Aerodynamics of the flying snake Chrysopelea paradisi: how a bluff body cross-sectional shape contributes to gliding performance

A prominent feature of gliding flight in snakes of the genus Chrysopelea is the unique cross-sectional shape of the body, which acts as the lifting surface in the absence of wings. When gliding, the flying snake Chrysopelea paradisi morphs its circular cross-section into a triangular shape by splaying its ribs and flattening its body in the dorsoventral axis, forming a geometry with fore–aft symmetry and a thick profile. Here, we aimed to understand the aerodynamic properties of the snake's cross-sectional shape to determine its contribution to gliding at low Reynolds numbers. We used a straight physical model in a water tunnel to isolate the effects of 2D shape, analogously to studying the profile of an airfoil of a more typical flyer. Force measurements and time-resolved (TR) digital particle image velocimetry (DPIV) were used to determine lift and drag coefficients, wake dynamics and vortex-shedding characteristics of the shape across a behaviorally relevant range of Reynolds numbers and angles of attack. The snake's cross-sectional shape produced a maximum lift coefficient of 1.9 and maximum lift-to-drag ratio of 2.7, maintained increases in lift up to 35 deg, and exhibited two distinctly different vortex-shedding modes. Within the measured Reynolds number regime (Re=3000–15,000), this geometry generated significantly larger maximum lift coefficients than many other shapes including bluff bodies, thick airfoils, symmetric airfoils and circular arc airfoils. In addition, the snake's shape exhibited a gentle stall region that maintained relatively high lift production even up to the highest angle of attack tested (60 deg). Overall, the cross-sectional geometry of the flying snake demonstrated robust aerodynamic behavior by maintaining significant lift production and near-maximum lift-to-drag ratios over a wide range of parameters. These aerodynamic characteristics help to explain how the snake can glide at steep angles and over a wide range of angles of attack, but more complex models that account for 3D effects and the dynamic movements of aerial undulation are required to fully understand the gliding performance of flying snakes.

[1]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[2]  M. Koehl,et al.  THE INTERACTION OF BEHAVIORAL AND MORPHOLOGICAL CHANGE IN THE EVOLUTION OF A NOVEL LOCOMOTOR TYPE: “FLYING” FROGS , 1990, Evolution; international journal of organic evolution.

[3]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[4]  Roddam Narasimha,et al.  Leading edge shape for flat plate boundary layer studies , 1994 .

[5]  C. Williamson Vortex Dynamics in the Cylinder Wake , 1996 .

[6]  D. Rockwell,et al.  FORCE PREDICTION BY PIV IMAGING: A MOMENTUM-BASED APPROACH , 1997 .

[7]  Shigeru Sunada,et al.  Airfoil Section Characteristics at a Low Reynolds Number , 1997 .

[8]  M. Selig,et al.  High-Lift Low Reynolds Number Airfoil Design , 1997 .

[9]  S. Balachandar,et al.  Mechanisms for generating coherent packets of hairpin vortices in channel flow , 1999, Journal of Fluid Mechanics.

[10]  George Em Karniadakis,et al.  Dynamics and low-dimensionality of a turbulent near wake , 2000, Journal of Fluid Mechanics.

[11]  M. G. McCay,et al.  Aerodynamic stability and maneuverability of the gliding frog Polypedates dennysi. , 2001, The Journal of experimental biology.

[12]  Pavlos Vlachos,et al.  Flow Control of a Sharp-Edged Airfoil , 2001 .

[13]  F. Scarano Iterative image deformation methods in PIV , 2002 .

[14]  Raghu Machiraju,et al.  A Novel Approach To Vortex Core Region Detection , 2002, VisSym.

[15]  J. Socha Kinematics: Gliding flight in the paradise tree snake , 2002, Nature.

[16]  M. Wernet Digital Particle Image Velocimetry , 2003 .

[17]  F. Lehmann The mechanisms of lift enhancement in insect flight , 2004, Naturwissenschaften.

[18]  Z. J. Wang,et al.  Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments , 2004, Journal of Experimental Biology.

[19]  M. Dickinson,et al.  The effect of advance ratio on the aerodynamics of revolving wings , 2004, Journal of Experimental Biology.

[20]  B. Tobalske,et al.  Aerodynamics of the hovering hummingbird , 2005, Nature.

[21]  M. Labarbera,et al.  Effects of size and behavior on aerial performance of two species of flying snakes (Chrysopelea) , 2005, Journal of Experimental Biology.

[22]  J. Westerweel,et al.  Universal outlier detection for PIV data , 2005 .

[23]  R. Adrian,et al.  On the relationships between local vortex identification schemes , 2005, Journal of Fluid Mechanics.

[24]  R. Adrian Twenty years of particle image velocimetry , 2005 .

[25]  Laurent David,et al.  Characterization by proper-orthogonal-decomposition of the passive controlled wake flow downstream of a half cylinder , 2005 .

[26]  Z. Jane Wang,et al.  DISSECTING INSECT FLIGHT , 2005 .

[27]  M. Labarbera,et al.  A 3-D kinematic analysis of gliding in a flying snake, Chrysopelea paradisi , 2005, Journal of Experimental Biology.

[28]  Troy R. Smith,et al.  Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial , 2005 .

[29]  R. Dudley,et al.  Directed aerial descent in canopy ants , 2005, Nature.

[30]  Joseph Katz,et al.  Instantaneous pressure and material acceleration measurements using a four-exposure PIV system , 2006 .

