Increasing of the imaging rate of conventional atomic force microscopy (AFM) is almost impossible without impairing of the imaging quality, since the probe tip tends to lose contact with the sample. We propose to apply the additional nonlinear force on the upper surface of a cantilever, which will help to keep the tip and surface in contact. In practice this force can be produced by the precisely regulated airflow. Such an improvement affects the AFM system dynamics, which were evaluated using a mathematical model presented in this paper. The model defines the relationships between the additional nonlinear force, the pressure of the applied air stream and the initial air gap between the upper surface of the cantilever and the end of the air duct. It was found that the nonlinear force created by the stream of compressed air (aerodynamic force) prevents the contact loss caused by the high scanning speed or higher surface roughness, and at the same time has minimal influence on the interaction force, thus maintaining stable contact between the probe and the surface. This improvement allows to effectively increase the scanning speed by at least 10 times using a soft (spring constant of 0.2 N/m) cantilever by applying the air pressure of 40 Pa. If a stiff cantilever (spring constant of 40 N/m) is used, the potential of accuracy improvement reaches 92 times. This method is suitable for use with different types of AFM sensors and can be implemented practically without essential changes in AFM sensor design.