Phase II Final Report - NASA's Institute for Advanced Concepts

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
Kα1 ⋅ A( 1,
1.159)
+ Kα3 ⋅ A( 3,
1.159)
+ Kα5 ⋅ A( 5,
1.159)
+ Kα7 ⋅ A( 7,
1.159)
+ Kα9 ⋅ A( 9,
1.159)
... Ωα2( 1.159)
Kα1 ⋅ A( 1,
0.927)
+ Kα3 ⋅ A( 3,
0.927)
+ Kα5 ⋅ A( 5,
0.927)
+ Kα7 ⋅ A( 7,
0.927)
+ Kα9 ⋅ A( 9,
0.927)
... Ωα2( 0.927)
Kα1 ⋅ A( 1,
0.644)
+ Kα3 ⋅ A( 3,
0.644)
+ Kα5 ⋅ A( 5,
0.644)
+ Kα7 ⋅ A( 7,
0.644)
+ Kα9 ⋅ A( 9,
0.644)
... Ωα2( 0.644)
Kα1 ⋅ A( 1,
0.451)
+ Kα3 ⋅ A( 3,
0.451)
+ Kα5 ⋅ A( 5,
0.451)
+ Kα7 ⋅ A( 7,
0.451)
+ Kα9 ⋅ A( 9,
0.451)
... Ωα2( 0.451)
( )
Kα := Find Kα1, Kα3, Kα5, Kα7,
Kα9
Ωα φ
() := Kα 0 sin()
φ
( )
( )
( )
( )
sin 3 ⋅ φ sin 5 ⋅ φ sin 7 ⋅ φ sin 9 ⋅ φ
⋅ + Kα 1 ⋅ + Kα 2 ⋅ + Kα 3 ⋅ + Kα 4 ⋅
3
5
7
9
⎛
⎜
⎝
σh() φ := C φ
()
+
( ( ))
( ) 1i J1( k()
φ )
1i ⋅ J1 k φ
J0 k()
φ − ⋅
⎞
⎠
⋅
⎛
⎜
⎝
()
( )
Ωh φ
Ωh2 φ
− 1
⎞
⎠
⎛
⎜
⎝
σα() φ := C φ
()
+
( ())
( ) 1i J1( k()
φ )
1i ⋅ J1 k φ
J0 k()
φ − ⋅
⎞
⎠
⋅
⎛
⎜
⎝
()
()
Ωα φ
Ωα2 φ
− 1
⎞
⎠
Fh() φ := F() φ + Re σh φ
( ())
Fα() φ := F() φ + Re σα φ
( ())
Gh() φ := G() φ + Im σh φ
( ())
Gα() φ := G() φ + Im σα φ
( ())
⎡
⎢
⎣
Ctθθ0() φ := π ⋅ Fα() φ + Gα() φ
2
− Fα φ
()
+
⎛
⎜
⎝
k() φ
2 ⋅ Fαφ () 2 + Gαφ () 2
− Fα φ
()
+
1
2
⎞⎤ ⎥⎦
⎠
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