Old rule divisions twelfs etc

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90/127

MichaelG.

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PostScript: __ You are guilty of conflating resolution, accuracy and precision, Dave

… There are important distinctions between them

Edited By Michael Gilligan on 29/09/2021 12:01:35

90/127.... Screw-cutting today, then, Michael?

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No … just answering Dave’s question.

MichaelG.

And this is what the inch fraction ¹⁄₁₂₇ scale looks like, magnified!

If the pictured scale looks uneven on your screen, its because ¹⁄₁₂₇" pushes display technology - jpeg photos and the your computer screen both struggle,

I'm pointing out the shortcomings of fractional rules rather than fractions, but Michael's 18mm conversion highlights a few problems:

• There is no standard ¹⁄₁₂₇" rule: it would have to be specially made
• ¹⁄₁₂₇" is too small for the human eye to read reliably
• ¹⁄₁₂₇" (about 8 thou) is about the width of a finely printed graduation, which introduces significant error
• There are no natural halves or other sub-graduations to help the user find which graduation represents ⁹⁰⁄₁₂₇" - mistakes are too easy
• In practice, with a standard inch rule gradated in say sixteenths, its necessary to translate ⁹⁰⁄₁₂₇" into the nearest sixteenth and interpolate. Finding the nearest twelfth, sixteenth or sixty-fourth to ⁹⁰⁄₁₂₇ is a challenge.
• Decimal scales are easier to interpolate by eye than fractional scales because there's no need to adjust the divisor.

I reluctantly agree conflating resolution, accuracy and precision is sinful and leave it to Michael to explain the difference! His concern isn't pedantry: in engineering, many words such as energy, work, power, stress, and strain have particular meanings that confuse when used carelessly, as I did with precision. All I can say is 'even Homer nods'. Please be gentle with me and I would like 98 other offences to be taken into consideration!

All I'm trying to say is that rules aren't much good compared with a Vernier or Digital Caliper, and they are inferior to a micrometer. And micrometers aren't the best measuring tools available either.

Dave

What fractional notation applies to 7490/18773 ?

Regards Ian.

Unsurprisingly, Dave …

A scale divided into 127ths of an inch would be interchangeable with one having 0.2mm divisions

MichaelG.

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7490/18773 … as you presumably well-know

What was the point of your question ?

MichaelG.

Hi Dave, I think you'll find that 45/64" is about as close as one might get with a rule if that is all that is available, 45/63.5 being equal to 90/127

Regards Nick.

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Having tapped on your picture of the scale, to expand it … then done a screenshot … then converted that .png back to .jpg for the forum … I think my iPad handles that pretty well : I can even see the dots on your Grid.

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Click for a larger view ^^^

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Certainly good enough to see the nominal resolution of the scale, even if not to assess its accuracy/linearity.

MichaelG.

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P.S. __ ‘sub-graduations’ could be added according to taste … there is no need for them to be integer divisions of 127 … they are simply an aid to counting.

Edited By Michael Gilligan on 30/09/2021 13:38:21

Michael, your 'clear' image is about 5" across on this device, and is therefore utterly useless as a defence of a scale that doesn't work in real life.

And Imperial measurements have enough stupid divisions without some idiot enthusing about 1/127s !

I must confess that however useful a rule calibrated in 127ths might be, I cannot easily make out anything much smaller than the 1/127" markings on my rule, needing a magnifier to read the 1/254" scale. There is evidently a market for unusual imperial rules as Starrett's "no.1" graduation for rules includes not only the usual 16ths, 32nds and 64ths but also 12ths, 24ths and 48ths as well as 10ths, 20ths, 50ths and 100ths (handy for thou dimensions) and even 14ths and 28ths. I can sort of see the point of 12ths for scale drawing but 14ths! Drawing year planners perhaps?

Brian G

I have seen scales in 1/128" graduations and at least one twist drill sized in 1/128ths. I have a wooden rule graduated in whole inches only.

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I will accept your written apology for that personal insult when you care to post it.

… You have evidently mis-understood the preceding discussion.

MichaelG.

Edited By Michael Gilligan on 30/09/2021 21:34:42

I am not quite clear where that 1/127 came in but I did have a steel rule that had one inch divided into 1/128.

Quite how the manufacturers thought anyone could read that, is anyone's guess!

More useful though not in the workshop, was an acrylic rule with one of those diagonal scales that allow measuring tiddly bits of inches without needing a microscope. I think I still have it, but have forgotten how they work, beyond using a similar-triangles principle, though was taught it at school.

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Dave asked for the ‘fractional inch’ equivalent of 18.0mm

… which is 90/127

MichaelG.

These exotic fractional inches may be accurate and precise, but of no practical use to model engineers until they are "translated" into practical measurements such as mm. How would you turn a piece to 90/27"  diameter and how would you measure it?

Edited By david bennett 8 on 01/10/2021 02:34:25

Edited By david bennett 8 on 01/10/2021 02:38:08

Edited By david bennett 8 on 01/10/2021 02:50:16

Edited By david bennett 8 on 01/10/2021 02:50:41

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David … Did you miss this ^^^ post that I made yesterday ?

… if so, I commend it to your attention.

MichaelG.

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P.S. __ I am assuming that your 90/27 should read 90/127 … that was the fraction under discussion.

[ once more … with feeling ]

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MichaelG.

Still with you Michael! My response is a rule graduated in 0.2mm increments isn't much practical use either - not without a microscope.

This table shows what I don't like about fraction rules. It spans one inch assuming the user has rules graduated in eighths, tenths, twelfths, twentieths, and sixty-fourths.

The table can be eyeballed to see 3/8" is smaller than 25/64" which is smaller than 2/5, which is smaller than 13/32". They all approximate 10mm and 25/64" is the closest. But, as a general way of measuring, it's fairly obvious from the decimal fractions that the usual common fractions don't step evenly: they jump.

The graph has a sawtooth rather than a straight line:

In practice, this means it's best to work with a limited range of common fractions when using rules. Although you could have several rules, making anything dimensionally complicated is clumsy compared with working throughout in decimal fraction such as thou. Thou and millimetres are smooth, for example it's easy to go to tenths or nanometres when more accuracy is needed. But not measured with a rule!

Michael: I suspect some of our exchanges are being misunderstood: we're perhaps being a tad pedantic or arcane for most tastes. For the avoidance of doubt, Michael and I aren't having an argument! And I don't think I'm doing a good job explaining myself, so apologies for not being clear. Maths isn't my best subject.

Dave

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Thanks for that comment, Dave

… I was going to describe our exchange as sparring

There is no winner or loser, we are just exercising our minds to mutual benefit.

MichaelG.

Edited By Michael Gilligan on 01/10/2021 11:18:40