Arc flash: other methods
Doughty–Neal incident energy, 600 V and below (open air and 508 mm box)
- where
- incident energy in open air and in a box (cal/cm²)
- working distance (in)
- arc duration (s)
- bolted fault current (kA)
- working distance (mm)
Explain this equation
Gives incident energy for 600 V and below from Doughty, Neal and Floyd’s tests, in open air or in a 20 in (508 mm) box, as listed in NFPA 70E Annex D.
F is the bolted fault current, tA the arc duration and DA or DB the working distance in inches. The quadratic in F reflects how arc power grows with current once the arc voltage and arcing current are taken into account.
The power of distance shows how energy spreads: −1.9593 in open air is close to inverse-square, while −1.4738 in a box shows the enclosure focusing energy out of the opening. Energy is linear in time.
Sense check: at 30 kA, 0.2 s and 18 in, open air gives about 7.7 cal/cm² and the box about 11.7 cal/cm², showing the effect of the enclosure.
Watch out: tested only between 16 and 50 kA and at distances of 18 in or more.
Doughty, Neal and Floyd’s empirical equations (NFPA 70E Annex D) for three-phase arcs at 600 V and below, in open air or in a cubic box up to 508 mm (20 in).
Enter your values to see the result.
Good to know
Distances are converted to inches inside the calculator, as the equations were fitted in inches. Test data were at 600 V and 480 V. Source transcriptions differ in the fourth decimal of the constants (0.8938 or 0.8939; 5.9675 or 5.9673); the effect is under 0.1 %. For new studies IEEE 1584-2018 is preferred because it covers enclosure size, electrode orientation and reduced arcing current.
Common mistake
Applying the box equation to larger switchboard sections or to HV equipment, or extrapolating below 16 kA where the polynomial in F behaves poorly.
Limits
Three-phase, ≤600 V, bolted fault 16–50 kA, working distance ≥ 18 in (455 mm), box no larger than 20 in (508 mm) cube. UK duty: under the Electricity at Work Regulations 1989 work on or near live conductors is allowed only where reg 14 is met (unreasonable to make dead, reasonable to work live, suitable precautions); regs 12 and 13 require isolation and precautions for dead working, and reg 4(4) requires suitable protective equipment. HSE HSG85 and your DNO or company safety rules (ENA-based distribution safety rules) take precedence. Apply the hierarchy of controls: de-energise first, then engineering controls (faster protection, maintenance switches, remote racking/operation, arc-resistant switchgear), then distance and procedures; arc-rated PPE is the last line of defence.
Sources
- R. L. Doughty, T. E. Neal, H. L. Floyd, Predicting incident energy to better manage the electric arc hazard on 600-V power distribution systems, IEEE Trans. Industry Applications 36(1), 2000
- NFPA 70E-2024 Standard for Electrical Safety in the Workplace: Informative Annex D (incident energy and arc flash boundary methods) and Table 130.7(C)(15)(c)
- ABB / Thomas Domitrovich et al.: Arc flash hazard analysis and mitigation (restates IEEE 1584-2002, Lee and Doughty–Neal equations)
- The Electricity at Work Regulations 1989 (SI 1989/635), regulations 4, 12, 13 and 14
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.