Thread: Discussion A non-aerodynamic proof that a lifting wing pushes down on the earth View Single Post
 Nov 17, 2012, 02:00 PM Registered User Germany, BW, Stuttgart Joined Mar 2012 1,081 Posts While there is no connection between centripetal acceleration and the change in pressure along the air's streamlines, there is a definite connection between centripetal acceleration and the change in pressure normal to the streamlines: pressure gradient perpendicular to flow direction = density * velocity^2 / radius of curvature Suppose you started at a point many spans above the wing. You would expect the pressure there to be roughly equal to atmospheric pressure. Imagine you followed a path to a point on the top of the wing by always moving perpendicular to the local flow direction. You could determine the pressure at that point on the wing by integrating the equation for the pressure gradient given above. As long as the streamlines predominantly curved downward, the pressure would decrease as you moved to the wing, meaning the pressure on the top of the wing would be less than atmospheric pressure. You could follow a similar path from well below the wing to the lower surface. As long as the streamlines again predominantly curved downward, the pressure would increase as you moved to the wing, meaning the pressure there would be greater than atmospheric pressure. By adjusting your starting point fore and aft, you could end up at any point on the surface of the wing. This would give you a (horribly inefficient) way to calculate the lift on the wing from the centripetal acceleration. This illustrates that the wing essentially creates an area of lower pressure on the top surface and a region of higher pressure on the lower surface by deflecting the air downward as it passes above and below the wing. Is there momentum exchange associated with this deflection? Absolutely. However, you have to remember that a 3D wing is elsewhere deflecting air upward, so you can't draw any conclusion about net momentum exchange.