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. / Ph. D. / Flying snakes are a group of snake species that are found primarily in lowland tropical forests of south and southeast Asia. These snakes possess a sophisticated gliding ability, with an aerial behavior which is fundamentally different from any other biological or man-made flyer. As flying snakes lack conventional wings or any other specialized flight surfaces, they use their entire body as a morphing ‘wing’ to produce lift and gain forward acceleration. While airborne, the snakes assume an undulating S-like posture, in which traveling waves move down the body. The role of this highly dynamic aerial behavior in the gliding of snakes is not known. In this study, we hypothesized that body undulation is likely to influence the dynamics and stability of snakes, because it continually redistributes mass and aerodynamic forces along the body. To study the dynamics of snake flight, we developed a number of theoretical models, starting from simple two-dimensional models, and then proceeding to more realistic three-dimensional models. Undulation was considered as periodic changes in the shape of the model. The models were shown to be passively unstable, but they could be stabilized with some control. Under certain conditions, it was shown that undulation could stabilize the trajectory without any control. Overall, our theoretical results suggested that the snakes need some extent of control in spite of the clear contribution of undulation to the stability of glide. We also considered the effects of aerodynamic interactions between the fore and the aft body on the aerodynamic performance of flying snakes. With two anatomically accurate airfoils placed in a water tunnel, the forces were measured by load cells, and the flow around the airfoils were captured by high-speed cameras. The results confirmed that the aerodynamic forces on the tandem airfoils would change when the airfoils are moved with respect to each other. Overall, the results of this study elucidate the underlying physical principles used by flying snakes in their unconventional mode of aerial locomotion. Therefore, these results can help to engineering novel biologically inspired vehicles.

This dissertation addresses the question, how and why do 'flying' snakes (Chrysopelea) undulate through the air? Instead of deploying paired wings or wing-like surfaces, flying snakes jump, splay their ribs into a bluff-body airfoil, and undulate through the air. Aerial undulation is the dominant feature of snake flight, but its effects on locomotor performance and stability are unknown. Chapter 2 describes a new non-equilibrium framework to analyze gliding animals and how the pitch angle affects their translational motion. Chapter 3 combines flying snake glide experiments and detailed dynamic modeling to address what is aerial undulation and how each kinematic component affects rotational stability and translational performance. Chapter 4 combines the kinematic data of Chapter 3, with elements of the non-equilibrium framework of Chapter 2, to examine the kinematics of snake flight in greater detail. This chapter also tests if our current understanding of flying snake aerodynamics is sufficient to explain the observed center of mass motion. / Ph. D. / Flying snakes can move unlike any other flying or slithering animal. Flying snakes have evolved the ability to glide safely to the ground by undulating through the air. Flapping flyers, like birds, bats, and insects, move through the air using wings and powerful flight muscles. In contrast, gliding animals fall through the air, using gravity to increase their speed, and air resistance to produce lift and drag forces such that they move over the ground. Flying snakes glide by jumping, flattening their bodies (similar to a cobra hooding), and undulating through the air using an ‘S’-shaped body. This dissertation addresses the question, how and why do flying snakes undulate through the air? First, I describe a new mathematical analysis of gliding animals, which provides a framework to understand how an animal’s size and orientation to the oncoming airflow affect its glide performance. Second, I describe glide experiments where the bodies of flying snakes were measured as they flew through a large indoor glide arena. From these measurements, we quantified how the body bends in the horizontal and vertical directions. Next, I describe a detailed mathematical model used to test how the different body configurations we measured affect glide performance and flight stability. The model result indicate that flying snakes likely use aerial undulation to stabilize their rotational motion. Third, I tested if our current measurements of the lift and drag properties of flying snakes, based on the quasi-steady assumption, can account for the trajectories we recorded. The force analysis suggests that flying snakes produce more force than the quasi-steady assumption can account for, and that future work is needed to understand unsteady aerodynamic mechanisms relevant for snake flight.