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

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
( ) := ⎡Cpθθ0 φ
⎣+
Cp φ,
t
+
⎡
⎢
⎢
⎣
() + Cpθθc() φ ⋅ cos⎡⎣
( 2) ⋅ ω ⋅ t + 2 ⋅ φα()
t ⎤⎦ ... ⎤ ⋅
Cpθθs() φ ⋅ sin( 2 ⋅ ω ⋅ t + 2 ⋅ φα()
t )
⎦
Cpθh0() φ ⋅ cos( φh() t − φα()
t − ψθh()
φ ) ... ⎤ ⋅ α1t () ⋅
+ ( Cpθhc() φ ⋅ cos( 2 ⋅ ω ⋅ t + φht () + φα()
t ))
... ⎥
+ Cpθhs() φ ⋅ sin( 2 ⋅ ω ⋅ t + φht () + φα()
t ) ⎥ ⎦
3.3.3.8 Results for the Baseline Case
The coefficient of lift is given in Figure 3-121.
α1() t
2
k()
φ
h1()
t
+ ⎡Cphh0() φ + Cphhc() φ ⋅ cos( 2 ⋅ ω ⋅ t + φht ())
... ⎤ ⋅ ⎜ k()
φ ⋅
⎣+ ( Cphhs() φ ⋅ sin( 2 ⋅ ω ⋅ t + φht ()))
⎦ ⎝ 2⋅
b φ
h1()
t
+ α0() t ⋅ kφ () ⋅ ⋅ Cpθhs()
φ ⋅ sin( ω ⋅ t + φht () + φα()
t )
2⋅
b()
φ
2.597
4
⎛
...
⋅
h1()
t
2⋅
b φ
()
()
2
⎞
⎠
...
...
2
Cl( acos( 0.75) , t)
0
− 1.881
2
0 0.1 0.2
0 t
Figure 3-121: Lift Coefficient vs. Time
0.167
The values of thrust coefficient are of the same shape and scale as that of the lift. The moment
produced in the upbeat is going to be neutralized by that produced by the downbeat, and is not
significant. It has high values once the angle of attack changes and that comports with the physics
of the problem. The graphs for moment and power coefficients are given in Figures 3-122
and 3-123.
139