A buried, coated pipeline behaves like a leaky electrical transmission line. Current from each rectifier's anode enters the steel at one point and bleeds outward through coating defects into the soil, so both the protective current and the pipe-to-soil potential shift decay exponentially with distance from that point:
α = √(R_L / R_C) attenuation constant (1/m)
λ = 1 / α attenuation length (m)
Z0 = √(R_L · R_C) characteristic impedance (Ω)
ΔV_i(x) = (I0_i/2)·Z0·e^(−α·|x−x_i|) shift from anode i
ΔV(x) = Σ ΔV_i(x) total shift (linear superposition)
E(x) = E_corr − ΔV(x) actual pipe-to-soil potential (V, Cu/CuSO4)
R_L is the pipe steel's resistance per unit length — adjustable here directly (typical 20-inch, 9.5 mm wall steel line: R_L ≈ 11.2 µΩ/m). R_C is the coating's resistance-length product — it falls sharply as holidays (coating defects) let more current leak to soil, so the Coating quality slider spans roughly three orders of magnitude in R_C. A larger λ means the same rectifier reaches farther before the potential decays back toward the unprotected native corrosion potential, E_corr ≈ −0.55 V. With two anodes the contributions add linearly (superposition), which is exactly why a second, weaker rectifier placed at a distant weak point can rescue coverage more cheaply than boosting the first one's current.
Per NACE SP0169, a point is considered protected once E(x) is more negative than −0.85 V; pushed past about −1.20 V, excess current risks coating disbondment and hydrogen embrittlement in high-strength steel — the "overprotected" band above.
- Coating quality — sets R_C; poor coating forces the CP current to dissipate within a short stretch of pipe.
- Pipe steel resistance R_L — a heavier wall or larger diameter lowers R_L and stretches λ for the same coating.
- Anode position / current — drag an anode along the pipe or use its sliders; add a second anode to see the combined potential profile.