Physical mechanisms of control of gliding in flying snakes

Abstract

Flying snakes possess a sophisticated gliding ability with a unique aerial behavior, in which they flatten their body to make a roughly triangular cross-sectional shape to produce lift and gain horizontal acceleration. Also, the snakes assume an S-like posture and start to undulate by sending traveling waves down the body. The present study aims to answer how the snakes are able to control their glide trajectory and remain stable without any specialized flight surfaces. Undulation is the most prominent behavior of flying snakes and is likely to influence their dynamics and stability. To examine the effects of undulation, a number of theoretical models were used. First, only the longitudinal dynamics were considered with simple two-dimensional models, in which the snake was approximated as a number of connected airfoils. Previously measured force coefficients were used to model aerodynamic forces, and undulation was considered as periodic changes in the mass and area of the airfoils. The model was shown to be passively unstable, but it could be stabilized with a restoring pitching moment. Next, a three-dimensional model was developed, with the snake modeled as a chain of airfoils connected through revolute joints, and undulation was considered as periodic changes in the joint angles. It was shown that undulation, when added to a linearization-based closed-loop control, could increase the size of the basin of stability. Our theoretical results suggested that the snakes need some extent of closed-loop control in spite of the clear contribution of undulation to the stability of glide. Next, we considered the effects of aerodynamic interactions between the fore and the aft body on the aerodynamic performance of flying snakes. Two-dimensional anatomically accurate airfoils were used in a water tunnel. Lift and drag forces were measured by load cells, and the flow field data were obtained using digital particle image velocimetry. The results confirmed strong dependence of the aerodynamic performance on the tandem arrangement. Flow fields around the airfoils were obtained to show how the tandem arrangement modified the separated flow and the wake; therefore altering the pressure field and resulting in changes in the lift and drag.