Experimental hydrodynamics imaging of four Pangasius sanitwongsei were considered. A quantitative characterization of caudal fin is presented in this article. Steady swimming of four P. sanitwongsei with different total length was studied experimentally and taped by high-speed digital video, and undulatory movement of each fish at different velocity was revealed. The pattern of body undulatory movement of the fish was drawn from the video images. Three main factors that determine the fish swimming behavior are Reynolds number, Strouhal number and shape. In this study, Lf/L was chosen as a characteristic of shape, where Lf was the distance from the start of the head to the end of the head. This is a major point and displays less variation of head to the more variation of the body and caudal fin. L is the length of the fish body. The relationship between Reynolds number and Strouhal number of four P. sanitwongsei with different Lf/L were studied here. Then, the relationship between effective non-dimensional parameters in thrust force and kinematic parameters was found. As a result, an experimental equation was formulated. This equation indicates that, as much as the ratio of the end part of fish with high undulatory movement (body and caudal fin) to the total length goes up, the ratio of amplitude to the total length increases. Consequently, there was an increase in displacement and thrust force also. Then, undulatory movement equation of fish swimming was calculated by fitting a second-order function that describes wave amplitude of this type of fish. All the finding in these researches could be applied to design a robotic fish.
movement equation, fish swimming, robot fish, video image, Pangasius, undulatory
 Arakeri, J.H., Fluid mechanics of fi sh swimming. Resonance, 14(1), pp. 32–46, 2009. doi: http://dx.doi.org/10.1007/s12045-009-0005-9
 Hu, H., Liu, J., Dukes, I. & Francis, G., Design of 3d swim pattern for autonomous robotic fi sh. IEEE, International Conference on Intelligent Robots and Systems, pp. 2406–2411, 2006.
 Streitlien, G.S. & Triantafyllou, M.S., Effi cient foil propulsion through vortex control. AIAA Journal, 34(11), pp. 2315–2319, 1996. doi: http://dx.doi.org/10.2514/3.13396
 Anderson, J.M., Streitlien, K., Barrett, D.S. & Triantafyllou, M.S., Oscillating foils of high propulsive effi ciency. Journal of Fluid Mechanics, 360, pp. 41–72, 1998.doi: http://dx.doi. org/10.1017/S0022112097008392
 Lauder, G.V., Nauen, J.C. & Drucker, E.G., Experimental hydrodynamics and evolution: function of median fi ns in ray-fi nned fi shes. I. & C. Biology, 42(5), pp.1009–1017, 2002.
 Gillbert, D., Quantitative characterization of three – dimensional pectoral fi n kinematics in Bluegill sunfi sh, Lepomis macrochirus. MURJ, 10, pp. 58–64, 2004.
 Lauder, G.V. & Madden, G.A., Learning from fi sh: kinematics and experimental hydrodynamics for roboticists. International Journal of Automation and Computing, 4, pp. 325–335, 2006. doi: http://dx.doi.org/10.1007/s11633-006-0325-0
 Bejan, A. & Marden, J.H., Unifying constructal theory for scale effects in running, swimming and fl ying. Journal of Experimental Biology, 209, pp. 238–248, 2006. doi: http://dx.doi.
 Bejan, A. & Marden, J.H., Constructing animal locomotion from new thermodynamics theory. American Scientist, 94, pp. 342–349, 2006. doi: http://dx.doi.org/10.1511/2006.60.1000
 Standen, E.M. & Lauder, G.V., Hydrodynamic function of dorsal and anal fi ns in brook trout (Salvelinus fontinalis). Journal of Experimental Biology, 210, pp. 325–339, 2007. doi: http:// dx.doi.org/10.1242/jeb.02661
 Masalo, I., Reig, L. & Oca, j., Study of fi sh swimming activity using acoustical Doppler velocimetry (ADV) techniques. Aquacultural Engineering, 38, pp. 43–51, 2008. doi: http://dx.doi. org/10.1016/j.aquaeng.2007.10.007
 Lauder, G.V., Swimming hydrodynamics: ten questions and technical approaches needed to resolve them. Experiments in Fluids, 51, pp. 23–35, 2011. doi: http://dx.doi.org/10.1007/ s00348-009-0765-8
 Stafi otakis, M., Lane, D.M. & Davies, J.B.C., Review of fi sh swimming modes for aquatic locomotion. IEEE Journal of Oceanic Engineering, 24(2), pp. 237–252, 1999. doi: http://dx.doi. org/10.1109/48.757275
 Lauder, G.V. & Drucker, E.G., Morphology and experimental hydrodynamics of fi sh fi n control surfaces. IEEE Journal of Oceanic Engineering, 29(3), pp. 556–571, 2004. doi: http:// dx.doi.org/10.1109/JOE.2004.833219
 Lindsey, C.C., Form function and locomotory habits in fi sh. Fish Physiology, Vol. 7, Academic Press: New York, pp. 1–100, 1987.
 Lauder, G.V., Nauen, J.C. & Drucker, E.G., Experimental hydrodynamics and evolution: function of median fi ns in ray-fi nned fi shes. Integrative and Comparative Biology, 42(5), pp.1009–1017, 2002. doi: http://dx.doi.org/10.1093/icb/42.5.1009
 Webb, P.W., Simple physical principles and vertebrate aquatic locomotion. American Zoologist, 28, pp. 709–725, 1988.
 Takeuchi, S., Kusada, S. & Kajishima, T., Optimisation of fi sh shape and swim mode in fully resolved 2-D fl ow fi eld by genetic algorithm with the least square prediction method. (Chapter13). Bio-mechanisms of Swimming and Flying, eds. N. Kato & S. Kamimura, Springer-V erlag: T okyo, pp. 155–166, 2007.
 Abbaspour, M. & Vaghefi , A.S., Experimental hydrodynamics imaging and undulatory movement equation of steady swimming fi sh (Pangasius sanitwongsei). WIT Transactions on Ecology and the Environment (Design and Nature VI), 160, pp. 171–181, ISSN 1743-3541 (on-line) WIT Press: Southampton, 2012, www.witpress.com, doi:10.2495/DN12016.
 Ziegler, M., Iida, F. & Pfeifer, R., Underwater locomotion: roles of morphological properties and behavioural diversity. Proceedings of the 9th International Conference on Climbing and Walking Robots (CLAWAR), Brussels, Belgium, 2006.
 Liao, J.C., Beal, D.N., Lauder, G.L. & Triantafyllou, M.S., The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street. Journal of Experimental Biology, 206, pp. 1059–1073, 2003. doi: http://dx.doi.org/10.1242/jeb.00209
 Liu, J. & Hu, H., A 3D simulator for autonomous robotic fi sh. International Journal of Automation and Computing, 1, pp. 42–50, 2004. doi: http://dx.doi.org/10.1007/s11633-004-0042-5
 Vaghefi , A.S. & Abbaspour, M., Experimental hydrodynamics imaging of Trout in steady swimming. IPCBEE, 32, pp. 135–139, 2012.