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Unformatted text preview: AA 311 Lecture 7: Drag; Finite Wing Effects; Induced Drag; Efficiency Factor Reading:  Chapter 5. Total drag on an airfoil can be written as the sum: D = D f + D p + D w , where • D : total drag on airfoil. • D f : skin friction drag. • D p : pressure drag (sometimes called form drag ). • D w : wave drag (present only at transonic and supersonic speeds; zero for subsonic speeds). At subsonic speeds the wave drag can be neglected, and we have D = D f + D p . The sum D f + D p is sometimes called profile drag , because it depends on the shape and size of the body, that is, the profile of the body. In terms of drag coefficient, we have c d = c d,f + c d,p . Remember that these coefficients are referenced for airfoils that are assumed to be unit span segments of an infinitely long wing, such that the flow is uniform everywhere in the span-wise direction. The question arises: Can we apply the same coefficients for a finite wing? That is, suppose we are given data for a NACA 2412 airfoil at α = 6 ◦ angle of attack: c l = 0 . 85 c d = 0 . 0077 . If we build an actual wing using NACA 2412 airfoil sections, will the lift and drag coefficients be C L = 0 . 85 C D = 0 . 0077 ? The answer is no, due to the finite wing effects discussed presently. Finite Wings The fundamental difference between flows over finite wings as opposed to infinite wings is the effect of wing-tip vortices. Consider Figure 1a. The pressure difference between the top and bottom surface causes air to leak around the edge, from bottom to top. The leakage creates vortices at the wing tips, each with opposite sense to the other. The effect of these wingtip vortices is that they introduce a small downward component of flow velocity in the neighborhood of the wing itself. This downward component of velocity is called downwash , and is denoted by the symbol, w . The effect of downwash is shown in Figure 2. Here V ∞ denotes the relative wind, however near the immediate vicinity of the wing, V ∞ and w add together to produce the “local” relative wind that is deflected downward from the original free-stream velocity. The consequences of downwash are: • The angle of attack is effectively reduced. 1 Figure 1: Wingtip vortices produced by finite wings. • There is an increase in drag. This increase is called induced drag . The term induced drag comes from the fact that the deflection of the relative wind downward results in the lift vector being tilted backwards, and hence the lift vector contributing a small amount to the total drag. This way dragbackwards, and hence the lift vector contributing a small amount to the total drag....
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- Fall '09
- Aerodynamics, Lift, Airfoil, Wing design