NEC Changes For #14 Ampacity

[FionaZuppa]

I haven't look at the N&M equations, but basic physics says for a unit length of wire of diameter d and _surface_ area A

P = I^2 * R
R varies as 1/d^2
So P varies as I^2/d^2
A varies with d
So P/A varies as I^2/d^3

Temperature rise of the wire should be an increasing function of P/A (power dissipated per unit surface area of the conductor). Certainly that is true for the radiant and conductive components of heat loss, not sure about convection. So at least to a first approximation, a given maximum temperature rise will mean a fixed maximum P/A.

Thus there's nothing linear here: ampacity should vary as diameter to the 3/2, or cross-sectional area to the 3/4. How does that compare to the trend in the NEC ampacity values?

Cheers, Wayne

sure, but the ohms/100ft tables for AWG sizes are already done, i simply took those R values, etc. the P for each of those using the NEC ampacity table is not constant. why is that? P has to dissipate somewhere. if XYZ wire generates 10w then its 10w (10J/sec) of energy that has to go somewhere, and this has temp associated with it. if N-M equations show that temp rise is not directly proportional to P in linear fashion for varying wire sizes then this may explain it, but i just didnt see it in the N-M equations. NEC tables list ampacities that shows an increase of P density (heat generation) as wire size gets bigger, etc.

 

[wwhitney]

if N-M equations show that temp rise is not directly proportional to P in linear fashion for varying wire sizes then this may explain it

I don't think that the exact relationship between P/A and temp rise matters at all, it certainly won't be linear. As long as temp rise is an increasing function of P/A, then under a particular set of conditions (ambient temperature, insulation temperature rating, etc), the conductors will have a particular allowed temperature rise, which will result in a particular allowed P/A, independent of wire size.

Cheers, Wayne

 

[mbrooke]

sure, but the ohms/100ft tables for AWG sizes are already done, i simply took those R values, etc. the P for each of those using the NEC ampacity table is not constant. why is that? P has to dissipate somewhere. if XYZ wire generates 10w then its 10w (10J/sec) of energy that has to go somewhere, and this has temp associated with it. if N-M equations show that temp rise is not directly proportional to P in linear fashion for varying wire sizes then this may explain it, but i just didnt see it in the N-M equations. NEC tables list ampacities that shows an increase of P density (heat generation) as wire size gets bigger, etc.

Not sure if I am explaining it correctly but an increase in wire size means more mass but less surface area to dissipate heat.

This is why larger wires get hotter for less voltage drop at the same length.

 

[wwhitney]

Hmm, my simple model of I varies as d^1.5 must be missing something, it doesn't match the trend in NEC ampacity values. Using a spreadsheet, the trend is close to I varies as d^1.25 (I got exponents between 1.22 and 1.28). Not sure what is going on.

I do notice that insulation thickness tends to increase with increasing wire diameter. The thermal resistance of the insulation will reduce the heat loss, so the allowable P/A will go down with increasing insulation thickness. I don't know how big an effect that is or whether it could explain the above discrepancy.

Cheers, Wayne

 

[mbrooke]

Is it possible rounding plays a role? I mean the numbers are always mice and even.

 

[FionaZuppa]

dielectic rated say 600v should remain same thickness no matter wire size, but vendor might add thickness for strength reasons. i dont think NEC accounts for any dielectric variations other than heat R value for types of wire insulation.

as wire size gets bigger the area of heatsink gets bigger. for same P value if the heatsink area gets bigger thus heatsink density goes down (P/area), hence the surface temp per area will also go down.

conduction of heat within the mass (wire) itself will still want to migrate to the surface, the mass itself will have some heat R and is a function of radius (heat at radius=0 has to move across wire radius (radial in angular 2pi) before that heat gets to the surface to transfer out). but this item is generalized when we define DC ohms per circular mil of the copper alloy of the wire, etc. the integration of heat generated across the cross sectional area is basically summarized in I^2R, etc. 60Hz is considered very low freq and for most values the equations in DC suffice.

i am still a tad baffled by the NEC ampacity table. i know everyone keeps saying "the table works so why question it?", well, because thats what i do.

