A Model of Rapid-Start Swimming at Intermediate Reynolds Number: Undulatory Locomotion in the Chaetognath Sagitta Elegans

Abstract

The mechanics and kinematics of accelerational undulatory locomotion by the chaetognath Sagitta elegans (Verrill, 1873) are studied with a combination of highspeed cinematography (200 frames s−1) and mathematical modeling. The model is constructed such that it predicts body velocity for an organism starting from rest and accelerating rapidly by swimming with prescribed wave kinematics. The speed of the undulatory propulsive waves and the number of these waves on the body is highly conserved across 11 individuals, while the wave amplitude is positively related to distance traveled in the first 65 ms of swimming. There is excellent agreement between these data and predictions of body translations that are based on a mathematical model for this mode of locomotion. The model also shows that instantaneous forces generated by the undulating body are much larger than average forces and consist of non-trivial inertial terms, even for such small organisms. The model also shows that the distance traveled over a fixed time interval is limited by the maximum muscle stress that can be physiologically generated. Peak instantaneous force represents a mechanical upper boundary to thrust production and, hence, a limit to performance.