Flying insects have evolved sophisticated sensory-motor systems, and here we argue that such systems are used to keep upright against intrinsic flight instabilities. We describe a theory that predicts the instability growth rate in body pitch from flapping-wing aerodynamics and reveals two ways of achieving balanced flight: active control with sufficiently rapid reactions and passive stabilization with high body drag.

Falling parallelograms exhibit coupled motion of autogyration and tumbling, similar to the motion of falling tulip seeds, unlike maple seeds which autogyrate but do not tumble, or rectangular cards which tumble but do not gyrate. This coupled tumbling and autogyrating motion are robust, when card parameters, such as aspect ratio, internal angle, and mass density, are varied. We measure the three-dimensional (3D) falling kinematics of the parallelograms and quantify their descending speed, azimuthal rotation, tumbling rotation, and cone angle in each falling.

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms' performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures.

Motivated by our interest in understanding collective behaviour and self-organization resulting from hydrodynamic interactions, we investigate the two-dimensional dynamics of horizontal arrays of settling cylinders at intermediate Reynolds numbers. To simulate these dynamics, we develop a direct numerical simulation based on the immersed interface method. A novel aspect of our method is its ability to efficiently and accurately couple the dynamics of the freely moving objects with the fluid.

A maple seed falls in a characteristic helical motion. A crude analogy with autorotation of a wind turbine suggests that the torque due to the aerodynamic force would initiate the gyration of the seed. We were therefore surprised that a seed with a torn wing gyrates in a similar manner as a full-winged seed. In fact, a seed with only a sliver of leading edge can still gyrate. Thus the gyrating motion appears not to fully depend on the aerodynamic force. If, on the other hand, the aerodynamic force is completely absent, a seed would fall from rest like a rock in a vacuum.

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.

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.

Just as the Wright brothers implemented controls to achieve stable airplane flight, flying insects have evolved behavioral strategies that ensure recovery from flight disturbances. Pioneering studies performed on tethered and dissected insects demonstrate that the sensory, neurological, and musculoskeletal systems play important roles in flight control. Such studies, however, cannot produce an integrative model of insect flight stability because they do not incorporate the interaction of these systems with free-flight aerodynamics.

Flapping flight is more maneuverable than steady flight. It is debated whether this advantage is necessarily accompanied by a trade-off in the flight efficiency. Here we ask if any flapping motion exists that is aerodynamically more efficient than the optimal steady motion. We solve the Navier-Stokes equation governing the fluid dynamics around a 2D flapping wing, and determine the minimal aerodynamic power needed to support a specified weight.