Thrust estimation of a flapping foil attached to an elastic plate using multiple regression analysis

  • Kumar, Rupesh (School of Naval Architecture and Ocean Engineering, University of Ulsan) ;
  • Shin, Hyunkyoungm (School of Naval Architecture and Ocean Engineering, University of Ulsan)
  • Received : 2018.07.31
  • Accepted : 2019.02.19
  • Published : 2019.02.18


Researchers have previously proven that the flapping motion of the hydrofoil can convert wave energy into propulsive energy. However, the estimation of thrust forces generated by the flapping foil placed in waves remains a challenging task for ocean engineers owing to the complex dynamics and uncertainties involved. In this study, the flapping foil system consists of a rigid NACA0015 section undergoing harmonic flapping motion and a passively actuated elastic flat plate attached to the leading edge of the rigid foil. We have experimentally measured the thrust force generated due to the flapping motion of a rigid foil attached to an elastic plate in a wave flume, and the effects of the elastic plates have been discussed in detail. Furthermore, an empirical formula was introduced to predict the thrust force of a flapping foil based on our experimental results using multiple regression analysis.


Supported by : Korea Institute of Energy Technology Evaluation and Planning, Korea Electric Power Corporation


  1. Belibassakis, K.A., Filippas, E.S., Touboul, J., Rey, V., 2015. Hydrodynamic analysis of oscillating hydrofoils in waves and currents. Towar. Green Mar. Technol. Transp. 185-192.
  2. Blondeaux, Paolo, Fornarelli, Francesco, G, L., 2005. Numerical experiments on flapping foils mimicking fish-like locomotion. Phys. Fluids 17.
  3. Bockmann, E., Steen, S., 2014. Experiments with actively pitch-controlled and spring-loaded oscillating foils. Appl. Ocean Res. 48, 227-235.
  4. Evangelos, S.F., 2015. Augmenting ship propulsion in waves using flapping foils initially designed for roll stabilization. In: YSC 2015. 4th Int. Young Sci. Conf. Comput. Sci. Elsevier B. V., Athens, pp. 103-111.
  5. Filippas, E.S., Belibassakis, K.A., 2014. Hydrodynamic analysis of flapping-foil thrusters operating beneath the free surface and in waves. Eng. Anal. Bound. Elem. 40, 47-59.
  6. Fish, F.E., 2013. Advantages of natural propulsive systems. Mar. Technol. Soc. J. 47, 37-44.
  7. Gause JA. Flexible Fin Propulsion Member and Vessels Incorporated Same. GB Patenet 1176559, 1966.
  8. Hover, F.S., Haugsdal, Triantafyllou, M.S., 2004. Effect of angle of attack profiles in flapping foil propulsion. J. Fluid Struct. 19, 37-47.
  9. Isshiki, H., 1994. Wave energy utilization into ship propulsion by fins attached to a ship. Bull Soc Nav Archit Japan III, 508.
  10. Jakobsen, E., 1981. The foilpropeller, wave power for propulsion. In: Second International Symposium on Wave & Tidal Energy. BHRA Fluid Engineering, pp. 363-369.
  11. Lee, J., Park, Y.J., Cho, K.J., Kim, D., Kim, H.Y., 2017. Hydrodynamic advantages of a low aspect-ratio flapping foil. J. Fluid Struct. 71, 70-77.
  12. Hermann Linden. Improved combination with floating bodies, of fins adapted to effect their propulsion. GB Patent 14,630. Filed Aug. 1, 1895. Patented Jul. 18, 1896. GBD189514630 (A), n.d.
  13. Liu, Z., Tian, F.B., Young, J., Lai, J.C.S., 2017. Flapping foil power generator performance enhanced with a spring-connected tail. Phys. Fluids 29.
  14. Liu, Peng, Liu, Yebao, Huang, Shuling, Jianfeng Zhao, Y.S., 2018. Effects of regular waves on propulsion performance of flexible flapping foil. Appl. Sci. 8, 934.
  15. Prempraneerach, P., Hover, F.S., Triantafyllou, M.S., 2003. The effect of chord wise flexibility on the thrust and efficiency of a flapping foil. In: Int Symp Unmanned Untethered Submers Technol.
  16. Read, D.A., Hover, F.S., Triantafyllou, M.S., 2003. Forces on oscillating foils for propulsion and maneuvering. J. Fluid Struct. 17, 163-183.
  17. Kazi Shah Nawaz Ripon, JMKG. Optimizing bio-inspired propulsion system using genetic algorithm. Comput. Intell. (SSCI), 2017 IEEE Symp. Ser., Honolulu, HI, USA: n.d. doi:10.1109/SSCI.2017.8285175.
  18. Silva, L.W.A.D., Yamaguchi, H., 2012. Numerical study on active wave devouring propulsion. J. Mar. Sci. Technol. 17, 261-275.
  19. Terao, Y., 1982. A floating structure which moves towards the waves (possibility of wave devouring propulsion. J Kansai Soc Nav Archit Japan 51-54.
  20. Ulysses S. Harkson; san mateo; WATER CRAFT HAVING HYDROPLANES, 2,821,948 United States patent office, claim. (CI. 114-66.5), 1958.
  21. Xie, Y.-H., Jiang, W., Lü, K., Zhang, D., 2016. Review on research of flapping foil for power generation from flow energy. Zhongguo Dianji Gongcheng Xuebao/Proceedings Chinese Soc Electr Eng 36, 5564-5575.
  22. Xu, G.D., Duan,W.Y., Zhou, B.Z., 2017. Propulsion of an active flapping foil in heading waves of deep water. Eng. Anal. Bound. Elem. 84, 63-76.
  23. Yu, J., Tan, M., Wang, S., Chen, E., 2004. Development of a biomimetic robotic fish and its control algorithm. IEEE Trans Syst Man Cybern 34, 1789-1810.
  24. Zhou, K., Liu, J., Chen, W., 2017. Study on the hydrodynamic performance of typical underwater bionic foils with spanwise flexibility. Appl. Sci. 7, 1120.