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

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

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)

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 < )

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

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

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

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

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

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

Total Lift and Drag Coefficient Estimation 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

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

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

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

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

(empirically based from Roskam Part II, p. 154) 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)

Wing Characteristics

Coming Attractions… CLmax Control Surface Sizing Tail Sizing

Questions?