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

Chapter 3.0 Vehicle Design
3.3 Wing Aerodynamics
h(t) = Instantaneous flapping height, or plunge as a function of time. It is defined as a cosine wave function of
angular velocity and time, with h0x as the intercept, h1x as the coefficient of cosine function and ωhx as phase
angle. x corresponds to different phases in the cycle. This has been explained in the model formulation.
α(t) = Instantaneous pitch angle, it is defined on the same lines as h(t)
φ = span location, span has been divided into 20 sub parts.
b(φ) = semichord as a function of span location φ
rchord = chord at semi span = root chord
U(φ) = Effective velocity at a span location φ (Euclidean of V, and angular velocity)
b1(φ) = semichord normalized by semi root chord
xt(φ) = location of trailing edge at span location φ
xl(φ) = location of leading edge at span location φ
k(φ) = Reduced Frequency at span location φ
zm(φ) = dimensionless coordinate of midchord line
k0 = reduced frequency at semispan
s = ratio of semispan to rootchord
F(φ) = Real part of Theoderson Lift Deficiency Factor as a function of reduced frequency at span location φ. It is
a combination of first and second kind of Bessel functions of first and second order. J and Y represent Bessel
function of first and second kind.
G(φ) = Imaginary part of Theoderson Lift Deficiency Factor as a function of reduced frequency at span location
φ.
C(φ) = Theoderson Lift Deficiency factor
µ(φ) = Function of Bessel Functions
Ωh2(φ) = Amplitude of two dimensional circulation function due to flapping
Ωα2(φ) = Amplitude of two dimensional circulation function due to pitching
Ωη(φ) = Amplitude of three dimensional circulation function due to flapping
Ωα(φ) = Amplitude of three dimensional circulation function due to pitching
σh(φ) = Finite span and planform correction factor for flapping
σα(φ) = Finite span and planform correction factor for pitching
Ctxxx, Clxxx, Cmxxx, Cpxxx = Different coefficients used to simplify the solution of equations for coefficients
of thrust, lift moment, and power calculation respectively [12]
ψθh(φ) = Phase angle between pitching and flapping.
Ct = Coefficeint of Thrust
C L = Coefficient of Lift
Table 3-8: List of Symbols (Continued)
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