Background Previously published versions of the ‘Balbi model’ describing surface fire propagation consist of a set of equations based on simplified conservation laws. Their main equation calculating the fire rate of spread (ROS) relied on an iterative process to account for the effect of environmental drivers. Aims We formulated a new version of this model that considers a 3D flame front composed of peaks and troughs, integrates distinct radiation and convection heat transfer mechanisms, and outputs the physical characteristics of a flame front as they are influenced by weather, fuel and topographical conditions. A simpler operational version, composed of only one equation, is also exhibited. Methods While maintaining its characteristics (physics-oriented, fully predictive and faster than real time) from older versions, the global structure of the proposed model is changed to obtain a set of algebraic equations easy to solve and to code. Key results We described the model and provided an analysis of model response to key environmental variables. Model evaluation against independent data is provided in a companion paper. Conclusions A simplified physical propagation model for surface fires has been exhibited. Implications The algebraic nature of the model’s equations makes it suitable to incorporate into fire management decision-making tools to support suppression activities.