 

[mbrooke]

dielectic rated say 600v should remain same thickness no matter wire size, but vendor might add thickness for strength reasons. i dont think NEC accounts for any dielectric variations other than heat R value for types of wire insulation.

as wire size gets bigger the area of heatsink gets bigger. for same P value if the heatsink area gets bigger thus heatsink density goes down (P/area), hence the surface temp per area will also go down.

conduction of heat within the mass (wire) itself will still want to migrate to the surface, the mass itself will have some heat R and is a function of radius (heat at radius=0 has to move across wire radius (radial in angular 2pi) before that heat gets to the surface to transfer out). but this item is generalized when we define DC ohms per circular mil of the copper alloy of the wire, etc. the integration of heat generated across the cross sectional area is basically summarized in I^2R, etc. 60Hz is considered very low freq and for most values the equations in DC suffice.

i am still a tad baffled by the NEC ampacity table. i know everyone keeps saying "the table works so why question it?", well, because thats what i do.

Keep questioning it. :thumbsup:

Assuming insualtion plays a minimal role, the surface area increases less relative to the mass of conductor. Mass means more current can flow by itself, however surface area not proportionally increasing to mass leads to less heat dissipation and thus lowered ampacity.

Try this, check your equations against voltage drop. Play around and see what happens:

http://www.electrician2.com/calculators/vd_calculatoradv.htm


http://cablesizer.com/

 

[FionaZuppa]

Keep questioning it. :thumbsup:

Assuming insualtion plays a minimal role, the surface area increases less relative to the mass of conductor. Mass means more current can flow by itself, however surface area not proportionally increasing to mass leads to less heat dissipation and thus lowered ampacity.

Try this, check your equations against voltage drop. Play around and see what happens:

http://www.electrician2.com/calculators/vd_calculatoradv.htm


http://cablesizer.com/

the mass per length is already accounted for in ohms per ft tables, etc. mass/length alone is not good enough to describe the heat density in the heatsink, the geometry is also needed. for this discussion we are limiting it conductors that have round x-section, etc.

your statement suggests that the ampacities are less than what wire size (mass) would suggest, but look at the NEC table #'s, the heatsink density (joules/sec/sq.in) goes up with larger wire sizes, so in essence a bigger wire is allowed to dissipate more heat (joules/sq.in/ft) than a smaller wire. this is where it is baffles me, etc. even with thicker insulation on bigger wire, the heat still needs to transfer out of that wire to surrounding environment.

 

[mbrooke]

the mass per length is already accounted for in ohms per ft tables, etc. mass/length alone is not good enough to describe the heat density in the heatsink, the geometry is also needed. for this discussion we are limiting it conductors that have round x-section, etc.

your statement suggests that the ampacities are less than what wire size (mass) would suggest, but look at the NEC table #'s, the heatsink density (joules/sec/sq.in) goes up with larger wire sizes, so in essence a bigger wire is allowed to dissipate more heat (joules/sq.in/ft) than a smaller wire. this is where it is baffles me, etc. even with thicker insulation on bigger wire, the heat still needs to transfer out of that wire to surrounding environment.

I think it might have to do with smaller wires being abused more. BTW, useing your equations, how does this compare?

 

[wwhitney]

your statement suggests that the ampacities are less than what wire size (mass) would suggest, but look at the NEC table #'s, the heatsink density (joules/sec/sq.in) goes up with larger wire sizes

My analysis says it goes down, in that P/A varies as I^2/d^3, and the observed trend in NEC ampacities is approximately I varies as d^1.25. Together that means with the NEC ampacities P/A is varying as d^-0.5, i.e. it goes down with wire diameter. Did I make a mistake in my first post today? (I'm using A for surface area, not cross-sectional area, probably should have used S for that from the beginning.)

Maybe this has something to do with convection? If you double the surface area, perhaps you don't actually double the convective heat rejection capability, so P/A isn't the right term to look at?

Cheers, Wayne

 

[FionaZuppa]

My analysis says it goes down, in that P/A varies as I^2/d^3, and the observed trend in NEC ampacities is approximately I varies as d^1.25. Together that means with the NEC ampacities P/A is varying as d^-0.5, i.e. it goes down with wire diameter. Did I make a mistake in my first post today? (I'm using A for surface area, not cross-sectional area, probably should have used S for that from the beginning.)

Maybe this has something to do with convection? If you double the surface area, perhaps you don't actually double the convective heat rejection capability, so P/A isn't the right term to look at?

Cheers, Wayne

take 100ft of each wires size, then P = ampacity(60C column) * ohms(100ft). now, calculate the surface area sq.in/ft for each wire size (i used AWG wire dia, no insulation). heatsink density = P/sq.in(ft) seems to go up with wire size using the NEC ampacity table, and not linear. the heat density is directly proportional to temp.

 

[wwhitney]

take 100ft of each wires size, then P = ampacity(60C column) * ohms(100ft).

That should be P = (ampacity)^2 * R, yes?

now, calculate the surface area sq.in/ft for each wire size (i used AWG wire dia, no insulation).

