16100lectre16_cg - Important Concepts in Thin Airfoil...

Important Concepts in Thin Airfoil Theory
1. This airfoil theory can be viewed as a panel method with vortex solutions
taking the limits of infinite number of panels & zero thickness & zero camber
{ }
0
1
0
0
1 ( )
1
2
2
lim lim vortex panel thin airfoil theory
c
N
j ij i
j
thickness N
camber
d dz
V
K V n
x dx
γ ξ ξ
α
γ
π ξ
π
∞
∞
=
→ →∞
→
 
= −
 
=
−
 
=
∫
∑
K
K
i
±²²²³²²²´
±²²²³²²²´
2. 2 ( )
l LO
C π α α = −
0
1
(1 cos )
(1 cos )
2
LO o o
o
dz
d
dx
c
x
π
α θ θ
π
θ
= −
= −
∫
• 0 =
LC
α for 0
dz
dx
= {i.e. symmetric airfoils}
•