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

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
1
1
30
30
75
75
80
φα() t := if⎛
t≤ , 0,
if⎛
t > ∧ t ≤ , Coeff3 1 , if⎛
t > ∧ t ≤ , 0,
if⎛
t > ∧ t ≤ , Coeff4 1 , 0⎞⎞⎞⎞
⎜
⎜
⎜
⎜
⎝ 4 ⋅ freq ⎝ 4 ⋅ freq 100 ⋅ freq ⎝ 100 ⋅ freq 100 ⋅ freq ⎝ 100⋅
freq 100 ⋅ freq ⎠⎠⎠⎠
( )
α() t := α0() t + α1() t ⋅ cos ω ⋅ t + φα()
t
The pitching motion produced is shown in Figure 3-119.
0.14
0.2
α()
t
0
− 0.14
0.2
0 0.02 0.04 0.06 0.08
0 t
0.063
Figure 3-119: Pitching Motion
The planform shape of Entomopter wing was defined as a five-degree polynomial to evaluate
chord in terms of span location, similarly five degree polynomials were formulated for leading
edge and trailing edge locations. Chord as a function of span location is shown in Figure 3-120.
φ := acos ( 0) , acos ( 0.05)
.. acos ( 1.0)
b() φ := ⎡ 6.9105⋅ ( cos () φ ) 5
− 19.883⋅
cos φ
⎢
⎣
( ()) 3
( ()) 4
( ()) 2
( ())
+ 21.551⋅ cos φ − 11.177⋅
cos φ + 2.3791⋅
cos φ + 0.3395
...
⎤ ⎥⎦
⋅
sspan
2
() := V 2 + ( cos () φ ⋅ ω ⋅ sspan ) 2
U φ
rchord = 0.339 • sspan
b1()
φ
:=
2⋅
b()
φ
rchord
xt() φ := ⎛ 1.9534⋅
cos () φ
5
− 7.7057⋅
cos () φ
4
...
⎜
+ 11.407⋅
cos φ − 7.7318⋅
cos φ + 1.9612⋅
cos φ + 0.1714
⎝
(
() 3
() 2
()
⎞
⎠
⋅ sspan
131