The erosive burning of ammonium perchlorate (AP) inert binder propellants is considered both experimentally and from the modeling viewpoint. The full modelization, developed earlier, is applied for various scales and reveals a pronounced scale effect. From these numerical results and preceeding others, a correlation law is thus extracted which gives an estimate of the wall shear stress with strong injection. This is the root of the concise model, in which a local one-dimensional description of the wall zone (including the combustion flame) is fed with the sole knowledge of the mean specific mass flow rate in the channel above the propellant. It shows that the propellant normal burning rate is the main parameter which influences the erosive burning response. Furthermore, this normal burning rate has a direct influence on the threshold for erosive burning. From this simple concise model, the influence of the scale upon the threshold is included in a universal correlation with appropriate nondimensional parameters, as found previously with complex turbulent flow computations.