Presets
Playback
Weather, water and shape
Colder, windier air freezes more water. If the supply is smaller than the amount that can freeze, nothing drips and growth is limited by the water; if it is larger, the extra water leaves as drops.
Model checks
The science
What is modelled
The icicle is a cone of fixed length-to-radius ratio. Heat leaves its surface to the cold air through a convective coefficient and freezes meltwater, up to the water supplied. Unfrozen water drips from the tip, and the drop mass follows Tate's law.
Equations
- Freezing rate
m = h (0 - Tair) A / Lf,h = 5.7 + 3.8 uW/m²K, cone areaA = π r √(r² + L²). - Volume balance
ρi dV/dt = m, coneV = π r² L / 3; with unlimited water the length grows linearly. - Ice wall growth:
ρ Lf (d²/2k + d/h) = ΔT t. - Drop mass
md ≈ 0.6 · 2π rtip γ / g. - Rayleigh-Plateau: fastest mode at
k R = 0.697.
Checks run in the page
- The volume-balance integration against the linear growth law.
- The Stefan freezing front against its closed form.
- Water mass and ice volume bookkeeping.
- The Rayleigh-Plateau fastest-growing mode.
Honest simplifications
Fixed cone shape, a single convective coefficient with no radiation or sun, ice at the water-film temperature, no heat conduction along the icicle and a constant water supply. Real icicle ripples are set by a thin water film and have a wavelength near 1 cm, which is shown as an observed value rather than derived here.
What to try
- Press Hard frost, no water: growth is limited by the small supply and nothing drips.
- Press Mild and wet: most of the water drips away and growth is slow.
- Raise the wind speed to see the heat transfer and the growth rate rise.