Arc flash: risk and PPE
Arc flash boundary from a known incident energy and distance exponent
- where
- arc flash boundary (mm)
- working distance (mm)
- incident energy at D (J/cm²)
- incident energy at the boundary (J/cm²)
- distance exponent
Explain this equation
Finds the arc flash boundary from an incident energy that is already known at a stated working distance, for example from a label or study.
E is the incident energy at distance D, EB the threshold energy at the boundary (5.0 J/cm², the onset of a curable burn on bare skin) and x the distance exponent of the method and configuration.
All the models treat energy as falling as a power of distance, E ∝ D^−x. Solving for the distance at which E equals EB gives D × (E/EB)^(1/x). The larger x is, the faster energy falls and the nearer the boundary.
Sense check: 20 J/cm² at 500 mm with x = 2 gives a 1 m boundary; with x = 1.6 it would be about 1.2 m.
Watch out: using x = 2 for an enclosed arc understates the boundary.
Works out the arc flash boundary from an incident energy you already have (from a study or label) at a stated working distance, using the distance exponent for the configuration.
Enter your values to see the result.
Good to know
Incident energy falls as D^−x. IEEE 1584-2018 distance exponents (−k12): at 600 V VCB 1.598, VCBB 1.809, HCB 2.03, VOA 1.598, HOA 1.99; at 2.7 kV 1.569, 1.742, 1.723, 1.515, 1.639; at 14.3 kV 1.568, 1.677, 1.655, 1.534, 1.633. IEEE 1584-2002: 2.0 open air and cable, 1.473 LV switchgear, 1.641 LV MCC/panel, 0.973 HV switchgear. Lee and the d.c. methods use 2. The boundary is where a person without arc-rated clothing would just receive a curable (second-degree) burn.
Common mistake
Using x = 2 for enclosed equipment. A box focuses energy out of the opening, so the true exponent is lower and the boundary is further out than inverse-square suggests.
Limits
Assumes the energy-distance relationship is a single power law between the working distance and the boundary. Between 600 V and 15 kV the 2018 model interpolates between three exponents, so this is approximate there (typically within a few %). 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
- IEEE Std 1584-2018 IEEE Guide for Performing Arc-Flash Hazard Calculations (equations 1–25, Tables 1–7, Annex D worked examples)
- IEEE Std 1584-2002 IEEE Guide for Performing Arc-Flash Hazard Calculations (superseded; empirical model and Lee method)
- 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)
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.