Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee (Bombus terrestris) were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study (the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0–0.66). The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed (advance ratio 0.66), i.e. the power curve is J-shaped. Except at the highest flight speed, storing energy elastically can save power up to 20%–30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque (due to the smaller stroke amplitude and stroke frequency used), the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.