Introduction to Aeronautics ARO 101 Sections 03 & 04 Sep 30, 2015 thru Dec 9, 2015 Instructor: Raymond A. Hudson Week #8 Lecture Material 1
Topics For Week #8 Airfoil Geometry & Nomenclature Identify the geometrical measures that define airfoil configuration: Chord, Camber, Thickness, Angle of Attack, etc. NACA Airfoil Numbering System Describe the 4-digit NACA airfoil series, what each digit in the designator means, and what they taught us about airfoil performance. Pressure, Lift & Drag Coefficient Equations The non-dimensional measures that quantify aerodynamic performance of any given shape. Airfoil Lift Vs. AOA Curve How lift varies linearly with angle of attack. Align Lift Curve Slope & Lift@Zero AOA with y = mx + b Airfoil Drag Polar How drag varies parabolically with lift. Zero-lift drag & the drag polar equation: C D = C D0 + K*C L 2 Wind Tunnel Data Analysis I will show you how I used MS Excel to analyze the data and prepare the final calculations for creating X-Y plots. 2
Airfoil Geometry CERTAINLY These Would Make Good Quiz Material, Right? LE = Leading Edge LE TE = Trailing Edge TE Chord Line = The straight line that connects the LE to the TE. Chord Length (c) = The distance measured from the LE to the TE, along the chord line. Thickness (t) = The maximum distance between the US and the LS. 3
Airfoil Geometry CERTAINLY These Would Make Good Quiz Material, Right? Mean Camber Line (MCL) = A line that connects the LE to the TE, and is equidistant from upper and lower surfaces. a Relative Wind (Airspeed) Velocity Vector V Camber (y c ) = The maximum distance between the chord line and the mean camber line. Angle of Attack (a) = The angle measured between the chord line and the relative wind velocity vector. 4
NACA 4 Digit Airfoil Series Numbering Scheme NACA National Advisory Committee on Aeronautics. Precursor to NASA. One research project NACA performed was to quantify how airfoils perform. The 4 digit series NACA airfoils were first defined to understand how thickness and camber affect lift, drag, and pitching moment performance. Numbering Scheme: NACA XYZZ X = Maximum airfoil camber measured as percent of total chord. Y = Maximum camber distance from airfoil leading edge in tenths of chord. ZZ = Maximum airfoil thickness measured as percent of total chord. Example Airfoil: NACA 2412 y c /c = 0.02 (i.e. 2% camber) Location of y c = 0.4 x c from the LE t/c = 0.12 (i.e. 12% thickness) 5
Pressure Coefficient Equation Pressure Coefficient A non-dimensional value that helps us visualize how a body that disturbs a uniform flow causes pressure changes from the freestream pressure (P) P V P LOCAL P C P = LOCAL - P ½*r*V 2 Note The Physical Significance Of Certain Values of C p : C P = 1 P LOCAL = P TOTAL C P = 0 P LOCAL = P C P < 0 P LOCAL < P (i.e. vacuum pressure, accelerated flow) C P > 0 P LOCAL > P (i.e. positive pressure, decelerated flow) 6
Plotting Pressure Coefficient On Airfoil C P < 0 C P > 0 7
Lift & Drag Coefficient Equations Lift & Drag Coefficients Non-dimensional values that helps us understand how a specific geometric shape performs, regardless of the specific dynamic pressure or specific size of the shape. Lift Coefficient (2-D Airfoil) C l = LIFT Force ½*r*V 2 *c Drag Coefficient (2-D Airfoil) C d = DRAG Force ½*r*V 2 *c Lift Coefficient (3-D Wing) LIFT Force C L = ½*r*V 2 *S REF Drag Coefficient (3-D Wing) DRAG Force C D = ½*r*V 2 *S REF 8
Airfoil Lift Variation With Angle Of Attack A linear relation when AOA < Stall AOA Lift-Curve Slope (C La ) Change in Lift Coefficient (DC L ) With respect to Change in AoA (Da) Equation for a straight line: y = m*x + b V 8º 1.4 2º Lift Coefficient (C L ) Non-Dim 1.0 0.6 0.2 1 Da 2 DC L V 2 4 6 8 10 12 14 16 18 Angle of Attack (a) Degrees C La = DC L Da (C L2 -C L1 ) = = (a 2 -a 1 ) (0.88-0.40) (8º - 2º) = 0.80 (1/Deg) 9
Airfoil Drag Variation With Lift Generation Referred To As The Drag Polar Equation for a parabola: y = y 0 + k*x 2 C D = C D0 + k*c L 2 y 0 = How far parabola is offset above the X axis. k = Controls how wide the bowl of the parabola is. 0.06 0.05 CD vs CL C D0 = Zero Lift Drag Coefficient 0.04 KC L2 = Induced Drag Coefficient 0.03 0-1.5-1 -0.5 0 0.5 1 1.5 Now let s examine the plots of CL and CD for NACA airfoils in Appendix D of our book. 10 0.02 0.01 K = 0.0497 C D0 = 0.003