Flying animals exhibit remarkable capabilities for both generating maneuvers and stabilizing their course and orientation after perturbation. Here we show that flapping fliers ranging in size from fruit flies to large birds benefit from substantial damping of angular velocity through a passive mechanism termed flapping counter-torque (FCT). Our FCT model predicts that isometrically scaled animals experience similar damping on a per-wingbeat time scale, resulting in similar turning dynamics in wingbeat time regardless of body size. The model also shows how animals may simultaneously specialize in both maneuverability and stability (at the cost of efficiency) and provides a framework for linking morphology, wing kinematics, maneuverability, and flight dynamics across a wide range of flying animals spanning insects, bats, and birds.

Specifically, the manoeuvres studied here were triggered by providing a sudden looming stimulus to a hovering moth, causing it to pitch up, fly backwards a short distance, and then pitch back Accepted 23 September 2011 SUMMARY Insects produce a variety of exquisitely controlled manoeuvres during natural flight behaviour. Here we show how hawkmoths produce and control one such manoeuvre, an avoidance response consisting of rapid pitching up, rearward flight, pitching down (often past the original pitch angle), and then pitching up slowly to equilibrium. We triggered these manoeuvres via a sudden visual stimulus in front of free-flying hawkmoths (Manduca sexta) while recording the animalsʼ body and wing movements via high-speed stereo videography. We then recreated the wing motions in a dynamically scaled model to: (1) associate wing kinematic changes with pitch torque production and (2)

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Hummingbirds are nature's masters of aerobatic manoeuvres. Previous research shows that hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g, and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g, and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees of freedom on a stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the 'helicopter model' that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.

tert-Butylperoxy radicals generated by TBHP and Ru(PPh3)3Cl2 or other catalysts adds to C60 and C70 to form stable multiadducts, C60(O)(OOtBu)4 and C70(OOtBu)10. The four tert-butylperoxy groups in the C60 mixed peroxide are located around a pentagon, and the epoxy O occupies the remaining 6,6-bond connected to the same pentagon. The C70 decaadduct shows an unprecedented C2 symmetry with the 10 tert-butylperoxy groups added around the central part of C70 by consecutive 1,4-addition. The compounds are fully characterized by spectroscopic data.