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 Post subject: Questions about Lee equations
PostPosted: Wed Jan 14, 2015 1:53 pm 
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I have gone through IEEE paper "The Other Electrical Hazard: Electric Arc Blast Burns" by Ralph H. Lee. The article's findings (equations 4 through 7) are commonly used for determining arc flash boundaries. I have come across some interesting discrepancies and I was wondering if anyone else has ever observed them.

As an example, I see a mismatch between data published in Table II comparing to the data from Figure 4. According to Figure 4, 2 in. diameter arc sphere corresponds to 17MW arc power (also exemplified on page 5 of the article). However, Table II shows arc power of 7.5MW only for 2 inch diameter sphere. As another example, according to Fig. 4, 5.14 inches diameter arc sphere corresponds to 100MW+ arc power but Table II shows arc power of 50MW only for 5.14 inch diameter sphere.

Image


There are more discrepancies I see, and I will address them one at a time. You can access the full text using the link below:

http://www.arcadvisor.com/pdf/arc-flash/the-other-electrical-hazard-electric-arc-blast-burns.pdf


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 Post subject: Re: Questions about Lee equations
PostPosted: Fri Jan 16, 2015 3:28 pm 
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Lee's arc blast equation is way off. At this time the CIGRE has provided algorithms and calculations which give extremely detailed and accurate measurements of pressures due to arcing faults based on far more research than Lee's theoretical guessing. Why not use the best out there?


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 Post subject: Re: Questions about Lee equations
PostPosted: Fri Jan 16, 2015 8:22 pm 
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PaulEngr wrote:
Lee's arc blast equation is way off. At this time the CIGRE has provided algorithms and calculations which give extremely detailed and accurate measurements of pressures due to arcing faults based on far more research than Lee's theoretical guessing. Why not use the best out there?


In fact, the Lee article "The Other Electrical Hazard: Electric Arc Blast Burns" I am talking about does not deal with arc blast pressures. Lee's equations for arc flash boundary calculations found in NFPA 70E come from this article. Ralph Lee had addressed arc blast phenomenon and provided the formula for calculating initial impulse force in a separate IEEE paper "Pressures Developed by Arcs".

Please provide references to CIGRE articles addressing arc blast calculations you have mentioned.


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 Post subject: Re: Questions about Lee equations
PostPosted: Sun Jan 18, 2015 6:39 am 
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Lee kind of started things off. The Doan paper refined it further and provided a basis for the IEEE 1584 empirical equations. Empirical is troubling because you can't extrapolate theory from it or handle non-standard cases. A different approach which is evident in the Wilkins paper on Mersen's site is likely to be the basis for the next 1584 standard. Wilkins starts with theoretical equations and uses empirical curve fitting to set the model parameters, then shows the results are predictive for non-fit cases. Wilkins also claims a better fit to 1584 data but this approach is a mathematical trap. As you add more adjustable parameters to any equation you get a better curve fit but the confidence intervals get excessive as well so predictive capabilities fall. The trouble with Wilkins paper is that it is incomplete. Several model equations are missing. A third model that I don't have now (in my work files) recognizes that arcs are partly driven by a quadratic term for current. The author almost goes as far as converting the 1584 empirical equation into a polynomial one with two terms that breaks the self-reference to current but stops just short. The equation removes the self reference issue with current. The equations were fit to 1584 calculations instead of the 1584 data set. The approach closely follows the form of the theoretical formulas but maintains the simplicity of the 1584 empirical equation. If it does as well as the 1584 equation on the data sets, it would be a convenient alternative to a Wilkins style model which requires a computer to run the calculation.


