When flying snakes glide, they use aerial undulation. To determine if aerial undulation is a flight control strategy or a non-functional behavioural vestige of lateral undulation, we measured snake glides using high-speed motion capture and developed a new dynamical model of gliding. Reconstructions of the snake’s wing-body reveal that aerial undulation is composed of horizontal and vertical waves, whose phases differ by 90° and whose frequencies differ by a factor of two. Using these results, we developed a three-dimensional mathematical model of snake flight that incorporates aerodynamic and inertial effects. Although simulated glides without undulation attained some horizontal distance, they are biologically unrealistic because they failed due to roll and pitch instabilities. In contrast, the inclusion of undulation stabilized the rotational motion and markedly increased glide performance. This work demonstrates that aerial undulation in snakes serves a different function than known uses of undulation in other animals, and suggests a new template of control for dynamic flying robots.
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All data that support the plots within this paper and other findings of this study are available in the Data subdirectories of the code repository and at https://drive.google.com/drive/folders/1FpSBUD1XY3guuWjGUE5V7dqluNkoXyKy for processed experiment and simulation data.
Code used to analyse the glide trials and perform the glide simulations is available at github.com/TheSochaLab/Undulation-enables-gliding-in-flying-snakes.
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We thank the Virginia Tech Institute for Creativity, Arts, and Technology (ICAT) for facility access, crew support and funding. In particular, we thank T. Upthegrove, N. McGowan and B. Knapp. We thank G. Nave, T. Weiss, M. Graham, J. Whitehead and J. Garrett for assisting with the kinematics experiments. We thank H. Pendar for help with developing the mathematical model of snake flight, and F. Jafari for discussions about the role of undulation. We thank G. Nave, P. Nolan, K. Tetreault, N. Hall, F. Jafari and M. Graham for critical reading of early versions of the manuscript. We thank B. Robert, J. Settlage and A. Rizzo for help with IACUC. We also thank M. LaBarbera for his original suggestion that undulation might function as a mechanism of dynamic stability. This work was supported by the National Science Foundation under grant 1351322 to J.J.S., grants 1537349 and 1922516 to S.D.R. and grant 0966125 to S.D.R. and J.J.S.
The authors declare no competing interests.
Peer review information Nature Physics thanks Daniel Goldman, Michael Shelley and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary figures, tables and text.
Side view of a long glide of the flying snake Chrysopelea paradisi. This slow-motion sequence shows the snake progress through the ballistic dive to the shallowing glide to landing. The sequence begins with the snake approximately 15 m above the ground, in the extended position just after a J-loop take-off (which was not recorded). During the ballistic dive, the tail is relatively up and the head is down in the pitch axis. As the snake undulates and the glide angle (relative to horizontal) decreases, the tail and posterior body move downward but continuously translate periodically in the vertical axis. Recorded in Penang, Malaysia, 2010, by producer Robert Wise, cameraman John Benam, and Jake Socha. Video provided courtesy of National Geographic Television.
Side view of take-off and flattening of the flying snake Chrysopelea paradisi. This slow-motion sequence shows the snake begin a glide using a J-loop take-off, become dorsoventrally flattened, and then gather the body into an S-shape as it falls through the ballistic dive portion and begins undulating. The body flattening that produces the snake’s aerial cross-sectional shape starts during the jump and is completed just after the snake becomes fully airborne. Recorded in Sabah, Malaysia, 2015, by producer Simon Bell, cameraman Pete McCowen, and Jake Socha. Video provided courtesy of the British Broadcasting Corporation.
Front view of take-off and flattening of the flying snake Chrysopelea paradisi. This slow-motion sequence shows the snake begin a glide using a J-loop take-off, become dorsoventrally flattened, and then gather the body into an S-shape as it falls through the ballistic dive portion and begins undulating. The snake appears momentarily ribbon-flat as it completes the jump, but this appearance results from the overexposure of the dorsal surface of the snake next to the bright sky. Near the end of the sequence, small bumps can be seen on the body near the tail; these bumps are sub-surface parasites that occur naturally in some wild-caught specimens. Recorded in Sabah, Malaysia, 2015, by producer Simon Bell, cameraman Pete McCowen, and Jake Socha. Video provided courtesy of the British Broadcasting Corporation.
Overhead view of a glide trial of the flying snake Chrysopelea paradisi. Recorded with two Photron APS-RX high-speed video cameras. This glide is from a snake with a mass of 71 g and snout–vent length of 77 cm.
Infrared markers tracked through a glide of the flying snake Chrysopelea paradisi. Top and side views are shown of 12 points on the snake as it moves through its trajectory.
Development of a 3D model of the flying snake Chrysopelea paradisi from motion-capture data. The interactive online visualization of the snake can be found in Visualization 1: https://sketchfab.com/models/5aea787df31d48e288915b94e3a4c9de.
Simulations of a flying snake gliding with and without aerial undulation. The co-moving frame, located at the center of mass, is indicated by the three orthogonal arrows (red, green, and blue), and the inertial coordinate system is indicated by the long lines. The instantaneous center of mass velocity is shown by the black arrow. The sheets emanating from the body are the local lift (blue) and drag (yellow) forces distributed over the body. In the first simulation, the undulating snake (Chrysopelea paradisi, f = 1.2 Hz) pitches down, but it glides 10 m vertically before any Euler angle exceeds 85°, indicating that the snake is relatively stable over short distances. In the second simulation, the snake has the same initial conditions as in the first, but with an undulation frequency of 0 Hz. The horizontal and vertical waves were selected such that the glide is generally stable in pitch. However, the snake is still unstable, as it yaws to the left more than 85° before falling 10 m vertically.
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Yeaton, I.J., Ross, S.D., Baumgardner, G.A. et al. Undulation enables gliding in flying snakes. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0935-4