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*α CL = W/S*q = from constraint
solve for a = 6.8 deg in order to match CL
CDi calculation
cl calculation

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

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 = = .0190

16. (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)

17. Wing Characteristics

18. Coming Attractions…
CLmax
Control Surface Sizing
Tail Sizing

19. Questions?