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 Post subject: Re: Questions about Lee equations
PostPosted: Mon Jan 19, 2015 11:24 am 
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PaulEngr wrote:
Lee kind of started things off. The Doan paper refined it further and provided a basis for the IEEE 1584 empirical equations. Empirical is troubling because you can't extrapolate theory from it or handle non-standard cases. A different approach which is evident in the Wilkins paper on Mersen's site is likely to be the basis for the next 1584 standard. Wilkins starts with theoretical equations and uses empirical curve fitting to set the model parameters, then shows the results are predictive for non-fit cases. Wilkins also claims a better fit to 1584 data but this approach is a mathematical trap. As you add more adjustable parameters to any equation you get a better curve fit but the confidence intervals get excessive as well so predictive capabilities fall. The trouble with Wilkins paper is that it is incomplete. Several model equations are missing. A third model that I don't have now (in my work files) recognizes that arcs are partly driven by a quadratic term for current. The author almost goes as far as converting the 1584 empirical equation into a polynomial one with two terms that breaks the self-reference to current but stops just short. The equation removes the self reference issue with current. The equations were fit to 1584 calculations instead of the 1584 data set. The approach closely follows the form of the theoretical formulas but maintains the simplicity of the 1584 empirical equation. If it does as well as the 1584 equation on the data sets, it would be a convenient alternative to a Wilkins style model which requires a computer to run the calculation.


I am neither questioning nor advocating Lee's approach in calculating arc flash boundaries. It is what it is with its advantages and disadvantages.

The purpose of my post was to bring attention this forum participants a seeming blunder in the Lee's paper. I am wondering if I missed something. I have used Lee's approach when arriving at equation for arc flash boundary similar to the equation (6) from "The Other Electrical Hazard: Electric Arc Blast Burns" article:

Df = (1.96 * MVAbf * t)^0.5

I get an equation similar to Lee's equation above but with a different multiplier under the square root while using the same methodology. I believe the discrepancy is caused due to introduction of the mistake when arriving on the equation as exemplified in Table II and Figure 4. The equation is included in NFPA 70E and is widely used for determining the arc flash boundary.

Please provide references to CIGRE articles addressing arc blast calculations you have mentioned CIGRE algorithms and calculations for determining pressures due to arcing faults. Could you provide references to CIGRE articles addressing arc blast calculations you have mentioned?


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 Post subject: Re: Questions about Lee equations
PostPosted: Mon Jan 19, 2015 5:12 pm 
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The table speaks of "Arc Power", while the figure speaks of "Available Arc MW." Could the figure be using the available bolted fault current expressed in MW while the table is using the power dissipated in the arc itself? As I recall, the maximum power transfer of any circuit occurs where half the total is dissipated in the load and the other half is dissipated in the source. In this case the "load" we wish to maximize is the arc. Definitely confusing as written.


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 Post subject: Re: Questions about Lee equations
PostPosted: Tue Jan 20, 2015 8:35 am 
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CIGRE article entitled "Tools for the Simulation of Effects of the Internal Arc in Transmission and Distribution Switchgear" has two models for simulating arc pressures in enclosures up to the point of even including the "outer" enclosure (room) in the calculations. This gives a lot of really good data. Where it falls down in terms of fully capturing "arc blast" is two items:
1. In a true open-air scenario, we have effectively a jet which rapidly loses pressure as it exits the enclosure. This rapidly diminishes the arc blast. There are other places to get this formula but it's not directly in the CIGRE data. This is specifically because CIGRE was primarily interested in a mathematical design tool for designing arc resistant gear. The second reason is because they model the gear sitting in an enclosure where potentially depending on the size of the room AND shape, it may affect development of the pressure waves.
2. As clearly delineated by CIGRE, arcing pressure reaches a peak when the enclosure is essentially "closed". Once it starts venting, pressure rapidly falls off. CIGRE fails to adequately model the physical pressure withstand rating of the enclosure itself. Up until the enclosure ruptures or vents, pressure climbs linearly and is really easy to model analytically without resorting to very complicated (iterative or finite volume/element) modelling. If the vent is "simple" (e.g. a small hole), analytical results are still easy to obtain. But large openings or restrictive ducts such as are used in arc resistant gear must resort to much more complicated finite element modelling, which the CIGRE paper also lays out in full detail.
3. You will probably notice right away that CIGRE starts with Lee as an arcing model, warts and all. You can probably either drop the use of Lee in favor of a better model or accept it. The experimental data sort of bypasses Lee by using actual measurements instead but then curve fits the model to the Lee equation, which confounds trying to do things without Lee.
4. Military data on concussive blasts shows that at around 20 PSI is the threshold for a fatality. It increases up to around 35 PSI at the point where a fatality is virtually guaranteed. However consider the IEEE 1584 "medium" box (roughly 20x20"). The pressure on the door at 20 PSI is 20x20x20=8,000 lbs. or 4 tons. Frankly you can knock the hinge out with an order of magnitude less force. At that point according to the CIGRE experimental data, the pressure would reach a maximum, or at around 2 PSI. So we are an order of magnitude below the force necessary to cause a fatality. I believe some of the recent experiemental data from the joint NFPA/IEEE arc flash study also showed more or less a constant at around 2 PSI. It may be possible to reach 8,000 PSI in some explosion proof enclosures I guess but the NEMA tests don't seem to support that level of protection.


