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1. Computational analysis of vortex dynamics and aerodynamic performance in flying-snake-like gliding flight with horizontal undulation

   https://doi.org/10.1063/5.0125546  

   Gong, Yuchen; Wang, Junshi; Zhang, Wei; Socha, John J.; Dong, Haibo (December 2022, Physics of Fluids)

   This paper numerically studies the flow dynamics of aerial undulation of a snake-like model, which is adapted from the kinematics of the flying snake (Chrysopelea) undergoing a gliding process. The model applies aerial undulation periodically in a horizontal plane where a range of angle of attack (AOA) is assigned to model the real gliding motion. The flow is simulated using an immersed-boundary-method-based incompressible flow solver. Local mesh refinement mesh blocks are implemented to ensure the grid resolutions around the moving body. Results show that the undulating body produces the maximum lift at 45° of AOA. Vortex dynamics analysis has revealed a series of vortex structures including leading-edge vortices (LEV), trailing-edge vortices, and tip vortices around the body. Changes in other key parameters including the undulation frequency and Reynolds number are also found to affect the aerodynamics of the studied snake-like model, where increasing of undulation frequency enhances vortex steadiness and increasing of Reynolds number enhances lift production due to the strengthened LEVs. This study represents the first study of both the aerodynamics of the whole body of the snake as well as its undulatory motion, providing a new basis for investigating the mechanics of elongated flexible flyers. 

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2. Vertical bending and aerodynamic performance in flying snake-inspired aerial undulation

   https://doi.org/10.1088/1748-3190/ad920b  

   Gong, Yuchen; Huang, Zihao; Dong, Haibo (November 2024, Bioinspiration & Biomimetics)

   Abstract This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs topological local mesh refinement mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes ( ${\psi }_m$). The vortex dynamics analysis unveiled alterations in leading-edge vortices formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production at ${\psi }_m={2.5}^{\circ }$and the highest lift-to-drag ratio (L/D) at ${\psi }_m=5^{\circ }$, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal–ventral bending amplitude ( ${\psi }_{\text{DV}}$), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% at ${\psi }_{\text{DV}}$= 5°, while a preferable L/D is found at ${\psi }_{\text{DV}}$= −5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body–body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding. 

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3. 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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4. The aerodynamics of flying snake airfoils in tandem configuration

   https://doi.org/10.1242/jeb.233635  

   Jafari, Farid; Holden, Daniel; LaFoy, Roderick; Vlachos, Pavlos P.; Socha, John J. (July 2021, Journal of Experimental Biology)

   null (Ed.)

   ABSTRACT Flying snakes flatten their body to form a roughly triangular cross-sectional shape, enabling lift production and horizontal acceleration. While gliding, they also assume an S-shaped posture, which could promote aerodynamic interactions between the fore and the aft body. Such interactions have been studied experimentally; however, very coarse models of the snake's cross-sectional shape were used, and the effects were measured only for the downstream model. In this study, the aerodynamic interactions resulting from the snake's posture were approximated using two-dimensional anatomically accurate airfoils positioned in tandem to mimic the snake's geometry during flight. Load cells were used to measure the lift and drag forces, and flow field data were obtained using digital particle image velocimetry (DPIV). The results showed a strong dependence of the aerodynamic performance on the tandem arrangement, with the lift coefficients being generally more influenced than the drag coefficients. Flow field data revealed that the tandem arrangement modified the separated flow and the wake size, and enhanced the lift in cases in which the wake vortices formed closer to the models, producing suction on the dorsal surface. The downforce created by the flow separation from the ventral surface of the models at 0 deg angle of attack was another significant factor contributing to lift production. A number of cases showing large variations of aerodynamic performance included configurations close to the most probable posture of airborne flying snakes, suggesting that small postural variations could be used to control the glide trajectory. 

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5. Dynamic Modeling and Validation of Soft Robotic Snake Locomotion

   https://doi.org/10.1109/ICCAR57134.2023.10151763  

   Arachchige, Dimuthu D.; Mallikarachchi, Sanjaya; Kanj, Iyad; Perera, Dulanjana M.; Chen, Yue; Gilbert, Hunter B.; Godage, Isuru S. (April 2023, 2023 9th International Conference on Control, Automation and Robotics (ICCAR))

   Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to date, soft robotic snakes are limited to emulating planar locomotion gaits, which are derived via kinematic modeling and tested on robotic prototypes. Given that the snake locomotion results from the reaction forces due to the distributed contact between their skin and the ground, it is essential to investigate the locomotion gaits through efficient dynamic models capable of accommodating distributed contact forces. We present a complete spatial dynamic model that utilizes a floating-base kinematic model with distributed contact dynamics for a pneumatically powered soft robotic snake. We numerically evaluate the feasibility of the planar and spatial rolling gaits utilizing the proposed model and experimentally validate the corresponding locomotion gait trajectories on a soft robotic snake prototype. We qualitatively and quantitatively compare the numerical and experimental results which confirm the validity of the proposed dynamic model. 

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