Paddling Mode of Forward Flight in Insects

By analyzing high-speed video of the fruit fly, we discover a swimminglike mode of forward flight characterized by paddling wing motions. We develop a new aerodynamic analysis procedure to show that these insects generate drag-based thrust by slicing their wings forward at low angle of attack and pushing backwards at a higher angle. Reduced-order models and simulations reveal that the law for flight speed is determined by these wing motions but is insensitive to material properties of the fluid. Thus, paddling is as effective in air as in water and represents a common strategy for propulsion through aquatic and aerial environments.

Figure 1

Reconstruction of forward flight in a fruit fly (body length 2.7 mm). Flight is recorded using three high-speed video cameras, and snapshots from each are displayed on the panels. Body and wing motions are extracted using a tracking algorithm, and these data are displayed on the rendered insect for one frame. The wings beat in horizontal arcs, and wing-tip trajectories for two strokes are shown in dark blue.

Figure 2

Comparison of hovering (speed $u=2\mathrm{cm}/\mathrm{s}$) and fast flight ($u=43\mathrm{cm}/\mathrm{s}$). (a) Each wing sweeps along a globe centered about its root on the body [17]. (b and c) Stroke diagrams show the wing as a line with a leading-edge circle (scale bars, 30°). The wings are darker with time and displayed at the frame rate of 8000 Hz. (d–f) Wing angles for hovering (blue, wing-beat period $T=4.0\mathrm{ms}$) and forward flight (red, $T=4.8\mathrm{ms}$). Stroke is the angle in the horizontal plane, deviation is the vertical excursion, and pitch is measured between the wing chord and the horizontal. Measurements (circles) are phase-averaged, and right and left wing data are pooled and used to form Fourier fits (solid lines). Mean values of pitch are shown as dashed lines in (f).

Figure 3

Dependence of flight speed on wing angles. (a) Comparison of experimentally measured speeds for hovering (blue) and fast flight (red) to those predicted by simulation. (b) Simulations of hovering and fast flight kinematics (top) compared to hybrid kinematics (bottom). For hybrid simulations, wing motions are formed by selecting each angle—stroke, deviation, and pitch—from either the hovering or fast flight set. Slow speeds are associated with pitch from hovering, and high speeds are associated with pitch from fast flight. The remaining spread in speeds is largely due to wing strokes that are faster in their backward sweep [Fig. 2d] (c) Simulations of hovering and fast flight (top) compared to those with swapped mean values of pitch (bottom). For example, blue stripes on the red box indicate that the fast flight kinematics have been modified only by shifting the pitch curve upward so as to have hovering’s mean value [dashed lines of Fig. 2f].

Figure 4

Paddling drives forward flight. (a) Hovering: each wing has equal attack angles for forward and backward sweeps. (b) Paddling: shifting the pitch downward by the paddling angle $\Delta \alpha$ (here, 30°) alters angle of attack. (c) Flight speed normalized by wing speed, $u/w$, correlates with $\Delta \alpha$. A minimal aerodynamic model [Eq. (2), dashed line] and simulation (solid line) account for the trend in the data (circles). Simulations show that the flight speed relation is insensitive to changes in the density of the fluid (d) and the drag coefficient (e).