Byram's Fireline Intensity

Fireline intensity is the heat a wildfire releases each second along each metre of its front. It is the product of the heat each kilogram of fuel gives, $H$ (kJ/kg), the mass of fuel burned from each square metre, $w$ (kg/m²), and the rate of spread, $R$ (m/s). Multiply them and the units come out as kW per metre of fire front. Each factor scales the answer in direct proportion.

Reading the answer. This is a physical intensity for a fire that is already burning, unlike the Canadian fire weather index, which rates the weather. The Forest Service's explanation of the Rothermel fire spread model uses the equation for the head of the fire. The intensity sets the flame length, which grows with the intensity to the power 0.46 (see Byram's flame length). The fuel term needs care: $w$ is the fuel consumed in the flaming front, not the whole of the fuel that is on the ground.

Worked examples. A fire that spreads at 0.5 m/s (30 m/min) through fuel that burns away 1 kg/m² at 18 000 kJ/kg has an intensity of 9 000 kW/m. The page also solves backward: 9 000 kW/m with 1 kg/m² and 30 m/min gives a heat yield of 18 000 kJ/kg. The Forest Service's own form uses Btu per pound, pounds per square foot and feet per second: 8 000 Btu/lb (the commonly used value, 18 600 kJ/kg) times 0.5 lb/ft² times 0.5 ft/s is 2 000 Btu per foot per second, which is 7 200 000 Btu per hour per foot, or 6 921 kW/m.

Source and limits. George Byram (1959, page 79) presented the model as $I = H\,w\,R$. It appears in the same form in Andrews (2018), the Forest Service report RMRS-GTR-371, section 4.4, and Alexander (1982) covers calculating and interpreting forest fire intensities. The number describes the front, per metre of its length, and it is only as good as its inputs, especially the fuel actually burned.