Thrust Force Generated by Heaving Motion of a Plate: The Role of Vortex-Induced Force
To understand the force acting on birds, insects, and fish, we take heaving motion as a simple example. This motion might deviate from the real one. However, since the mechanism of force generation is the vortex shedding due to the motion of an object, the heaving motion is important for understanding the force generated by unsteady motion. The vortices released from the object are closely related to the motion characteristics. To understand the force acting on an object, information about momentum change is necessary. However, in vortex systems, it is impossible to estimate the usual momentum. Instead of the momentum, the “virtual momentum,” or the impulse, is needed to generate the force. For calculating the virtual momentum, we traced all vortices over a whole period, which was carried out by using the vortex-element method. The force was then calculated based on the information on the vortices. We derived the thrust coefficient as a function of the ratio of the heaving to travelling velocity.