Most reduced forest fire spread models, Such as the Rothermel model (Rothermel, 1972) have been developed to provide the stationary rate of spread such as the fire is propagating at the equilibrium between the fuel consumption and the energy of ignition. Nevertheless, some of the assumption (flat radiating panel, front depth corresponding to the residence time) may not be appropriate in real world condition where the topography, wind speed, wind direction and vegetation is constantly changing. This paper proposes a formulation of a physical rate of spread model that explicitly takes into account the front depth and local curvature in order to prognoses the instantaneous, non stationary rate of spread. Three idealized simulations results run with the stationary and non-stationary model shows that the curvature, acceleration and front depth effects are well reproduced.