On Fri, 1 Dec 2006 15:57:55 +0000 (UTC) Michael Moroney wrote:
|>Of course. The reality is the supply is a statistical range. But it does |>have a center. A given service drop may have a long term center that is |>offset from 120 maybe even by quite a few volts. But the _basis_ voltage |>is still 120 volts. I could run all my calculations on various voltages |>in the range, and the extremes of the range, and get range results with |>precision. | | Such precision isn't necessary in that case, unless you're pulling a stunt | like wiring two big substation transformers to have a zero voltage | difference between two terminals, and using your two hands to "measure" | the difference. In that case the accuracy doesn't matter (you don't care | if the transformers are putting out 69 kv or 68 kv) but you do want the | difference to be very precisely 0.
You're using "precision" and "accuracy" interchangeably here.
|>Only to people that misunderstand the difference between precision and |>accuracy. | | I know the difference perfectly well.
|>First of all, saying "120" does NOT say that it is 3 significant figures. | | Right. To an engineer it's ambiguous, but it implies accuracy to two | figures. "120.", to an engineer, states 3 figures accuracy.
You're using "precision" and "accuracy" interchangeably here.
|>It could be a reference label to the connection that is defined nominally |>as 120 volts can could be found to be anywhere from 114 to 126 volts in |>places where the voltage is within 5%, or even further at 108 to 132 volts |>when 10% is the margin. And you can find different ranges based on long |>pr short term statistics. | | There are different usages to an engineer and, say an electrician or a | lineman working on something. Even today, electricians often speak of | "two twenty" although the nominal voltage has been 240V (or at least | larger than 220V for decades)
Indeed. "two twenty" is a label, not a measure. So is "220V" and "240V" and even "207.84609690826527522329356". As labels they imply certain meanings which have nothing to do with precisions or even measures. The label "207.84609690826527522329356" means "120 times the square root of 3 with an extremely high degree of confidence" as opposed to "some number that just happens to come out really close" (as often does happen when many formulas with irrational numbers are involved).
|>Nevertheless, I run my calculations at precision (not accuracy) based on |>the "definition voltage". This lets me double check things, and assures |>that where multiple steps should end up back at a whole number they very |>likly will, or will be so damned close it's obvious to anyone. If you |>do some calculations and the end result is 119.999999997 you can just |>tell it was "meant to be" 120. But if the result is 119, that's not so |>obvious. | | Unnecessary, and misleading.
Tell that to the calculator or computer giving the results.
|>| This becomes ambiguous when the number of sig figs is less than the number |>| of digits left of the decimal point (what does 69,000 volts mean?), |>| but that's one of the reasons for scientific notation as well as metric |>| prefixes. 69 kV has 2 figures accuracy, 69.0 kV 3 figures, 69.00 kV four |>| figures etc. | |>I really don't know their basis voltage. If that is the L-N voltage on |>a system with a L-L basis voltage of 120 kV, then the L-N _basis_ voltage |>would be 69282.032302755 ... rounded to 9 fractional digits :-) That |>would be the center point in a range. | | Specifying "69282.032302755" as a center point in a range that can be a | few hundred volts is absurd.
That depends on the context. If I want to specifically make a reference to a baseline value related by a specific irrational number, more precision increases the confidence of correctly matching the numbers. If I just want to refer to a "69kv" circuit to by common label, to distinguish it from a "12kv" circuit, those terms are enough. But if I do some arithmetic and what I end up with is 68971.54879012, even though all steps used many digits of precision, then I know one of two things: either an error was made somewhere in the arithmetic, or the result happens to be close to, but is not the same as, "69282.032302755". If I express either one to 2 digits, each would be "69k". Precision in the arithmetic is more than just getting all the digits (even though so many are not actually needed for use), but it is about understanding what the number is. ONE of those numbers relates to exactly
120000 as a definition point by a ratio of the square root of three, whereas the other does not. When doing arithmetic, this is important to perceive, especially if you may be dealing with formulas that come full circle back to numbers you already work with.
|>| And when designing something, you must be sure the added digits don't come |>| back and bite you. | |>Don't worry. I know how to handle high precision arithmetic. | | YOU know, but does anyone using your design documents, should you be | designing something?
Lots of people certainly don't know how to deal with precision. Lots of people say "accuracy" when precision is what is meant ... or visa-versa.
And who says I would put that on a design document. I would where I feel it is important to identify that meaning of a number. But where meaning is unimportant and construction value is all that is needed, I would supply the value and its tolerance.
BTW, everything would all be different if we used base 8 or base 12 instead of base 10. We "quantize" to base 10 when we round things to make values fit available accuracy. Then we force precision to that level. It would end up at different points in a different arithmetic base. Thus we can actually have differences in engineering or construction that relate to what base we use.
| If you needed to specify the rating of a capacitor to connect line-line | in a 120 volt line-neutral 3 phase circuit, would you specify a capacitor | with a breakdown voltage of 293.9387692 volts (120V * sqrt(3) * sqrt(2) | sine wave peak voltage, plus a hundred picovolts safety margin) ?
293.93876913398137178367408896470696703591369767880041541192310807 :-)
Seriously, it depends on the context. If I'm trying to match numbers, I'd use more digits just to be sure the matching confidence is high. Normally, for a capacitor, I'd want a lot more margin to account for variation in voltage, environment, manufacturing, and aging. So I am likely to say "at least 600 volts" and may even go higher.