Surface area will just have units of square inches, if you do something like surface area/foot, that's just the perimeter of the circular cross-section of the wire.

heatsink density = P/sq.in(ft) seems to go up with wire size using the NEC ampacity table, and not linear.

Not sure what you mean by heatsink density, I was looking at P/A (power over surface area), which is required rate of heat loss per unit area per unit time. Using the NEC ampacities, I find that P/A goes down with increasing diameter.

the heat density is directly proportional to temp.

I'm pretty sure that's not going to be true, the temperature will rise until the heat loss due to radiation, conduction, and convection matches the power dissipation, achieving equilibrium. For conduction, the heat loss is proportional to the temperature difference. However, for radiant heat loss, the radiant flux of a black body is proportional to the 4th power of the absolute temperature. I don't know how convection works.

Even though the rate of heat loss may not be proportional to temperature rise, the rate of heat loss will increase with temperature, so for given conditions, a particular maximum temperature rise will have an associated maximum allowable power dissipation and vice versa.

Cheers, Wayne

 

[FionaZuppa]

yes, I^2, was typing too fast.
the heatsink density is same as your P/A and directly proportional, etc.
the reference to P/A/ft is more like a reference "P/A (ft)" because when i got to power density for the heatsink of insulation i did it for 1ft of wire, kinda like how N-M equations are. but, the initial P/ft calc is unified with wire length of 100ft (ampacity^2* Rohms(100ft)/100), etc. N-M doc also talks about temp of wire for areas where ambient air is not the same for the full wire length.

i am running the P/A #'s for 14/12/10 awg sizes and will list the % diffs between them as the wire size goes up.

Even though the rate of heat loss may not be proportional to temperature rise, the rate of heat loss will increase with temperature, so for given conditions, a particular maximum temperature rise will have an associated maximum allowable power dissipation and vice versa.

Cheers, Wayne

i suspect you are getting into heat flows (and "flux" densities). you can wrap all that up into net heat loss per unit time which basically defines the temp per unit area.

Teertstra, P., Yovanovich, M.M., and Culham, J.R., “Analytical Forced Convection Modeling of Plate Fin Heat Sinks,” Proceedings of 15th IEEE Semi-Therm Symposium, pp. 34-41, 1999.

this reference shows that thermal resistance is parabolic as sink area increases in linear fashion. but its not significant for common AWG wire sizes.

 

[FionaZuppa]

notice the % increase in P/A from #14 to #12, and then from #12 to #10. the % increase in area is almost linear, but power jumps quite a bit in #10 wire. even with some of the other deep-dive factors accounted for (as N-M equations do) why does NEC allow this increase in power density as wire size goes up? some are suggesting rounding of the #'s that accounts for this ?? or, this is a case where the bigger wire P/A is still at acceptable levels, but because #12 and #14 is used more the ampacities were knocked down some, but this logic doesnt make sense to me.

updating table, 1sec

 

[jim dungar]

...why does NEC allow this increase in power density as wire size goes up?

Most likely the NEC did not perform any of these analysis for their Small Conductors.
Their 'restrictions' are likely not much more than feel good values that address cable construction, conductor insulation and installation considerations over the past 100 years of electrical installations. As such the report values bear no relationship to real world physics.

Your deep dive analysis may be more germane to equipment standards, like those that allow #18AWG in fixtures.

 

[wwhitney]

updating table, 1sec

When I looked at the numbers, the heat flux P/A is decreasing with wire diameter, except for #10 and #3. #10 is likely rounding errors since 15, 20 and 30 are such small numbers. Not sure what is going on with #3.

Anyway, if you just look at #14, #12, and #10, you will be misled as to the trend, I looked at #14 through 1000 kcmil.

Cheers, Wayne

 

[FionaZuppa]

When I looked at the numbers, the heat flux P/A is decreasing with wire diameter, except for #10 and #3. #10 is likely rounding errors since 15, 20 and 30 are such small numbers. Not sure what is going on with #3.

Anyway, if you just look at #14, #12, and #10, you will be misled as to the trend, I looked at #14 through 1000 kcmil.

