I’ve heard two explanations for how flight is achieved: (A) through lift generated by differential pressure (Bernoulli’s effect) and (B) through elastic collisions between air molecules and the underside of a wing. Which is correct? How does the fact that planes can fly upside down enter into this picture?
Explanation A is entirely correct and explanation B is partly correct. If you extended explanation B to include all collisions between air molecules and the entire wing, then it would also be correct. Explanation A is the continuous fluid picture of flight and the revised explanation B is the granular fluid picture of flight. To the extent that gases are incompressible fluids (as required for Bernoulli’s equation to be completely valid), these two explanations are essentially equivalent.
The lift experienced by a plane’s wing depends on its shape and on its tilt or “angle of attack” into the wind. In general, wings are airfoils—curved shapes that are designed to obtain significant lift forces while experiencing minimal drag forces. Most airplane wings are more highly curved on their tops than on their bottoms and obtain upward lift forces as a result. These lift forces occur because the stable airflow that forms around such a wing involves faster-moving and thus lower-pressure air above the wing than beneath it. However, some airplane wings are symmetric—they have equal curvatures on top and on bottom. These symmetric wings compensate for their symmetry by attacking the air at an angle. When they are tipped so that their leading edges are higher than their trailing edges, these wings also experience upward lift forces. The air again flows more rapidly over than under the wings and the pressure is lower above the wings than beneath them. Even an inverted non-symmetric wing can adjust its angle of attack to obtain an upward lift force, which is how a plane can fly upside down.
In all of these cases, the forces are really exerted on the plane’s wings by the impacts of countless air molecules. These air molecules hit harder and more often beneath the wings than above them and thus exert a net upward force on the plane. The fact that some wings have more surface area on their highly curved tops doesn’t lead to larger downward forces because many of the collision forces exerted by molecules on the top surface of the wing cancel one another, in the same way that forces exerted on opposite sides of a sheet of paper cancel one another.