... Diameter of 1 strand = .22mm ... Area of 1 strand = 3.1415 * (.11 ^ 2) = 0.0380132711
Tot area of cable (26 wires) = 0.0380132711 * 26 = 0.98834504881 ... So original is 1mm² ... Method seems to work well, even with thin wire and crappy callipers. I guess I might have pinched the malleable copper a bit.
No way am I working that out, but it looks more like 1.5mm2 in your picture, and, as you have indicated, you need 1.5mm2.
Interesting, it could well not be a good method then.
Your calculation was correct, and I have to say that your answer was so close to 1.0 mm that I would have been tempted to think that your measurement was probably also fairly correct.
Working backwards if the original wire was was 1.5mm² then the diameter of each strand would be: 2 * (sqrt(1.5/(3.1415*26))) = 0.27mm .... This is 0.05mm off my measurement of 0.22mm.
Your calculation is again correct
My callipers say they are accurate to +/- 0.03mm. Which is probably generous for this usage, measuring a very thin malleable copper wire. So yes I could well believe I'm wrong and this isn't an accurate way of doing things. The trouble is I guess any inaccuracy in the initial measurement is magnified by a factor of 26 when calculating the total area.
It's actually a lot 'worse' than that. Not only would an error in your calculated area of one strand be multiplied by 26, but the error in the one-strand error would be related to the
square of the error in your measured diameter.
Do I take it that you measured several strands? Also, all that can really go wrong (other than the intrinsic error of the callipers) is that the measuring device can 'squash' a malleable strand. If that happens, the diameter at right angles to one's initial measurement will presumably increase. I therefore always measure at least two or three strands and, at least in some, measure (very gently!) in two planes at right angles - and then take an average of everything. As I said, when I do that, I virtually always get what seems to be a credible (correct?) answer!
I have very little experience of callipers for this sort of measurement (! always use a micrometer) but one with a possible error of 0.03 mm is clearly not really 'fit for purpose' for measuring the sort of small strands we are talking about - since ±0.03 mm is about ±11% of, say, 0.27 mm - and an 11% error in measuring diameter will lead to about a ±23% error in the calculated area.
Having said all that, it wouldn't fully explain how you managed (if you did) to measure 0.27 mm as 0.22 mm, unless you were very 'heavy handed' in squashing the strand with your callipers. I would imagine that the effects of squashing are fairly pro-rata - so if you squashed 27 mm down to 0.22 mm, one might expect that the 'other diameter'; would have increased from0.27 to about 0.32 mm.
Kind Regards, John
Edit: Incorrect attribution of quotes corrected
