Originally Posted by ciurpita
this is becoming frustrating ... do you need to consider the state of the air behind or to the side of the wing when trying to understand the mechanism of lift at the surface of the wing?
You dont need to consider the state of the air anywhere but right at the surface of the wing to calculate the lift. I think you do need to consider the air elsewhere if you want to understand what gives rise to the state of the air at the surface. I can't pretend that I really understand the mechanism behind lift. Nmasters said it well in the "Understanding Flaps" thread...
"Fluid dynamics is the hardest problem in classical physics."
I've written a lot in this thread, but I haven't been trying to peddle an explanation for lift. I've been trying to show that a simple explanation based on pure vertical momentum exchange is flawed.
I first encountered this problem as a graduate student in the following context... For a jet engine to produce a given amount of thrust, it needs to impart momentum to the air at a given rate. In imparting momentum to the air, the jet inevitably also imparts energy. If you can reduce the rate at which a jet engine imparts energy to the air, you can improve its propulsive efficiency. A jet that imparts a small change in velocity to a large mass of air can achieve the same momentum exchange with less energy expenditure than a jet that imparts a large change in velocity to a small mass of air (one of the reasons you see big engine diameters where fuel economy is important).
In a conversation with my thesis advisor, I tried extend this concept to a lifting wing. I suggested that a higher aspect ratio wing imparts less velocity to a larger mass of air and therefore can impart the same downward momentum with less energy. His reply was basically: "Interesting observation, but at what rate does a wing impart downward momentum to the air?". I answered: "At a rate equal equal to the lift... Obviously". He challenged me to actually calculate the air's rate of vertical momentum change. After going through the exercise, I was very surprised to find that my intuition (based on incorrect application of Newton's 2nd Law) was completely incorrect. It turns out that the rate at which the air's vertical momentum changes depends on how the air is bounded (even when the boundaries are very far from the wing).
I'm glad I had that conversation because it has helped me grasp some subtle features of a lifting wing that I otherwise would have missed.