Saltwater Atmospheric Icing on Power Lines & Ships Simulator
Estimate ice accretion on overhead power lines, ship decks, wind-turbine blades and offshore structures using ISO 12494 and the Makkonen model. Adjust air temperature, wind speed, liquid water content, droplet MVD and exposure time to see how collision efficiency alpha1, accretion rate, ice thickness, self-weight load and ISO 12494 class respond.
Parameters
Ice type
Drives sticking/accretion efficiency and density
Air temperature
°C
Wind speed
m/s
Liquid water content (LWC)
g/m³
Median volume diameter (MVD)
μm
Cylinder diameter
mm
e.g. conductor diameter (standard ACSR ~28 mm), leading-edge characteristic dimension
Exposure time
hr
Location
Assumed structure category (used for the diagram label)
Results
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Collision eff. α₁
—
Accretion rate (kg/m/hr)
—
Total ice (kg/m)
—
Radial ice thickness (mm)
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Self-weight (N/m)
—
ISO 12494 class
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Cross-section — Ice layer growth
Blue arrows show the wind, white dots are supercooled droplets (MVD), and the white-to-blue layer is the accreted ice. Colour reflects the ISO 12494 class (green = minor, orange = moderate, red = severe).
Ice thickness vs exposure time
Ice-type comparison (current weather)
Theory & Key Formulas
$$\frac{dM}{dt} = \alpha_1 \alpha_2 \alpha_3 \cdot V \cdot w \cdot A,\quad K = \frac{d_{drop}^2 \rho_w V}{9 \mu_{air} D}$$
α₁ collision efficiency, α₂ sticking, α₃ accretion, V wind speed [m/s], w LWC [kg/m³], A projected area [m²/m], K Langmuir-Blodgett inertia parameter.
Radial ice thickness from ice volume per unit length V_ice [m³/m] and ice density ρ_ice [kg/m³] (concentric annulus assumption).
Saltwater icing on power lines & ships — ISO 12494 / Makkonen model
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I've seen news about transmission towers collapsing after an ice storm. How thick can the ice on a relatively thin conductor really get?
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It gets surprisingly thick. During the 1998 Quebec ice storm in eastern Canada, conductors grew more than 50 mm of radial ice in just five days, more than 1,000 towers collapsed, and the damage bill was around US$5 billion. The conductor itself is thin, but supercooled rain and fog keep adding to the radius for hours. That's why this tool reports the radial thickness on the cylinder and the corresponding ISO 12494 class.
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Supercooled droplets are still liquid below 0°C and freeze on contact, right? But why split Makkonen's equation into three separate alphas?
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Good question. A droplet has to pass three gates before it ends up as ice. alpha1 is the collision efficiency — how many of the droplets carried by the wind actually hit the cylinder. Small droplets follow the airflow around the body and miss, so alpha1 drops. alpha2 is the sticking efficiency — how many of the impacting drops stay on the surface. Wet snow near 0°C bounces off, so alpha2 falls. alpha3 is the accretion efficiency — what fraction of the captured water actually freezes. Glaze ice forms at higher temperatures and some water runs off before freezing, which depresses alpha3. They multiply, so the smallest factor dominates.
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If I raise the wind speed V on the left, both the inertia parameter K and alpha1 go up. So is more wind always more dangerous?
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Wind acts twice: it brings more water per second and it raises the collision efficiency. dM/dt is proportional to V and K is proportional to V too, so the ice load at 25 m/s is an order of magnitude beyond what you get at 5 m/s. Real-world icing maxima sit on ridges and saddles where wind concentrates. Now switch the location to "Ship deck" — instead of cloud LWC, sea spray supplies the water and the dominant ice density jumps to about 850 kg/m^3 because of the salt. Same equation, very different load.
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Does a ship actually sink under that much ice?
