Lift for a Finite Wing SRM University（提升为一个有限的翼SRM大学）.pdfVIP

Lift for a Finite Wing • all real wings are finite in span (airfoils are considered as infinite in the span) The lift coefficient differs from that of an airfoil because there are strong vortices produced at the wing tips of the finite wing, which trail downstream. These vortices are analogous to mini-tornadoes, and like a tornado, they reach out in the flow field and induce changes in the velocity and pressure fields around the wing Imagine that you are standing on top of the wing you will feel a downward component of velocity over the span of the wing, induced by the vortices trailing downstream from both tips. This downward component of velocity is called downwash. The local downwash at your location combines with the free-stream relative wind to produce a local relative wind. This local relative wind is inclined below the free- stream direction through the induced angle of attack αi . Hence, you are effectively feeling an angle of attack different from the actual geometric angle of attack of the wing relative to the free stream; you are sensing a smaller angle of attack. For Example if the wing is at a geometric angle of attack of 5°, you are feeling an effective angle of attack which is smaller. Hence, the lift coefficient for the wing is going to be smaller than the lift coefficient for the airfoil. This explains the answer given to the question posed earlier. High-Aspect-Ratio Straight Wing The classic theory for such wings was worked out by Prandtl during World War I and is called Prandtls lifting line theory. dc a0 l airfoil lift slope per radian and e1 is a factor that dα depends on the geometric shape of the wing, dC including the aspect ratio and taper ratio. L a wing dα 2 Prandtls lifting line theory does not apply to b A