As of this time the only thing that is done in an engineering study on arc flash is quantifying the thermal energy. Plasma and arc blast (pressure forces) are not considered.

There was a paper by Ralph Lee which calculated the theoretical force of an arcing fault in terms of pressure, and there is data available from military tests and standards showing that above around 20 PSI there is a risk and this increases up to around 80-100 PSI where the risk goes to around 100% that internal organs (heart) and ruptured and thus we get a fatality for sure. Ralph Lee's arc blast calculation does not in any way, shape, or form, correlate at all with arc flash and has to be treated separately. Second, it is purely theoretical.

The only data that I have seen so far is a graph provided from some of the preliminary joint IEEE/NFPA study that showed that essentially arc blast is a constant of around 2 PSI (hard to make out from the graphics I saw) for pretty much any input conditions. This seems to at a minimum completely invalidate the Lee theoretical calculation that seems to show that even for relatively low level (10-15 cal/cm^2) arcs, an arc blast is 100% fatal.

Note also that what you are referring to at all is the 40 cal/cm^2 "rule" which is being removed from NFPA 70E. It was originally suggested that as an upper limit at some point arc blast becomes a more serious threat than arc flash. The cutoff suggested in the fine print note (note==explanatory, not part of the actual Code) was 40 cal/cm^2. An alternative interpretation is that although the equipment may not be inherently dangerous, a "heightened awareness" is warranted. Since as of this point at least the preliminary data from the joint IEEE/NFPA arc flash study invalidates the "40 cal cutoff" and Ralph Lee's theoretical calculation (correct or not) also invalidates it, the note is being DELETED from the Code.

The term "Danger" and "Warning" comes from labelling as per ANSI Z535. Hazards which can cause an immediate life threatening injury are labeled with the signal word "DANGER". This would apply for instance to access panels on medium voltage switchgear bus which as per NEC Code must be labeled "DANGER--HIGH VOLTAGE---KEEP OUT". The signal word "WARNING" is reserved for hazards which again can cause a life threatening injury but the effect is not immediate and would for instance occur if appropriate action is not taken. Note that prior to the most recent editions of ANSI Z535, these definitions were not clear and thus there was a lot of confusion about how to differentiate the signal words "DANGER" and "WARNING". Thus there is a lot of misuse. This has been fixed in the more recent editions of the Z535 Code.

Some practitioners have made a practice in the past of labelling equipment which is over 40 cal/cm^2 with the "DANGER" signal word in keeping with the note in 70E. However clearly there is no immediate danger from the equipment unless there is some obvious visible threat such as water pouring directly onto it from a leaking pipe. Upgrading from "WARNING" to "DANGER" does provide heightened awareness but is also a clear violation of the meaning and intent of the signal words, and unlike 70E, ANSI Z535 is referenced directly by OSHA regulations. Also 70E states that only activities which would be considered interacting with equipment in such a way as to cause an arc flash need to be considered, the equipment itself is not considered inherently dangerous in any way or that it forms an immediate, life threatening hazard. Thus it is inappropriate to use the word "DANGER" and a violation of OSHA for equipment over 40 cal/cm^2 even if the original text in 70E were being retained.

Much appreciated response. This has become the Friday morning office chatter topic.

Thermal energy calculations are not directly relateable to blast force.

The blast that generates 40cal/cm^2 in 10 msec is certainly different than one that does 40 cal/cm^2 in 10sec, even though the heat energy is the same.

Many instructors like to 'shock and awe' their students, so they don't get burdened down with detailed facts and reasoning.

Which makes sense.. it's like comparing the cal/cm^2 of a space heater over the span of 40 years as opposed to the energy after just a few seconds. It was time that threw me off. Thanks!

The formula I saw was based on the current and the distance from the blast - unfortunately nothing about duration
which is like looking at cal/cm2 without the tA factor

I am pretty sure that there is testing being conducted in an effort to better understand the arc blast forces that occur for a wide variety of circumstances (i.e., voltage, current, protective devices, etc.). This testing has been going on for several years now, so it's hard to say when definitive results will be available.

What is published is that it takes time...at least a cycle or two, to develop an arc blast in the first place. Then once the airis heated and released under pressure, further time has zero impact. So the relevant factors would be arc power (current, voltage), and enclosure dimensions. Time plays a factor but in a nonlinear way. There might also be some material factors (contributions of vaporized metals), but without data this is all speculation. Details related to time are published in a lot of European manufacturer documents for arc resistant gear that many tout as arc proof.

