WEIHS, D.: Stability versus Maneuverability in Aquatic Locomotion

The dictionary definition of stability as “Firmly established, not easily to be changed” immediately indicates the conflict between stability and maneuverability in aquatic locomotion. The present paper addresses several issues resulting from these opposing requirements. Classical stability theory for bodies moving in fluids is based on developments in submarine and airship motions. These have lateral symmetry, in common with most animals. This enables the separation of the equations of motion into two sets of 3 each. The longitudinal set, which includes motions in the axial (surge), normal (heave) and pitching directions, can thus be separated from yaw, roll and sideslip motions. This has been found useful for longitudinal stability studies based on coasting configurations (e.g. Weihs, 1993) but is not applicable to the analysis of turning, fast starts and vigorous swimming, where the lateral symmetry of the fish body is broken by bending motions. The present paper will examine the stability vs. maneuverability aspects of these asymmetric motions, starting off with an analysis of the conditions under which the separation of equations of motions is legitimate, and a definition of the equations to be used in cases where the separation is not accurate enough. Several examples are presented, including: 1) BCF locomotion is inherently unstable in yaw due to the sideways excursions of the rear body and the flexibility of the body. a) in rectilinear swimming, the pectorals are used to counteract and damp yawing motions of the head. b) turning motions, in which the instability is utilized, to improve performance. c) rapid starting, where various combinations of a and b are applied. 2) An analysis of the influence of the highly elliptic shape of body cross-sections in certain species in enhancing stability by reducing the interaction of yawing and rolling motions.