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Aerodynamics PDR AAE451 – Team 3 October 21, 2003

This document outlines the aerodynamic design process for a wing, including airfoil selection, lifting-line theory calculations, and drag estimation. It also discusses the criteria for airfoil selection and provides calculations for total lift and drag coefficients. The document concludes with future considerations for the wing design.

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Aerodynamics PDR AAE451 – Team 3 October 21, 2003

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  1. Aerodynamics PDR AAE451 – Team 3 October 21, 2003 Brian Chesko Brian Hronchek Ted Light Doug Mousseau Brent Robbins Emil Tchilian

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

  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 - aL=0)

  4. 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 < )

  5. 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  A2, A4,… are zero • take only A1, A3,… as unknowns • take only control points on half of the wing: 0 < i  /2 • Example for N=30: • take A1, A3, A5 as unknowns • take control points (equidistant in ):  = /(2N) stepping • take lift-slope of the airfoil a0 = 5.66, and wing aspect ratio A = 5

  6. Lifting-Line Calculation • Sample Output N = 3 • CL calculation from lifting line theory CL = πAR*A1*αCL = W/S*q = .4873 from constraint solve for a = 6.8 deg in order to match CL • CDicalculation • clcalculation

  7. Lifting-Line Theory Outputs: CDi = 0.0131 Cdi distribution CL = 0.4873 Cl distribution Section Lift Coefficient Varies from ~ 0 – 0.6

  8. 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

  9. Airfoil Selection Region of Interest Clark Y Clark Y Airfoil is Best

  10. Clark Y Airfoil • Geometry • Drag Polar • cl vs a cl vs. a cd vs. cl dcl/da = 5.66

  11. 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 • CDifound 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

  12. Parasitic Drag Calculation • Used Polynomial Function to Fit Airfoil’s Drag Polar

  13. Parasitic Drag Calculation • Plugged wing cl distribution into polynomial function to get corresponding parasitic cd distribution along span

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

  15. Total Wing Drag Coefficient • CD = CDi + CDp • CD = .0131 + .0059 = .0190

  16. Wing Characteristics Wing Sweep = 0º Taper Ratio = 1 Dihedral Angle = 5º AR = 5 S = 40 ft2 Tail Airfoil = NACA 0012 (empirically based from Roskam Part II, p. 154) (subject of future trade study)

  17. Wing Characteristics

  18. Coming Attractions… • CLmax • Control Surface Sizing • Tail Sizing

  19. Questions?

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