.


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