Touch and step
Tolerable touch and step voltages (IEEE 80, 50 kg or 70 kg body)
- where
- surface layer derating factor
- native soil resistivity (Ω·m)
- surface layer resistivity (Ω·m)
- surface layer thickness (m)
- tolerable touch voltage (V)
- body constant: 0.116 for 50 kg, 0.157 for 70 kg (A·s½)
- shock duration (s)
- tolerable step voltage (V)
Explain this equation
Gives the IEEE 80 tolerable touch and step voltages for a chosen fault duration, body weight and surface layer, as used on IEEE-based substation designs.
k/√ts is Dalziel's body current that a person of that weight can tolerate for ts seconds without fibrillation: k is 0.116 for 50 kg and 0.157 for 70 kg. 1000 Ω is the body resistance. Each foot is modelled as a small disc with resistance about 3Cs·ρs; two feet in parallel give 1.5Cs·ρs for touch and in series 6Cs·ρs for step. Cs reduces the effective surface layer resistivity when it is thin or the soil below is conductive.
The tolerable voltage is the tolerable current multiplied by the total resistance in the circuit, so a high-resistivity surface layer raises the limit directly.
With no surface layer on 100 Ω·m soil, 1 s and 50 kg, Etouch is about 133 V. With 100 mm of 2500 Ω·m rock, 0.5 s and 70 kg it rises to about 840 V.
Watch out: this is the IEEE method. UK designs use BS EN 50522 and ENA TS 41-24, whose limits are based on IEC 60479-1.
IEEE 80 limits for touch and step voltage, based on Dalziel’s fibrillation threshold, a 1000 Ω body and the foot resistance on a high-resistivity surface layer.
Enter your values to see the result.
Good to know
k = 0.116 (50 kg) or 0.157 (70 kg) from IB = k/√ts. Each foot is a 0.08 m radius disc of resistance 3Cs·ρs, giving 1.5Cs·ρs for feet in parallel (touch) and 6Cs·ρs in series (step). Cs is the empirical IEEE 80 Eq. 27 (accurate to about 5 %). IEEE 80 Example 1 (400 Ω·m soil, 0.102 m of 2500 Ω·m rock, 0.5 s, 70 kg): Cs = 0.74, Etouch = 838.2 V, Estep = 2686.6 V.
Common mistake
Using the 70 kg criterion by default. IEEE 80 suggests 50 kg where the public may have access; the 50 kg limit is 26 % lower.
Limits
IEEE 80 approach only; it is not the UK method (use BS EN 50522 / ENA TS 41-24 for UK designs). Cs formula is the simplified expression; IEEE 80 Figure 11 gives the exact curves. Gloves, shoes and contact resistance other than the surface layer are ignored.
Sources
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.