The Rothermel Equation Divides Propagating Heat Flux by a Fuel Heat Sink
Rothermel's 1972 surface-fire model is an energy balance written as a ratio. The numerator is the heat arriving at the unburned fuel just ahead of the front, written as the reaction intensity \( I_R \) — the heat released per unit area per unit time inside the flaming zone — multiplied by the propagating flux ratio \( \xi \), the fraction of that heat that actually reaches forward rather than radiating away. The denominator is the heat sink: the bulk density of the fuel bed \( \rho_b \) times the effective heating number \( \epsilon \) times the heat of preignition \( Q_{ig} \), which is the energy needed to dry and raise one kilogram of fuel to ignition. In the no-wind, no-slope case the spread rate is \( R_0 = \frac{I_R \xi}{\rho_b \epsilon Q_{ig}} \). The confusion this resolves: spread rate is not a measure of how hot the fire is, it is a race between heat delivered and heat demanded, so a hot fire in wet, dense fuel spreads slowly. Fuel moisture raises \( Q_{ig} \) and is the term that stops the fire at the moisture of extinction. After this Concept you can name each term in the Rothermel ratio and say which way spread rate moves when it changes.
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Rothermel's 1972 surface-fire model is an energy balance written as a ratio. The numerator is the heat arriving at the unburned fuel just ahead of the front, written as the reaction intensity \( I_R \) — the heat released per unit area per unit time inside the flaming zone — multiplied by the propagating flux ratio \( \xi \), the fraction of that heat that actually reaches forward rather than radiating away. The denominator is the heat sink: the bulk density of the fuel bed \( \rho_b \) times the effective heating number \( \epsilon \) times the heat of preignition \( Q_{ig} \), which is the energy needed to dry and raise one kilogram of fuel to ignition. In the no-wind, no-slope case the spread rate is \( R_0 = \frac{I_R \xi}{\rho_b \epsilon Q_{ig}} \). The confusion this resolves: spread rate is not a measure of how hot the fire is, it is a race between heat delivered and heat demanded, so a hot fire in wet, dense fuel spreads slowly. Fuel moisture raises \( Q_{ig} \) and is the term that stops the fire at the moisture of extinction. After this Concept you can name each term in the Rothermel ratio and say which way spread rate moves when it changes.
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