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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 c l found using Lifting-Line Theory Airfoil Selection Drag Integration. Lifting-Line Theory. - PowerPoint PPT Presentation
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Aerodynamics PDR
AAE451 – Team 3
October 21, 2003
Brian CheskoBrian HronchekTed LightDoug MousseauBrent RobbinsEmil Tchilian
2
AAE 451Team 3Team 3 Aerodynamics PDR
Design Process
• Span-wise distribution for cl found using Lifting-Line Theory
• Airfoil Selection
• Drag Integration
3
AAE 451Team 3Team 3 Lifting-Line Theory
Inputs:a = dcl/d5.66 (airfoil specific)
Constant Chord = 2.8
AR = 5
= 6.85 deg (to match CL)
(actually L=0)
• Wing modeled as distribution of horseshoe vortices
• Fourier Series for circulation along span
nAbV
N
nn sin2)(
1
4
AAE 451Team 3Team 3 Prandtl’s Lifting-Line
• Solve Prandtl’s wing equation
• Substitute
iLl
cVaa
c
000
2
nAbVN
nn sin2)(
1
sin
sin)(
1
nnA
N
nni
0110 sin
sinsin
4
L
N
nn
N
nn
nnAnA
ca
b
•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
AAE 451Team 3Team 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 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
i
N
nn
i
nAn
a
Asin
sin
4
1 0
6
AAE 451Team 3Team 3 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 = 6.8 deg in order to match CL
• CDi calculation
• cl calculation
1
1
1
975
464.80464.4
7103
3
2
1
A
A
A
0040.0
0277.0
2316.0
3
2
1
A
A
A
0where)1(2
2
1
2
N
n
nLD A
An
A
CC
i
nAbVN
nn sin2)(
1
iL
l
cVaa
c
000
2
7
AAE 451Team 3Team 3 Lifting-Line Theory
Outputs:
CDi = 0.0131
Cdi distribution
CL = 0.4873
Cl distribution
Section Lift Coefficient Varies from ~ 0 – 0.6
0 1 2 3 4 5 6 70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Span/2 (ft)
Cl,
Cdi
, al
phai
ClCd*10alpha
i*10
8
AAE 451Team 3Team 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
9
AAE 451Team 3Team 3
-1 -0.5 0 0.5 1 1.50.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
Section Lift Coefficient, cl
Sec
tion
Dra
g C
oeff
icie
nt,
c d
Drag Polar for Candidate Airfoils
NACA 441244154425241823018ClarkY
Airfoil Selection
Region of Interest
Clark Y Airfoil is Best
Clark Y
10
AAE 451Team 3Team 3 Clark Y Airfoil
-10 -8 -6 -4 -2 0 2 4 6 8 10-1
-0.5
0
0.5
1
1.5
2
Angle of Attack
Sec
tion
Lift
Coe
ffic
ient
, c l
-0.2
-0.1
0
0.1
0.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x/c
y/c
•Geometry
•Drag Polar
•cl vs
-1 -0.5 0 0.5 1 1.5 20.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Section Lift Coefficient, cl
Sec
tion
Dra
g C
oeff
icie
nt,
c d
dcl/d = 5.66
cl vs. cd vs. cl
11
AAE 451Team 3Team 3 Total Lift and Drag Coefficient Estimation
• Lift:• CL – Found at cruise, can be obtained at any
• cl - Found using lifting line theory
• Drag:• CD = CDi + CDp
• CDi found using lifting line theory, can be obtained at any
• From Drag Polar of airfoil (cl vs. cd), cdp can be obtained and integrated to obtain CDp for the entire wing
12
AAE 451Team 3Team 3 Parasitic Drag Calculation
• Used Polynomial Function to Fit Airfoil’s Drag Polar
-1 -0.5 0 0.5 1 1.5 20.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
Cl
Cd
AIRFOIL DRAG POLAR
ActualPolynomial Fit
13
AAE 451Team 3Team 3 Parasitic Drag Calculation
• Plugged wing cl distribution into polynomial function to get corresponding parasitic cd distribution along span
14
AAE 451Team 3Team 3 Parasitic Drag Calculation
• Integrated Parasitic Drag Distribution Along Span to get 3-D Wing Parasitic Drag
• CDp = .0059
15
AAE 451Team 3Team 3 Total Wing Drag Coefficient
• CD = CDi + CDp
• CD = .0131 + .0059 = .0190
16
AAE 451Team 3Team 3 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
AAE 451Team 3Team 3 Wing Characteristics
18
AAE 451Team 3Team 3 Coming Attractions…
• CLmax
• Control Surface Sizing
• Tail Sizing
19
AAE 451Team 3Team 3 Questions?
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