Gap crossing is a regular locomotor activity for arboreal animals. The distance between branches likely plays a role in determining whether an animal is capable of crossing a given gap, and what locomotor behavior it uses to do so. Yet, despite the importance of gap distance as a physical parameter influencing gap crossing behavior, the precise relationships between gap distance and movement kinematics have been explored in only a very small number of species. One particularly interesting group of arboreal inhabitants are the flying snakes (Chrysopelea). This species is able to use a dynamic "J-loop" movement to launch its glides, but it is not known whether it is also capable of using such jumps to cross smaller gaps between tree branches. This dissertation addresses this knowledge gap, and investigates the influence of gap distance on crossing behavior and kinematics in three closely-related species of snake: Chrysopelea paradisi, a species of flying snake, and two species from the sister genus, Dendrelaphis, neither of which can glide. Chapter 2 is a literature review of the biomechanics of gap crossing, specifically focusing on the role played by gap distance, and establishes the context for the rest of the work. Chapter 3 presents a detailed study of how increasing gap size influences the behavior and kinematics of gap crossing in C. paradisi, showing that this species uses increasingly dynamic movements to cross gaps of increasing size. Chapter 4 explores the same relationships between gap size and kinematics in D. punctulatus and D. calligastra, revealing remarkable similarities between the three species, suggesting the possibility that dynamic gap crossing may have evolved prior to gliding in this clade. Finally, chapter 5 addresses the role played by gap distance in limiting the non-dynamic, cantilever movements used by these species to cross small gaps, comparing observed stopping distances to those predicted by various torque-related limitations. / Doctor of Philosophy / To successfully cross a gap, an animal must be able to reach or jump from one side to the other. Animals who live in trees must do this quite frequently, as they live among the branches and there are often not connected paths from one place to another. But we don't know very much about how the distance between two structures (the "gap distance") affects the ways an animal moves between them. In this dissertation, I explore how gap distance changes the way a few special species of snakes cross a gap. The species I am studying are special because one species, the paradise tree snake, can glide. Because this 'flying' snake launches its glides by doing a big jump, it is possible that the snake can also jump between tree branches, but this question has never been examined before. We also don't know how the ability to do big jumps evolved, so I studied how distance affects the way two very closely related species of snake, the common tree snake and the northern tree snake, cross gaps. By looking at all of these species, we can understand more about what kinds of behavior are specific to the flying snakes, and which are present in related species. Finally, I also explore how gap distance limits the way the snakes cross gaps when they are not jumping. When the snakes do not jump, they have to hold themselves out straight off the end of a branch. This requires a lot of muscular effort, which means they can't go as far. The fact that the non-jumping behavior is distance-limited might help explain why the snakes need to jump. Altogether, the projects in this study help us understand how gap distance influences what behavior an animal chooses to cross the gap, and increases our knowledge of how flying snakes and their relatives cross gaps in particular.

The genus Chrysopelea encompasses the "flying" snakes. This taxon has the ability to glide via lateral aerial undulation and dorsoventral body flattening, a skill unique to this group, but in addition to other functions common to all colubrids. The skin must be extensible enough to allow this body shape alteration and undulation, and strong enough to withstand the forces seen during landing. For this reason, characterizing the mechanical properties of the skin may give insight to the functional capabilities of the skin during these gliding and landing behaviors. Dynamic and viscoelastic uniaxial tensile tests were combined with a modified particle image velocimetry technique to provide strength, extensibility, strain energy, and stiffness information about the skin with respect to orientation, region, and species, along with viscoelastic parameters. Results compared with two other species in this study and a broader range of species in prior studies indicate that while the skin of these unique snakes may not be specifically specialized to deal with larger forces, extensibility, or energy storage and release, the skin does have increased strength and energy storage associated with higher strain rates. The skin also has differing properties with respect to dorsoventral location, and regional differences in strength in the circumferential orientation. This may indicate that, although the properties of the skin may not be different, the rate at which the skin is strained in the different species may vary, thus altering the apparent properties of the skin during specific behaviors. / Master of Science

