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

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
40
30
20
10
0
0.02 0.12 0.22 0.32 0.42 0.52 0.62 0.72 0.82 0.92
-10
r = 0.1
r = 0.2
r = 0.3
r = 0.4
r = 0.5
r = 0.6
-20
-30
-40
Wing Flap Cycle
Figure 3-103: Wing-velocity Profile Due to Wing Motion Through One-flap Cycle
This figure shows the velocity profile throughout one flap cycle at various points along the
radius of the wing. Wing-velocity profiles were generated for a flapping rate of 5.79 Hz and
maximum flap angle of 65°. As these parameters vary, the absolute values of the curves will
change, but the relative shape of the profiles will remain the same.
The equations for generating these velocity profiles are given below. The velocity calculation is
broken up into three segments. The velocity profiles (V w1 , V w2 , and V w3 ) for the three segments
are given in Equations 3-32 through 3-34, where r is the length along the wing where the velocity
is calculated, θ is the maximum flap angle for the wing, t is the time from the beginning of
the cycle in seconds, and f is the flapping frequency of the wing in Hz.
V w1 =32 θ rtf Equation 3-32
V w2 = 16 θ rf – 32 θ rtf 2 Equation 3-33
V w3 = -32 θ rf + 32 θ rtf 2 Equation 3-34
This wing-velocity profile coupled with the free stream-air velocity produces the relative air
velocity and angle of attack the wing sees during flight. The angle of attack (a) is given by
Equation 3-35. Figures 3-104 through 3-107 show the angle of attack along the wing length
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