240 volts

Get an appropriate star delta transformer, perhaps?

Move to a country where the distribution companies are actually helpful?

Connect the supply that you *do* have to the heater on a *large* jacuzzi, ideally overlooking a large beautiful mountain range. The jacuzzi to have a wine cooler and suitable quantities of a fine wine or two. Chill the parts that benefit from chilling. Warm the parts that don't. Life really is too short...

These days a lot of people are going to VFDs when they don't have the flavor of power they need. They are getting cheaper than transformers and a lot better than MG sets although the MG does a great job of isolating line hits.. Even years ago we had solid state converters to get the 36KVA 400hz they needed in computer rooms. It was part of the UPS system.

I've just finished making myself a 5kW TIG inverter - standard components that cost me

A Rockwell Allen Bradley VFD is the answer. The smaller one's that do up to 10 hp cost less than a PC. The last one I used took about 160 variables programmed in using a little key pad. They can be connected to a PC for even more fun.

Is this a residential application?

Obvious but not yet mentioned are autotransformers on each 208 volt phase. Also, the utility will probably supply 480 volt delta and you can use a 480-240 volt transformer. Choice of solution would depend on other 3 phase equipment that might require Y, delta at different voltages and the magnitudes of these loads.

I'd put the phase converter at the bottom of the list no matter what its initial cost advantage over a transformer.

But you know all of this so what's up?

Chuck

Do your own homework.

Bill

On Tue, 26 Feb 2008 16:11:51 -0500 Chuck wrote: | On 26 Feb 2008 19:20:30 GMT, snipped-for-privacy@ipal.net wrote: | |>You have a machine that requires 240 volt three phase power. It requires |>connection to 3 phase lines and ground, but not neutral. You ask your |>utility to supply 240 volt delta and they say no. The machine fails to |>operate on 208 volts. What do you do? How many different solutions could |>you think of to explore? | | Is this a residential application?

It's three phase. I didn't mention country. But in the USA, three phase power to residential users is rare. But I'm not really asking about the type of service, just how to get a picky 240 volt machine to work.

| Obvious but not yet mentioned are autotransformers on each 208 volt | phase. Also, the utility will probably supply 480 volt delta and you | can use a 480-240 volt transformer. Choice of solution would depend on | other 3 phase equipment that might require Y, delta at different | voltages and the magnitudes of these loads.

They might supply 480Y/277, too.

At least one utility I found would provide 240Y/139 in certain locations. I don't know how they accomplish that. Maybe they found some transformers they can get the 138.564 volts out of, or approximate it some other way. But I do know utilities prefer not to have delta secondary services these days, presumably due to phase feedback situations and blowing lots of MV fuses.

| I'd put the phase converter at the bottom of the list no matter what | its initial cost advantage over a transformer.

I didn't think of that. But I don't think I would consider it, either.

| But you know all of this so what's up?

I'm just checking to see all the creative solutions. Personally, if I were faced with this, I'd take the 208Y/120 and add the autotransformer in boost configuration to get closer to that 240 volt need.

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. The closest one I figured out would get 239.7 Y / 138.4 volts. It would use a 240->24 volt transformer with primary connected C-A and secondary wired in series from A, giving a "bent" leg. The primary would have 208 volts at a 30 degree phase angle relative to the N-A leg, giving a boost of 20.8 volts at the same angle. That would give 138.4 volts with a sum angle of 4.3 degrees for a L-L voltage of 239.7. There are configurations for more than 240 volts, as well.

Another option is a 208/120 to Scott-T.

On Wed, 27 Feb 2008 00:53:02 GMT Salmon Egg wrote: | In article , snipped-for-privacy@ipal.net | wrote: | |> You have a machine that requires 240 volt three phase power. It requires |> connection to 3 phase lines and ground, but not neutral. You ask your |> utility to supply 240 volt delta and they say no. The machine fails to |> operate on 208 volts. What do you do? How many different solutions could |> you think of to explore? | | Do your own homework.

I already did. I'm just checking to see if I missed any creative ideas and to see what kind of diversity others as a group would have.

|---------------------------------------/----------------------------------|

|------------------------------------/-------------------------------------|

I actually have this issue Phil. I used a buck boost transformer. This is a light and intermittent load. A bank of relays at the end of a long cable run.

|> I already did. I'm just checking to see if I missed any creative ideas | and |> to see what kind of diversity others as a group would have. |>

|> -- |>

| |---------------------------------------/----------------------------------| |> | Phil Howard KA9WGN (ka9wgn.ham.org) / Do not send to the address below | | |> | first name lower case at ipal.net / snipped-for-privacy@ipal.net | | |>

| |------------------------------------/-------------------------------------| | | | I actually have this issue Phil. I used a buck boost transformer. This is a | light and intermittent load. A bank of relays at the end of a long cable | run.

