Rail Catenary Icing - 2D Ice Load, Wire Sag and Joule De-icing Lab

Ice accretion

Freezing rain of intensity p falls at about 9 m/s and sweeps past the wire with relative speed √(v_d² + U²). The water caught per metre is ρ_w p D_ice √(1 + (U/v_d)²), where D_ice = D + 2r grows as ice thickens, so accretion accelerates (Makkonen-style glaze model). The mass per metre M gives the radial thickness from π ρ_i ((D/2 + r)² - (D/2)²) = M with ρ_i = 900 kg/m³.

Load, sag and de-icing

Vertical load w = (m₀ + M) g, wind load F_w = ½ ρ_a C_d U² D_ice, resultant w_r = √(w² + F_w²). For a flexible wire with constant horizontal tension H the mid-span sag is s = (H/w_r)(cosh(w_rL/2H) - 1), close to the parabola w_rL²/(8H) when sag is small. Current I heats the wire at I²R′; ice melts at (I²R′ - convective loss h π D_ice ΔT) / (L_f + c_i ΔT) kilograms per metre per second.

Honest simplifications: a single wire with constant tension (real catenaries use droppers and counterweights), the frozen fraction is a crude ramp with temperature, no runoff or wet growth, fixed convective coefficient 20 W/m²K, wind drag coefficient 1. Values are illustrative, not a design calculation.

• Run the Freezing rain event: ice thickens faster as the wire gets thicker.
• Open Severe ice storm and watch the sag grow to several times its bare value.
• Use Current de-icing: above a threshold current the ice mass falls while the rain continues.
• Compare Long span, slack wire: a longer span and lower tension sag far more for the same ice.