100 years ago you could be a "1000 pound rope" and never see it break even with 2000 pounds of load on it. Today, you buy a "1000 pound rope" and you can't sue the manufacturer for it breaking under your 1005 pound load. That's a misuse of the numbers. And it certainly is not precision. It's just being cheap.
|>When I was in school in the 1970's, courses in sciences and engineering |>never explained anything about precision vs. accuracy. I found a lot of |>people, including professors, didn't understand the distinction. More |>recently I was reading a (rather heavy) college freshman chemistry book |>(a chemistry prof my dad knew gave to him) and it actually did address |>the precision vs. accuracy issue. | | This is an accuracy issue, but it fails on precision grounds as well. | Are the three transformers in a 3 phase circuit _precisely_ identical | to that many degrees precision? Is the phase angle _precisely_ 120.000000 | degrees? Is the resistance/capacitance/indeuctance of the 3 supplying | conductors _precisely_ the same? Etc.
This is called "tolerance".
Of course not.
But when one is discussing the bounds of theoretical and comparing results to confirm formulas, the numbers have a different set of semantics.
|>So would you change "197.45379 +/- 0.5" to be "197 +/- 0.5" or would you |>change it to be "197.5 +/- 0.5"? Is 196.9530 within the range? What about |>197.9536? | | What is this "197.45379" figure? A one time measurement? A calculation? | If a calculation, what is the accuracy of the figures used in the | calculation? What is the "+/- 0.5" figure? A specification? An observed | range? An error figure carried through the calculation (say double a | figure of 98.726895 +/- 0.25) ? What is the accuracy of the "0.5" figure? | Where did all those decimal points come from, was it multiplication or | division of something with few significant figures by an irrational number | such as sqrt(3)? Depending on the answer to these, it may be appropiate | to write it as 197. or 197.5.
It also depends on whether you are talking about real physical things that can be measured to a certain accuracy, or discussing theory and the mathematics behind it.
| There are instances where you have to bring both a figure and the error | specification through the calculation. | |>What you are doing when you change it to either 197 or 197.5 is called |>quantization. It really is possible to have more precision than accuracy. |>You could have a 6 digits voltmeter that reads 207.846 volts. Then you |>can watch it waver up and down between 206.846 and 208.846. The accuracy |>of the supply is +/- 1 volt while the precision of the meter _may_ be |>+/- less than 0.001 volt. If the meter is calibrated to 0.0005 volts |>accuracy, then its precision is easy to deal with. However, if it is |>out of calibration, it can still give you precision. If you have a |>reference voltage you can check the error. But even if it is out of |>calibration by an unknown voltage, you might still read a figure around |>120 volts on a circuit that should have around 120 volts and know that |>it is at least not too far off. Then with the precision and lack of |>accuracy, you can still measure the _other_ phase and see _about_ how |>many volts different they are. You cannot do that if you misunderstand |>precision and assume it is always bound to accuracy (sometimes it is, |>but not in this case). | | Again, in many cases, you have to bring both the figure and the error | range through the calculations. But unless the accuracy error somehow | cancels (such as subtracting two figures known to have total inaccuracy | from the same source) that extra precision is useless.
And where I need to bring the error range through, I sure will. And it sometimes influences things in unexpected ways (especially with things like non-linear effects). But that wasn't needed in my recent posts.
|>BTW, the square root of three is approximately: | |>1.7320508075688772935274463415058723669428052538103806280558069794519330169088 | | Irrelevant to every engineering application I can think of.
However, keep in mind that is an irrational number. It is always in some amount of error. Depending on what kind of math is involved, you might need more precision for _this_ number and the calculations using it. For example, if a calculation has to be repeatedly multiplied and divided by this number as new factors keep being introduced, this error builds up. More precision to match the scale of the arithmetic (e.g. how many times a program loop doing this has to run).
Chaos theory describes how this affects calculations. It is also termed the "butterfly effect". Was that storm that came through caused by a butterfly somewhere? No. Could it have been influenced in some minute way? Yes. Not in ways you could measure, but in ways much larger than it's small size and mass would suggest.
|>but most electrical engineers will use 1.732 or even 1.73 because it is quite |>adequate where precision isn't needed. | | Exactly.
... where precision isn't needed ... but engineers need to know where it is not needed, and where it _is_ needed. I think too few can do this well.
|>The later is how far I have memorized the square root of three. But I can |>calculate it with a program I wrote to many million digits if you'd want it. |>When I want to know things like "does this calculation involving the square |>root of 3 produce a result that is supposed to be at a whole number", then |>I intentionally use more precision to be sure of it. | | Good engineering can justify calculations without that, plus anything | beyond the simplest it really can't be done anyway.
|>And I can also give you some whole number fractions that get very close to |>the square root of 3. Here are some examples: | | Useless except to a math geek. | | I can tell you for a fact that in introduction to engineering course, | writing the line-line voltage of a 120.V line-neutral circuit as | 207.8460969V will be marked wrong.
Most likely what is being asked for is a label, not mathematical matching.
What would you write for the line to line voltage for a circuit with 230V as the line to neutral voltage? 398V? 400V?
Did you see my proposal for an electrical system (if I could go back in time ... a hypothetical exercise that could not really happen today) where I proposed a standard voltage of 288 volts line to line, and mentioned that it would be based on 144 volts line to neutral from single phase sources and 166 volts line to neutral from three phase sources. Then I went on to indicate that a higher voltage system could use that same 288 volts in a line to neutral way and have 499 volts line to line. I mentioned that I thought the voltages were "catchy" because they all ended in two like digits. But I wonder if such a system have been used, how many people would still end uo just calling the latter "500V".
Humans LOVE round numbers. I think this is excessively so. So did you pick 398V or 400V above? I bet it was 400V. Nice round number.