Tradeoffs for bluegill sunfish turning at different rates

When fish turn using their caudal fins, they face a tradeoff. To turn rapidly, they must produce high torque or reduce their rotational moment of inertia or both, but these two things may pose opposite constraints. The moment arm for torque from forces from the caudal fin is highest when the body is straight, but the moment of inertia is lowest when the body is bent. Torque depends on the distance of body segments from the center of mass, but moment of inertia depends on this distance squared. Therefore, we hypothesized that fish would resolve this tradeoff differently at different turning rates, producing torque first at low speeds but reducing moment of inertia first at higher speeds. We developed a device that elicits 180° turns repeatedly at controlled speeds. The device constrained fish to perform a turn with a defined radius (a property referred to as maneuverability) while varying the speed of the turn (the agility of the turn). Using this device, we compare the swimming kinematics of bluegill sunfish (Lepomis macrochirus) during fast (high agility) and slow (lower agility) turns, while maintaining maneuverability. Across all speeds of turns, lower moment of inertia correlated with faster turns, and minimum moment of intertia tended to coincide with maximum angular velocity. In faster turns, fish began with higher linear momentum, which they then converted to angular momentum. Slower turning fish also took more strokes with their pectoral fins while faster turning fish took higher frequency strokes with their pectoral fins. Therefore we found partial support for our hypothesis: despite substantial variability in the data, for faster turns, fish more often minimized moment of inertia before they maximized torque.