C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory

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1 ROAD MAP... AE301 Aerodynamics I UNIT C: 2-D Airfoils C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory AE301 Aerodynamics I : List of Subjects Wings and Airfoils Lift Curves Airfoils NACA Conventional Airfoils NACA Airfoil Data

2 Page 1 of 10 Wings and Airfoils NOMENCLATURE FOR WINGS (3-D) 3-D Wing Geometry Nomenclature: Leading edge (LE) Trailing Edge (TE) Airfoil (a cross section of wing) Recall that the lift, drag, and moment coefficient for 3-D wing can be defined as: L D M CL CD CM qs qs qsc NOMENCLATURE FOR AIRFOILS (2-D) 2-D Airfoil Geometry Nomenclature: Chord Line Mean Camber Line Chord (c) Thickness (t) Camber: (difference between chord line and mean camber line) For 2-D airfoil, the aerodynamic coefficients are per unit span basis: Lb L' Db D' Mb M ' cl cd cm 2 qc 1 qc qc 1 qc q c1 c qc Note: b = wing span

3 Page 2 of 10 Lift Curves LIFT OF AIRFOILS Lift on an airfoil depends on the following properties: V (freestream velocity) (freestream density) S (wing area) Hence, lift coefficients are normalized by these properties: C L L and qs c l L '. qc LIFT CURVE OF AIRFOILS The behavior of lift ( lift curve characteristics) depends on the following properties: (angle of attack) Lift-curve (or often called, cl - curve) provides important relationship between angle of attack and lift coefficient, under a certain condition of Reynolds number. Interestingly, lift-curve is fairly close to a linear line, as long as it is not under the stall condition (hence, we often assume it is a simple linear function in our aerodynamic analysis for simplification). (viscosity) Lift curve depends on the Reynolds number. a (freestream speed of sound, or compressibility ) Lift curve will also depend on the compressibility of the flow field (Mach number).

4 Page 3 of 10 Airfoils (1) AIRFOILS The shape of airfoil: the design of 2-D airfoil will have a significant impact on aircraft performance. Airfoils represent performance of a given cross-section of a wing. The shape of an airfoil has tremendous effects on the overall performance of wing (thus, airplane). Airfoils can be considered as a model for a unit span of an infinite wing of constant crosssection. The performance of an airfoil can be determined by a quasi-2-d wind tunnel tests. A Quasi-2-D is actually a 3-D, but constant cross section. Thus, the cross-sectional properties (i.e., lift, drag, and moment per unit length ) can be determined. GEOMETRIC AND AERODYNAMIC TWISTS OF WINGS Geometric twist of wing is varying angle of attack along the span, but retains the same airfoil. Aerodynamic twist of wing is varying airfoil (cross section of the wing) along the span, but retains the angle of attack.

5 Page 4 of 10 Airfoils (2) CAMBERED V.S. SYMMETRICAL AIRFOIL The camber in airfoil is the asymmetry between the top and the bottom curves of an airfoil. Cambered airfoils generate lift at positive, zero, or even small negative angle of attack, whereas a symmetric airfoil only has lift at positive angles of attack. a 0 dc l : lift curve slope the slope of the cl curve (straight line) d The lift curve slope of a thin airfoil (either symmetric or cambered) is: a 2 (1/rad) = (1/deg) 0 L 0 : zero lift angle of attack ( alpha zero-lift ) the angle of attack (negative value), where the cambered airfoil generates no lift. LIFT EQUATIONS Assuming the linear relationship between angle of attack () and lift coefficient (cl), one can estimate the lift coefficient at a given angle of attack: For symmetrical airfoil ( L 0 0 ): a cl 0 For cambered airfoil ( L 0 0 ): cl a0 L 0 NOTE: these lift equations are based on assumptions that angle of attack () and lift coefficient (cl) are perfectly in linear relationship (these are simple linear algebraic equations, such as: y ax b ). Is it always true???

6 Page 5 of 10 Class Example Problem C-1-1 Related Subjects... Airfoils Can airplane fly upside-down? To answer this question, make the following simple calculation. Consider a positively cambered airfoil with a zero-lift angle of attack of 3 degrees. The lift slope of this airfoil is 0.11 per degree. (a) Calculate the lift coefficient at an angle of attack of 10 degrees. (b) Now imagine the same airfoil turned upside-down, but at the same 10 degrees angle of attack as part (a). Calculate its lift coefficient. (c) At what angle of attack must the upside-down airfoil be set to generate the same lift as that when it is right-side-up at a 10 degrees angle of attack? (a) Assuming the linear relationship between cl (valid only in the certain range of ): c a ( ) 0.11[10 ( 3)] 1.43 l 0 L 0 (b) Upside-down means that the airfoil is now negatively cambered. The zero lift AOA is now + 3 degrees. Thus, 10 degrees AOA is essentially equivalent to only 7 degrees AOA, so: cl a0( L 0) 0.11[10 ( 3)] 0.77 (c) In order to maintain the same lift coefficient (1.43 at 10 degrees AOA), the upside-down airfoil must be pitched to a higher AOA. c a ( ) l 0 L 0 cl 1.43 => L 0 (3) 16 (degrees) a0 0.11

