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As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2–0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.