Voltrael wrote:

We have some labels (which I hope to change out sooner, rather than later) that just tell you the voltage and table category of the equipment. For something labeled a category 4, I am going to assume the equipment is at 40 cal/cm2, and we need to use that value for our arc flash boundary. But what I'm wondering is what is the arc flash boundary given an incident energy of 40 cal/cm2?

The hands down easiest approach is to use the assumptions section of the tables in 70E which at least in the 2015 edition give you the arc flash boundaries. That is the method that I recommend. If you don't have a copy it is a little time consuming but you can page through the entire thing or jump chapter-by-chapter to get the values from the nfpa.org web site.

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Keep in mind that there is no one-size-fits all result. In 2015, we have 3 subtables: a task/risk table, an equipment table, and a PPE table. You get the PPE level from the equipment table which also includes all the assumptions, arc flash boundaries, etc. The PPE table is very similar to 2012 and earlier editions. The equipment won't change so you can just jump to that table to get the information you seek.

You can't just convert to a single result. The issue is what is known as "radiative view factors". A long enclosed box such switchgear tends to "focus" the thermal radiation compared to a relatively flat shallow box such as a panelboard. Thus IEEE 1584 includes different exponents to deal with differences in enclosure shapes. So the arc flash boundary for a row of medium voltage starters is going to be a lot farther away than a panelboard even if both are rated for 40 cal/cm^2, even if the working distance was set to be the same for both of them (which it isn't).

As per IEEE 1584 (and Annex D in NFPA 70E) the first step in doing an empirical arc flash calculation is to determine the arcing current followed by the normalized incident energy (normalized to 610 mm, 0.2 seconds arcing time). The next step (and what we need for this discussion) is to run the denormalizing formula backwards. E = Cf * En * (t / 0.2) * (610^x)/(D^x) where:

Cf is a calculation factor (1.0 for >= 1 kV, 1.5 for < 1 kV). I'm assuming you have this.

En is the normalized energy (what you need).

t is arcing time. This is given in the 70E tables.

x is the calculation exponent and D is the working distance.. This information is given in IEEE 1584 and restated again in the table in Annex D.

Once you have recovered the normalized distance, rerun the formula "forwards" while adjusting the distance D until you get to 1.2 cal/cm^2 or do the math to solve for D in the above calculation to determine the arc flash boundary directly.

Note that while doing all this work though you will have to look for the arcing time on the tables in the exact same place where the arc flash boundary is already given.