Fruit Flies Modulate Passive Wing Pitching to Generate In-Flight Turns

Flying insects execute aerial maneuvers through subtle manipulations of their wing motions. Here, we measure the free-flight kinematics of fruit flies and determine how they modulate their wing pitching to induce sharp turns. By analyzing the torques these insects exert to pitch their wings, we infer that the wing hinge acts as a torsional spring that passively resists the wing’s tendency to flip in response to aerodynamic and inertial forces. To turn, the insects asymmetrically change the spring rest angles to generate asymmetric rowing motions of their wings. Thus, insects can generate these maneuvers using only a slight active actuation that biases their wing motion.

Figure 1

(a) Fly body position and orientation vs time. Measurement uncertainties are 0.05 mm and 3°, respectively [6]. (b) Motion reconstruction of the 120° turn. The side panels show 6 of 821 frames recorded by high speed videography. Labeled on the fifth frame are the Euler angles that quantify the fly’s orientation. (c) Fly wing orientation relative to body vs time. Measurements are accurate to approximately 3° [6]. The wings are chiefly driven by the same large flight muscles resulting in motion that is nearly in phase [10]. (d) Trajectory and orientation of wing chords during a typical flapping stroke. The ball and sticks on the globe depict the chord’s orientation at equal time snapshots, with the ball depicting the wings leading edge. Three Euler angles describe each wing’s orientation within the stroke plane ($\varphi$), deviation from the stroke plane ($\theta$), and orientation around its span ($\psi$). (e) The unwrapped ball-and-stick diagram highlights the 9° asymmetry in the midstroke angle of attack $\alpha$ that induces the maneuver. The uncertainty in $\alpha$ is approximately 1°.

Figure 2

(a) Pitching torque vs wing pitch for the wing beats during steady flight. Circles are instantaneous values corresponding to frames of the flight sequence. Triangles are the result of fitting ${\tau }_p$ with a damped torsional spring model. The counterclockwise direction of propagation indicates that the motion is damped. (b) Phase-averaged ${\tau }_p$ vs $\psi$ for strokes associated with symmetric wing movements compared to asymmetric wing movements.

Figure 3

(a)–(c) Torsional spring parameters vs time extracted with error bars from experimental data. Dashed lines are the parameter values simulated in the minimal turning model. (d) Yaw angle vs time. Measurements (solid line) are compared with turning model simulations (dashed line). (e) Phase-averaged wing pitch vs time in the three labeled regions for measurements (solid lines) and the turning model (dashed lines). The area between the left and right wing curves is shaded to correspond to the wing whose pitch is shifted up. The mean shift $\Delta \psi$ in the three regions are 6.5° (asymmetric $\Delta {\psi }_0<0$), 2.5° (asymmetric $\Delta {\psi }_0>0$), and $<1.0°$ (symmetric $\Delta {\psi }_0\approx 0$). The corresponding $\Delta \psi$ for the turning model are 8°, 2.9°, and 0°, respectively.

Figure 4

(a) Minimal model of turning dynamics. Biasing the spring rest angle produces an asymmetric stroke that generates thrust and a yaw torque on the fly. (b) The average values of $\Delta \psi$ vs $\Delta {\psi }_0$ for 147 strokes (circles) compared with simulations of the turning model (dashed line). Measurement errors are on the order of the data spread and omitted for clarity. (c) Turn angle vs cumulative pitch asymmetry. Measurements (circles) are compared with predictions of the turning model (dashed line). Measurement errors are on the order of the marker size and omitted for clarity.