Lift is created by forcing air downward. The pushing (accelerating) of the air downward creates an equal and opposing force upward on wing (see Newton's third law.) The displacement of air downward during the creation of lift is known as downwash. The diversion of the airflow downwards can be seen to create a higher pressure below the wing and a lower one above it. An aerofoil is so shaped to accomplish this as efficiently as possible. One puzzle is why the airflow "sticks" to the wing as it changes direction - this is known as the Coanda Effect, but the reason for it is not fully understood.
Any shape will produce lift if tilted to the air flow direction (inclined) or cambered (curved). However, most shapes will be very inefficient and waste a great deal of energy in the creation of drag. Lift itself creates drag - this is called lift-induced drag, or just induced drag.
The force on the wing can also be found using the pressure differences above and below the wing. This method of explanation is mathematically equivalent to the Newton's 3rd law explanation as developed above. The relationship between the velocities and pressures above and below the wing are nearly predicted by Bernoulli's Equation. The differences between the Bernoulli-predicted values and the true values are small and related to viscosity, which is neglected in the Bernoulli equation. However, one common misconception is that the pressure differences result from the velocity changes needed for the air that separates at the front of the airfoil to meet at the trailing edge. This does not happen, in fact, if it were to happen, no lift would be generated, as explained in the circulation section below.
A third way of conceptualizing lift is a mathematical construction called circulation. Again, it is mathematically equivalent to the two explanations above. It is often used by practicing aerodynamicians as a convenient quantity, but is not often useful for a layperson. The circulation is the line integral of the velocity of the air, in a closed loop around the boundary of the airfoil. It can be understood as the total amount of "spinning" of air around the airfoil. When the vorticity is known, the section lift can be calculated using:
where is the air density, is the free-stream airspeed, and is the circulation.
The boundary layer is a thin region close to the airfoil, defined for convenience in order to ignore viscosity outside the boundary layer. There are two types of flow in the boundary layer. Around the leading edge the air flows smoothly and behaves like a stack of sheets (laminae) sliding over each other - laminar flow. Further along the wing there is a transition to a turbulent flow. The laminar layer produces less drag, but the turbulent layer more stable, that is, less likely to move away from the surface. As flow speed increases the boundary layer starts to separate at the trailing edge of the wing and a vortex begins to form, moves back and then leaves the surface. This is the starting vortex which disrupts the symmetry of the air flow, causing differences in flow pressure and speed between the upper and lower surfaces of the wing - Lift. The vortex extends in a closed circuit of two real vortices trailing from near the wing tips (wing-bound vortex) and the starting vortex, forming a horseshoe shape and sometimes called the horseshoe vortex system.
Aerodynamicians are one of the most frequent users of dimensionless numbers. The coefficient of lift is one such term. When the coefficient of lift is known, for instance from tables of airfoil data, lift can be calculated using the Lift Equation: