The power-speed relationship is U-shaped in two free-flying hawkmoths ().

A flying animal can minimize its energy consumption by choosing an optimal flight speed depending on the task at hand. Choice of flight speed can be predicted by modelling the aerodynamic power required for flight, and this tool has previously been used extensively in bird migration research. For insects, however, it is uncertain whether any of the commonly used power models are useful, as insects often operate in a very different flow regime from vertebrates. To investigate this, we measured aerodynamic power in the wake of two flying freely in a wind tunnel at 1-3.8 ms, using tomographic particle image velocimetry (tomo-PIV). The expended power was similar in magnitude to that predicted by two classic models. However, the most ubiquitously used model, originally intended for vertebrates, failed to predict the sharp increase in power at higher speeds, leading to an overestimate of predicted flight speed during longer flights. In addition to measuring aerodynamic power, the tomo-PIV system yielded a highly detailed visualization of the wake, which proved to be significantly more intricate than could be inferred from previous smoke trail- and two-dimensional-PIV studies.