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 Post subject: Re: Questions about Lee equations
PostPosted: Tue Jan 20, 2015 10:17 am 
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stevenal wrote:
The table speaks of "Arc Power", while the figure speaks of "Available Arc MW." Could the figure be using the available bolted fault current expressed in MW while the table is using the power dissipated in the arc itself? As I recall, the maximum power transfer of any circuit occurs where half the total is dissipated in the load and the other half is dissipated in the source. In this case the "load" we wish to maximize is the arc. Definitely confusing as written.


Indeed, Lee's model for calculating arc flash boundary is based on the assumption that equivalent system impedance is fully inductive. In such case, the maximum power dissipated in the load is observed when the arc voltage drop is 70.7 percent of the supply voltage. The arc power is than equal half the short circuit MVA. The Figure 4 horizontal axis should than read something like "Available Fault MVAR" instead of "Available Arc MW".

Assuming this is what the author meant by putting the Table II and Figure 4 together, I still don't understand how Mr. Lee had arrived on the values published there. According to the text, the surface area of arc sphere in Table II is calculated as S = MW * 10^6 / h, where MW is arc power in Megawatts, h is the heat generated by 20,000K hot source per unit of surface area and h is equal to 3.68 * (20,000)^4 * 10^-11 W/in^2 (see Equation 2). Than S is equal to 0.17 * MW. However, the values from Surface area column in Table II are exactly 10 times higher than predicted. For example the surface area for 0.25MW arc in Table II should read 0.043 sq.in., not 0.43 sq.in. etc.


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 Post subject: Re: Questions about Lee equations
PostPosted: Mon Feb 02, 2015 9:17 am 
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The 1584 committee is currently reviewing the latest data. Preliminary data show interesting results. I am not on the committee but I was at the meeting at the ESW and I hope they can have some new info within the year or two. This is a large machine and moves slowly but it sounded like progress is going to ramp up.

I hope the new data will improve on what was know previously - which does have several "holes"


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 Post subject: Re: Questions about Lee equations
PostPosted: Fri Feb 06, 2015 9:53 am 
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engrick wrote:
The 1584 committee is currently reviewing the latest data. Preliminary data show interesting results. I am not on the committee but I was at the meeting at the ESW and I hope they can have some new info within the year or two. This is a large machine and moves slowly but it sounded like progress is going to ramp up.

I hope the new data will improve on what was know previously - which does have several "holes"


I like the term "holes" :D
I don't also understand were the 75 to 100V/in voltage drop number comes from in the paper? More recent studies indicate average 34V/in value [1].

1. Ammerman, R.F. ; Golden, Gammon, T. ; Sen, P.K. ; Nelson, J.P. "DC-Arc Models and Incident-Energy Calculations" Industry Applications, IEEE Transactions on Industry Applications Vol.46, Issue 5, 2010


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 Post subject: Re: Questions about Lee equations
PostPosted: Sun Feb 08, 2015 4:29 pm 
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arcad wrote:
engrick wrote:
I don't also understand were the 75 to 100V/in voltage drop number comes from in the paper? More recent studies indicate average 34V/in value [1].

1. Ammerman, R.F. ; Golden, Gammon, T. ; Sen, P.K. ; Nelson, J.P. "DC-Arc Models and Incident-Energy Calculations" Industry Applications, IEEE Transactions on Industry Applications Vol.46, Issue 5, 2010


