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Thin Airfoil Theory Summary
•
Replace airfoil with camber line (assume small
c
τ
)
•
Distribute vortices of strength
)
(
x
γ
along chord line for
0
x
c
≤
≤
.
•
Determine
)
(
x
by satisfying flow tangency on camber line.
0
()
0
2(
)
c
dZ
d
V
dx
x
γξ ξ
α
πξ
∞
−−
=
−
∫
•
The pressure coefficient can be simplified using Bernoulli & assuming small
perturbation:
x
z
c
τ
(x) = thickness
z(x) = camber line
x
z
c
z(x) = camber line
x
z
c
γ
(x)dx
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View Full Document Thin Airfoil Theory Summary
16.100
2002
2
{}
2
22
2
2
2
2
2
2
higher order
1
2
11
()
1
1
2
2
1
2
p
pp
c
V
p
Vu
V
p
V
V u V
V
V
VV
u
u
V
V
uuV
ρ
∞
∞
∞∞
∞
∞
∞
∞
−
=
++
+
=
+
−+
+
⇒=
−
+
=−
+
−
±
±
±
±
±
±±
±
²³´³µ
2
p
u
C
V
∞
−
±
•
It can also be shown that
2
lower
upper
upper
lower
p
p
p
upper
lower
xu
x
CC
C
u
u
V
γ
∞
⇒∆
=
−
=
−
() 2
p
x
Cx
V
∞
Symmetric Airfoil Solution
For a symmetric airfoil (i.e.
0
dz
dx
=
), the vortex strength is:
θ
α
sin
cos
1
2
)
(
+
=
∞
V
But, recall:
(1
cos )
2
c
x
Thin Airfoil Theory Summary
16.100
2002
3
2
2
cos
1
2
sin
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Dynamics, Aerodynamics

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