Fig. 6.
Using an inertia-spring-damper model for body yaw, we infer that lovebirds combine passive and active control to reach the goal perch in gusts. (A) Slip angles range up to 30° in the cross environment ( 3; separated by bird in SI Appendix, Fig. SF19). Neck angles are sufficient for proprioceptive input (dark green, gaze aligns with perch; medium green, gaze within ±150% of the perch). (B) When landing in the shear environment (left side of plot), slip angles are larger and the head is fixated on the perch more often. (C) The slip angle passively goes to zero for an ornithopter, except for a small offset (8°) due to minor wing asymmetries (Movie S4). (D) The nondimensional restoring torque on the ornithopter is proportional to slip angle over angles relevant to lovebirds (95% of lovebird data occurred between shaded boxes). Gray, tracking data; black, linear fit. (E) In our minimalistic model, body yaw is driven by a passive torque proportional to slip angle and an active torque proportional to neck angle , and is dampened by a passive flapping counter torque. (F) The average corroborated coefficients in Eqs. 1 and 2 are similar across visual/gust environments, leading to similar damping coefficients and yaw response times in wingbeats . (G) A scaling analysis of the lovebird yaw gust response model applied for a steplike gust across animals in flapping flight shows they also can infer the direction of gusts based on neck twist within several wingbeats. Air density and nondimensional ratios can change the yaw response time in wingbeats up to an order of magnitude. See SI Appendix, section S5 for scaling details. Mean and SD by species group was derived from literature (58) for evaluating the scaling trend (light gray, insects; medium gray, hummingbirds; dark gray, birds; see SI Appendix, Fig. SF37 for all species). The Inset shows the corroborated lovebird response time varies little with visual condition.