Ammerman's paper is a bit vague on this and you are getting down into arc physics at this point. The short answer is that it depends. The voltage drop near the electrodes is relatively fixed for any arc. All of the background papers that Ammerman used bring this point home. There is something like 25 or so Volts (28 seems to be a popular number for copper electrodes) which is relatively speaking a constant that doesn't go away but is material dependent. Below that voltage no matter what the gap, fault current, etc., an arc is just plain impossible. Under reasonable assumptions even up to 50-75 V, an arc simply isn't possible. And under actual testing (which showed that Ammerman's model is still off by a factor of 200-400%), only under the most extreme conditions can DC arcs at 130 V or less get up over 1.2 cal/cm^2, and they don't sustain except under extreme conditions. The voltage drop through the rest of the arc column is a function of the current and the arc gap. The arc gap affects the high/low current cutoff quite a bit so for low voltages (like under 250 VAC) it confounds nice "linear" assumptions. This is why, and Ammerman's charts show it quite distinctly, the arc voltage increases only slowly in the "high current" zone, which leads to what looks like it is somewhat inversely proportional to current but this is only partly true...there is a slight slope. And this is all DC. At AC we are seeing the effects of a constantly varying voltage so at low voltages, the DC "low voltage" effects are more pronounced, and arc extinguishment is also a (currently unquantified) factor. At 1 kV and higher typically these "low voltage" effects though are so small that they disappear and hence the reason that the 1 kV empirical equation is so much simpler.

This is why the time domain model is so important. A lot of the very strange things that go on in the world under 250-300 Volts can be modeled better wiht the time series model which basically takes the DC model and applies it to AC after curve fitting the parameters that can't be calculated or measured.

See the public (free) papers on EPRI's web site because they are testing and attempting to model arcs that are feet long, not inches. The impact is dramatic and pretty wild, and you can see arc physics phenomena on a much larger scale. And this sort of thing is very necessary in the utility world if ever we are to improve on the theoretical model driving ArcPro.


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 Post subject: Re: Questions about Lee equations
PostPosted: Mon Feb 09, 2015 10:36 am 
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PaulEngr wrote:
There is something like 25 or so Volts (28 seems to be a popular number for copper electrodes) which is relatively speaking a constant that doesn't go away but is material dependent. Below that voltage no matter what the gap, fault current, etc., an arc is just plain impossible. Under reasonable assumptions even up to 50-75 V, an arc simply isn't possible. And under actual testing (which showed that Ammerman's model is still off by a factor of 200-400%), only under the most extreme conditions can DC arcs at 130 V or less get up over 1.2 cal/cm^2.


I disagree with your statement that an arc is not possible under 75V. What "reasonable assumptions" you are implying? Consider arc welding with typical welding voltage in the 40 to 70V AC range. Also, the Ammerman's findings are reportedly based on "set of data totaling some two million current and voltage points". What "actual testings" showing that Ammerman's model is off by a factor of 200-400 are you talking about? Also, why keeping the incident energy benchmark limited to 1.2 cal/cm^2, and not to some other arbitrary value? One should primary take into account how fast the energy is delivered. The issue of NFPA 70E using 1.2 cal/cm^2 as onset energy for a second degree burn on a bare skin had been addressed on this forum. See the thread located at http://www.arcflashforum.com/viewtopic.php?f=34&t=2221 for more information.


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 Post subject: Re: Questions about Lee equations
PostPosted: Tue Feb 10, 2015 2:05 pm 
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arcad wrote:
PaulEngr wrote:
There is something like 25 or so Volts (28 seems to be a popular number for copper electrodes) which is relatively speaking a constant that doesn't go away but is material dependent. Below that voltage no matter what the gap, fault current, etc., an arc is just plain impossible. Under reasonable assumptions even up to 50-75 V, an arc simply isn't possible. And under actual testing (which showed that Ammerman's model is still off by a factor of 200-400%), only under the most extreme conditions can DC arcs at 130 V or less get up over 1.2 cal/cm^2.


I disagree with your statement that an arc is not possible under 75V. What "reasonable assumptions" you are implying? Consider arc welding with typical welding voltage in the 40 to 70V AC range.


Reduce arc gap down to around 0.1" (2-3 mm) and apply the studies Ammerman references. The arc gap in electric arc welding is much less than this and the energy released is very controlled, not "arc flash" levels. It is operating in the "low current" region that Ammerman essentially ignores in order to get to a tractable equation to solve. So far though arc modelling has been concerned with arc gaps that are 1/4" or larger so the typical electrode gap for arc welding is way below that. Even with arc welding, dipping below around 30 V is not practical.

Quote:
Also, the Ammerman's findings are reportedly based on "set of data totaling some two million current and voltage points".

