Spider web dew - 2D night cooling timeline

Why a strand gets colder than the air

At night a surface radiates to the cold sky and receives little back. The net radiative loss is q = ε σ (T⁴ - T_sky⁴), with the clear-sky temperature estimated by Swinbank's relation T_sky = 0.0552 T_air^1.5 (kelvin), about 15 to 20 K below the air. Cloud cover returns radiation and shrinks the deficit. Air touching the strand warms it by convection, h (T_air - T), with h from the Churchill-Bernstein correlation for a cylinder, Nu = 0.3 + 0.62 Re^1/2 Pr^1/3[…]. Steady state is where loss and gain balance, so thin threads and windy nights stay close to the air temperature.

Dew point and condensation

Water vapour condenses when the surface falls below the dew point T_d, found from the Magnus formula e_s(T) = 611.2 exp(17.62 T / (243.12 + T)) Pa. The vapour flux onto the strand is ṁ'' = h_m (ρ_v,air - ρ_v,sat(T)) with h_m = h / (ρ c_p Le^2/3). Condensation releases latent heat L ṁ'', which warms the strand and brakes further cooling, so the dew rate settles near the net radiative cooling divided by L, a few tenths of a millimetre per night at most.

Honest simplifications: a single cylinder at one temperature (a real web has droplets, silk with water-attracting properties, and thread-to-thread shading), dew appears as an average water depth on the strand surface rather than per-droplet growth, vapour content stays constant through the night (a real night also loses moisture to dew and fog), the sky model is a one-parameter fit, and the thread-thickness range goes beyond spider silk (3 micrometres) up to grass-stalk size. Real hair-thin silk barely cools below the air, which is why webs gather dew mostly near saturation or in fog.

• Compare the clear calm night with the cloudy night: clouds return radiation and the dew almost vanishes.
• Raise the wind speed to 4 m/s and watch the strand temperature climb back towards the air.
• Shrink the strand to 0.01 mm (silk): its temperature hugs the air and dew only forms near saturation.
• Pick the dry desert air preset: the dew point sits far below the strand and nothing condenses.