Aerodynamics PDR AAE 451 Team 3 October 21

Aerodynamics PDR AAE 451 – Team 3 October 21, 2003 Brian Chesko Brian Hronchek Ted Light Doug Mousseau Brent Robbins Emil Tchilian

AAE 451 Team 3 Aerodynamics PDR Design Process • Span-wise distribution for cl found using Lifting-Line Theory • Airfoil Selection • Drag Integration 2

AAE 451 Team 3 Lifting-Line Theory • Wing modeled as distribution of horseshoe vortices • Fourier Series for circulation along span Inputs: a = dcl/da = 5. 66 (airfoil specific) Constant Chord = 2. 8 AR = 5 a = 6. 85 deg (to match CL) (actually a - a. L=0) 3

AAE 451 Team 3 Prandtl’s Lifting-Line • Solve Prandtl’s wing equation • Substitute • System of N equations with N unknowns (Solve N N matix) • Take N different spanwise locations on the wing where the equation is to be satisfied: 1, 2, . . N; (but not at the tips, so: 0 < 1 < ) 4

AAE 451 Team 3 Lifting-Line For Rectangular Wing • Consider: • rectangular wing: c = constant; span = b; b/c = A = 5 without twist: = constant; L=0 = 0 Evaluate the wing equation at the N control points at i : • The wing is symmetrical A 2, A 4, … are zero • Example for N=30: – take only A 1, A 3, … as unknowns – take only control points on half of the wing: 0 < i /2 – take A 1, A 3, A 5 as unknowns – take control points (equidistant in ): = /(2 N) stepping – take lift-slope of the airfoil a 0 = 5. 66, and wing aspect ratio A = 5 5

AAE 451 Team 3 • Lifting-Line Calculation Sample Output N=3 • CL calculation from lifting line theory CL = πAR*A 1*α CL = W/S*q =. 4873 from constraint solve for a = 6. 8 deg in order to match CL • CDi calculation • cl calculation 6

AAE 451 Team 3 Lifting-Line Theory Outputs: CDi = 0. 0131 Cdi distribution CL = 0. 4873 Cl distribution Section Lift Coefficient Varies from 7

AAE 451 Team 3 Airfoil Selection Airfoils Selection Criteria: • Low drag over range of specified cl values • Easy construction – Round Leading Edge – Relatively Flat Bottom • Easy to construct on tabletop – Constructible Trailing Edge 8

AAE 451 Team 3 Airfoil Selection Region of Interest Clark Y Airfoil is Best 9

AAE 451 Team 3 Clark Y Airfoil • Geometry • Drag Polar • cl vs a cl vs. a cd vs. cl dcl/da = 5. 66 10

AAE 451 Team 3 Total Lift and Drag Coefficient Estimation • Lift: • CL – Found at cruise, can be obtained at any a • cl - Found using lifting line theory • Drag: • CD = CDi + CDp • CDi found using lifting line theory, can be obtained at any a • From Drag Polar of airfoil (cl vs. cd), cdp can be obtained and integrated to obtain CDp for the entire wing 11

AAE 451 Team 3 Parasitic Drag Calculation • Used Polynomial Function to Fit Airfoil’s Drag Polar 12

AAE 451 Team 3 Parasitic Drag Calculation • Plugged wing cl distribution into polynomial function to get corresponding parasitic cd distribution along span 13

AAE 451 Team 3 Parasitic Drag Calculation • Integrated Parasitic Drag Distribution Along Span to get 3 -D Wing Parasitic Drag • CDp =. 0059 14

AAE 451 Team 3 Total Wing Drag Coefficient • CD = CDi + CDp • CD =. 0131 +. 0059 =. 0190 15

AAE 451 Team 3 Wing Characteristics Wing Sweep = 0º Taper Ratio = 1 Dihedral Angle = 5º (empirically based from Roskam Part II, p. 154) AR = 5 (subject of future trade study) S = 40 ft 2 Tail Airfoil = NACA 0012 16

AAE 451 Team 3 Wing Characteristics 17

AAE 451 Team 3 Coming Attractions… • CLmax • Control Surface Sizing • Tail Sizing 18

AAE 451 Team 3 Questions? 19