  Large-amplitude oscillations of foils have been observed to yield greater
propulsive efficiency than small-amplitude oscillations. Using scaling
relations and experiments on foils with peak-to-peak trailing edge amplitudes
of up to two chord lengths, we explain why this is so. In the process, we
reveal the importance of drag, specifically how it can significantly reduce the
efficiency, and how this effect depends on amplitude. The scaling relations and
experimental data also reveal a fundamental tradeoff between high thrust and
high efficiency, where the drag also plays a crucial role.
