Doan / NFPA 70E Maximum Power Method Verified

Concept: the worst-case DC arc flash occurs at the point of maximum power transfer — when arc resistance equals the system's upstream resistance, which happens when the arcing current is exactly half the bolted fault current. That single assumption makes this the simplest method here: no iteration, no gap measurement needed, just system voltage, bolted fault current, arc duration, and working distance.

Source: D.R. Doan, "Arc Flash Calculations for Exposures to DC Systems," IEEE Transactions on Industry Applications, Vol. 46 No. 6, 2010 — reproduced in NFPA 70E's Informative Annex D as the Maximum Power Method (confirmed at §D.8.1.1 in the 2015 edition; later editions have renumbered this annex, so we cite the paper itself rather than guess at a current locator). Stated in NFPA 70E's own text to be conservatively high, and validated by testing performed for Bruce Power. Explicitly limited to systems up to 1000 Vdc.

Use it for: a fast, conservative first-pass screen, or when you don't have (or don't want to assume) an electrode gap. Watch out for: it can be very conservative — one independent comparison found it overestimated measured incident energy by a wide margin under some test conditions — so treat a Doan result as a worst-case ceiling, not a best estimate.

Stokes-Oppenlander / Ammerman Method Verified

Concept: models the arc as a resistance that depends on both the electrode gap and the arcing current itself, which means the arc current can't be solved directly — it's found by iterating the circuit equation (upstream resistance plus arc resistance) until it converges, starting from the same 50%-of-bolted-current first guess Doan uses as its final answer.

Source: A.D. Stokes & W.T. Oppenlander, "Electric Arcs in Open Air," Journal of Physics D: Applied Physics (1991) — the original arc-resistance research. R.F. Ammerman, T. Gammon, P.K. Sen & J.P. Nelson, "DC-Arc Models and Incident-Energy Calculations," IEEE Trans. Ind. Appl., Vol. 46 No. 5, 2010, adopt this same V-I model and add R. Wilkins' (2004) enclosure geometry constants for boxed equipment — this calculator uses the one Wilkins constant pair independently verifiable (an enclosed panelboard); other equipment types from Wilkins' table aren't offered rather than guessed at.

Use it for: the most realistic estimate of these four — independent comparisons against real DC arc-flash test data found this model tracked measured results more closely than any other method here. Watch out for: that same accuracy cuts both ways — because it isn't deliberately conservative, one test-data comparison found it under-predicted the actual measured energy about half the time. Don't treat it as a safety margin the way you would a Doan result.

Paukert Method Verified via secondary reproduction

Concept: J. Paukert compiled arc-fault test data from seven researchers (AC and DC, currents from 0.3 A to 100 kA, gaps from 1 to 200 mm) and fit an empirical power-law voltage/current curve for each of seven tabulated gap widths. The calculator interpolates between those tabulated gaps for whatever electrode spacing you enter, then solves the same iterative circuit equation as Stokes-Oppenlander.

Source: J. Paukert, "The Arc Voltage and Arc Resistance of LV Fault Arcs," 7th International Symposium on Switching Arc Phenomena, 1993. The original 1993 proceedings paper predates open digital archives; the tables used here are reproduced from a training reference that cites Paukert's original tables directly — not independently verified against the 1993 proceedings text itself.

Use it for: a middle-ground estimate — independent comparisons consistently place Paukert's results between Doan (higher) and Stokes-Oppenlander (lower) for the same inputs. Watch out for: it's only validated within its tabulated range (gaps 1–200 mm, currents to 100 kA) — outside that range you're extrapolating past what the underlying data actually covers.

DGUV Information 203-077 (Germany) Verified — primary source

Concept: the German DC arc flash method, published by DGUV (Deutsche Gesetzliche Unfallversicherung). It offers the same two-tier structure as the others here — a quick worst-case screen (a fixed 25% of bolted-fault power for DC systems) and a more detailed iterative calculation using its own arc voltage/current relationship — but reports the result in an entirely different framework: total arc energy in kilojoules, compared against IEC 61482-1-2 "Box-Test" Arc Protection Class (APC) thresholds, not cal/cm² and NFPA 70E PPE categories.

Source: DGUV Information 203-077, 2nd edition, September 2020, "Thermische Gefährdung durch Störlichtbögen" — read directly as a primary source, not a secondary description.

Use it for: facilities operating under German or broader European PPE frameworks, where IEC 61482-1-2-rated arc-protective clothing (rated by Arc Protection Class, not by a cal/cm² ATPV rating) is what's actually available and specified. Do not convert its kJ output to cal/cm² or cross-reference it against an NFPA 70E PPE category — the standard itself states explicitly that no valid conversion exists between the two systems, which is why the calculator reports the DGUV result on its own terms rather than force-converting it.

Conservative vs. Aggressive — A Real Comparison

Independent comparisons that ran the same inputs through multiple methods found a consistent ranking, most conservative (highest incident energy) to least:

Practical guidance that follows from this: use Doan (or DGUV's quick screen) for a fast, defensibly conservative first pass or when you're missing an electrode gap measurement. Use Stokes-Oppenlander/Ammerman or Paukert when you have real gap data and want an estimate that's less likely to grossly overstate the hazard — but don't treat either as inherently "safe" the way a deliberately conservative method is; they're aiming for accuracy, not margin.

A Note on Electrode Gap

Three of these four methods need an electrode gap as an input, and it matters — Paukert's own tables show arc voltage roughly doubling as gap increases from 1 mm to 20 mm, and the same trend holds in Stokes-Oppenlander's formula. There's no universal "voltage determines gap" chart, because electrode gap is a physical/mechanical property of the equipment (bus spacing, terminal clearance), not something derived from system voltage alone — though higher-voltage equipment does tend toward larger designed clearances as a matter of general practice. If you're unsure what gap to use, check the equipment manufacturer's drawing rather than estimating from voltage class alone. The AC arc flash calculator on this site's home page has a library of typical IEEE 1584 gap values by equipment type, which is a reasonable starting reference even though it's calibrated for AC equipment.