[31]  Fulvio Scarano,et al.  Non-intrusive load characterization of an airfoil using PIV , 2006 .

[32]  John J Socha,et al.  Becoming airborne without legs: the kinematics of take-off in a flying snake, Chrysopelea paradisi , 2006, Journal of Experimental Biology.

[33]  K. Breuer,et al.  Direct measurements of the kinematics and dynamics of bat flight , 2006, Bioinspiration & biomimetics.

[34]  A. Hedenström,et al.  Bat Flight Generates Complex Aerodynamic Tracks , 2007, Science.

[35]  Kristin L Bishop Aerodynamic force generation, performance and control of body orientation during gliding in sugar gliders (Petaurus breviceps) , 2007, Journal of Experimental Biology.

[36]  Bret W Tobalske,et al.  Biomechanics of bird flight , 2007, Journal of Experimental Biology.

[37]  Robert Dudley,et al.  Gliding and the Functional Origins of Flight: Biomechanical Novelty or Necessity? , 2007 .

[38]  Anders Hedenström,et al.  Beyond robins: aerodynamic analyses of animal flight , 2008, Journal of The Royal Society Interface.

[39]  Adric Eckstein,et al.  Phase correlation processing for DPIV measurements , 2008 .

[40]  Ferry Schrijer,et al.  Effect of predictor–corrector filtering on the stability and spatial resolution of iterative PIV interrogation , 2008 .

[41]  P. Vlachos,et al.  The Physical Mechanism of Heat Transfer Augmentation in Stagnating Flows Subject to Freestream Turbulence , 2008 .

[42]  Fritz-Olaf Lehmann,et al.  Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl , 2008, Journal of The Royal Society Interface.

[43]  Kenneth Breuer,et al.  Aeromechanics of Membrane Wings with Implications for Animal Flight ArnoldSong, ∗ XiaodongTian, † EmilyIsraeli, ‡ RicardoGalvao, § KristinBishop, ¶ SharonSwartz, ∗∗ , 2008 .

[44]  Jian Chen,et al.  Quantifying the complexity of bat wing kinematics. , 2008, Journal of theoretical biology.

[45]  Anders Hedenström,et al.  PIV-based investigations of animal flight , 2009 .

[46]  P. Vlachos,et al.  Digital particle image velocimetry (DPIV) robust phase correlation , 2009 .

[47]  A. Hedenström,et al.  A quantitative comparison of bird and bat wakes , 2010, Journal of The Royal Society Interface.

[48]  F. Lehmann Wing–wake interaction reduces power consumption in insect tandem wings , 2009 .

[49]  Fulvio Scarano,et al.  Surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image velocimetry , 2009 .

[50]  P. Vlachos,et al.  A mechanism for mitigation of blade–vortex interaction using leading edge blowing flow control , 2009 .

[51]  Yu Zhou,et al.  Aerodynamic Characteristics of Asymmetric Bluff Bodies , 2009 .

[52]  Adric Eckstein,et al.  Assessment of advanced windowing techniques for digital particle image velocimetry (DPIV) , 2009 .

[53]  Kyung-Soo Yang,et al.  Numerical Study of Flow past a Square Cylinder with an Angle of Incidence , 2009 .

[54]  Jeffery T. Murphy,et al.  An Experimental Investigation on a Bio-inspired Corrugated Airfoil , 2009 .

[55]  Christophe Sarraf,et al.  Thickness effect of NACA foils on hydrodynamic global parameters, boundary layer states and stall establishment , 2010 .

[56]  John J Socha,et al.  Non-equilibrium trajectory dynamics and the kinematics of gliding in a flying snake , 2010, Bioinspiration & biomimetics.

[57]  Haecheon Choi,et al.  Aerodynamic characteristics of flying fish in gliding flight , 2010, Journal of Experimental Biology.

[58]  Cameron V. King,et al.  Assessment of pressure field calculations from particle image velocimetry measurements , 2010 .

[59]  Brenden P. Epps,et al.  An error threshold criterion for singular value decomposition modes extracted from PIV data , 2010 .

[60]  Hongxing Yang,et al.  The ultra-low Reynolds number airfoil wake , 2010 .

[61]  K. Breuer,et al.  Wake structure and wing kinematics: the flight of the lesser dog-faced fruit bat, Cynopterus brachyotis , 2010, Journal of Experimental Biology.

[62]  M. Labarbera,et al.  Effects of Body Cross-sectional Shape on Flying Snake Aerodynamics , 2010 .

[63]  Enpu Gong,et al.  Model tests of gliding with different hindwing configurations in the four-winged dromaeosaurid Microraptor gui , 2010, Proceedings of the National Academy of Sciences.

[64]  R. Dudley,et al.  Animal aloft: the origins of aerial behavior and flight. , 2011, Integrative and comparative biology.

[65]  John J Socha,et al.  Gliding flight in Chrysopelea: turning a snake into a wing. , 2011, Integrative and comparative biology.

[66]  R. Dudley,et al.  Evolution and ecology of directed aerial descent in arboreal ants. , 2011, Integrative and comparative biology.

[67]  Joseph W Bahlman,et al.  Glide performance and aerodynamics of non-equilibrium glides in northern flying squirrels (Glaucomys sabrinus) , 2013, Journal of The Royal Society Interface.

[68]  A. Strauß Theory Of Wing Sections Including A Summary Of Airfoil Data , 2016 .