Precision measurements of a nanoscale sample surface using an atomic force microscope (AFM) require a precise quantitative knowledge of the 3D tip shape. Blind tip reconstruction (BTR), established by Villarrubia, gives an outer bound with larger errors if the tip characterizer is not appropriate. In order to explore the errors of BTR, a series of simulation experiments based on a conical model were carried out. The results show that, to reconstruct the tip precisely, the cone angle of the tip characterizer must be smaller than that of the tip. Furthermore, the errors decrease as a function of the tip cone angle and increase linearly with the sample radius of curvature, irrespective of the tip radius of curvature. In particular, for sharp (20 nm radius) and blunt (80 nm radius) tips, the radius of curvature of the tip characterizer must be smaller than 5 nm. Based on these simulation results, a local error model of BTR was established. The maximum deviation between the errors derived from the model and the simulated experiments is 1.22 nm. Compared with the lateral resolution used in the above simulated experiments (4 nm/pixel), it is valid to ignore the deviations and consider the local error model of BTR is indeed in quantitative agreement with the simulation results. Finally, two simulated ideal structures are proposed here, together with their corresponding real samples. The simulation results show they are suitable for BTR.