Investigation of chordwise functionally graded flexural rigidity in flapping wings using a two-dimensional pitch-plunge model

A numerical study on the aerodynamic effects of dynamic twisting on forward flight flapping wings

To better understand the secret of natural flying vertebrates such as how humming-birds twist their wings to achieve superb flight ability, we presented a numerical investigation of dynamic twisting based on a hummingbird-like flapping wing model. Computational fluid dynamic simulations were performed to examine the effects of dynamic twisting on the unsteady flow field, the generation of instantaneous aerodynamic forces, and the time-averaged aerodynamic performance. This research reveals the details of leading-edge vortices (LEVs) and the underlying mechanisms behind the positive effects of wing torsion. The results demonstrated that wing torsion can effectively maintain the favorable distribution of effective angle of attack along the wing spanwise, resulting in a higher time-averaged thrust and vertical force. Further, the proper parameters of dynamic twisting can also improve the propulsive efficiency in forward flight. Dynamic twisting also showed a superior ability in controlling the airflow separation over the wing surface and maintaining the stability of the LEV. The amplitudes of effective angle of attack associated with the highest peak thrust and the maximum thrust-to-power at different advanced ratios were also explored, and it was found that the amplitudes decrease with increasing advanced ratio. To improve the efficiency during larger advanced ratio, specific modifications to the pitching of the wing were proposed in this work. The research in this paper has promising implications for the bio-inspired flapping wing.

Modeling and Analysis of a Simple Flexible Wing-Thorax System in Flapping-Wing Insects

Small-scale flapping-wing micro air vehicles (FWMAVs) are an emerging robotic technology with many applications in areas including infrastructure monitoring and remote sensing. However, challenges such as inefficient energetics and decreased payload capacity preclude the useful implementation of FWMAVs. Insects serve as inspiration to FWMAV design owing to their energy efficiency, maneuverability, and capacity to hover. Still, the biomechanics of insects remain challenging to model, thereby limiting the translational design insights we can gather from their flight. In particular, it is not well-understood how wing flexibility impacts the energy requirements of flapping flight. In this work, we developed a simple model of an insect drive train consisting of a compliant thorax coupled to a flexible wing flapping with single-degree-of-freedom rotation in a fluid environment. We applied this model to quantify the energy required to actuate a flapping wing system with parameters based off a hawkmoth Manduca sexta. Despite its simplifications, the model predicts thorax displacement, wingtip deflection and peak aerodynamic force in proximity to what has been measured experimentally in flying moths. We found a flapping system with flexible wings requires 20% less energy than a flapping system with rigid wings while maintaining similar aerodynamic performance. Passive wing deformation increases the effective angle of rotation of the flexible wing, thereby reducing the maximum rotation angle at the base of the wing. We investigated the sensitivity of these results to parameter deviations and found that the energetic savings conferred by the flexible wing are robust over a wide range of parameters.

Derivative-Free Observability Analysis for Sensor Placement Optimization of Bioinspired Flexible Flapping Wing System

Observability analysis of a bioinspired flexible flapping wing system provides a measure of how well the states of flexible flapping wing micro-aerial vehicles can be estimated from real-time measurements during high-speed flight. However, the traditional observability analysis approaches have trouble in terms of lack of quantitative analysis index, high computational complexity, low accuracy, and unavailability in stochastic systems with memory, including bioinspired flexible flapping wing systems. Therefore, a novel derivative-free observability analysis method is proposed here based on the generalized polynomial chaos expansion. By formulating a surrogate model to represent the relationship between the cumulative measurement and the random initial state, the observability coefficient matrix is calculated and the observability rank condition is stated. Consequently, several observability indices are proposed to quantity the observability of the system. Altogether, the proposed method avoids the disadvantages of the traditional approaches, especially in assessing the observability degree of each state and the effect of stochastic noise on observability. The validation of the proposed method is first provided by demonstrating the equivalence between the traditional and proposed methods and subsequently by comparing the observability of the Lorenz system calculated via three different approaches. Finally, the proposed method is applied on a bioinspired flexible wing system to optimize the placement of sensors, which is consistent with the natural configuration of campaniform sensilla on the wing of the hawkmoth.