The study of DC arcs has a long history, not the least of which is due to studying neon lamps and similar lighting. Ammerman's research is based on taking several of the popular papers and plotting them on the same chart and then coming up with a new equation where he sort of draws a "straight line" through the data. The general shape of the curve has not been questioned, only the form of the equation over time. And yes, they are all pretty much empirical.

Quote:
What "actual testings" showing that Ammerman's model is off by a factor of 200-400 are you talking about?

http://www.battcon.com/PapersFinal2012/ ... 0Flash.pdf
See table 3. Note that this is all normalized data, and normalized badly. The 20 kA arc at 1/2" gap only lasted for 0.8 seconds, and the working distance in this data is 12" so you have to de-normalize both the time and working distance to arrive at a more typical 18" distance and also factor out the actual arcing time of only 0.8 seconds. When you do, it barely gets above 1.2 cal/cm^2, and this is for a DC arc at a gap distance that is usually never found in substation battery systems.

Quote:
Also, why keeping the incident energy benchmark limited to 1.2 cal/cm^2, and not to some other arbitrary value? One should primary take into account how fast the energy is delivered. The issue of NFPA 70E using 1.2 cal/cm^2 as onset energy for a second degree burn on a bare skin had been addressed on this forum. See the thread located at http://www.arcflashforum.com/viewtopic.php?f=34&t=2221 for more information.


I know you want to float this threshold. But its worse than that. We'd have to ask why the Stoll curve is the threshold at all and why not some other point, and why estimate the distance to the face/chest instead of some other point on the body? At the end of the day, the standard used in IEEE 1584 and 70E for acceptable incident energy is a purely arbitrary one. We probably need not even mention the fact that in ASTM 1959, it's not a constant but a curve (Stoll curve). As to the "proof", right now we have a lack of reported major injuries while using the IEEE 1584 estimate and a 1.2 cal/cm^2 cutoff. Granted there are major reasons why this is really an extremely conservative number. For instance IEEE 1584 estimates a numerical calculation accuracy of 95% based on threshold data. ASTM 1959 estimates a protective value at the d50 point. But workers are rarely exposed to arcs right at the threshold because we don't stock PPE in an infinite number of ratings. So far more often than not, they are overprotected. So we likely will not have a "real" test of any of this for decades. By then, the IEEE 1584 committee's can just point to the "95%" result and say, "see I told you it wasn't perfect, and we admitted it." We will go on with life as we know it with years of "successful tests" to backup the claimed validity of the methodology, whether the right threshold is a constant 1.2 cal/cm^2 or if it floats from zero up to around 2-3 as you are suggesting. So by that time the general feeling will be to leave well enough alone, just as it is today. The argument is the same reason that the academics will slow down updates to the IEEE 1584 update process...because they won't accept anything unless it is "perfect" or at least their version of "perfect" while avoiding the word smithing, the special interests, and just the general bureacracy of the process. So although I agree with your stance in principal to some degree, as a practical matter unless NFPA 70E changes to reflect it, using the actual Stoll curve might be more accurate but using the fixed value follows a consensus safety standard, and we reach the point where we are arguing for both the validity of the threshold and whether it is met, rather than having only an argument about whether or not the safety standard has been met. That is both the power and the disadvantage of going for or against a standard.


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 Post subject: Re: Questions about Lee equations
PostPosted: Wed Feb 11, 2015 11:38 am 
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PaulEngr wrote:
Reduce arc gap down to around 0.1" (2-3 mm) and apply the studies Ammerman references. The arc gap in electric arc welding is much less than this and the energy released is very controlled, not "arc flash" levels. It is operating in the "low current" region that Ammerman essentially ignores in order to get to a tractable equation to solve. So far though arc modelling has been concerned with arc gaps that are 1/4" or larger so the typical electrode gap for arc welding is way below that. Even with arc welding, dipping below around 30 V is not practical.


Done it. Reducing arc gap to 2mm results in approx 10A transition current and 28V arc confirming the fact the arc is very much possible well under 75V. Also, Ammerman's equation (7) Varc = (20 + 0.534*Zg)*Iarc^0.12 is based in particular on Stokes and Oppenlander study and application to "50Hz arcs with amplitudes decaying from 20kA to 30A" which extends ong way beyond the "low current" range. Also, the equation shows approx 10V/cm voltage drop which is roughly 3 times less the value published in Lee's paper. I have also increased the gap to 20mm and arcing current to 1000A, and both Stokes and Paukert's equations are still predicting arcing voltage less than 75V.

