Batoid locomotion: effects of speed on pectoral fin deformation in the little skate, Leucoraja erinacea.

Most batoids have a unique swimming mode in which thrust is generated by either oscillating or undulating expanded pectoral fins that form a disc. Only one previous study of the freshwater stingray has quantified three-dimensional motions of the wing, and no comparable data are available for marine batoid species that may differ considerably in their mode of locomotion. Here, we investigate three-dimensional kinematics of the pectoral wing of the little skate, Leucoraja erinacea, swimming steadily at two speeds [1 and 2 body lengths (BL) s-1]. We measured the motion of nine points in three dimensions during wing oscillation and determined that there are significant differences in movement amplitude among wing locations, as well as significant differences as speed increases in body angle, wing beat frequency and speed of the traveling wave on the wing. In addition, we analyzed differences in wing curvature with swimming speed. At 1 BL s-1, the pectoral wing is convex in shape during the downstroke along the medio-lateral fin midline, but at 2 BL s-1 the pectoral fin at this location cups into the flow, indicating active curvature control and fin stiffening. Wing kinematics of the little skate differed considerably from previous work on the freshwater stingray, which does not show active cupping of the whole fin on the downstroke.

Rajiform locomotion: three-dimensional kinematics of the pectoral fin surface during swimming in the freshwater stingray Potamotrygon orbignyi.

Rajiform locomotion in fishes is dominated by distinctive undulations of expanded pectoral fins. Unlike other fishes, which typically interact with the fluid environment via multiple fins, undulating rays modulate a single control surface, the pectoral disc, to perform pelagic locomotion, maneuvering and other behaviors. Complex deformations of the broad, flexible pectoral fins occur as the undulating wave varies in three dimensions; pectoral fin kinematics and changes in waveform with swimming speed cannot be fully quantified by two-dimensional analyses of the fin margin. We present the first three-dimensional analysis of undulatory rajiform locomotion in a batoid, the freshwater stingray Potamotrygon orbignyi. Using three cameras (250 frames s(-1)), we gathered three-dimensional excursion data from 31 points on the pectoral fin during swimming at 1.5 and 2.5 disc lengths s(-1), describing the propulsive wave and contrasting waveforms between swimming speeds. Only a relatively small region of the pectoral fin (~25%) undulates with significant amplitude (>0.5 cm). Stingrays can maintain extreme lateral curvature of the distal fin margin in opposition to induced hydrodynamic loads, 'cupping' the edge of the pectoral fin into the flow, with potential implications for drag reduction. Wave amplitude increases across both anteroposterior and mediolateral fin axes. Along the anteroposterior axis, amplitude increases until the wave reaches mid-disc and then remains constant, in contrast to angulliform patterns of continuous amplitude increase. Increases in swimming speed are driven by both wave frequency and wavespeed, though multivariate analyses reveal a secondary role for amplitude.

A robotic fish caudal fin: effects of stiffness and motor program on locomotor performance.

We designed a robotic fish caudal fin with six individually moveable fin rays based on the tail of the bluegill sunfish, Lepomis macrochirus. Previous fish robotic tail designs have loosely resembled the caudal fin of fishes, but have not incorporated key biomechanical components such as fin rays that can be controlled to generate complex tail conformations and motion programs similar to those seen in the locomotor repertoire of live fishes. We used this robotic caudal fin to test for the effects of fin ray stiffness, frequency and motion program on the generation of thrust and lift forces. Five different sets of fin rays were constructed to be from 150 to 2000 times the stiffness of biological fin rays, appropriately scaled for the robotic caudal fin, which had linear dimensions approximately four times larger than those of adult bluegill sunfish. Five caudal fin motion programs were identified as kinematic features of swimming behaviors in live bluegill sunfish, and were used to program the kinematic repertoire: flat movement of the entire fin, cupping of the fin, W-shaped fin motion, fin undulation and rolling movements. The robotic fin was flapped at frequencies ranging from 0.5 to 2.4 Hz. All fin motions produced force in the thrust direction, and the cupping motion produced the most thrust in almost all cases. Only the undulatory motion produced lift force of similar magnitude to the thrust force. More compliant fin rays produced lower peak magnitude forces than the stiffer fin rays at the same frequency. Thrust and lift forces increased with increasing flapping frequency; thrust was maximized by the 500× stiffness fin rays and lift was maximized by the 1000× stiffness fin rays.