Physical Mechanisms of Control of Gliding in Flying Snakes Farid Jafari Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering Mechanics John J. Socha, chair Nicole Abaid Shane D. Ross Pavlos P. Vlachos Craig A. Woolsey August 12, 2016 Blacksburg, VA Keywords: Flying snakes, glide, stability, control, and aerodynamics Physical Mechanisms of Control of Gliding in Flying Snakes Farid Jafari 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. Physical Mechanisms of Control of Gliding in Flying Snakes Farid Jafari GENERAL AUDIENCE ABSTRACT 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. ACKNOWLEDGEMENTS The experimental part of this study could never be accomplished without the unstinting help of my dear friends Dr. Sevak Tahmasian, Dr. Ayoub Yari, Dr. Mohammad Mostafavi, and Mr. Khaled Adjerid, to whom I will always be grateful. Also, I would like to thank Dr. Christopher Williams and other members of DREAMS lab at Virginia Tech who made the snake model with 3D printing. I would like to thank my dissertation committee for their support and helpful advice. I am especially indebted to my advisor Dr. Jake Socha for his generous support and invaluable guidance. I learned much more than science from him and my respect for him is beyond words. My greatest appreciation is due to my wife, who never stopped encouraging me during all of these years. Without her, this work would never be accomplished. I dedicate my dissertation to my wife and to my son who are my life’s delights. iv TABLE OF CONTENTS Abstract ……………………………………………...……………...………………….… ii General audience abstract ……………………………...………………………………… iii Acknowledgements ……………………………...…………………………...……...…… iv Table of contents ……………………………………………….………………...…….… v List of figures …………………………………………..…………………...……………. vii List of tables ……………………………………………………...………………………. xv Chapter 1. Introduction ……………………………..……………………….…………… 1 1. Motivation …………………………………………………...…………...……. 1 2. Background ………………………………………...……………….…………. 2 3. The present work …………………………………………….……...........……. 5 References …………………………………………………………...……...……. 13 Chapter 2. A theoretical analysis of pitch stability during gliding in flying snakes ……... 18 Abstract ………………….………………………………………..…………........ 18 1. Introduction ………………….……………………………………………........ 18 2. Methods …………………………..…………………………..………............... 20 2.1. Modeling of forces ………….……………………….…….……........ 22 2.2. Model 1 ………………………….…….…………….…….………… 22 2.3. Model 2 …………………………….…….…………….….………… 24 2.4. Equations of motion for model 2 ……….……………...….………… 26 2.5. Determination of parameters for model 2 ……….……..….……........ 27 2.6. Stability analysis ………………………...…………..…….………… 29 2.7. Simulations ……………………………….……………......……....... 31 3. Results …………………………………………….…………..……..……........ 32 3.1. Trajectory simulations ………………………..……...…….……....... 32 3.2. Stability analysis …………………………...……….….….………… 34 4. Discussion ………………………………………………….………..……........ 35 4.1. Stability analysis of the models ……………………..…….………… 35 4.2. Implications about gliding snakes ………………..…….….……........ 37 4.3. Gliding trajectories ………………………….….........…….……........ 39 4.4. Conclusion …………………………………......…....…….………… 39 References …………………………………………….………………..……........ 49 Chapter 3. Dynamical analysis of undulatory motions in a 3D model of flying snakes …. 51 Abstract ………………….…………………………………………..………........ 51 1. Introduction ………………….……………………………………………........ 51 2. Methods …………………………..…………………………..………............... 55 2.1. Modeling of forces ………….……………………….…….……........ 56 2.2. Equations of motion ……………………...………….…….……........ 57 2.3. Controlled motion about a fixed point ………...……….….……........ 58 v 2.4. Motion with undulation ……….……………...…………....……........ 59 2.5. Simulations ……………………………….……………......……....... 60 3. Results …………………………………………….…………..……..……........ 61 4. Discussion ………………………………………………….………..……........ 65 4.1. Glide simulations ……………………..…………………...………… 65 4.2. Implications about gliding snakes ………………..…….….……........ 67 4.3. Modeling limitations ………………………….…......…….……........ 68 4.4. Conclusion …………………………………...……...…….……….... 69 References …………………………………………….………………..……........ 80 Chapter 4. Experimental study of the aerodynamics of snake-like airfoils in tandem configuration ……………………………………………………………….....…………. 84 Abstract ………………….……………………………..……………………........ 84 1. Introduction ………………….……………………………………………........ 84 2. Methods …………………………..…………………………..………............... 87 2.1. Experimental models and test facility ……………….…….……........ 88 2.2. Load cell measurements ……………….…………….…….……........ 89 2.3. Flow field measurements …………………...………….….………… 90 2.4. Spectral analysis ……….…………………………….....….……........ 91 2.5. PIV-based aerodynamic force calculation ……………..….………… 91 2.6. Proper orthogonal decomposition …………….……..…….……........ 92 2.7. Uncertainty analysis …………………..….……………......……........ 93 3. Results …………………………………………….…………..……..……........ 93 3.1. Lift and drag coefficients …………………………....…….……........ 93 3.2. Spectral analysis ……….…………………………….....….……........ 96 3.3. Velocity field ……….……………………….……….....….……......