Square Mil to Circular Mil?

[Boognish]

Hello, I have a homework question. This is the first and hopefully last time that I will ask for others help when doing homework, as I prefer finding out answers for myself ( thus actually learning ). So, here's the question.

What is the CM area of a buss bar 1/2 inches by 2 inches?

Are either of these formulas correct? If not, could you provide me with the correct formula?

( 0.5 x 1000 )(2)( 1.273 ) = 1273
or
( 0.5 x 1000 )(2 x 1000 ) (1.273 ) = 1,273,000

Thanks.

 

[mivey]

Area of 1 circular mil = d^2

Area of circle = 0.25*Pi*d^2 => d^2 = Area * 4 / Pi (mils^2)

Thus, 1 cmil = d^2 = Area * 4 / Pi

Take your area in square mils times 4 and divided by Pi and you will get the cmil. 4/Pi = 1.273

Your second equation is correct.

 

[Besoeker]

Area of 1 circular mil = d^2

Area of circle = 0.25*Pi*d^2 => d^2 = Area * 4 / Pi (mils^2)

Thus, 1 cmil = d^2 = Area * 4 / Pi

Take your area in square mils times 4 and divided by Pi and you will get the cmil. 4/Pi = 1.273

Your second equation is correct.

Makes me pleased that we (UK) don't have such a complicated system.
You have AWG, circ mils, square mils.....etc.
From Wikipedia:

By definition, No. 36 AWG is 0.0050 inches in diameter, and No. 0000 is 0.4600 inches in diameter. The ratio of these diameters is 92, and there are 40 gauge sizes from No. 36 to No. 0000, or 39 steps. Using this common ratio, wire gauge sizes vary geometrically according to the following formula: The diameter of a No. n AWG wire is

d_n = 0.005~\mathrm{inch} \times 92 ^ \frac{36-n}{39} = 0.127~\mathrm{mm} \times 92 ^ \frac{36-n}{39}

or equivalently

d_n = e^ {-1.12436 - .11594 \times n}\ \mathrm{inch} = e^ {2.1104 - .11594 \times n}\ \mathrm{mm}

The gauge can be calculated from the diameter using

n = -39\log_{92} \left( \frac{d_{n}}{0.005~\mathrm{inch}} \right)+36 = -39\log_{92} \left( \frac{d_{n}}{0.127~\mathrm{mm}} \right)+36 [3]

and the cross-section area is

A_n = \frac{\pi}{4} d_n^2 = 0.000019635~\mathrm{inch}^2 \times 92 ^ \frac{36-n}{19.5} = 0.012668~\mathrm{mm}^2 \times 92 ^ \frac{36-n}{19.5},

Shame you can't copy and paste the symbols but I'm sure you get the point.
You guys really need to take on board SI.
It is SO much simpler.

And I say that on the basis that I'm old enough to have dealt with both Imperial and metric (SI) units.

All our conductor sizes are in mm^2. Busbar dimensions are in mm.
I don't have to convert between horsepower and kW, gallons and litres, pounds and kg etc.
Conveniently, one litre of water weighs one kg. I don't have to know that one horsepower is 550 ft-lb/sec. A tonne (metric ton to some) is 1000 kg.
All of the basic electrical units are defined using SI.
There is no Imperial equivalent for the Volt or the Amp.

And the OP would have been more like "What is the area of a 12mm by 50mm busbar? It's obviously 600mm^2 and a very much simpler calculation.

 

[480sparky]

Silly me. I just use a 0.7854 multiplier.

 

[mivey]

Makes me pleased that we (UK) don't have such a complicated system.

We used to have problems a while back. But to make a long story short, it ended with : "... and stay there!" :grin:

 

[Besoeker]

We used to have problems a while back. But to make a long story short, it ended with : "... and stay there!" :grin:

At that point we were using the Imperial system that you still have.
We have since moved on....

 

[mivey]

At that point we were using the Imperial system that you still have.
We have since moved on....

England's legacy lingers on in our antiquated ways.

12mm by 50mm busbar? It's obviously 600mm^2 and a very much simpler calculation.

It would have been a simple calculation had the OP used root-cmil units:
A 564rcm x 2257rcm busbar? It would obviously be 1,273 kcmil. Very simple.

 

[cadpoint]

Hello, I have a homework question. This is the first and hopefully last time that I will ask for others help when doing homework, as I prefer finding out answers for myself ( thus actually learning ). So, here's the question. ...

Welcome to the Forum, the pleasure of learning is here!

By all means use your brain, don't be shy use all the resources that can be found here and at the host page,

Enjoy!

 

[Besoeker]

England's legacy lingers on in our antiquated ways.

Perhaps I ought to remind you that I'm not English!!
:grin:

It would have been a simple calculation had the OP used root-cmil units:
A 564rcm x 2257rcm busbar? It would obviously be 1,273 kcmil. Very simple.

Nice one.

 

[Boognish]

Area of 1 circular mil = d^2

Area of circle = 0.25*Pi*d^2 => d^2 = Area * 4 / Pi (mils^2)

Thus, 1 cmil = d^2 = Area * 4 / Pi

Take your area in square mils times 4 and divided by Pi and you will get the cmil. 4/Pi = 1.273

Your second equation is correct.

