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Unformatted text preview: AA 311 Lecture 6: NACA Airfoils; Pressure Coefficient; High-lift De- vices; Aerodynamic Similarity Reading:  Chapter 5. The National Advisory Committee for Aeronautics (NACA) was founded in 1915 as a federal agency aiding the advancement of the aeronautical sciences. Today NACA doesnt exist any more, its role, assets and personnel was overtaken by the newly established National Aeronautics and Space Administration (NASA) in 1958. In the early years of aeronautics, NACA was responsible for developing standards and recommendations, many of which are still in use today. Among others, NACA developed a large bulk of experimental data for many airfoil shapes in low-speed subsonic wind tunnels. The measurements for lift, drag, and moment coefficient were carried out for constant-chord wings that entirely spanned the tunnel test section from one wall to the other. Thus the flow essentially saw an infinite wing section, where the wingtip effects of a finite wing (discussed in a later lecture) were not included. NACA airfoils were designed from 1929 through 1947 under the direction of Eastman Jacobs at NACAs Langley Field Laboratory. NACA airfoils are constructed by combining a chord-wise thickness envelope along the mean camber line. The equations that describe this procedure are Chord-wise length: x . Thickness function: y t ( x ). Camber line function: y c ( x ). Camber line slope: = arctan dy c dx . (1) Upper surface: x u = x- y t ( x )sin (2) y u = y c ( x ) + y t ( x )cos . (3) Lower surface: x l = x + y t ( x )sin (4) y l = y c ( x )- y t ( x )cos . (5) The NACA 4-digit series The NACA 4-digit series numbering system is the following: NACA MPXX M : Maximum camber in percent of chord. P : Position of maximum camber in 10ths of chord. XX : Is the maximum thickness ratio, t/c in percent of chord. For example, Figure 1 shows a NACA 2415 airfoil. The airfoil has a maximum thickness ratio of 15%, that is t/c = 0 . 15. The maximum camber is 0 . 02 c that is located at 0 . 4 c , that is 40% aft measured from the leading edge. 1 Figure 1: NACA 2415 4-digit series airfoil. For the NACA 4-digit series the camber line is given by the following formula. If x/c < P y c /c = M P 2 2 P ( x c- x c 2 (6) dy c dx = 2 M P 2 P- x c (7) If x/c P y c /c = M (1- P ) 2 1- 2 P + 2 P ( x c- x c 2 (8) dy c dx = 2 M (1- P ) 2 P- x c (9) The NACA 4-digit thickness distribution is given by y t c = t c a r x c- a 1 x c- a 2 x c 2 + a 3 x c 3- a 4 x c 4 , where a = 1 . 4845 a 1 = 0 . 6300 a 2 = 1 . 7580 a 3 = 1 . 4215 a 4 = 0 . 5075 . The camber line slope is found from equation (1) using (7) and (9). The upper and lower surface ordinates are then computed using equations (2)-(5). This is precisely the method how the airfoil shape in Figure 1 was obtained....
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This document was uploaded on 02/05/2012.
- Fall '09