Slide rule with a log scale?
70's wiring in new sockets
- Thread starter sxturbo
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Slide rule with a log scale?
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I used Knotts log tables on Castles, and yes the slide rule did have a log scale, but significant figures much reduced, today I use the go/no go gauge i.e. will a blue terminal fit. I would guess a 2.5 mm² is around 0.070 inches? but in real terms this is the problem, have I made a mistake? Is 89 thou 4 mm²? or 6 mm² 109 thou? I have a micrometer but I don't know off hand what the reading should be, so easy to forget it's radius not diameter and end up out be a factor of 2. OK today with excel or java script you can make a converter. But in the main we don't use the micrometer we use red, blue, yellow crimps as see which fits. This means it is all too easy to think a 2.9 mm² cable is 4 mm² it will not fit in blue, and slack in yellow so must be 4 mm², that is only true if cable is metric.
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TBH I'd have thought that the ease 2.5mm²7X goes into a blue crimp [and 2x 1.5mm² tri-rated usually fits] that 7/0.029" would also fit. That's D=2.045mm/80.5thou Vs 2.21mm/87thou.
I think it's been a long time since I've had to crimp onto 7/0.029", so I'm not able to give a definitive answer.
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Indeed - and that is remarkably close to the 'true' answer. It assumes that pi = 22/7, and that's almost true - pi is actually 3.1415925..... and 122/7 is 3.1428571 (recurring) - so the approximation is accurate to within about 0.04%.
Kind Regards, John
Not sure that there is any difference but -
rather than assuming that pi is 22/7, surely it realises that 7 x pi is near enough 22, namely 21.99(11485etc.).
If one needs to be more accurate and one's calculator has a pi key then there there is no bother in using the full equation.
rather than assuming that pi is 22/7, surely it realises that 7 x pi is near enough 22, namely 21.99(11485etc.).
If one needs to be more accurate and one's calculator has a pi key then there there is no bother in using the full equation.
There isn't a difference - you've just said the same thing in two different ways - if 7 x pi is 'near enough 22", then pi is also 'near enough' to 22/7
If you change the "near enough" to "equals", and change pi to P, then ...
if 7 x P = 22, then P = 22/7
Kind Regards, John
Agreed, but surely people didn't begin by dividing 22 by 7 and seeing what the answer was; they would have multiplied pi by 7 because that is the number of strands.
Quite possibly, but so what?
I wasn't speculating about how the rule of thumb came about - I was merely indicating how very accurate it is, and that's because (to state it one way) 22/7 is very close to pi. If you prefer an alternative, but mathematically equivalent way of expressing that, that's fine
Perhaps far more to the point, particularly before calculators (with 'pi' built in), or slide rules (with 'pi' marked on their scales) came along, mathematicians and engineers have, 'since the start of time', been using 22/7 as a (very close) approximation to pi (which was the point I was making).
It so happens that this particular discussion related to 7-stranded conductors, but the pi=22/7 approximation applies in any situation or context (e.g. for 5-stranded or 11-stranded conductors), and it's a pure co-incidence that the "7" related, in this case to the number of strands in the conductor.
Kind Regards, John
Ok, but I just don't think they discovered the 22/7 by doing it that way round - unless you think they might have tried 23/7 first and found that it was too much.
As I implied, I can't read what was in 'their' minds.
However, as I said, it's only in relation to 7-stranded conductors that your way of looking at it would work, and that's is due to a 'co-incidence'.
In the absence of calculators or slide rules etc., people will have still needed a simple (i.e. 'using whole numbers') approximation to pi - and that would always have been 22/7, regardless of the number of strands (or, indeed, the nature of the calculation - which could be anything in maths or engineering). For example, if it were a 5-strand conductor, the total CSA would have to be calculated (using 'whole numbers') as:
5 x (22/7) x r²
... so the 22/7 approximation for pi works with any number of strands (or any other application that requires pi), whereas your way of looking at it only 'works' in the special case of 7-strand cable (and that because a "7" appears, co-incidentally, in the approximation to pi).
Kind Regards, John
I think we are at crossed purposes.
All I am saying is that anyone using 22/7 would not have come to that fraction by dividing 22 by 7.
They would have realised or just known that 0.14(159etc.) is all but a seventh and therefore pi is all but 3 1/7, i.e. 22/7.
All I am saying is that anyone using 22/7 would not have come to that fraction by dividing 22 by 7.
They would have realised or just known that 0.14(159etc.) is all but a seventh and therefore pi is all but 3 1/7, i.e. 22/7.
pi is actually 3.14159265...
I'm not realy sure where this is leading either but I'll stick a bit in just because I can.
I assume, guess, suppose, think or any other word to add vagueness that in the early days the value of π (the symbol used on this site for pi) was derived by wrapping a piece of string, creeper etc around, or rolling something round along the ground and then discovering that represented 22/7 times the diameter, as more accurate round things were made and measurement accuracy improved we discovered we were a whole 1/25% out.
I dare say in the early days a figure of 3 was used and was close enough for many applications, even now I'll often aproximate to 3 +10% when ordering cable/rope etc as an example.
Or is the discussion actually about the accuracy of 22/7 Vs 3.14.............?
I assume, guess, suppose, think or any other word to add vagueness that in the early days the value of π (the symbol used on this site for pi) was derived by wrapping a piece of string, creeper etc around, or rolling something round along the ground and then discovering that represented 22/7 times the diameter, as more accurate round things were made and measurement accuracy improved we discovered we were a whole 1/25% out.
I dare say in the early days a figure of 3 was used and was close enough for many applications, even now I'll often aproximate to 3 +10% when ordering cable/rope etc as an example.
Or is the discussion actually about the accuracy of 22/7 Vs 3.14.............?
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