Modeling non-equilibrium glides in flying snakes

Flying snakes of the species Chrysopelea paradisi glide without the use of limbs. These gliders use the speed of free fall and the change in their body shape to generate lift. Despite their lack of appendages, their ability to glide has piqued the interest of many. Hence, modeling the flight of these snakes has received considerable attention in the recent past. Experimental studies have been done in the past on live flying snakes to understand their unusual glide mechanism. Equilibrium glide-in which the speed of the center of gravity of the snake is more or less constant - is relatively easier to model than nonequilibrium glide where this speed changes with time. Flying snakes spend most of their flight in non-equilibrium glide than on equilibrium glide. An earlier model for generating the undulating shape generated realistic shapes at a specified time. However, many parameters needed to be fine-tuned along with unforeseen singularities. Further, it generated the centerline shape of the snake in a plane, but could not consider out of plane undulation of the snake. In the current work, a better model for the undulating motion of the snake is proposed which is extended to include out of plane motion of the snake's centerline. The aerodynamic forces acting on the snake at an instant of time are computed using thin airfoil theory and blade element theory. With the help of these, the velocities and trajectory of the snake's flight path are computed and compared with data available in literature. This model has potential for application in biological and biomechanical study of the flight of flying snakes, study of unconventional Micro-aerial vehicle and physics based computer animation.

I. Introduction

Flying snakes were noted and recorded as early as 1899 [1]. Further, flying snakes of the species Chrysopelea paradisi glide without the use of limbs. These gliders use the speed of free fall and the change in their body shape to generate lift.