Chrysopelea paradisi, also known as the flying snake, possesses one of the most unique forms of aerial locomotion found in nature, using its entire body as a dynamic lifting surface without the use of wings or membranes. Unlike other airborne creatures, this species lacks appendages to aid in controlling its flight trajectory and producing lift. The snake exhibits exception gliding and maneuvering capabilities compared with other species of gliders despite this lack of appendages. While gliding, C. paradisi morphs its body by expanding its ribs, essentially doubling its width and utilizing its entire length as a reconfigurable wing. Its cross-sectional shape transforms into a thick, airfoil shape with a concave ventral surface, outwards protruding lips at the leading and trailing edges, a somewhat triangular dorsal surface with a round apex, and fore-aft symmetry. This study investigated the aerodynamic performance of this unique shape by simulating a single, static segment of the snake's body over a wide range of Reynolds numbers (3,000 to 15,000) and angles of attack (-10 to 60o) to simulate the full range of the snake's flight kinematics. This is the first study on an anatomically accurate snake model, and few aerodynamic studies have been performed in this low Reynolds number regime. Load cell measurements and time-resolved digital particle image velocimetry (TRDPIV) were performed on a 2D anatomically accurate model to determine the lift and drag coefficients, wake dynamics, and vortex shedding characteristics. This geometry produced a maximum lift coefficient of 1.9 and maximum lift to drag ratio of 2.7, and maintained increases in lift up to 35o. Overall, this geometry demonstrated robust aerodynamic behavior by maintain significant lift production and near maximum lift to drag ratios over a wide range of test parameters. These aerodynamic characteristics may enable the flying snake to glide at steep angles and over a wide range of angles of attack, often encountered in gliding trajectories. This geometry also produced larger maximum lift coefficients than many other bluff bodies and airfoils in this low Reynolds number regime. This thesis is organized as follows. The first section contains a broad introduction on gliding flight and C. paradisi's unique mode of gliding. The following section is a manuscript that will be submitted to a journal and contains the experimental analysis on the snake's cross-sectional shape. Several appendices attached to the end of this thesis contain additional analysis and work performed throughout the duration of this project and unique Matlab algorithms developed during this research. / Master of Science

Immersed boundary methods are a class of techniques in computational fluid dynamics where the Navier-Stokes equations are simulated on a computational grid that does not conform to the interfaces in the domain of interest. This facilitates the simulation of flows with complex moving and deforming geometries without considerable effort wasted in generating the mesh. The first part of this dissertation is concerned with the aerodynamics of the cross-section of a species of flying snake, Chrysopelea paradisi (paradise tree snake). Past experiments have shown that the unique cross-section of this snake, which can be described as a lifting bluff body, produces an unusual lift curve--with a pronounced peak in lift coefficient at an angle of attack of 35 degrees for Reynolds numbers 9000 and beyond. We studied the aerodynamics of the cross-section using a 2-D immersed boundary method code. We were able to qualitatively reproduce the spike in the lift coefficient at the same angle of attack for flows beyond a Reynolds number of 2000. This phenomenon was associated with flow separation at the leading edge of the body that did not result in a stall. This produced a stronger vortex and an associated reduction in pressure on the dorsal surface of the snake cross-section, which resulted in higher lift. The second part of this work deals with the analysis of the direct forcing method, which is a popular immersed boundary method for flows with rigid boundaries. We begin with the fully discretized Navier-Stokes equations along with the appropriate boundary conditions applied at the solid boundary, and derive the fractional step method as an approximate block LU decomposition of this system. This results in an alternate formulation of the direct forcing method that takes into consideration mass conservation at the immersed boundaries and also handles the pressure boundary conditions more consistently. We demonstrate that this method is between first and second-order accurate in space when linear interpolation is used to enforce the boundary conditions on velocity. We then develop a theory for the order of accuracy of the direct forcing method with linear interpolation. For a simple 1-D case, we show that the method can converge at a range of rates for different locations of the solid body with respect to the mesh. But this effect averages out in higher dimensions and results in a scheme that has the same order of accuracy as the expected order of accuracy of the interpolation at the boundary. The discrete direct forcing method for the Navier-Stokes equations exhibits an order of accuracy between 1 and 2 because the velocities at the boundary are linearly interpolated, but the resulting boundary conditions on the pressure gradient turn out to be only first-order accurate. We recommend linearly interpolating the pressure gradient as well to make the method fully second-order accurate. We have also developed two open source codes in the course of these studies. The first, cuIBM, is a two-dimensional immersed boundary method code that runs on a single GPU. It can simulate incompressible flow around rigid bodies with prescribed motion. It is based on the general idea of a fractional step method as an approximate block LU decomposition, and can incorporate any type of immersed boundary method that can be made to fit within this framework. The second code, PetIBM, can simulate both two and three-dimensional incompressible flow and runs in parallel on multiple CPUs. Both codes have been validated using well-known test cases.