Nowadays, the needs for decision making tools useful for people involved in firefighting and/or in landscape management becomes more and more crucial, especially with the dramatic increase of the fire dangerousness and fire severity. These tools have to be accurate enough and faster than real time. Up to now, simulators and other tools are mainly based on empirical or semi-empirical models but the lack of physics in their formulation is a major flaw. The Balbi model is a simplified physical propagation model for surface fires which explicitly depends on the topography, the wind velocity and several fuel characteristics. It is a set of algebraic equations built from usual physical conservation laws (mass, momentum etc.) with some strong assumptions. This work aims at providing a new version of the Balbi model in which the resolution of the rate of spread (ROS) does not need any iterative method any more. This simplification is helpful in implementing the equations set into a fire propagation simulator or a coupled fire-atmosphere simulator. It needs a complete change in the structure of the model and the predicted ROS was tested at the field scale against 179 shrubland fires (burnt in Australia, South Africa, Turkey, Portugal, Spain, New Zealand) and 178 Australian grassland fires with a very good agreement with the observed ROS. Two statistical tools are used to check this agreement (Normalized Mean Square Error, NMSE and Mean Absolute Percentage Error, MAPE) and the Fractional Bias (FB) aims at understanding when the model over-predicts or under-predicts the ROS. The proposed model is accurate and its model parameters are calibrated against a small training dataset which makes it fully predictive whatever the environmental and topographic conditions and the fuel bed characteristics. Its more simple structure allows it to be a good candidate for the heart of a simulation or land management decision making tool.