I see your location is Western Australia. I just returned from Victoria and NSW, Australia last week. A very long trip but always worth it. A great place. I even finally learned to drive on the left side of the road this time. A bit of a challenge when the first traffic I hit is downtown Sydney. Everyone survived.
Back when I worked at Square D Company in the very early 1980’s the Chief Electrical Engineer was instrumental in the 277 V Arcing Fault Damage tests. (Harry Stanback). It was to assist in developing ground fault protection requirements. It has all progressed a great deal since those days.
I’m not as familiar with this publication as many others but I’ll give my 2 cents. Perhaps others can join in.
For your first question about 2.42 in^3 of copper being vaporized in 0.3 seconds. Based on the calculations you seem to have the correct number. In the lab, copper vaporizes at an amazing rate under fault conditions so I would not be surprised if this value is close to what happens.
This issue is also addressed in the Australian / New Zealand AS/NZS Standard 3000 Wiring Rules for internal arcing faults and uses the following equation to calculate the damage limit:
Clearing Time t = (Ke x Ir) / (If^1.5)
If = 30% of prospective fault current
Ke = 250 constant (same as you have)
Ir = current rating of switchboard
T = clearing time in seconds.
It looks like the AS Standard follows a similar logic to NEMA (or vice-versa). However, they don’t seem to take into account the difference between copper and aluminum.
As far as your comments:
I^2*t is typically thought of as the thermal energy and damage characteristics. Interesting to see 1.5 being used for both.
I’m not sure I would say incident energy is proportional to arcing current. There are logarithms and exponents involved in the calculations (non-linear). Many factors come into play.
You are correct - IEEE 1584 is only for 3 phase. It assumes Line-Ground (Line-Earth) can escalate to 3 Phase.