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Aspect Ratio Calculator - Next Generation
Article © MAIL User: ZiLi

After some 'development iterations' I show my version of an aspect ratio calculator slide rule. As this enhanced version has undergone significant changes and additions compared to the basic version provided by 'Workshop Warlock' in his article Aspect Ratio Calculator, I will provide a new manual now, that shows and explains these changes - for the basic explanations please follow the instructions of my forerunner, as they are not only sufficient, but excellent. But I try to give them here as well.

Image: arcalc-article.jpg

Download, print (and feel free to save a local copy) of the PDF file to be found by clicking the image above. You need Adobe Acrobat Reader(TM), Foxit Reader or another software that can handle PDF files to be installed on your PC for this. Alternatively I can provide a .GIF file for you per mail - just ask for it.

Note: Scroll down to the bottom - there is a link to the newest version of this AR calculator, incorporating changes made after original submission of this article...

After printing the slide rule page on approx. 160gsm (~8 mils thick) strong paper or maybe light cardboard (letter or A4 format preferred, just check 'fit to page' to get the largest possible result), you should cut out, separate parts, fold and glue the item together, as noted on the left margin of that page. After gluing the body part, you may cut notches at its left and right ends to be able to push the slider easier out of its centered "parking" position (as shown above) - or simply cut the body a bit shorter, if you like to do so. Then stick the slider into the body, so its scales are visible through the slots (I note that, because some people seem being too d... to imagine this - but I guess these would be unable to use this tool at all, so I don't worry too much about them). The slider should be relatively easy movable, but without any wobbling, as that would destroy the principally high precision of this tool. So you might be forced to make corrections or even a repetition of the print and cut, until it works out well. Just be as precise as you can achieve, and do NOT use less effort as when making a fine piece of maille - using ruler and knife for cutting may be a good idea.

The basic principle of that AR calculator, and explaining the principles of logarithmic scaling are beyond the goals of this article - I propose the interested ones to look up Wikipedia or a good maths book for "slide rule" and/or "logarithm". But the shortest possible explanation I can give is, that the use of logarithms is to enable someone to MULTIPLY numbers by ADDING their logarithms looked up at a precalculated table, and looking up the number accompanied to the addition's result at the same table (divisions are made by subtracting logarithms). And that principle can be embedded in a device made from two rulers, where numbers are shown in a logarithmic scaled grid instead of a linear one, so direct multiplications can be made by adding lengths in that grid.

Complicated explanation aside - the mode of use is really simple: Shift the slider in a manner, that the wire diameter on the body scale is aligned with the used ring inner diameter - and the AR can be read directly at the lowest tongue scale at the point aligned with the triangular 'Aspect Ratio' mark. Naturally you can do this calculation in different directions, e.g. for determining a needed ring ID by given wished AR and existing wire diameter - set the AR on the lower scale, and simply read the corresponding ring IDs for given wire diameters. And last but not least needed wire diameters for given ring size and AR can be determined the same way. For a more 'graphic' description on the tool's use you maybe look up the article of the original AR calculator linked at the top of this article.

Just align the given known data, and read the to be determined ones. Easy, isn't it?

To the changes and enhancements: While the original AR calculator had the upper scale reserved for the wire gauges, and the lower one for decimal inches, that is compressed now a bit by combining all inch related scales on the upper scale area, and a fractional inch scale included - to free up the lower scale space for an additional - corresponding - metric one. The imperial and metric scales are shifted by the factor 25.4 against each other, so direct unit conversions between metric [mm] and imperial [in]/gauge values can be made easily, as well as AR calculations using mixed metric and imperial ring and wire dimensions. And finally there are a springback correction scale added to the AR mark at the bottom, and scale alignment lines. The use of the springback correction scale is easy - if you know the typical springback ratio of your wire type, you can simply use the mark you experienced already (or were reported) as valid for your material choice, coiling and cutting method on that correction scale to estimate real ring data - be it a resulting real AR with mandrel size and wire diameter given, or one of the other parameters with remaining ones known. For example most welding wire types I know have a ratio of around 5 to 10% (depending on cutting method; saw cut will have less than score'n'break), as these wires have all to be stiff enough to feed well through the welding machine, but must not be much stiffer as necessary at the same time, to not impair the useability of the welding device. That this correction scale can be used to 'guesstimate' a needed mandrel for a given wire and wished REAL Aspect Ratio, should be 'straightforward thinking'. Note that springback is not constant - larger mandrels result in more springback, so the springback correction is only an estimation; but it's better than noncorrected anyway, and very often right on the spot. And finally the scale alignment lines are to enable the user to align data on the upper imperial scale and the corresponding lower metric scale without the necessity to introduce a cursor to this shift stick when making unit conversions or mixed metric/imperial calculations.

-ZiLi-

Edit 2009-10-20: A more recent version, including Industrial rod sizes 1..52, A..Z as additional ring ID scale, can be downloaded HERE; replace '.pdf' in the url by '.gif' to get an editable image file - but please provide the results of your changes, as I may like to embed some of them into mine. And let me know per PM or email about needed, wished, or desirable changes or additions, as it is a continuing effort to enhance that item - and I simply need feedback for that.
Edit 2010-04-01: If you have a color printer, you might like a colored version: HERE; again alternatively available as .GIF by manual changing the file extension in URL.
Edit 2011-07-01: Besides some enhancements a mandrel diameter reference table has been added to the calculator's back side now: HERE; .GIF alternative as usual...
Edit 2013-09-01: There's a new version, with a bit cleaned-up scales, and extra 'helpline' markers for the most common wire diameters: HERE; .GIF alternative as usual...
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=535