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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
Ωα2()
φ
:=
()
( ( ) Y1( k()
φ ))
4⋅
1i⋅
C φ
k() φ ⋅ J1 k()
φ −
1i ⋅ km ( φ )
⎡
⎢
⎣
()
⋅ e ⋅ 1 + 1i⋅
k φ ⋅
⎛
⎜
⎝
1
2
− a
⎞⎤ ⎥⎦
⎠
⋅
b1()
φ
⋅ αamp
n = 1,3,5,7,9
( )
Sn n,
φ
( )
sin n ⋅ φ
:= ...
sin()
φ
π
1i ⋅ k0 ⋅ s ⌠
+ ⋅
⎮
π ⎮
⎮
⎮
⎮
⎮
⎮
⌡
0
cos() φ − cos θ
cos() φ − cos θ
( )
( )
⋅ ⎡⎡
−ln( k0 ⋅ s ⋅ cos () φ − cos ( θ)
) − 0.270...
⎤ ...
θ
⎢
⎤ ⋅ cos( n ⋅ θ)
d
⎢
+ 0.764⋅ ( k0 ⋅ s ⋅ cos() φ − cos( θ)
) − 0.129⋅
( k0 ⋅ s ⋅ cos () φ − cos ( θ)
) 2 ... ⎥ ⎥
⎢⎢
⎥ ⎥
⎢⎣
+ 0.011⋅
( k0 ⋅ s ⋅ cos() φ − cos( θ)
) 3
⎦ ⎥
⎢ + 1i ⋅ ⎡ 1.319−
0.757⋅
( k0 ⋅ s ⋅ cos () φ − cos( θ)
) ...
⎤ ⎥
⎢ ⎢
⎣ + 0.202⋅ ( k0 ⋅ s ⋅ cos() φ − cos( θ)
) 2 − 0.020⋅
( k0 ⋅ s ⋅ cos () φ − cos( θ)
) 3 ⎥⎦
⎣
⎥
⎦
Anφ ( , )
:=
( )
sin n ⋅ φ
n
+
π
s
⋅
b1()
φ
⋅
µ () φ
⋅
Sn( n,
φ)
Kh1 ⋅ A( 1,
1.369)
+ Kh3 ⋅ A( 3,
1.369)
+ Kh5 ⋅ A( 5,
1.369)
+ Kh7 ⋅ A( 7,
1.369)
+ Kh9 ⋅ A( 9,
1.369)
... Ωh2( 1.369)
Kh1 ⋅ A( 1,
1.159)
+ Kh3 ⋅ A( 3,
1.159)
+ Kh5 ⋅ A( 5,
1.159)
+ Kh7 ⋅ A( 7,
1.159)
+ Kh9 ⋅ A( 9,
1.159)
... Ωh2( 1.159)
Kh1 ⋅ A( 1,
0.927)
+ Kh3 ⋅ A( 3,
0.927)
+ Kh5 ⋅ A( 5,
0.927)
+ Kh7 ⋅ A( 7,
0.927)
+ Kh9 ⋅ A( 9,
0.927)
... Ωh2( 0.927)
Kh1 ⋅ A( 1,
0.644)
+ Kh3 ⋅ A( 3,
0.644)
+ Kh5 ⋅ A( 5,
0.644)
+ Kh7 ⋅ A( 7,
0.644)
+ Kh9 ⋅ A( 9,
0.644)
... Ωh2( 0.644)
Kh1 ⋅ A( 1,
0.451)
+ Kh3 ⋅ A( 3,
0.451)
+ Kh5 ⋅ A( 5,
0.451)
+ Kh7 ⋅ A( 7,
0.451)
+ Kh9 ⋅ A( 9,
0.451)
... Ωh2( 0.451)
Kh := Find( Kh1, Kh3, Kh5, Kh7,
Kh9)
Ωh φ
() := Kh 0 sin()
φ
( )
( )
( )
( )
sin 3 ⋅ φ sin 5 ⋅ φ sin 7 ⋅ φ sin 9 ⋅ φ
⋅ + Kh 1 ⋅ + Kh 2 ⋅ + Kh 3 ⋅ + Kh 4 ⋅
3
5
7
9
Kα1 ⋅ A( 1,
1.369)
+ Kα3 ⋅ A( 3,
1.369)
+ Kα5 ⋅ A( 5,
1.369)
+ Kα7 ⋅ A( 7,
1.369)
+ Kα9 ⋅ A( 9,
1.369)
... Ωα2( 1.369)
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Phase II Final Report