I'm curious what the configuration is. I have a list of many different configurations near to, and far from, 240 volts, than can be derived from

208Y/120.

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.

You have some unique and original ideas, but it almost seems that you are off in a different electrical world somewhere, with your own standards and conventions.

On Wed, 27 Feb 2008 17:42:21 GMT Beachcomber wrote: | |>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.

It is an accuracy vs. precision issue. Accuracy is needed in order to correctly reflect the mathematical formula used. In the event some other formula results in a value somewhere near there, that would when rounded in the practical manner yield the very same result, the accuracy value is what will distinguish the different formulas. Precision is then how the value is expressed to carry the accuracy (of the calculation).

Although in this case I do not know of another formula that could give a result close enough to, when rounded, appear to be the same, I cannot rule out some formula existing. In the past I have run into cases where entirely different formulas ... formulas that are not mathematically the same (e.g. one cannot be transformed into the other), give results that are closer to each other than the practical precision normally used.

So ... as a standard practice, when numbers are produced as a result of doing mathematical/arithmetic calculations, I use enough precision to give a very high level of confidence in matching the correct formula. Sometimes I express a precision as extreme as arithmetic being performed can do. Sometimes I reduce it some for convenience, but leave enough to be sure there is likely no ambiguity as to which formula is used.

Someone wishing to review my calculations can then match the numbers very closely to be sure that not only am I using the correct formula, but am also using valid trigonmetry implementations (e.g. code I did not write).

If I measure a voltage with a voltmeter, I will express it as precisely as the device is capable of accurately measuring and precisely displaying. If it has an accuracy of 1/10 of a volt in a 200 volt range (rather good) I'll use that and might state the voltage as "119.1" or "121.0". But if it only has an accuracy of 1 volt, I'll state it as "119" or "121".

So when you see me use a highly precise expression like "235.5589", it is coming from a mathematical calculation done with at least 6 or 7 digits of precision (probably more since I default to using the double type which has 14 or so digots), using a formula I believe to be accurate.

If I ever manage to make a real physical measurement with such accuracy, I'll be sure to let you know about that miracle device capable of doing such a thing.

| You have some unique and original ideas, but it almost seems that you | are off in a different electrical world somewhere, with your own | standards and conventions.

Like doing mathematical formula based programming to automatically explore lots of models?

Here is the output of one of my programs that explores a variety of ways to configure different buck-boost transformers, including 480/240/120 volt transformers, and running transformers at much lower than design voltage just as a means to get a desired ratio (e.g. 208 volts being fed to a transformer designed step 480 volts down to 120 just because that is the only common transformer to get a 4:1 ratio).

The first 2 mumeric colums give the resultant system (at calculation level precision slightly reduced to fit the output format). The 4th and 5th give the voltage being added to 120 volts, and the phase angle of that added voltage vector. The 6th gives the buck-boost transformer primary voltage, and the 7th and 8th describe the buck-boost transformer being used.

Notice the two "103.923048" volt results. They are really the same thing in a geometric/vector sense, even if the configuration to arrive at them are different. The precision of the expression reveals that.

Notice the rows with "228.630707" and "228.945408". Those are _different_ kinds of configurations that are _not_ the same as vector math goes. The fact that the numbers are different reveals this. If these had been rounded, that fact would be hidden. If you measured them with a typical voltmeter, you wouldn't know as both might read "229".

There are other examples of close numbers in this list.

