AERODYNAMIC theories predict that the mechanical power required for flapping animal flight varies with flight speed according to a 'U-shaped' curve1–6. At some intermediate speed there is a pronounced power minimum, typically half the power required for hovering flight. These theories are widely used for birds and bats, but the predictions are not well supported by measurements of the rate of energy expenditure, or metabolic rate—usually determined from the rate of oxygen consumption—of animals flying in wind tunnels. This rate follows a distinctly U-shaped curve in a few species, but quantitative agreement with theoretical predictions is nevertheless unsatisfactory7–9. In other species either the curve is much flattened or the rate shows no significant change with flight speed10–13. In one case the agreement between theory and experiment is remarkable over the limited speed range under test6,14, but there is a discrepancy in the shapes of the two curves which would lead to large differences outside that speed range. Hummingbirds show no significant difference in their flight metabolism over speeds from hovering up to 7 m s−1 (ref. 15). At even higher speeds the metabolic rate increases, presumably as a result of the increased power needed to overcome body drag. The theories can also be applied to insects, but there are no equivalent data against which they can be tested. Here we report such measurements for bumblebees in free, controlled, forward flight over a speed range of 0–4 m s−1. The metabolic rate does not vary significantly with flight speed, suggesting that the theories are inadequate for insect flight.