PaulEngr wrote:
The study of DC arcs has a long history, not the least of which is due to studying neon lamps and similar lighting. Ammerman's research is based on taking several of the popular papers and plotting them on the same chart and then coming up with a new equation where he sort of draws a "straight line" through the data. The general shape of the curve has not been questioned, only the form of the equation over time. And yes, they are all pretty much empirical.


Well, consider Paukert's arc voltage equations per electrode gap featured in Table III of the Ammerman paper if you don't trust Stokes and Oppenlander. Paukert's arcing currents ranged from 0.3A to 100kA, electrode gaps ranging 1 to 200mm. The equations reinforce the fact an arc is very well possible at low voltages.

PaulEngr wrote:
http://www.battcon.com/PapersFinal2012/ ... 0Flash.pdf
See table 3. Note that this is all normalized data, and normalized badly. The 20 kA arc at 1/2" gap only lasted for 0.8 seconds, and the working distance in this data is 12" so you have to de-normalize both the time and working distance to arrive at a more typical 18" distance and also factor out the actual arcing time of only 0.8 seconds. When you do, it barely gets above 1.2 cal/cm^2, and this is for a DC arc at a gap distance that is usually never found in substation battery systems.


I don't quite understand how table 3 data proves that Ammerman's model is off by a factor of 200-400? The table 3 shows battery specs only as far I can tell.

PaulEngr wrote:
We will go on with life as we know it with years of "successful tests" to backup the claimed validity of the methodology, whether the right threshold is a constant 1.2 cal/cm^2 or if it floats from zero up to around 2-3 as you are suggesting. So by that time the general feeling will be to leave well enough alone, just as it is today. The argument is the same reason that the academics will slow down updates to the IEEE 1584 update process...because they won't accept anything unless it is "perfect" or at least their version of "perfect" while avoiding the word smithing, the special interests, and just the general bureacracy of the process. So although I agree with your stance in principal to some degree, as a practical matter unless NFPA 70E changes to reflect it, using the actual Stoll curve might be more accurate but using the fixed value follows a consensus safety standard, and we reach the point where we are arguing for both the validity of the threshold and whether it is met, rather than having only an argument about whether or not the safety standard has been met. That is both the power and the disadvantage of going for or against a standard.


There is plenty of old and recent scientific evidence available proving the NFPA 70E methodology of adopting the 1.2 cal/cm^2 constant threshold for a second degree burn by an exposure of unprotected skin to radiated heat is plain wrong. You can pick other than Stoll's thermal radiation dose but no matter what threshold for damage during one second exposure is picked, one will always arrive at a threshold value less than the one (1) second threshold when the heat flux is increased. Consensus works in marriage, it may or may not work in social life but as a matter of fact it does not work in science. The notion of a flat Earth was one of scientific consensus in old days too. I expected a big and influential safety association would acknowledge error once it had been revealed, address and correct it instead of pretending there is no error. I am glad that more and more people, including this forum contributors, start realising the scope of problem with the existing NFPA 70E methodology.


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 Post subject: Re: Questions about Lee equations
PostPosted: Thu Feb 12, 2015 10:24 am 
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arcad wrote:
PaulEngr wrote:
Reduce arc gap down to around 0.1" (2-3 mm) and apply the studies Ammerman references. The arc gap in electric arc welding is much less than this and the energy released is very controlled, not "arc flash" levels. It is operating in the "low current" region that Ammerman essentially ignores in order to get to a tractable equation to solve. So far though arc modelling has been concerned with arc gaps that are 1/4" or larger so the typical electrode gap for arc welding is way below that. Even with arc welding, dipping below around 30 V is not practical.


Done it. Reducing arc gap to 2mm results in approx 10A transition current and 28V arc confirming the fact the arc is very much possible well under 75V. Also, Ammerman's equation (7) Varc = (20 + 0.534*Zg)*Iarc^0.12 is based in particular on Stokes and Oppenlander study and application to "50Hz arcs with amplitudes decaying from 20kA to 30A" which extends ong way beyond the "low current" range. Also, the equation shows approx 10V/cm voltage drop which is roughly 3 times less the value published in Lee's paper. I have also increased the gap to 20mm and arcing current to 1000A, and both Stokes and Paukert's equations are still predicting arcing voltage less than 75V.