7 Page 6 of 10 NACA Conventional Airfoils NACA 4-Digit Series: NACA X X XX One digit describing maximum camber (in % of chord). One digit describing the distance to the maximum camber location measured from the leading edge (in 10% of chord). Two digits describing maximum thickness of the airfoil (in % of chord). NACA AIRFOIL DATA NACA 5-Digit Series: NACA X XX XX One digit, when multiplied by 1.5, gives the lift coefficient in 1/10. Two digits, when divided by 2, describe the distance to the maximum camber location measured from the leading edge in 1/10 of chord. Two digits describing the maximum thickness of the airfoil in % of chord. NACA airfoils are airfoil shapes developed by the National Advisory Committee for Aeronautics (NACA). The lift, drag, and moment coefficients for these airfoils were obtained through wind tunnel tests conducted in 1950s (NACA Report 824). NACA FOUR/FIVE DIGIT SERIES AIRFOILS The normalized coordinates (x/c, y/c) of NACA 4 digit or 5 digit series conventional airfoils can be computer-generated (NASA-96-TM4741). NACA 4/5 digit series airfoils are usually called as: NACA Conventional Airfoils. NACA conventional airfoils have maximum thickness (usually) at quarter chord. For a conventional airfoil, the maximum thickness location is designed to be at the location of aerodynamic center. If the maximum thickness location is moved (usually aft not forward ), the airfoil design is usually considered non-conventional (i.e., NACA 6-series Natural Laminar Flow or NLF airfoils).

8 Page 7 of 10 NACA Airfoil Data THIS FIGURE IS FOR EXPLANATION PURPOSES ONLY = NOT VERY ACCURATE!!! OTHER NACA AIRFOILS NACA 1-Series: Mathematically derived airfoil shape from the desired lift characteristics. Prior to this, airfoil shapes were only determined using a wind tunnel. NACA 6-series: An improvement over 1-series airfoils with emphasis on maximizing natural laminar flow (NLF). Maximum thickness is moved (close) to the half chord location. NACA 7-series: Further advancement in maximizing laminar flow achieved by separately identifying the low pressure zones on upper and lower surfaces. NACA 8-series (NASA-SC): Supercritical (SC) airfoils designed to optimize transonic flow characteristics.

9 Page 8 of 10 Class Example Problem C-1-2 Related Subjects... NACA Airfoil Data A model wing of constant chord length is placed in a low speed subsonic wind tunnel, spanning across the test section (this is called, a quasi-2-d test). The wing has a NACA 4412 airfoil and a chord length of 1.0 m. The test section airspeed is 44 m/s at standard sea-level condition. If the wing is at a 2 degrees angle of attack, determine: (a) c l, c d, and c m,c/4 (b) the lift, the drag, and the moment about the quarter chord (per unit span) NACA 4412 (a) At standard sea-level condition with 44 m/s airspeed: = kg/m 3 = kg/ms c = 1.0 m Vc (1.225)(44)(1) The test section Reynolds number: Re = Let us look at the NACA 4412 airfoil data (Reynolds number ): At 2 degrees of AOA: cl = 0.6 cd = cm,c/4 = 0.08

10 Page 9 of 10 Class Example Problem C-1-2 (cont.) Related Subjects... NACA Airfoil Data 2 2 (b) The dynamic pressure is: q 1 V 1 (1.225)(44) = 1,185.8 N/m Therefore, L' qcc l (1,185.8)(1)(0.6) = N (per unit span) D' qcc d (1,185.8)(1)(0.0067) = N (per unit span) M ' qc c (1,185.8)(1) ( 0.08) = N (per unit span) 2 2 c/4 m, c/4

11 Page 10 of 10 Class Example Problem C-1-3 Related Subjects... NACA Airfoil Data Once again, can airplane fly upside-down? To answer this question, we will use the same wind tunnel test as in Class Example Problem C-1-2. Consider NACA 4412 airfoil. (a) Determine the lift coefficient at an angle of attack of 10 degrees. (b) Now imagine the same airfoil turned upside-down, but at the same 10 degrees angle of attack as part (a). Determine its lift coefficient. (c) At what angle of attack must the upside-down airfoil be set to generate the same lift as that when it is right-side-up at a 10 degrees angle of attack? NACA 4412 Upside-down flight is equivalent to the NACA data in the range of negative angle of attack. The only difference is that the negative angle of attack produces downforce (means negative lift coefficient), while upside-down flight produces lift (positive lift coefficient). Thus, one can read-out the lift coefficient from the NACA data (in the range of negative angle of attack). (a) From NACA 4412 data (assuming the Reynolds number ): At 10 degrees => cl 1.34 (b) If the data is read-off from negative angle of attack: At 10 degrees => c 0.64 l (c) Impossible. The airfoil stalls out at about negative angle of attack of 12 degrees (maximum c 0.8 ) l