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It's capsize, not sinking, that gets vessels. Ice builds on bow, mast and superstructure, raising the centre of gravity. The restoring moment collapses on a single heavy roll. The US Coast Guard logs 15-20 spray-icing capsizes per year on Arctic and Bering Sea trawlers. That's why polar vessels keep the superstructure low and symmetric and run deck heaters and de-icing crews on a schedule. Each industry has its own failure mode — tower collapse, capsize or aerodynamic loss on a turbine — but the underlying physics is the same.
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What about mitigation? You can't send a crew every time.
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Two families: prevent it (anti-icing) or remove it (de-icing). Norway's Statnett embeds heating cables in 380 kV conductors and pre-heats them when icing is forecast. Vestas combines electrothermal leading-edge heaters with aggressive pitch changes that throw ice off the blade. Lines can also use Joule heating by deliberately raising the current. Removal techniques include pneumatic boots, electrothermal pulse de-icing, infrared and laser ablation, and even helicopter strikes for transmission lines. The right mix depends on power budget, geography and how costly an outage is.
Frequently asked questions
In Makkonen's icing model dM/dt = alpha1 * alpha2 * alpha3 * V * w * A, alpha1 is the collision efficiency (fraction of supercooled droplets that strike the cylinder), alpha2 is the sticking efficiency (fraction of those that adhere), and alpha3 is the accretion efficiency (fraction of the remaining water that freezes). For dry rime ice alpha2 and alpha3 are typically 1, wet snow lowers alpha2, and glaze ice lowers alpha3 because the heat balance forces runoff. alpha1 is governed by the Langmuir-Blodgett inertia parameter K and depends strongly on droplet MVD, wind speed and cylinder diameter.
ISO 12494 "Atmospheric icing of structures" organises ice loads on structures and classifies radial ice thickness from G1 (~10 mm) up to G5+ (100 mm and above). IEC 60826 references the same scheme when defining mechanical load cases for transmission line towers. In Japan the Honshu-Hokkaido mountain corridors are typically G2-G3 territory, while heavily ice-prone routes reach G3-G4. This tool reports the class that corresponds to the ice thickness derived from the meteorological inputs you provide.
Sea spray icing builds dense (~850 kg/m^3) saline ice on the bow, deck and superstructure of small vessels within hours, raising the centre of gravity and destroying stability. The USCG records 15-20 trawler capsize events per year in the Arctic and Bering Sea attributed to spray icing. Mitigation combines mechanical de-icing hammers, electric de-icers, deck heaters and a low, symmetric superstructure design to maintain restoring moment.
Anti-icing (prevention) includes heating cables (Statnett 380 kV lines), super-hydrophobic coatings and aerodynamic shedding via pitch control on Vestas wind turbines. De-icing (removal) covers mechanical methods (rollers, pneumatic boots), electrothermal pulse de-icing, infrared and laser melting. Power lines can also self-heat by raising current to exploit I^2R losses. The choice depends on energy budget, accessibility and the cost of an outage.
Real-world applications
Transmission and distribution design loads: IEC 60826 and ISO 12494 treat atmospheric icing as a primary mechanical load for towers and conductors in cold or mountainous corridors. The 1998 North American ice storm in Quebec deposited about 50 mm of radial ice on conductors, collapsed more than 1,000 towers and caused roughly US$5 billion of damage. This tool gives you a first-pass thickness for a given conductor diameter and meteorological scenario, which is enough to pick a design class between G1 and G5+.
Arctic and Bering Sea vessel design: US Coast Guard data lists 15-20 capsizing incidents per year linked to sea spray icing on fishing vessels. Heavy seas, low temperatures and strong wind can deposit hundreds of kilograms on the superstructure within a few hours and erase stability. Select the "sea-spray" type, substitute a representative cylinder diameter for a railing, mast or pipe, and you obtain an order-of-magnitude estimate of the spray ice load.
Wind-turbine and offshore wind output losses: In the Nordics, North America and northern China, leading-edge icing of wind-turbine blades degrades aerodynamic performance by 20-40% and visibly reduces annual energy production. Vendors such as Vestas and Siemens Gamesa offer electrothermal Ice Protection Systems (IPS). Treat the leading edge as a cylinder, plug in your MVD and LWC, and the tool gives a comparative accretion rate across typical weather windows.
