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1. Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

   https://doi.org/10.3390/fluids3040081  

   Pohly, Jeremy; Salmon, James; Bluman, James; Nedunchezian, Kabilan; Kang, Chang-kwon (December 2018, Fluids)

   Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model. 

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2. Quasi-steady aerodynamic theory under-predicts glide performance in flying snakes

   https://doi.org/10.1242/jeb.247989  

   Yeaton, Isaac J; Ross, Shane D; Socha, John J (October 2024, Journal of Experimental Biology)

   Flying snakes (genus Chrysopelea) glide without the use of wings. Instead, they splay their ribs and undulate through the air. A snake's ability to glide depends on how well its morphing wing-body produces lift and drag forces. However, previous kinematics experiments under-resolved the body, making it impossible to estimate the aerodynamic load on the animal or to quantify the different wing configurations throughout the glide. Here, we present new kinematic analyses of a previous glide experiment, and use the results to test a theoretical model of flying snake aerodynamics using previously measured lift and drag coefficients to estimate the aerodynamic forces. This analysis is enabled by new measurements of the center of mass motion based on experimental data. We found that quasi-steady aerodynamic theory under-predicts lift by 35% and over-predicts drag by 40%. We also quantified the relative spacing of the body as the snake translates through the air. In steep glides, the body is generally not positioned to experience tandem effects from wake interaction during the glide. These results suggest that unsteady 3D effects, with appreciable force enhancement, are important for snake flight. Future work can use the kinematics data presented herein to form test conditions for physical modeling, as well as computational studies to understand unsteady fluid dynamics effects on snake flight. 

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3. Sparse Reduced-Order Modeling of a Hovering Hawkmoth’s Wake

   https://doi.org/10.1115/FEDSM2024-130651  

   Lionetti, Seth; Hedrick, Tyson L; Li, Chengyu (July 2024, American Society of Mechanical Engineers)

   Abstract As insects fly, their wings generate complex wake structures that play a crucial role in their aerodynamic force production. This study focuses on utilizing reduced order modeling techniques to gain valuable insights into the fluid dynamic principles underlying insect flight. Specifically, we used an immersed-boundary-method-based computational fluid dynamics (CFD) solver to simulate a hovering hawkmoth’s wake, and then identified the most energetic modes of the wake using proper orthogonal decomposition (POD). Furthermore, we employed a sparse identification of nonlinear dynamics (SINDy) approach to find a simple reduced order model that relates the most energetic POD modes. Through this process, we formulated multiple different models incorporating varying numbers of POD modes. To compare the accuracy of these models, we utilized a force survey method to estimate the aerodynamic forces produced by the hawkmoth’s wings. This force survey method uses an impulse-based approach to calculate the aerodynamic lift and drag based solely on the velocity and vorticity information provided by the model. By comparing the estimated aerodynamic force with the actual force production calculated by the CFD solver, we were able to find the simplest model that still provides an accurate representation of the complex wake produced by the hovering hawkmoth wings. We also evaluated the stability and accuracy of this model as the number of flapping cycles increases with time. The reduced order modeling of insect flight has important implications for the design and control of bio-inspired micro-aerial vehicles. In addition, it holds the potential to reduce the computational cost associated with high-fidelity CFD simulations of complex flows. 

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4. CFD Analysis and Design Optimization of Dandelion-Inspired Flying Sensors for Remote Sensing in Inaccessible Environments

   https://doi.org/10.2514/6.2025-4131  

   Orlando, Matteo; Quayson, Gifty; Hassanalian, Mostafa (July 2025, American Institute of Aeronautics and Astronautics)

   This study investigates the aerodynamic performance of different flying sensors inspired by dandelion seeds, using COMSOL Multiphysics CFD simulation. Dandelion seeds are well known for their ability to remain suspended in the air for extended periods due to their lightweight structure, higher porosity, high drag, and the formation of a separated vortex ring (SVR) above the seed. Mimicking this behavior, five 2D and one 3D geometry were developed and analyzed first through steady-state simulations to explore how different design geometries influence passive flight performance. The primary aim is to identify an optimized structure that can achieve slower descent when realized from an altitude by drones for remote sensing. Steady-state results showed that although the drag coefficient generally decreased with increase in Reynolds numbers, porosity did not exhibit a constant trend across all designs. In some cases, geometries with lower porosity outperformed more porous ones. This may be due to their structural differences. SVR was observed in all designs. However, the distance between these SVR and geometry’s surface was small. While steady-state results give a fair indication of the aerodynamic behavior and relative performances of the various geometries, there are limitations. To address this, transient drop tests, currently under verification, will give a better understanding of the performances of these designs from which the best will be selected. 

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5. Birds can transition between stable and unstable states via wing morphing

   https://doi.org/10.1038/s41586-022-04477-8  

   Harvey, C.; Baliga, V. B.; Wong, J. C.; Altshuler, D. L.; Inman, D. J. (March 2022, Nature)

   Abstract Birds morph their wing shape to accomplish extraordinary manoeuvres 1–4 , which are governed by avian-specific equations of motion. Solving these equations requires information about a bird’s aerodynamic and inertial characteristics 5 . Avian flight research to date has focused on resolving aerodynamic features, whereas inertial properties including centre of gravity and moment of inertia are seldom addressed. Here we use an analytical method to determine the inertial characteristics of 22 species across the full range of elbow and wrist flexion and extension. We find that wing morphing allows birds to substantially change their roll and yaw inertia but has a minimal effect on the position of the centre of gravity. With the addition of inertial characteristics, we derived a novel metric of pitch agility and estimated the static pitch stability, revealing that the agility and static margin ranges are reduced as body mass increases. These results provide quantitative evidence that evolution selects for both stable and unstable flight, in contrast to the prevailing narrative that birds are evolving away from stability 6 . This comprehensive analysis of avian inertial characteristics provides the key features required to establish a theoretical model of avian manoeuvrability. 

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