250.122-B "Size of Equipment Grounding Conductors.--Increased in Size.

[chris huckins]

This article says the EGC shall be increased in size proportionately according to circular mil area of the ungrounded conductors. I came up with a formula for this requirement, but I was wondering if a standard formula exists?

 

[stevee]

I don't know of any standard formulas other than simple math.

If you increase your ungrounded conductors by 50% of their circular mil area then you are required to increase the circular mil area of your egc by 50% as well.

 

[Smart $]

The question I always have in this matter is: how accurate must the calculation be?

Take for instance a #8 circuit w/#10 EGC upsized to #4 circuit. The calculation goes:

41,740 ? 16,510 ? 10,380 = 26,242 cmil

#6 has a cmil area of 26,240... shy by 2 cmil. So do we upsize to #6 or #4 EGC?

 

[don_resqcapt19]

The math results in the minimum size permitted. You have to use a conductor that has at least that amount of area. You need a #4 for the EGC.

 

[sandsnow]

I have an excel table that will calculate the size for you. A very generous person created it. I think the person was from this forum. If you would like a copy, please PM me and I will email it to you.

 

[Smart $]

The math results in the minimum size permitted. You have to use a conductor that has at least that amount of area. You need a #4 for the EGC.

I agree that is how it appears. The problem, however, is the fact that I know the cmil areas of AWG sizes in NEC tables are rounded. Below is a list of these values and the corresponding AWG cmil values rounded to a whole number:

AWG	NEC Table	AWG Formula [Diameter = 0.005*92^(36-n/39)] 
18	1620		1624
16	2580		2583
14	4110		4107
12	6530		6530
10	10380		10383
8	16510		16510
6	26240		26251
4	41740		41741
3	52620		52634
2	66300		66371
1	83690		83693
1/0	105600		105535
2/0	133100		133077
3/0	167800		167806
4/0	211600		211600

If we calculate the problem given earlier using the AWG cmil values, we get:

41,741 ? 16,510 ? 10,380 = 26,243​

Note the discrepancy between #6 @ 26,251 cmil and the result of 26,243. This is due to rounding of the AWG values to whole numbers. So I have a variance of 8 cmil area using more accurate values than the rounded ones in the NEC tables... and these values are technically more proportional to each other than the NEC values, i.e. #10 - (#8 ? #4) = #6 exactly when calculated to the full extent attainable.

So this still leaves me questioning how accurate must the calculation be???

 

[winnie]

I think that Smart $ just said this, so to amplify: if you use the _definition_ of AWG, rather that the rounded values of the NEC tables, then a given numeric difference in AWG always corresponds to the same exact proportional area difference. Smart gave the defining formula for diameter:
Diameter = 0.005*92^((36-n)/39)

Consider two different wire gauges, n and (n-x) and ask 'What is the proportionate diameter of #n relative to #n-x?'

Diameter/Diameter(n-x) = 92^((36-n)/39) / 92^((36-(n-x))/39)
by the rules of exponents, this gives
=92^( ((36-n)/39) - ((36-(n-x))/39) )
=92^( ((36-n) - (36-(n-x)))/39 )
=92^(x/39)

A 4 AWG difference should always equate to the larger conductor being 1.5900...the diameter of the smaller, with an area 2.52829... the area of the smaller, for _any_ pair of AWG 4 apart.

-Jon

 

[iwire]

So this still leaves me questioning how accurate must the calculation be???

Accurate. :grin:

Just like parallel conductors 'shall be the same length'.

I don't care how careful you are, two conductors will never be the same length.

 

[Smart $]

Accurate. :grin:

Just like parallel conductors 'shall be the same length'.

I don't care how careful you are, two conductors will never be the same length.

I agree... but that's another subject in itself

So what is your opinion on this issue? Should we be stringent on the exact result of cmil area proportions using NEC table values? ...or can we base the proportions using the AWG gauge number?

Is there a definitive, authoratative solution?

 

[sandsnow]

I don't get it. The Code calls out proportional to cmil area, so why are we talking about AWG and diameter? Why don't we just use the values in the table and forget about it?

The math to figure it is not hard, just time consuming if you have a lot of feeders to check.

 

[Smart $]

I don't get it. The Code calls out proportional to cmil area, so why are we talking about AWG and diameter? Why don't we just use the values in the table and forget about it?

The math to figure it is not hard, just time consuming if you have a lot of feeders to check.