This time element is in regards to the effects of the blast. It is not the same as the arc clearing time that is used in determining incident arc flash incident energy (Ie).

I will not be surprised to find that we will have blasts at low Ie which are equal in effect to some associated with Ie>40cal/cm².

I was thinking more along the lines of duration of the arc.

For example in welding, the welder draws an arc - albeit a controlled arc for a long duration. The energy from the arc can be considerable. You can most assuredly get burned from exposure to welding (Granted it does take a long time to get to a second degree burn from this exposure). I have experienced first degree burns whilst doing extended welding while wearing a plain cotton T shirt (The shirt was fine - it was my skin that received rather extensive sunburn)

On the other hand, an arc flash is a very short time frame. The same amount of energy creates a very different result.

But, you don't know that, when all you see is the label that says >40cal/cm².
On the secondary side of a transformer is there a 'giant blast' or is it continued arcing due to the slow performance of the primary protective device that causes the 'Dangerous' condition?

Blast effects and thermal effects may not be closely related.

I meant relatively, perhaps I could have chosen my words better. Compared to a shift of arc-welding, even a 2-second arc flash event is short - unless, of course, you are the one having the first-hand arc flash experience.

Of course, you are right. I do not know of any studies that confirm - or disprove - a correlation between arc flash thermal effects and arc blast pressure.

It just stands to reason - given the laws of physics - that if there is any release of energy over a long duration, the results are going to be less spectacular than if you release the same amount of energy in a much shorter (say 8.33 mS) time frame.

Absolutely,

But the arcing current for a 1.2 cal/cm² event and a >40cal/cm² are the same (the difference is, one is cleared in .2 sec and the other in 2sec), therefore the blast should be the same based on the circuit characteristics and equipment construction.
The length of time of the blast, is not the same as the length of time of the arcing event.

We need to emphasis taking steps for 'blast protection' (e.g. ear plugs, hard hats, fastened covers) even when the label says there are low cal/cm² and not over emphasize 'the end of the world' possibilities because there may be high cal/cm² due to long arcing times.

I would be interested in seeing a study on arc blast duration and the profile of the blast wave.

All that I've seen so far is a very fuzzy chart from a slide show for the joint NFPA/IEEE testing that was being done.

Some of this stands to reason. PV=nRT. If we have a relatively fixed V and we increase T then obviously P has to increase until we rupture the enclosure. At that point, V goes essentially to infinity. P returns to 1 atmosphere more or less, and T can rise to pretty much any value once the pressure wave has been released. Now obviously this all happens in an adiabatic way so one would expect some sort of wave dynamics to occur and I'm only describing the end points.

The gas (nR) is a relatively fixed volume. There might be some contribution from the solid metals (vaporized copper or aluminum), and the rest of the contribution comes from the air in the enclosure. Thus V of the original enclosure is a factor and that would be just the only factor other than materials IF metals actually vaporize and contribute (this is a very big if). There is a lot of speculation but no evidence I've not yet seen that copper actually vaporizes (no Cu residue on all the surfaces of exploded enclosures) so if this happens at all then the effect is very subtle.

As to my speculation (purely speculative here):

As the size of the enclosure grows though then the surface area of the door and thus the force on the hinges grows as well. If we assume everything is a cube then V=x^3 where x is the length of a cube. The door pressure is then P=x^2. So if the size of the enclosure linearly doubles then the volume increases 8 fold while the pressure on the door quadruples. So even though the hinges get larger in realiy the pressure is going up a lot faster so we should see the failure happen at 1/4 the time assuming that the force to blow the doors off, F, is relatively constant. Meanwhile P/V=x^2/x^3 so we should see the amount of expanded gas vary inversely with enclosure size, which will actually decrease the size of the arc blast even though the enclosure is larger. Not sure where this is leading but there doesn't seem to be any theoretical reason that we would expect that larger enclosures = exponentially more dangerous. Quite the contrary. Also, arcing temperatures generally tend to stabilize around 4000-6000 degrees regardless of the current (the arc column simply increases in diameter) so with T not being dependent on current at all beyond a certain point, one would expect that the arc blast would be either relatively fixed or weakly (and negatively) correlated with enclosure size. If vaporization even occurs this should be a relatively fixed amount or else dependent on current only and not time or voltage. If this is the case due to the huge amount of expansion of solids into gasses then I would expect that this effect alone is the dominant force behind an arc blast.