How do wings work ?

This is an interesting article from the wonderful journal I posted in my last entry. It tries to poke the usual (even textbook) explanation of how wings work [2003 Phys. Educ. 38: 497].

Now Bernoulli’s equation is quoted, which states that larger velocities imply lower pressures and thus a net upwards pressure force is generated. Bernoulli’s equation is often demonstrated by blowing over a piece of paper held between both hands as demonstrated in figure 2. As air is blown along the upper surface of the sheet of paper it rises and, it is said, this is because the average velocity on the upper surface is greater (caused by blowing) than on the lower surface (where the air is more
or less at rest). According to Bernoulli’s equation this should mean that the pressure must be lower above the paper, causing lift. The above explanation is extremely widespread. It can be found in many textbooks and, to my knowledge, it is also used in the RAF’s instruction manuals. The problem is that, while it does contain a grain of truth, it is incorrect in a number of key places.

What’s wrong with the ‘popular’ explanation?
The distance argument;
The ‘equal time’ argument;
The Bernoulli demonstration.

Next, examine a particle moving along a curved streamline as shown in figure 7. For simplicity we can assume that the particle’s speed is constant3. Because the particle is changing direction there must exist a centripetal force acting normal to the direction of motion. This force can only be generated by pressure differences (all other forces are ignored), which implies that the pressure on one side of the particle is greater than that on the other. In other words, if a streamline is curved, there must be a pressure gradient across the streamline, with the pressure increasing in the direction away from the centre of curvature.