Generalized Byram's formula for arbitrary fire front geometries

• A formula generalizing the Byram's law is mathematically derived and validated by numerical simulations of fire spread.
• This formula extends the estimation of the heat release rate to an arbitrary geometry of the front.
• The scaling behaviour allows the heat release estimation from the fractal dimensions of satellite or airplane images.
• The front curvature radius, its convexity/concavity influences significantly the heat release rate.
• A reformulation using predictive parameters such as the wind speed is proposed.

The expression proposed a half century ago by Byram allowing the estimation of wild land fire front heat flux was extensively used in fire research and by firefighters. However, this formula does not account for wild land fuel heterogeneity and local weather changes. Its validity is limited to stationary spreads, and fails in describing the behavior of curved fronts and non-spreading fires. A new formula is derived to generalize heat flux estimation to any fire front with arbitrary geometry. Heat flux is found to depend on the front local radius as well as its convexity/concavity. The front curvature induces also a quadratic dependence on the rate of spread. The derived equation is validated by numerical simulations using the small world network model for line and curved fronts. Extensions of generalized Byram formula including fractal dimension of the front and wind speed effect are also proposed.