Operational forecasting at utilities and met services: National weather services and utility control centres extract LWC, MVD, air temperature and wind from numerical weather prediction output and feed Makkonen's equation to estimate transmission line icing in real time. Sections likely to cross a threshold trigger pre-heating, helicopter inspections or robotic de-icing dispatch. This page reproduces the core of that calculation in your browser.
Common misconceptions and pitfalls
The most common myth is "colder air means more icing". In reality, the most aggressive icing happens in the narrow window of -2 to -10°C. Below about -20°C the air carries far less water, supercooled droplet concentration drops, and so does the icing rate. Above 0°C nothing freezes. This tool exposes that effect only if you adjust LWC together with the temperature; real meteorological inputs (humidity and LWC) should be co-varied, not edited in isolation.
A second pitfall is "a thicker cylinder collects more ice". Yes, the projected area A scales with diameter, but the collision efficiency alpha1 falls because larger bodies deflect more of the airflow, so small droplets bypass them. The net result is sub-proportional growth in icing per unit length for fatter cables. Conductor sizing uses empirical icing atlases (Nordic, Canadian, EPRI) that capture this nonlinearity rather than relying on Makkonen alone.
Finally, Makkonen's equation is not universal. It is the 1981/2000 empirical form for clean circular cylinders. It cannot rigorously handle (i) non-cylindrical sections such as H-beams or lattice members, (ii) high LWC regimes where the heat balance drives alpha3 far below 1, or (iii) the time-dependent change of D as the ice layer itself grows. Detailed design should be cross-checked with CFD-based icing codes (ANSYS Fluent with LEWICE, FENSAP-ICE) and wind-tunnel data from NTNU (Norway) or McMaster (Canada). Treat this page as a fast first estimate, not a substitute for certification.
How to Use
Enter air temperature in °C (typically −5 to −15°C for icing events on power lines and offshore structures)
Input wind speed in m/s; marine icing intensifies above 10 m/s due to spray entrainment
Set liquid water content (LWC) in g/m³ (0.1–0.5 g/m³ for cloud icing; 0.5–3.0 g/m³ for sea-spray icing)
Specify median volume diameter (MVD) in microns; typical cloud droplets range 10–30 μm, sea-spray 50–200 μm
Read collision efficiency α₁, accretion rate (kg/m/hr), total ice mass, radial thickness (mm), and self-weight (N/m)
Cross-reference ISO 12494 icing class (Light, Medium, Heavy, Extreme) for design standard compliance
Worked Example
A 25 mm diameter aluminum conductor, 500 m span, experiences −8°C air, 12 m/s wind, 1.2 g/m³ LWC (sea-spray), 80 μm MVD. Collision efficiency α₁ = 0.78. Accretion rate = 1.8 kg/m/hr. After 4 hours: total ice = 7.2 kg/m, radial thickness = 18.5 mm, self-weight = 285 N/m. ISO class = Heavy. Total load on conductor = (conductor 0.7 kg/m + ice 7.2 kg/m) × 500 m × 9.81 = 38.4 kN, exceeding design tension of 30 kN.
Practical Notes
Sea-spray icing on ship deck railings (−12°C, 15 m/s, 2.0 g/m³ LWC) produces radial ice 25–40 mm in 3–6 hours; prioritize mechanical removal before structural compromise
Wind-turbine blade leading edges at northern latitudes (Norway, Canada) experience mixed cloud/spray icing; MVD >100 μm requires thicker certification margins per IEC 61400-2
ISO 12494 Heavy class (ice density ~900 kg/m³, thickness 25–50 mm) governs transmission line design in coastal Nordic and Russian regions
Collision efficiency decreases sharply for MVD <15 μm (cloud-only, α₁ ~0.4) versus sea-spray >150 μm (α₁ >0.9); use meteorological LWC sensors to validate input ranges