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Rates are per 100 km per year. Backflashover of GSW strokes depends on tower footing resistance and insulation — evaluate separately; this tool gives stroke incidence and shielding-failure only.
Geometric construction
exposed arc Dc (phase strike)
shielded (GSW / ground wins)
GSW arc rS
ground-capture line rg
Formulas used
Shielding angle
α = atan( (x_c − x_g) / (h_g − h_c) )
Average height (sag toggle)
h_avg = h − (2/3) · (sag%/100 · span)
Classical EGM striking distances (I in kA, r in m)
IEEE Std 1243: r_c = 10·I^0.65 ; r_g = (3.6 + 1.7·ln(43 − h_c))·I^0.65 (h_c < 40 m; else 5.5·I^0.65)
Love / CIGRE: r_c = 10·I^0.65 ; r_g = γ·r_c
Brown–Whitehead: r_c = 7.1·I^0.75 ; r_g = 6.4·I^0.75
Armstrong–Whitehead: r_c = 6.7·I^0.8 ; r_g = 6.0·I^0.8
Love / CIGRE: r_c = 10·I^0.65 ; r_g = γ·r_c
Brown–Whitehead: r_c = 7.1·I^0.75 ; r_g = 6.4·I^0.75
Armstrong–Whitehead: r_c = 6.7·I^0.8 ; r_g = 6.0·I^0.8
Eriksson improved EGM (attractive radii)
R_s = 0.67·h_g^0.6·I^0.74 (shield wire)
R_c = 0.67·h_c^0.6·I^0.74 (phase)
ground line at y = R_c
R_c = 0.67·h_c^0.6·I^0.74 (phase)
ground line at y = R_c
Simplified LPM (approximate)
k_L = 10·(500 / E_i) (calibrated: k_L = 10 at E_i = 500 kV/m ≡ Love)
r_S = k_L·I^0.65·(h_g/10)^0.15 ; r_C = k_L·I^0.65·(h_c/10)^0.15 ; r_g = k_L·I^0.65
r_S = k_L·I^0.65·(h_g/10)^0.15 ; r_C = k_L·I^0.65·(h_c/10)^0.15 ; r_g = k_L·I^0.65
Exposed arc D_c
Vertical leader at x strikes the highest first contact among: arc(S, r_S), arc(C, r_C), line y = r_g.
D_c = width of { x : phase arc is the first contact }. D_c(I_max) = 0 (found by bisection).
D_c = width of { x : phase arc is the first contact }. D_c(I_max) = 0 (found by bisection).
Shielding-failure flashover rate
SFFOR = 0.2 · N_g · ∫₀^Imax D_c(I)·f(I) dI [per 100 km/yr]
f(I) = 1 / (I·σ_ln·√(2π)) · exp( −(ln I − ln I_med)² / (2σ_ln²) ) (log-normal PDF)
Numerical: I = 1 … I_max, ΔI = 0.5 kA, D_c in metres.
f(I) = 1 / (I·σ_ln·√(2π)) · exp( −(ln I − ln I_med)² / (2σ_ln²) ) (log-normal PDF)
Numerical: I = 1 … I_max, ΔI = 0.5 kA, D_c in metres.
Total stroke incidence (Eriksson)
N_L = N_g · (28·h_g^0.6 + b) / 10 , b = GSW separation = 2·x_g (twin GSW) [flashes/100 km/yr]