Arc flash: risk and PPE
Stoll curve: second-degree burn threshold for an exposure time
- where
- second-degree burn threshold energy (cal/cm²)
- exposure duration (s)
- equivalent heat flux (cal/cm²·s)
- incident energy received (cal/cm²)
Explain this equation
Shows how much heat bare skin can take before a second-degree burn, depending on exposure time, to set the fixed 1.2 cal/cm² threshold in context.
Eb is the threshold energy for an exposure of t seconds, qb the equivalent constant heat flux, and the ratio compares a received energy E with the threshold.
Skin conducts heat away from the surface, so a slow exposure can be absorbed with less damage than the same energy delivered quickly. The power law 1.2 × t^0.3 fits the Stoll and Chianta tolerance data: shorter exposures need less total energy to burn.
Sense check: at 1 s Eb is 1.2 cal/cm²; at 0.1 s about 0.6 cal/cm²; at 2 s about 1.5 cal/cm² (Stoll table 1.46).
Watch out: the standards use 1.2 cal/cm² regardless of time, which is not conservative for very fast arcs.
Uses a published fit to the Stoll and Chianta tissue tolerance data to show how the energy needed for a second-degree burn on bare skin depends on exposure time.
Enter your values to see the result.
Good to know
Stoll’s data give the time to a second-degree burn under a constant heat flux: about 1.2 cal/cm²·s for 1 s, 0.73 for 2 s, and falling total-energy thresholds for shorter exposures. Furtak and Silecky’s fit Eb = 1.2 t^0.3 (equivalently t = 1.3 q^−1.43) reproduces the curve; at 1 s it gives exactly 1.2 cal/cm² (5.0 J/cm²), which is the fixed value IEEE 1584 and NFPA 70E use for the arc flash boundary. For fast arcs (0.1 s) the threshold is nearer 0.6 cal/cm², so the fixed 1.2 cal/cm² boundary is not conservative for very short arcs; for long exposures it is conservative. ATPV (ASTM F1959, IEC 61482-1-1) is defined against this Stoll response.
Common mistake
Treating 1.2 cal/cm² as a safe dose. It is the onset of a curable burn on bare skin, and only exactly so for a 1 s exposure. Ordinary clothing can ignite at a few cal/cm² and cause far worse injury.
Limits
Empirical fit to human/animal skin data for constant radiant flux; arc exposures are not constant flux. Stoll’s data cover roughly 1–30 s with extensions to about 0.1 s. For information and comparison only; boundaries are set by the 1.2 cal/cm² convention in the standards.
Sources
- A. M. Stoll, M. A. Chianta, Method and rating system for evaluation of thermal protection, Aerospace Medicine 40(11), 1969
- M. Furtak, L. Silecky, Evaluation of onset to second degree burn energy in arc flash hazard analysis, IAEI Magazine, July 2012
- ASTM F1959/F1959M Standard test method for determining the arc rating of materials for clothing (ATPV, EBT, Stoll response)
- IEEE Std 1584-2018 IEEE Guide for Performing Arc-Flash Hazard Calculations (equations 1–25, Tables 1–7, Annex D worked examples)
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.