For harmonic oscillations, the Theodorsen function C(k) accounts for the contribution of the wake to the lift
Question:
For harmonic oscillations, the Theodorsen function C(k) accounts for the contribution of the wake to the lift and moment. Plot a vector diagram of the real and imaginary parts of its complex conjugate C(k) versus the frequency k ∈ [0, ∞). Also, plot its magnitude and phase.
Plunging oscillations are an approximation of bending oscillations. Plot a vector diagram of the total lift coefficient of a thin airfoil undergoing plunging oscillations versus the reduced frequency. Also, plot its magnitude and phase.
Pitching oscillations are an approximation of torsional oscillations. Plot a vector diagram of the total lift coefficient of a thin airfoil undergoing torsional oscillations about the mid chord versus the reduced frequency. Also, plot its magnitude and phase. Repeat if the oscillations are about the airfoil leading edge.
Hint: use the following equation to approximate the Theodorsen function:
Chemistry The Central Science
ISBN: 978-0321696724
12th edition
Authors: Theodore Brown, Eugene LeMay, Bruce Bursten, Catherine Murphy, Patrick Woodward