Analytical Sensitivity Analysis of an Unsteady Vortex-Lattice Method for Flapping-Wing Optimization

Optimal thickness distributions of aeroelastic flapping shells

“…Two scalar functions are considered, averaged over the final flapping cycle once the behavior has become time-periodic: thrust coefficient (referencing Eq. (6), g = C T ,ave ) and efficiency (g = η), which is given as the ratio of the average thrust to the average power [21]. The derivative of these two functions with respect to the thickness of each finite element (where the thickness is uniform, set to the value of 0.5 mm given in Table 1) is given in Fig.…”

“…5 (θ y ). The topological details of the wing structure (discussed below) provide the wing with a negative bend-twist coupling (i.e., adaptive feathering [21]). This change in angle of attack shifts the lift coefficient of the flexible wing at stroke reversal, when the bending (and hence the torsion) is peak.…”

“…A similar optimization problem would use maximum efficiency as an objective function, but this was not done here. Maximizing efficiency would provide the optimizer with some incentive to improve the thrust [21], when theoretically, only a certain amount of thrust is needed for trim. For Eq.…”

“…The local streamline at each wake ring can be computed through the wing-wake and wake-wake interactions, and subsequently deformed [21].…”

Deterministic Global Optimization of Flapping Wing Motion for Micro Air Vehicles

“…w wake c control point te trailing edge x x-translation degree of freedom y y-translation degree of freedom θ rotational degree of freedom E pitching point 6 and L 7 denote the induced velocity obtained from the Biot-Savart law L 3 represents the impact of the freestream velocity on each control point L 4 updates the indices of the wake vortices at each time step L 8 represents the impact of the freestream velocity on each on each wake vortex location…”