Cheers, Wayne

indeed, here's the #'s in excel. i have to do multiple posts to show the tables i ran. this 1st one is NEC #'s, 2nd is fixed watts/ft, and the 3rd one is fixed P/A, the these two latter tables are base on 60C 20A ampacity for #14. if NEC is concerned about wire temp then fixed P/A makes sense to me, if NEC is concerned about total W/ft then fixed W/ft makes sense to me, the current NEC #'s dont make 100% sense to me.

awg	dia(in)	circumference(in)	area(in^2) per ft	% increase of area	60C ampacity A	Rohms(1000ft)	Rohms/ft	P (W/ft)	P/A (ft) watts/sq.in.	% increase in P/A
14	0.0641	0.402548	4.830576	0	15	2.525	0.002525	0.568125	0.117610198	0
12	0.0808	0.507424	6.089088	26.05304212	20	1.588	0.001588	0.6352	0.104317757	-11.30211635
10	0.1019	0.639932	7.679184	26.11386139	30	0.9989	0.0009989	0.89901	0.117071033	12.22541238
8	0.1285	0.80698	9.68376	26.10402355	40	0.6282	0.0006282	1.00512	0.103794394	-11.34066929
6	0.162	1.01736	12.20832	26.07003891	55	0.3951	0.0003951	1.1951775	0.097898605	-5.68025736
4	0.2043	1.283004	15.396048	26.11111111	70	0.2485	0.0002485	1.21765	0.079088478	-19.21388706
2	0.2576	1.617728	19.412736	26.08908468	95	0.1563	0.0001563	1.4106075	0.072664023	-8.123123246
1	0.2893	1.816804	21.801648	12.30590062	110	0.1239	0.0001239	1.49919	0.068764985	-5.365844014
0	0.3249	2.040372	24.484464	12.30556516	125	0.0983	0.0000983	1.5359375	0.062731106	-8.774639249

 

[FionaZuppa]

fixed watts/ft

awg

dia(in)

circumference(in)

area(in^2) per ft

% increase of area

60C ampacity A

Rohms(1000ft)

Rohms/ft

P (W/ft)

P/A (ft) watts/sq.in.

% increase in P/A

14	0.0641	0.402548	4.830576	0	20.00	2.525	0.002525	1.01	0.209084797	0
12	0.0808	0.507424	6.089088	26.05304212	25.22	1.588	0.001588	1.01	0.165870488	-20.66831683
10	0.1019	0.639932	7.679184	26.11386139	31.80	0.9989	0.0009989	1.01	0.131524391	-20.70657507
8	0.1285	0.80698	9.68376	26.10402355	40.10	0.6282	0.0006282	1.01	0.10429833	-20.70038911
6	0.162	1.01736	12.20832	26.07003891	50.56	0.3951	0.0003951	1.01	0.082730466	-20.67901235
4	0.2043	1.283004	15.396048	26.11111111	63.75	0.2485	0.0002485	1.01	0.06560125	-20.70484581
2	0.2576	1.617728	19.412736	26.08908468	80.39	0.1563	0.0001563	1.01	0.0520277	-20.69099379
1	0.2893	1.816804	21.801648	12.30590062	90.29	0.1239	0.0001239	1.01	0.046326773	-10.95748358
0	0.3249	2.040372	24.484464	12.30556516	101.36	0.0983	0.0000983	1.01	0.041250648	-10.95721761

 

[FionaZuppa]

forget post #94.

fixed P/A

awg

dia(in)

circumference(in)

area(in^2) per ft

% increase of area

60C ampacity A

Rohms(1000ft)

Rohms/ft

P (W/ft)

P/A (ft) watts/sq.in.

% increase in P/A

14	0.0641	0.402548	4.830576	0	20.00	2.525	0.002525	1.01	0.20908	0
12	0.0808	0.507424	6.089088	26.05304212	28.31	1.588	0.001588	1.27	0.20908	0
10	0.1019	0.639932	7.679184	26.11386139	40.09	0.9989	0.0009989	1.61	0.20908	0
8	0.1285	0.80698	9.68376	26.10402355	56.77	0.6282	0.0006282	2.02	0.20908	0
6	0.162	1.01736	12.20832	26.07003891	80.38	0.3951	0.0003951	2.55	0.20908	0
4	0.2043	1.283004	15.396048	26.11111111	113.81	0.2485	0.0002485	3.22	0.20908	0
2	0.2576	1.617728	19.412736	26.08908468	161.15	0.1563	0.0001563	4.06	0.20908	0
1	0.2893	1.816804	21.801648	12.30590062	191.81	0.1239	0.0001239	4.56	0.20908	0
0	0.3249	2.040372	24.484464	12.30556516	228.20	0.0983	0.0000983	5.12	0.20908	0

 

[wwhitney]

indeed, here's the #'s in excel.

Very nice. Your circumferences are off by a factor of 2, and hence the surface areas and the quantities derived from that. Since it is a consistent error, it doesn't affect any of the trends shown.

Cheers, Wayne.