Clock 00:00Burned 0 haHead 0 m/minVillage safe

Wildfire Front Lab — 2D Map and Cross-Section

The top-down companion of the 3D fire lab. Same Rothermel physics module, same scenarios; here you see the predicted ellipse, the wind / slope / resultant vectors, a terrain cross-section with flames, and the spread laws as plots.

Tool (click or drag on the map)

Firebreak budget: 250 cells.

Weather and fuel

Cross-section line

Live readouts

Measured vs predicted

Re-runs the front solver on a flat, uniform grass plain at the current wind and moisture, and compares it with the closed-form Rothermel + Anderson ellipse written out separately in this page.

Controls

Ignite: click or tap the map to light a fire on grass, shrub or timber. Firebreak: drag to remove fuel in a line before the front arrives (burning cells cannot be cut). Look only: no changes.
Changing wind, direction or moisture mid-run changes only the future: burned ground stays burned and the front is re-solved from the current fire edge.
Map: dashed cyan = predicted ellipse from the ignition cell's own rates; blue / green / orange arrows = wind effect, slope effect and their vector sum (resultant spread direction). White lines = where the front was every hour.

The science

Rate of spread. Rothermel (1972): head-fire speed on flat ground without wind is a fuel property R₀ (here an illustrative round value per fuel), reduced by fuel moisture η_M = 1 − 2.59 r + 5.11 r² − 3.52 r³, r = M_f/M_x (zero at the moisture of extinction), and increased by wind and slope: R = R₀ η_M (1 + φ_w + φ_s). Wind factor φ_w = C (196.85 U)^B (β/β_op)^−E with mid-flame wind U in m/s; slope factor φ_s = 5.275 β^−0.3 tan²θ. The 10 m wind is cut to mid-flame height by a wind adjustment factor (grass 0.40, shrub 0.35, timber 0.25: typical sheltering values).

Fire shape. Wind and slope combine as vectors in φ (the arrows on the map). The equivalent effective wind gives the length-to-width ratio of Anderson (1983), L/W = 0.936 e^{0.2566 U_e} + 0.461 e^{−0.1548 U_e} − 0.397 (U_e in mph, capped at 8). Each burning point spreads as an ellipse with the ignition at its rear focus (Richards 1990): R(ψ) = R_head (1 − e)/(1 − e cos ψ), e = √(1 − (W/L)²). This is also the polar equation of the dashed ellipse on the map. The real front is the envelope of all those ellipses (Huygens principle), found as minimum ignition time over the grid (Dijkstra, 32-neighbour stencil, 25 m cells). Terrain and fuel patches bend the real front away from the ideal ellipse.

Intensity and flames. Byram's fireline intensity I = H w R (H = 18 000 kJ/kg, w = fuel consumed in kg/m², R in m/s) in kW per metre of front; flame length L_f = 0.0775 I^0.46 m. Above about 4 000 kW/m hand crews cannot work at the front; above 10 000 kW/m no ground attack works. In the cross-section, flames are drawn five times their computed length so they stay visible against the ridge.

Spotting. Burning cells may loft embers that land downwind. A simple seeded stochastic stand-in, not a validated ember-transport model.

What is simplified. Surface fire only (no crown fire, no fire-induced wind), one fuel per cell, uniform wind and moisture for 12 h, constant fuel loads, no suppression except your firebreak. R₀, wind factors, loads and residence times are illustrative, not a calibrated fuel model: use it to understand why fires behave this way, not to predict a real fire. The terrain is the height grid of the 3D model.