103.923048 Y / 60.000000 : 120.000 + 60.000 @ 180 (120.000 via 240 -> 120) 103.923048 Y / 60.000000 : 120.000 + 103.923 @ 150 (207.846 via 240 -> 120) 137.477271 Y / 79.372539 : 120.000 + 51.962 @ 150 (207.846 via 480 -> 120) 152.420471 Y / 88.000000 : 120.000 + 32.000 @ 180 (120.000 via 120 -> 32) 166.276878 Y / 96.000000 : 120.000 + 24.000 @ 180 (120.000 via 120 -> 24) 168.000000 Y / 96.994845 : 120.000 + 27.713 @ 150 (207.846 via 240 -> 32) 177.583783 Y / 102.528045 : 120.000 + 20.785 @ 150 (207.846 via 240 -> 24) 180.000000 Y / 103.923048 : 120.000 + 60.000 @ 120 (120.000 via 240 -> 120) 180.133284 Y / 104.000000 : 120.000 + 16.000 @ 180 (120.000 via 120 -> 16) 181.865335 Y / 105.000000 : 120.000 + 15.000 @ 180 (120.000 via 120 -> 15) 183.597386 Y / 106.000000 : 120.000 + 14.000 @ 180 (120.000 via 120 -> 14) 185.329436 Y / 107.000000 : 120.000 + 13.000 @ 180 (120.000 via 120 -> 13) 186.418883 Y / 107.628992 : 120.000 + 32.000 @ 120 (120.000 via 120 -> 32) 187.061487 Y / 108.000000 : 120.000 + 12.000 @ 180 (120.000 via 120 -> 12) 187.445992 Y / 108.221994 : 120.000 + 13.856 @ 150 (207.846 via 240 -> 16) 190.494094 Y / 109.981817 : 120.000 + 24.000 @ 120 (120.000 via 120 -> 24) 192.468179 Y / 111.121555 : 120.000 + 10.392 @ 150 (207.846 via 240 -> 12) 193.989690 Y / 112.000000 : 120.000 + 8.000 @ 180 (120.000 via 240 -> 16) 195.468668 Y / 112.853888 : 120.000 + 16.000 @ 120 (120.000 via 120 -> 16) 196.150452 Y / 113.247517 : 120.000 + 15.000 @ 120 (120.000 via 120 -> 15) 196.845117 Y / 113.648581 : 120.000 + 14.000 @ 120 (120.000 via 120 -> 14) 197.453792 Y / 114.000000 : 120.000 + 6.000 @ 180 (120.000 via 240 -> 12) 197.552525 Y / 114.057003 : 120.000 + 13.000 @ 120 (120.000 via 120 -> 13) 198.272540 Y / 114.472704 : 120.000 + 12.000 @ 120 (120.000 via 120 -> 12) 201.275930 Y / 116.206712 : 120.000 + 8.000 @ 120 (120.000 via 240 -> 16) 202.849698 Y / 117.115328 : 120.000 + 6.000 @ 120 (120.000 via 240 -> 12) 208.624064 Y / 120.449159 : 120.000 + 10.392 @ 90 (207.846 via 240 -> 12) 209.227149 Y / 120.797351 : 120.000 + 13.856 @ 90 (207.846 via 240 -> 16) 210.940750 Y / 121.786699 : 120.000 + 20.785 @ 90 (207.846 via 240 -> 24) 213.232268 Y / 123.109707 : 120.000 + 6.000 @ 60 (120.000 via 240 -> 12) 213.316666 Y / 123.158435 : 120.000 + 27.713 @ 90 (207.846 via 240 -> 32) 215.109275 Y / 124.193398 : 120.000 + 8.000 @ 60 (120.000 via 240 -> 16) 218.238402 Y / 126.000000 : 120.000 + 6.000 @ 0 (120.000 via 240 -> 12) 218.979451 Y / 126.427845 : 120.000 + 12.000 @ 60 (120.000 via 120 -> 12) 219.970453 Y / 127.000000 : 120.000 + 13.000 @ 60 (120.000 via 120 -> 13) 220.970586 Y / 127.577427 : 120.000 + 14.000 @ 60 (120.000 via 120 -> 14) 221.702503 Y / 128.000000 : 120.000 + 8.000 @ 0 (120.000 via 240 -> 16) 221.979729 Y / 128.160056 : 120.000 + 15.000 @ 60 (120.000 via 120 -> 15) 222.997758 Y / 128.747816 : 120.000 + 16.000 @ 60 (120.000 via 120 -> 16) 223.615742 Y / 129.104609 : 120.000 + 10.392 @ 30 (207.846 via 240 -> 12) 226.495033 Y / 130.766968 : 120.000 + 51.962 @ 90 (207.846 via 480 -> 120) 228.630707 Y / 132.000000 : 120.000 + 12.000 @ 0 (120.000 via 120 -> 12) 228.945408 Y / 132.181693 : 120.000 + 13.856 @ 30 (207.846 via 240 -> 16) 230.362757 Y / 133.000000 : 120.000 + 13.000 @ 0 (120.000 via 120 -> 13) 231.447618 Y / 133.626345 : 120.000 + 24.000 @ 60 (120.000 via 120 -> 24) 232.094808 Y / 134.000000 : 120.000 + 14.000 @ 0 (120.000 via 120 -> 14) 233.826859 Y / 135.000000 : 120.000 + 15.000 @ 0 (120.000 via 120 -> 15) 235.558910 Y / 136.000000 : 120.000 + 16.000 @ 0 (120.000 via 120 -> 16) 239.699812 Y / 138.390751 : 120.000 + 20.785 @ 30 (207.846 via 240 -> 24) 240.399667 Y / 138.794813 : 120.000 + 32.000 @ 60 (120.000 via 120 -> 32) 249.415316 Y / 144.000000 : 120.000 + 24.000 @ 0 (120.000 via 120 -> 24) 250.567356 Y / 144.665131 : 120.000 + 27.713 @ 30 (207.846 via 240 -> 32) 263.271723 Y / 152.000000 : 120.000 + 32.000 @ 0 (120.000 via 120 -> 32) 274.954542 Y / 158.745079 : 120.000 + 60.000 @ 60 (120.000 via 240 -> 120) 274.954542 Y / 158.745079 : 120.000 + 103.923 @ 90 (207.846 via 240 -> 120) 289.309523 Y / 167.032931 : 120.000 + 51.962 @ 30 (207.846 via 480 -> 120) 311.769145 Y / 180.000000 : 120.000 + 60.000 @ 0 (120.000 via 240 -> 120) 374.699880 Y / 216.333077 : 120.000 + 103.923 @ 30 (207.846 via 240 -> 120)

