About Bernoulli. It has been a number of years since I took the meassurements in a wind tunnel. There is a pressure difference due to the differences in speed on airfoils. But the delta p is not significant. I can't remember the exact number but I think it is down around 5% of the total force the airfoil creates. We also have to keep in mind that Bernoulli worked on experiments in enclosed systems like pipes. In open systems, like airfoils, very different things happen to the fluid flow. Carburetors, venturis, and subsonic jet engines all work on Bernoulli.
Two more things happen on an airfoil. One, it is very rare that an airfoil is heading into the apparent wind such that the lower surface (if it were flat) is perpendicular to the apparent wind. Since it usually has a positive angle of attack, the airfoils redirect the wind downward. These changing angles of attack are where the force vector diagrams come into effect. You are comparing drag force to lifting force. As the shapre presented to the apparent wind changes the magnitude of the drage force and the magnitude of th lifting force caused by the redirection of the wind chage drastically. I am not sure of the amount of lift this contributes to the total number as we had a hard time isolating just the underside of the airfoil in the wind tunnel.
Two, the coanda effect on the top of the wing. This is where the airfoil needs to have that curved geometry. We are all familiar with the water on the back of the spoon effect. The top of the wing is the back of the spoon and the air is the water. This being said, the air is then accelerated downward causing a force (F=ma). Again, I am not sure of the portion of the total lifting force this contributes, but I believe it is the majority of it.
Here's why... Wings stall. We know this happens when the air separates from the top surface of a wing. When tis happends, the coanda effect is lost and this component of the lift force is lost. If we look at Bernoulli here, we see there still is a delta p present. All of the separated air is trying to fill the void on the top of the wing. If you keep the airspeed the same, but increase the angle of attack until the airfoil stalls the lift will drastically drop off. By keeping the airspeed the same in a wind tunnel you remove the issue of too much drag for the engine to pull the wing through the air at sufficent speed, therefore removing one of the variable (velocity of the airfoil) from the equation.
Also, look at hydrofoils versus airfoils. Why do hydrofoils have to be much smaller in chord and thickness to create the same amount of lifting force? I'm not sure here, but wouldn't the delta p be less on the hydrofoil than on the airfoil? If this is true then the larger force must be produced by water having more mass than air and when you redirect it (accelerate it) downward it will produce a larger force according to F=ma.
Again. Wouter, thanks for having this discussion with me (and the bow lifting discussion). I am learning how to better explain my side. I hope everyone following is gleaning something as well about how sails work.