Realistically it’s not an easy thing to do by hand. Few people who work with it even know how to do this.
Arc flash calculations starts with the short circuit current. There are lots of very simple calculation methods that give you short circuit currents that are useful for checking AIC for instance, but they give unrealistically high results. With arc flash this will underpredict the danger so simplified methods can’t be used. Probably the most approachable hand calculation method is the Bussman point to point method. In fact if you have a fuse only system Cooper-Bussmann gives you a simplified method that is pretty close to the more accurate IEEE 1584-2018 method. If you have breakers you are out of luck with Bussmann. There is software but at usually around $5,000 for a license it’s not cheap, it usually uses either the IEC or ANSI methods but it uses the full impedance (L and R) where the standards are designed back in the days of slide rules so only the inductance is used. This is the most difficult part of the entire calculation.
Next the actual arcing current is calculated using the system voltage, the short circuit current above,’and the arc gap. It’s a fairly straight forward calculation but pretty long in the current standard. Depending on the various factors the actual arcing current is about 40-85% of the short circuit current.
Next once you have this, take the arcing current and use the time-current curve of the fuse or breaker protecting the bus to determine the fault time before it trips and the arc is extinguished. This is pretty simple but finding this information especially on older or foreign equipment can be difficult.
Finally using all the above information plus the size of the bus can (LxWxH) and the distance between the arc and the prospective victim, you can calculate the heat flux in cal/cm2. Again the calculation is long and tedious but the sort of thing that you can do in a spreadsheet.
You can purchase the IEEE 1584-2018 book for around $600. They actually produced a little over 3000 arc flashes at several testing labs and collected a ton of data in order to arrive at the calculations. Understandably they charge that much to help with paying off the cost of the research. Older versions of NFPA 70E give the older 2002 version of the equations in IEEE 1584 and is available for under $100. The new calculations are not included partly because of space.
I know this is not the answer you are looking for but it should give you a flavor of what is involved and why realistically arc flash calculations are done in software.
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