|
| |> |
|> |>Although 208 volts might not work on some 240 volt machines, hopefully
|> |>just a few volts away would achieve that. Boosting each 120 volt leg
|> |>to 136 volts with a 120->16 volt transformer would give you 235.5589
|> |>volts line-to-line. That might be enough. But if one really needs to
|> |>get closer, there are other configurations.
|> |
|> | Phil, why do you use terms like 235.5589 volts? No electrical
|> | engineers do that. It is improper usage and unprofessional to imply
|> | precision to 4 decimal places for common electrical circuits.
|>
|> The precision _IS_ there ... because the number is the result of an
|> arithmetic calculation using a high level of precision with a formula
|> I believe to be accurate. This is very different than if I were to
|> physically measure the voltage of a circuit with a voltmeter that has
|> 4 digits of accuracy and precision. In the latter case you would see
|> me write "235.6" or whatever it happens to be.
|>
|
| Just to be pendantic, just because the sqrt(3) can be known to a high degree
| of precision, you're multiplying a number that has as many significant
| digits as you could want, with a number that is stated to only have three
| significant digits (120. with the decimal is three sig. digits, 120 without
| the decimal is only two significant digits). Mathematical purists will tell
| you that any multiplication or division can only be carried out to the same
| number of significant digits as the least significant term. So...
|
| 120. * sqrt(3) = 236. (three significant digits in 120.)
I get something closer to 207.84609690826527522329356098070468403313663
If I use 1.732 I get 207.84
If I use 1.73 I get 207.6
If I use 1.7 I get 204
If I use 2 I get 240
I have no idea where the 236 came from. Did you mean to start with 208
and just copied the number I was using before?
| 120 * sqrt(3) = 240 (only two significant digits in 120)
That's as bad as sqrt(3) = 2.
| And backing up a bit further, when you add you have to be even more careful
| about precision.
|
| 120. + 16. = 136. (because 120. (with the decimal point) is three
| significant digits.)
In the three phase wye buck-boost example, I consider the 136 to be
accurate and precise because the transformer can have an exact 15:2
winding ratio to derive 16 volts from 120 volts.
| But ...
|
| 120 + 16 = 140 (because the '16' has to be shifted to at least the same
| decade as the least significant digit of 120 and that means you round it off
| to...
| 120 + 20 = 140
You won't be able top tell the difference between using a 16 volt boost
transformer and a 24 volt boost transformer, if you express the result
as 140 volts.
| Most of us skimp on the rules a bit, but taking a number like 120 * sqrt(3)
| and claiming the answer to seven significant digits is over the top.
It depends on the context. If I am doing a calculation that _should_
come up with the same value as 120 volts times the square root of three,
but want to just express the result value to let someone else match it,
I will use more digits. Usually 6 is enough to not just identify the
system, but identify that the calculation did more than just get into
the right ball park.
| daestrom
| I told you I was going to be pendantic ....
I consider myself to be pedantic. My practice is that if there is a known
statistical error in the values I'm calculating with, I let those errors
work their way through in the appropriate way. I do NOT increase those
error artificially. So if I am working with 120 volts plus or minus 10
volts (at 95% confidence), then in three phase wye, the line to line value
is 207.846096908265275 volts plus or minus 17.3205080756887729 volts (at
95% confidence). THEN I round that result down to 208 volts plus or minus
17 volts, and let the confidence figure get a little fuzzy.
I would disagree with your "mathematical purist" (mentioned way above)
because I feel that is being quit UNpure to allow TWO sources of error
to operate in a formula when only one value (the measurement) has error
and the other (the mathematically defined square root of three) has no
error.
How much I round depends on the context. If I'm talking about a type of
electrical system, I'll say something like 208Y/120 or 220Y/127 as the
case may be. Accuracy is not important there as it is just identification,
not a measurement or calculation (which can be an identification of the
formula used).
Back when I was in junior high school, without the aid of any calculator
or computer, I pondered the meaning of the frequency 3.58 MHz as it related
to the TV broadcast standards (which at the time I "knew" to be 15,750 Hz
horizontal and 60 Hz vertical. But I found a book in the school library
that gave the value as 3.579545 MHz. Just that much information allowed
me to "reverse engineer" this number to determine it came from 5 MHz times
63 divided by 88, and really had "454545" repeated (3579545.45[45..] Hz),
and that the horizontal frequency was really 15734.265734[265734..] Hz,
and that the vertical frequency was really 59.940059[940059..] Hz. All
that semantic understanding came out of just getting 4 more digits of
precision. Over a decade later I found that the FCC broadcast rules
actully defined the value the same way, as 5 MHz times 63/88. It is still
identifiable as 3.58 MHz. But if I want to compare it to something else
semantically, I need a much more precise value. Would you recognize it
as the NTSC color subcarrier frequency if I called it 3.6 MHz? or 4 MHz?
Now along comes the new ATSC standard. Yes, I have very precise values
for it. What is _really_ scary about the exact DEFINED bits per second
rate it has is that the fractional part (in either MHz or Hz) in decimal
repeats only after 312 digits! But it is a lot easier to express it as
its exactly defined value in the form of 867996/44759 Mbps. Work out
that division on a calculation with thousands or more digits precision
adn you will get the repeat every 312 digits. Fortunately I only need
to express 11 digits to nail the value dead on.
How many digits of precision is needed from a calculation that _should_
give a result of exactly 1 do you need to see as a value just shy of 1
(e.g. 0.999....) to know that it _should_ be exactly one as opposed to
merely being _nearly_ 1? Does 0.999 do it? Does 0.999999 do it? How
about 0.999999999999999999999999999999999999999999999999? I would never
say 0.9 is 1. But as the number of 9's continues, the confidence that
the valus really should have been exactly 1 increases rapidly.
Do you do any computer programming? If so, do you just add up a long
list of floating point values in the order given, or do you sort them
so you accumulate the sum by adding the lowest values first?
How many digits do you want for the square root of three expressed as a
ratio of two integers with a precision in digits equal to or greater than
the SUM of the digits in the numerating AND denominator?
Anyone can just say:
17320508075688772935274463415058723669428052538103806280558069794519330169088
divided by:
10000000000000000000000000000000000000000000000000000000000000000000000000000
but that is only 77 digits of precision for 154 digits expressed.
But if I give you:
81637354237035839875406774706916734691676867556988461166524491402570869800626
divided by
47133348444681477624409145446409554706879415291771528507046516487702731598175
then you can be sure you have 154 digits of precision. Try it.
Remember 355/113 for the value of PI? I have way better fractions. You
won't _need_ them, of course. But I have them.