tgrayson
New Member
I know very little about Fourier analysis, so I can't give you a blow by blow. But the basic idea is that of a "vortex sheet", an infinite number of vortices that have an axis of rotation along the wing span. The math sums up their effects. The up and down portions cancel, but the part tangential to the wing do not, resulting in the velocities across the top and bottom of the airfoils.
John D. Anderson's "Fundamentals of Aerodynamics devotes a dozen or so pages to the math, if you're interested. But at the end, he says
Therefore, the local velocities tangential to the airfoil surface are equal to the local values of γ (gamma). In turn, the local pressure distribution can be obtained from Bernoulli's equation.
The significance of the above depends on his previous emphasis, such as
In Section 1.5, we emphasized that the resultant aerodynamic force on a body immersed in a flow is due the the net integrated effect of the pressure and shear stress distributions over the body surface. Moreover, in "Section 4.1, we noted that lift on an airfoil is primarily due to the surface pressure distribution, and that shear stress has virtually no effect on lift. It is easy to see why. Look at the airfoil shapes in Figures 4.12 and 4.13, for example. Recall that the pressure acts normal to the surface, and for these airfoils the direction of this normal pressure is essentially in the vertical direction, that is, the lift direction. In contrast, the shear stress acts tangential to the surface, and for these airfoils, the direction of this tangential shear stress is mainly in the horizontal direction, that is, the drag direction. Hence, pressure is the dominant player in the generation of lift and shear stress has a negligible effect on lift. It is for this reason that the lift on an airfoil below the stall can be accurately predicted by inviscid theories such as that discussed in this chapter.
Rather than debate theory with your buddies, you may find experimental data more user-friendly. I highly recommend "Theory of Wing Sections," which has lots of good stuff and is cheap.