Performance Analysis of a Self-Propelling Flat Plate Fin with Joint Compliance

  • N. Srinivasa ReddyEmail author
  • Soumen Sen
  • Sumit Pal
  • Sankar Nath Shome
Original Contribution


Fish fin muscles are compliant and they regulate the stiffness to suit different swimming conditions. This article attempts to understand the significance of presence of compliance in fin muscle with help of a flexible joint flat plate fin model. Blade element method is employed to model hydrodynamics and to compute the forces of interaction during motion of the plate within fluid. The dynamic model of self-propelling fin is developed through multi-body dynamics approach considering the hydrodynamic forces as external forces acting on the fin. The derived hydrodynamic model is validated with experiments on rigid flat plate fin. The effect of the joint stiffness and flapping frequency on the propulsion speed and efficiency is investigated through simulations using the derived and validated model. The propulsion efficiency is found to be highly influenced by the joint stiffness at a given flapping frequency. The fin attained maximum propulsion efficiency when the joint stiffness is tuned to a value at which flapping frequency matches near natural frequency of the fin. At this tuned joint stiffness and flapping frequency, the resulted Strouhal numbers are observed to fall within the optimum range (0.2 to 0.4) for maximized propulsion efficiency of flying birds and swimming aquatic animals reported in literature.


Fish propulsion Caudal fin Propulsion efficiency Joint compliance Hydrodynamic force 



Projected area of the fin-carrying-body


Plane area of the flapping fin


Area of the blade element i (i = 1, 2, 3,…, n)


Unsteady drag coefficient


Input power coefficient


Thrust coefficient


Damped natural frequency

\({\text{F}}_{{{\text{AM}}_{\text{i}} }}\)

Added mass force acting on the blade element i


Total hydrodynamic force acting on the fin-carrying-body due to its motion

\({\text{F}}_{{{\text{d}}_{\text{i}} }}\)

Drag force acting on the blade element i


Hydrodynamic force acting along j-direction in global frame (j = X, Y, Z)


Average thrust force. Bar indicates averaging


Joint stiffness


Total mass of the fin-carrying-body including added mass


Motor input power


Average input power


Distance of the blade element i from the axis of rotation


Strouhal number


Average propulsion speed


Oncoming water velocity


Instantaneous velocity of the blade element i along its normal


Wake width at the mid of the fin


Fin angle


Motor angle


Hydrodynamic torque acting on the fin


Motor torque


Height of the blade element i


Motor amplitude


Fin amplitude


Width of each blade element


Frequency of oscillation/flapping


Total number of blade elements




Time period of flapping cycle


Propulsion speed


Instantaneous acceleration of the blade element i along its normal


Added mass factor


Propulsion efficiency or Froude efficiency


Density of the fluid media (water)


Phase difference between the motor and fin angles



This work is carried out at CSIR-CMERI, Durgapur under the activities of the project (GAP-152812) funded by Department of Science and Technology, Government of India and the project UnWaR (ESC-0113) funded by Council of Scientific and Industrial Research (CSIR), Govt. of India.


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Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  1. 1.CSIR-Central Mechanical Engineering Research InstituteDurgapurIndia

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