E2 Control with multiple fins

Topic

The fish possesses a distributed hydrodynamic control system composed of several distinct surfaces—the pectoral, pelvic, dorsal, anal, and caudal fins—each responsible for generating a specific type of force. Unlike the rigid control surfaces used by aircraft, fish fins are flexible, deformable surfaces capable of actively altering their own geometry—area, angle of attack, and curvature—via intrinsic musculature within each fin; this allows the fish to precisely control the forces acting upon its body across all six degrees of freedom: three of translation and three of rotation.

Each of these fins acts as a lifting surface, generating a force normal to its surface (lift) and a tangential force along it (drag); both forces depend on lift and drag coefficients specific to each fin, which in turn depend on the angle of attack at which the fin cuts through the flow and the Reynolds number at which it operates.

Among these fins, the pectoral fins are primarily responsible for maintaining pitch and yaw balance, as well as for propulsion during slow swimming—a mode known as labriform swimming.

The stability resulting from the combined action of all these fins can be of two types: static stability is achieved when the point of application of the resultant force from all the fins coincides exactly with the fish's center of gravity, whereas dynamic stability arises not merely from this force geometry but requires the fish to actively maintain it through neural feedback.

The maneuvering torque generated by each fin is the product of the lift force produced by that fin and the moment arm separating it from the fish's center of mass. For rapid maneuvers, however, the fish employs a mechanism distinct from the previously described maneuverability torque: the generation of transient vortices via the so-called "added mass" effect. By abruptly accelerating or decelerating a fin, the fish imparts or removes momentum from the surrounding fluid, generating impulsive forces proportional to the acceleration of the fin surface itself.

The expected behavior of this distributed hydrodynamic control system is that, during steady, straight-line swimming, the resultant of all forces produced by the fish's various fins is exactly zero, ensuring that no fin deflects the fish from its path. Conversely, during a maneuver, the fish introduces a controlled asymmetry between the forces of opposing fins—such as between the pectoral fins on either side—and it is precisely this asymmetry that generates the torques required to change direction.

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