16.810
Engineering Design and Rapid Prototyping
Dept of Aeronautics & Astronautics
Massachusetts Institute of Technology
IAP 2005
Prof. O. de Weck
A. Bell, C. Graff
January 6, 2005
Version 1.0
XFOIL and Low Speed Airfoil Design/Analysis
Notes from presentation by Mark Drela
Equations
2
Coefficient of Drag
b
S
S = Area
b = Span
L = Lift
S
c = = chord
b
C
αi = L
πAR
α 3D = α 2 D + α i
L
CL =
1
ρV 2 S
2
1
L = ρV 2 SC L
2
C L ≈ Cl
1
D = ρV 2 SC D
2
CD = Cd + CDi
Induced Drag
C Di =
(9)
Center of Lift
( )
(10)
Aspect ratio:
Induced angle
3D angle
Lift coefficient
Lift
3D Lift ≈ 2D Lift
Drag
AR =
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
C L2
πAR
1 C
x
= − m
c cp 4 C
l
Vc
Re =
ν
Reynolds Number
(11)
2
ν = 1.45 ⋅10 m s
−5
For a 20” chord, Re ≈ 10 7
1
Procedure
Step 1: 2D simulation in XFOIL
Obtain Cl , Cd , Cm & α 2 D for your airfoil
Get AR
(equation 1)
x
Get
(equation 10)
c cp
( )
Step 2: Calculating Lift
Get CL
(equation 6)
Get L
(equation 5)
Step 3: Calculating Drag
Get C Di
(equation 9)
Get C D
Get D
(equation 8)
(equation 7)
Step 4: Calculating the Angle of Attack
Get α i
(equation 2)
(equation 3)
Get α 3 D
Structural Considerations
( c)
Center of Lift along chord: x
cp
is normally between 0.3 & 0.4
Place the spar at this location to avoid twisting of the airfoil. This is usually the thickest point.
Apply fiberglass at 45° to the leading edge of the airfoil, (not 0° & 90°) for torsional stiffness. If
you are not using a spar then you need to apply fiberglass at 0° & 90°, allowing the fibers to act
as a spar and bear the load.
To transfer load out of the wing, you must add hard points to the foam wing.
It is recommended to fiberglass and vacuum bag the wing for trailing edge strength, especially if
you are using a thin trailing edge.
2