Introduction
Steel in seawater corrodes unless its potential is pulled below about −0.80 V (Ag/AgCl). Sacrificial anodes of zinc or aluminium alloy do that by corroding instead, and designing them is a bookkeeping exercise: how much current the structure draws over its life (area × current density × coating breakdown), how much charge each kilogram of anode can supply (its electrochemical capacity, discounted by a utilisation factor), and whether the anodes can push that current through the water (their resistance). DNV-RP-B401 is the reference method for offshore structures; ship hulls use the same arithmetic with class-rule current densities per area. This calculator does both.
It is for naval architects and superintendents sizing hull anodes for a docking interval, offshore and port engineers protecting structures and tanks, and students of marine corrosion.
Formulas
Current demand (A), with coating breakdown f_c:
I_ci = A i_ci f_ci I_cm = A i_cm f_cm I_cf = A i_cf f_cf
f_ci = a, f_cm = a + b t_f / 2, f_cf = a + b t_f (≤ 1; bare steel f_c = 1)Anode mass, count and life:
Q = I_cm × t_f × 8760 [Ah] M = Q / (u ε) N = ceil(M / m_anode)
life = N m_anode u ε / (I_cm × 8760)Anode current output (initial, new anode):
I_a = (E_c − E_a) / R_a, E_c = −0.80 V
long slender stand-off (L ≥ 4r): R_a = ρ/(2πL) [ln(4L/r) − 1], r = periphery / 2π
short slender stand-off: R_a = ρ/(2πL) [ln(2L/r (1 + √(1 + (r/2L)²))) + r/2L − √(1 + (r/2L)²)]
long flush-mounted: R_a = ρ / (2S), S = (length + width)/2
short flush, bracelet, hull: R_a = 0.315 ρ / √A_exposed
check: N I_a ≥ I_ci and I_cfRP-B401 data (2021): bare-steel mean current density 0.070 (tropical) to 0.120 A/m² (arctic) at 0–30 m, with initial/final values per Table 8-1; coating constants a = 0.10/0.05/0.02/0.02 and b = 0.10/0.025/0.012/0.008 per year for categories I–IV at 0–30 m (b = 0.05/0.015/0.008/0.005 below 30 m); Al-Zn-In 2 000 Ah/kg at −1.05 V, zinc 780 Ah/kg at −1.03 V; utilisation 0.90 long stand-off, 0.85 short stand-off and long flush, 0.80 bracelet/flush.
Ship hulls: coated hull 10–20 mA/m² (+5 mA/m² for dockings beyond 30 months), bonded propeller about 500 mA/m², uncoated steel 100–150 mA/m²; design life = docking interval.
Assumptions and limitations
- Inventory calculation, not a layout: anode distribution, current drain to chains, wells or reinforcement, stray currents and ICCP interaction are outside the scope.
- The final output check uses the new-anode resistance; RP-B401 requires the resistance of the anode consumed to its utilisation factor, which is higher. Treat the final check as indicative.
- Table values are for open-sea, average-flow, uncoated steel at the stated temperatures; capacities drop in sediments and at high temperature.
- Hull current densities are typical class-practice values entered by the user; the actual class table (DNV-CG-0288, ABS) governs.
Worked example
A 6 000 m² coated hull with a bonded 40 m² propeller and 50 m² of uncoated appendages, docking every 2.5 years, protected with 20 kg zinc hull anodes in 0.25 Ω·m water.
- Current demand: 6 000 × 0.015 + 40 × 0.5 + 50 × 0.12 = 90 + 20 + 6 = 116 A (the propeller alone draws a sixth of it).
- Charge over 2.5 years: 116 × 2.5 × 8 760 = 2.54 MAh. Zinc at 780 Ah/kg and u = 0.80: M = 2.54 × 10⁶ / 624 = 4 070 kg → 204 anodes of 20 kg, 3.4 per 100 m².
- Output: a 0.6 × 0.15 m hull anode has R_a = 0.315 × 0.25/√0.09 = 0.26 Ω and delivers (−0.80 + 1.03)/0.26 = 0.88 A; 204 anodes give 179 A, above the 116 A demand.
- With a 3-year docking interval the hull density becomes 20 mA/m², the demand 146 A and the mass 6 150 kg.
Offshore check (RP-B401): 1 000 m² of category II coated steel in temperate water at 0–30 m for 25 years: f_cm = 0.05 + 0.025 × 12.5 = 0.36, I_cm = 1 000 × 0.100 × 0.36 = 36 A, mass 4 410 kg of aluminium at u 0.90; but the final demand is 1 000 × 0.130 × 0.675 = 88 A, so fifteen 300 kg stand-off anodes (3.1 A each) are too few by output and 29 are needed: output, not mass, governs.
FAQ
Zinc or aluminium?
Aluminium alloy gives 2.5 times the charge per kilogram and is standard offshore and on most hulls; zinc is used in ballast tanks (no spark risk) and where aluminium alloys may passivate (low salinity, buried).
Why does the coating matter so much?
A sound coating cuts the current demand to a few per cent of bare steel; the design life then depends on how fast it breaks down. Category III/IV systems halve the anode mass compared with a thin primer.
What is the utilisation factor?
The fraction of the anode mass that can be consumed before the anode stops working (core exposed, output too low): 0.90 for long slender anodes down to 0.80 for bracelets and hull anodes.
My mass is enough but the output check fails.
Large anodes have low resistance per anode but there are few of them; the peak (initial or final) demand needs more or longer anodes. Count can be governed by current, not by mass, exactly as in the offshore example.
How do I use this for a ballast tank?
Offshore mode with the appropriate current density (tanks are often treated as temperate, 0–30 m) and coating category; design life equals the special survey interval; aluminium is restricted in tanks adjacent to cargo tanks by SOLAS.
Does the propeller really need 500 mA/m²?
A bonded bronze propeller is a large bare cathode; if it is earthed to the hull through a slip ring it draws roughly that. If it is not bonded it is unprotected and does not load the anodes.
What about ICCP?
Impressed-current systems replace hull anodes; the current demand calculation is the same, but the output comes from a rectifier and the design is a different document.
Related calculators
- Paint coverage and quantity — the coating whose breakdown sets the demand.
- Hydrostatics basics — wetted surface area of the hull.
- Tank volume and partial fill — tank surface and volume.
- Thin-wall pressure vessel — the steel being protected.