ALTSHULER, Douglas L.; DICKSON, William B.; DICKINSON, Michael H.; Caltech; Caltech; Caltech: Kinematics, aerodynamics, and increased wing-wake interactions in the hovering flight of honeybees, Apis mellifera.

During hovering flight, an animal�s wing tip velocity is a function of its wing length (R), wingbeat frequency (f) and stroke amplitude (Φ). f is inversely correlated with R in insects, whereas the Φ of most hovering animals ranges from 130 to 160&deg. Thus, wingtip velocity exhibits a tight allometric relationship for hovering animals. One notable exception to the allometric relationship with f is the honeybee, Apis mellifera, which has a much higher f than other similarly-sized insects. Compared to a 1 mg fruit fly, which flaps its wings at 200 Hz, a 80 mg bee uses a f of 225 Hz. However, the wingtip velocity of bees is not unusually large relative to body size, because their Φ is quite low � a mere 90&deg compared to 145&deg for a fruit fly. We measured the aerodynamic consequences of the bee�s high f-low Φ stroke pattern by programming the flapping motion of a dynamically-scaled robotic insect. The kinematics of a hovering honeybee produce three prominent force peaks during the beginning, middle, and end of each half stroke, consistent with forces due to wake capture, translation, and rotation. We also measured the forces generated by a series of artificial wingbeat patterns in which we systematically varied Φ. These kinematic patterns were constructed in two ways, to maintain either constant wingtip velocity or constant f. For the constant wingtip velocity trials, increases in Φ were marked by a decrease in the magnitude of wake capture and an increase in the importance of translational forces. For constant f trials, wing-wake interactions persisted as Φ increased, and translational forces increased as expected from the overall increase in wing velocity. We conclude that the small Φ-high f wingstroke pattern of bees results in a relatively large contribution of wake capture and added mass forces.