1. Performance of Ray Fins in Fish Locomotion Qiang Zhu and Kourosh Shoele Department of Structural Engineering University of California San Diego

2. Characteristics of Ray Fins Characteristics:   Structural lightness   Deployability   Multi-dimensional controllability   3D anisotropic flexibilty Ray fins of bluegill sunfish (Alben et al. 2007) rays membrane base branches tendons Cartilage pad ligament dorsal fin pectoral fin pelvic fin anal fin caudal fin Tangorra et al. 2007 Lauder Lab Videos

3. Fluid-Structure Interaction Model   Potential flow model with boundary element method   Wakes are modeled as shear layers and mathematically represented by distributions of dipoles   Valid in high Reynolds numbers   Nonlinear Euler-Bernoulli beam model for embedded rays   Fully-coupled fluid-structure interactions Zhu et al. JFM 2002, Zhu & Kourosh JEB 2008

4. Caudal Fin Dynamics Advantages of a fin with flexible rays:  Reduced lateral force  Increased propulsion efficiency  Reduced dependence on kinematic parameters  Achievement of different locomotion modes (homocercal, heterocercal) Zhu & Kourosh JEB 2008

5. Pectoral Fins in Labriform Swimming Thorsen et al. 2005 Shape and structure Rigid Rays: All the rays are rigid (red lines) Fin A: All the rays have the same stiffness (green lines) Fin B: The ray at the leading edge is strengthened (blue lines) Kourosh & Zhu JEB 2009, 2010 Kinematics Flapping+rowing+baseline rotation

6. Summary   The ray-fin structure enables detailed control of fin motion (since each ray can be controlled individually), and is essential to the performance of the fin in locomotion.   Flexibility of the rays may enhance fin performance. It, however, depends upon detailed distribution of the stiffness (e.g. reinforcement at the leading edge).

7. Broader View Other Skeleton-Reinforced Membranes in Nature Venation structure in the wing of a Manduca sexta (from Combes & Daniel 2003). Insect Wings Cell Membrane Cell membrane contains a lipid bilayer supported by a protein scaffold (the cytoskeleton) (T. Wittmann, Science Photo Library). Mollusk Nacre Mollusk (e.g. abalone) nacre contains a chitin network that controls the growth and mechanical properties of the shell (Asaro & Harley 2004). Zhu et al. Biophy. J 2007; Zhu & Asaro Biophy. J. 2008; Peng et al. Phys. Review E. 2010

8. This study is supported by NSF. Acknowledgements