Hi, thanks for the response. I have a CM of 1,273,000 posted with the correct formula yet you say that 1.273 is correct. So, which number is correct and why not the other?

Anyone?

 

[mivey]

Perhaps I ought to remind you that I'm not English!!
:grin:



Nice one.

Now that you've uprooted our sister and planted her in the UK, she will have to become a Unitedkindoman. :grin:

Since they are set on mm over there and you can't get your hands on a good ruler, here is one you can print out to use in emergencies that includes scales up to 2 inches:

 

[mivey]

Hi, thanks for the response. I have a CM of 1,273,000 posted with the correct formula yet you say that 1.273 is correct. So, which number is correct and why not the other?

Anyone?

1.273 is the multiplier for conversion from mil^2 to cmil. You used this in your second equation and your second equation and answer are correct.

The first equation had mils*inches and gave you the wrong result.

 

[winnie]

There is a quote about making things as simple as possible but no simpler.

While I absolutely agree that the particular selection of limit values and number of steps in the 'AWG' system makes little sense today, the basic concept of using an exponential series of different wire sizes probably makes lots of sense.

You don't bother selecting between a 100mm^2 wire or a 101mm^2 wire; in real world applications the two would be indistinguishable. But the difference between a 1mm^2 wire and a 2mm^2 wire is huge. Thus even if you report your wire sizes as mm^2, you will still end up using an array of wire sizes that looks lots like AWG.

European paper sizes seem as odd as AWG sizes until you discover their basis in a very nice series; the mathematics of the situation requires strange non-round numbers. Why is A4 paper 210x297mm rather than a nice 'round' metric number such as 200x300mm? Because A0 was defined to have the property that if you divide its longer dimension in half, you would get two A1 size sheets with the same shape, combined with the definition that A0 was 1m^2 in area.

I would personally prefer that standard wire gauges were such that a given number of 'gauges' would exactly double wire area. Under the current system, going 3 steps in AWG ever so slightly more than doubles wire area. I'd also be happy with a wire gauge system where going some number of steps would exactly change the wire area by a factor of 10, perhaps even starting at 1mm^2. IEC 60228 doesn't do this.

-Jon

 

[Boognish]

1.273 is the multiplier for conversion from mil^2 to cmil. You used this in your second equation and your second equation and answer are correct.

The first equation had mils*inches and gave you the wrong result.

Ah, I see. Thank you.

 

[Besoeker]

Now that you've uprooted our sister and planted her in the UK, she will have to become a Unitedkindoman. :grin:

My good lady retains her US citizenship (not that she would dream of relinquishing it) but has indefinite leave to remain in UK.

Since they are set on mm over there and you can't get your hands on a good ruler, here is one you can print out to use in emergencies that includes scales up to 2 inches:

Thank you. That could be useful if I do any work over there.

 

[Besoeker]

There is a quote about making things as simple as possible but no simpler.

Occam's razor maybe?

While I absolutely agree that the particular selection of limit values and number of steps in the 'AWG' system makes little sense today, the basic concept of using an exponential series of different wire sizes probably makes lots of sense.

I think it does. It's just the different measurement systems used that make it seem overly complicated to me at least. When do you decide ir should be kcmil or AWG? And, with AWG, as the number goes up, the conductor size goes down. With mm^2, you get mm^2 with no conversion required.

You don't bother selecting between a 100mm^2 wire or a 101mm^2 wire; in real world applications the two would be indistinguishable. But the difference between a 1mm^2 wire and a 2mm^2 wire is huge.

Standard sizes for installation work go 1.0, 1,5, 2.5, 4, 6, 10 etc.

Because A0 was defined to have the property that if you divide its longer dimension in half, you would get two A1 size sheets with the same shape, combined with the definition that A0 was 1m^2 in area.

I didn't know that A0 was 1m^2. Thank you for that.

 

[mivey]

That could be useful if I do any work over there.

Just stay on your side of the road.:grin: I used cabs instead of renting when visiting the UK because I was afraid I would forget to stay left. That was after I found I had unknowingly violated other rules of the road in western Europe, and discovered my driving was not aggressive enough for Paris. Tourists :roll:!

 

[Besoeker]

Just stay on your side of the road.:grin: I used cabs instead of renting when visiting the UK because I was afraid I would forget to stay left.

Not the sort of thing you are likely to do more than once!!

That was after I found I had unknowingly violated other rules of the road in western Europe, and discovered my driving was not aggressive enough for Paris. Tourists :roll:!

The Boulevard P?ripherique isn't for the faint hearted and round the Arc de Triomphe it seems to be a complete laissez-faire. Think of us poor Brits used to driving on the other side of the road.....I commuted between London and Paris for the start-up of electrical equipment of the Orient Express.

But we have our own secret weapon - the "magic" roundabout.

http://www.youtube.com/watch?v=ih223jffmek
Enjoy!

 

[mivey]

But we have our own secret weapon - the "magic" roundabout.

An un-teathered teacup ride. Wheee!