| 219.970453 Y / 127.000000 : 120.000 + 13.000 @ 60 (120.000 via 120 -> 13)

I didn't even notice this one before. But I checked. It is correct that a vector of exact whole number length 120 at 0 degrees plus a vector of exact whole number length 13 at 60 degrees (1/6 of the arc of a circle) yields a sum vector that is an exact whole number length 127 (though at an angle I am unable to find a rational relationship to PI for). While it is possible to have triangles at any whole number lengths you pick, as long as no side is equal to or greater than the sum of the other sides, perhaps it is interesting when some can be formed with at least some corners having a rational relation to PI (e.g. 1/6 of a full circle).

And I would not have noticed it had I rounded all the numbers to whole.

OK, so I like precision in calculations, like the square root of 3 is:

1.7320508075688772935274463415058723669428052538103806280558069794519330169088

But some people seem to prefer whole numbers. So for them I have:

13005325352767864879663023255649031427 / 7508628093319191445537920541850040962

` These digital volt meters may have 4 digits of "precision" but nobody says they have that degree of "accuracy". Most will give you an inaccurate answer precise out to 4 decimal places unless you just got them back from the calibration lab and you haven't done anything to change the calibration (dropped it, had a static discharge while you were using it, left in in a hot car or whatever) Considering the utility only uses a +/- 10v "guideline" (they won't give you your money back if it is worse) who cares about tenths of a volt or less.

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.)

120 * sqrt(3) = 240 (only two significant digits in 120)

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.)

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

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.

daestrom I told you I was going to be pendantic .... :-)

| These digital volt meters may have 4 digits of "precision" but nobody | says they have that degree of "accuracy". Most will give you an | inaccurate answer precise out to 4 decimal places unless you just got | them back from the calibration lab and you haven't done anything to | change the calibration (dropped it, had a static discharge while you | were using it, left in in a hot car or whatever)

Suppose you know that there is a 95% probability that the meter will be off by plus or minus 1 volt. You get a reading of 121.3 volts. What is the probability that the real voltage is 120.1 volts? Which of these is a more correct sattement:

1. 95% probability the voltage is between 120.3 and 122.3
2. 95% probability the voltage is between 120 and 122

The interplay of accuracy and precision can be an interesting one. For more information, see:

is, if you have more than a 50% trust in the accuracy and precision of Wikipedia :-)

|> 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.

Many mid to high end multimeters are more accurate than that.

You are only talking about 1ppm or 0.1ppm. A lot of equipment exists with that accuracy. I have calibration instruments in my lab that will do it. However, that is several orders of magnitude better than any field measurements that I make. Even if you did make measurements with that accuracy on an electrical power system , it would be meaningless from a practical standpoint. It would be difficult to measure the difference in winding temperatures, for example, with a voltage variation of 0.0001%.

You are presenting a great mental excercize, but if you need to go that far down to differentiate between the results of two formulas, then as a practical matter in most power work, they are the same.

Great theory, but you will get plenty close using 1.732 for almost any power calculation.

-- Benjamin D Miller, PE