Research on the Hydrodynamic Forces of the Torsional Wave Propulsion by Extended Large-Amplitude Elongated-Body Theory

Abstract

Torsional wave propulsion is different from transversal wave propulsion. Based on the characteristic feature of fin ray’s motion, we divide the dorsal fin along the radial direction into a series of long narrow bands. For each band, the analysis method is the same as the method computing hydrodynamic force of transversal wave propulsion. Then we give an integral calculation over fin ray’ length. We analyze the influence of the swing amplitude, frequency and length of fin as well as wave numbers and ratio of wave speed to swimming speed on hydrodynamic force. The calculated results show that: 1. the average thrust on the dorsal fin is directly proportional to the square of swing amplitude and frequency of fin ray. 2. The average thrust on the dorsal fin is directly proportional to the biquadrate of ray’s length. 3. As the wave numbers increase, the average thrust begins with a little increase and then turns to decrease. When the wave number roughly equals to 1.5, it reaches to a maximum. 4. If the fin frequency is fixed, the average thrust is of maximum when the ratio of wave speed to swimming speed roughly equals to 1.4.