Go back and look at the Stokes & Oppenlander or Ayrton data. The equations developed show an asymptote at around 28 V. This is the region where it transitions to a low current region. Ammerman's model linearizes this and thus gives arc voltages that are incorrect at low voltage/current conditions. His model is specifically intended only to be applied in the high current region where a stable arc occurs. It is otherwise unremarkable and the arcing currents and voltages from the equation are substituted into the Lee equation for incident energy purposes. So whereas Stokes, Oppenlander, and Ayrton were more concerned with making sure that for instance an arc initiates for some kind of process and thus the minimum arcing voltage was important to them (and they give equations for it), Ammerman's approach was to focus instead on the "power arc" region and ignore the minimum arcing conditions.

Quote:
PaulEngr wrote:
The study of DC arcs has a long history, not the least of which is due to studying neon lamps and similar lighting. Ammerman's research is based on taking several of the popular papers and plotting them on the same chart and then coming up with a new equation where he sort of draws a "straight line" through the data. The general shape of the curve has not been questioned, only the form of the equation over time. And yes, they are all pretty much empirical.


Well, consider Paukert's arc voltage equations per electrode gap featured in Table III of the Ammerman paper if you don't trust Stokes and Oppenlander. Paukert's arcing currents ranged from 0.3A to 100kA, electrode gaps ranging 1 to 200mm. The equations reinforce the fact an arc is very well possible at low voltages.


No doubt that it exists. It is the principle behind neon lamps. But Ammerman makes the case as well that at low current conditions there isn't enough heat energy to worry about...his focus was on predicting arc flash, not whether or not a neon light works. Paukert and others were focussed more on the practical aspects of arcs such as predicting what happens in a neon lamp or predicting arcing in a breaker or switch as the contacts separate. This is a controlled, low power condition. See this presentation from Paul Sen that is showing the development of Ammerman's model:
http://www.efcog.org/wg/esh_es/events/D ... rkshop.pdf

Oppenlander and Stokes never went below 5 mm gaps. I don't have Ayrton's paper and there were some later improvements but see "Electric Arc Phenomena, Derdinand and Rasch (1913). It's publicly available on the internet and includes the etended version with other electrode materials. Suffice to say that Ayrton's equation after substituting values for copper electrodes in air is:
V=A+LB+(C+LD)/I where V is the minimum voltage to sustain an arc, I is the maximum available fault current, L is the gap length and must be greater than 1.1 mm (minimum depth of a pit formed during an arc...has to do with physics of the edges), A=21.38, B=2.074, C=10.68, D=15.24. So th eabsolute cutoff voltage under any condition is 21.38 volts. For a 1.3 mm gap, the minimum voltage is 24 V with an infinite bus. And you can then clearly extrapolate from there. In most realistic industrial cases for DC that I've looked at either the voltage is too low or the incident energy is too low to even consider anything beyond 1.2 cal/cm^2. The few exceptions such as a very large 125 VDC substation battery don't get to realistic cases such as 20 kA over a 12.5 mm gap. That's why the DC tables in 70E are a load of crap in my opinion...because the input conditions are both unrealistic and ignore real world testing.

Quote:
PaulEngr wrote:
http://www.
Quote:
battcon.com/PapersFinal2012/ ... 0Flash.pdf
See table 3. Note that this is all normalized data, and normalized badly. The 20 kA arc at 1/2" gap only lasted for 0.8 seconds, and the working distance in this data is 12" so you have to de-normalize both the time and working distance to arrive at a more typical 18" distance and also factor out the actual arcing time of only 0.8 seconds. When you do, it barely gets above 1.2 cal/cm^2, and this is for a DC arc at a gap distance that is usually never found in substation battery systems.


I don't quite understand how table 3 data proves that Ammerman's model is off by a factor of 200-400? The table 3 shows battery specs only as far I can tell.


Reading through it you are correct on page 7-7. There are two "table 3"s. Look on page 7-8. This data originates from a test done by Kinetrics for Duke. It's the only place I know of where it has been published publicly.


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