A methodology for the estimation of ignition delay times in forest fire modelling

A methodology for the estimation of ignition times on solid materials is presented. It is based on the observation that the time to ignition is proportional to the squared time integral of the incident heat flux. This relationship can be readily demonstrated for the classical solutions for time to ignition which consider constant incident heat fluxes. Thus, ignition times can be calculated only with the knowledge of the incident heat flux on the sample (gas-phase calculations) and experimental ignition results. This method is particularly useful when modelling wildfire propagation, where grid resolution is larger than some solid objects. Analytical solutions of the transient conduction problem for constant and ramping incident heat fluxes are discussed. The proportionality between the time to ignition and the squared integral of the incident heat flux was verified experimentally for constant and time-varying incident heat fluxes, showing that the proposed methodology can be applied to both cases. The methodology is outlined and an example is presented.