I believe it goes to intent... it has to! For the requirement certainly is not specific enough to eliminate different approaches.

Observe the following depiction of conductor cmil areas, using the problem I posed earlier.

The requirement:

(B) Increased in Size. Where ungrounded conductors are increased in size, equipment grounding conductors, where installed, shall be increased in size proportionately according to the circular mil area of the ungrounded conductors.

Where in there does it say proportionately must be mathematically decided?

Additionally, some assume the result of mathematical proportionating is the minimum cmil area of the upsized EGC (depicted in image above). Where in the requirement does it say that?

What if I decide to upsize EGC by visual proportions? Would that violate the code? Technically, no... for the requirement is not that specific.

I can just as easily do the proportioning calulation and choose whichever size conductor is closest by cmil area. Would that violate the code? Technically, no... for the requirement is not that specific.

I demonstrated above that using more accurate cmil area values than published in NEC tables that the calculation can result in a larger difference than performing the same calculation with NEC table values. Yet the result points a two different sizes for the upsized EGC (assuming the result iis indicative of the minimum cmil area).

I'm willing to wager a grand that the 2 and 8 cmil area differences noted earlier are well within manufacturing tolerances of a 6 AWG conductor!!!

Let's take a poll:

Looking at the image above, which do you believe best represents the intent of 250.122(B), the pair on the left or right?​

 

[iwire]

Smart as unusual as it is I agree with you. :smile:

But I think it is much about little, it's really up to the AHJ (IMO).

IMO if you use the tables from the NEC it would be difficult for the AHJ to say they are not valid.

However if you start picking and choosing other methods or sources, perhaps intentionally to your own advantage the AHJ could say that they do not recognize those methods or sources.

I'm willing to wager a grand that the 2 and 8 cmil area differences noted earlier are well within manufacturing tolerances of a 6 AWG conductor!!!

I bet your right.

I also bet that in practice the actual measured dimension will be running on the small end of the range and drops below the range frequently.

 

[Smart $]

...I think it is much about little, it's really up to the AHJ (IMO).

(Not an opinion ) ...so the first course of action is to determine, and question, the method by which AHJ's enforce the requirement. It's only much ado about little if it falls on deaf ears. The requirement is in the code, and therefore opens debate on its implementation.

IMO if you use the tables from the NEC it would be difficult for the AHJ to say they are not valid.

However if you start picking and choosing other methods or sources, perhaps intentionally to your own advantage the AHJ could say that they do not recognize those methods or sources.

It is not really a matter of using NEC tables or some other source. Using the NEC tables is fine. In fact, AWG gauge numbers are listed in the same table It is more a matter of interpretation of the requirement. I would say many assume the result of calculating a required cmil area for the EGC results in a strict minimum size. The requirement does not indicate anything of the sort. It only requires upsizing to be done proportionately. Any mental processing beyond that is an assumption.

I also bet that in practice the actual measured dimension will be running on the small end of the range and drops below the range frequently.

It should also be noted this occurs with the ungrounded conductor, too!!!

 

[sandsnow]

Let me throw this out real quick.

Is this in line with what you are saying?

If the base combination is say ungrounded conductor three sizes bigger than the EGC, then proportionatley we can just maintain that relationship as we increase the ungrounded conductor size.

 

[Smart $]

Let me throw this out real quick.

Is this in line with what you are saying?

If the base combination is say ungrounded conductor three sizes bigger than the EGC, then proportionatley we can just maintain that relationship as we increase the ungrounded conductor size.

Sort of yes... depends on what you consider "three sizes" bigger. #10 is two sizes larger than #12, and four sizes larger than #14. So even though we only use the even numbered smaller gauges, the odd numbered gauges still count as a size. No proportional cmil calculation necessary until one gets into the kcmil range of conductor sizes. Using AWG gauge numbers, subtraction and addition is all that is necessary to determine the proportional EGC size...

Where:

a = Base ungrounded AWG size
b = Base EGC AWG size
c = Upsized ungrounded AWG size
d = Upsized EGC AWG size​

Use the following formula:

c + (b – a) = d​

For x-ought sizes:

1/0 or 0 = 0 AWG
2/0 or 00 = (-1) AWG
3/0 or 000 = (-2) AWG
4/0 or 0000 = (-3) AWG​

If d results in an uncommon gauge number, go one size larger on the EGC. This may occur in the ungrounded conductor range of #2 and larger.