Since the above observed flow phenomena are related to lift, a good explanation of lift should naturally incorporate all these interrelated physical aspects into a unified framework. Of course, the well-known empirical fact is that surface pressure on the upper surface is lower than that on the lower surface, and the pressure difference between the upper and lower surfaces is the main source of lift. It is also observed that the incoming flow is deflected downward in the wake of the airfoil, while the incoming flow near the leading edge is induced upward. The two pieces of a marker line separated at the leading edge never meet at the trailing edge, and the marker line on the upper surface moves much faster. 1, the flow field around the airfoil is visualized by vertical maker lines (oil-smoke lines or dye lines in experiments) generated upstream at sequential times. A direct evidence on the faster motion of fluid particles can be obtained in flow visualizations.

The cross sectional area of streamline tubes on the upper surface is reduced near the leading edge and enlarged downstream. Streamlines are significantly influenced by the airfoil, and the cross sections of streamline tubes are pinched. Figure 1 illustrates the flow over an airfoil with streamlines, marker lines and aerodynamic force vectors. To understand the physical mechanisms of lift generation, the phenomenological aspects of the flow over an airfoil should be described based on flow visualizations and computational fluid dynamics (CFD) simulations. The aerodynamic force (lift and drag) of an airfoil is generated as a result of interaction between the incoming flow and airfoil. Therefore, it is still required to elucidate the physical mechanisms of lift generation. These explanations capture certain physical aspects of lift generation at different levels of fidelity, but they fail to reconstruct a complete and consistent picture with all the main physical processes. There are various popular explanations for lift generation. This is evidenced by the widely popularized myth that the laws of aerodynamics prove that the bumblebee cannot fly. Unfortunately, people who are interested in flight are still misled by some misconceptions and even wrong “theories” in non-technical literature. Since modern aviation has become relatively mature, people might think that how lift is generated seems such a trivial question that they could find a standard answer by just searching on the Internet. The recurring questions on how aerodynamic lift is generated might have arisen when people wonder how birds and bats could fly effortlessly. The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition. The vortex-force theory is described to provide a solid foundation for consistent treatment of lift, form drag, Kutta condition, and downwash. In particular, the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed, including Newton’s sine-squared law, Rayleigh’s lift formula, thin-airfoil theory and viscous-flow lift formula. The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model. This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations, particularly focusing on the critical effect of the fluid viscosity.

Airfoil diagram