Elliptical Wildfire Perimeter Growth & Moisture Extinction

Fuel & Weather

Dead fuel moisture M_f 8%

Wind speed 15 km/h

Slope 10°

Fire Behavior

Unignited

Head-fire ROS

0.0 m/min

Damping η_M

100%

Area burned

Length : Breadth

1.00

How it works

This companion sim traces the fire perimeter itself instead of a grid of cells. A single ignition point grows outward every frame as a Huygens-wavelet fire ellipse — the analytic front-tracking method (Richards 1990) used by real spread-prediction tools such as FARSITE — rather than a cellular automaton. In uniform wind, an unobstructed ignition point always grows into an ellipse with the ignition point sitting at one focus, not the centre, so the head and the back of the fire race away from the origin at different rates:

R(θ) = R_head · (1 − e) / (1 − e·cos θ)      θ measured from the downwind bearing
R_back = R(π) = R_head · (1 − e) / (1 + e)

The eccentricity e comes from the fire's length-to-breadth ratio, itself a real published empirical fit — Anderson's (1983) formula against effective wind speed U (mph), also the ratio BehavePlus and FARSITE use internally:

L∶B = 0.936·e^(0.2566U) + 0.461·e^(−0.1548U) − 0.397
e   = √(L∶B² − 1) / L∶B

R_head itself is scaled by the same Rothermel moisture damping coefficient η_M as the 3D companion sim — sampled locally at each point on the growing perimeter, not just at the ignition cell:

η_M = 1 − 2.59·r + 5.11·r² − 3.52·r³,   r = M_f(x,y) / M_x
η_M = 0  once r ≥ 1  (that stretch of perimeter cannot advance)

Because moisture is sampled independently along every bearing from the ignition point, the perimeter genuinely stalls and dents inward wherever it meets a damp pocket while the rest of the front keeps racing ahead — a distinctly different failure signature from the 3D grid's blocky cell-by-cell extinguishing, even though both share the same underlying physics.

M_f slider — raises moisture everywhere; push the head-fire direction past M_x≈30% and R_head collapses to zero.
Wind / Slope — combined into one effective wind vector that sets both the L∶B ellipse shape and the head-rate multiplier — a genuinely different combination rule from the 3D sim's separate φ_w·φ_s multipliers.
Ignite — starts a single point fire at the upwind edge; Reset Fuel Bed reseeds the moisture terrain and clears the burn.

Simplified teaching adaptation — real analysts still need fuel load, surface-area-to-volume ratio and heat content to get quantitative rates; the elliptical growth method itself, however, is exactly the one professional tools use to propagate a fire perimeter through time.

Unburned fuel (moist → dry) Actively burning front Burned out Perimeter (fire ellipse edge)