The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.

https://science.sciencemag.org/content/sci/288/5463/100.full.pdf

How Animals Move: An Integrative View

The flight of insects has fascinated physicists and biologists for more than a century. Yet, until recently, researchers were unable to rigorously quantify the complex wing motions of flapping insects or measure the forces and flows around their wings. However, recent developments in high-speed videography and tools for computational and mechanical modeling have allowed researchers to make rapid progress in advancing our understanding of insect flight. These mechanical and computational fluid dynamic models, combined with modern flow visualization techniques, have revealed that the fluid dynamic phenomena underlying flapping flight are different from those of non-flapping, 2-D wings on which most previous models were based. In particular, even at high angles of attack, a prominent leading edge vortex remains stably attached on the insect wing and does not shed into an unsteady wake, as would be expected from non-flapping 2-D wings. Its presence greatly enhances the forces generated by the wing, thus enabling insects to hover or maneuver. In addition, flight forces are further enhanced by other mechanisms acting during changes in angle of attack, especially at stroke reversal, the mutual interaction of the two wings at dorsal stroke reversal or wing-wake interactions following stroke reversal. This progress has enabled the development of simple analytical and empirical models that allow us to calculate the instantaneous forces on flapping insect wings more accurately than was previously possible. It also promises to foster new and exciting multi-disciplinary collaborations between physicists who seek to explain the phenomenology, biologists who seek to understand its relevance to insect physiology and evolution, and engineers who are inspired to build micro-robotic insects using these principles. This review covers the basic physical principles underlying flapping flight in insects, results of recent experiments concerning the aerodynamics of insect flight, as well as the different approaches used to model these phenomena.

/pdf/the-aerodynamics-of-insect-flight-4ladwfpmp7.pdf

The aerodynamics of insect flight

We are witnessing the advent of a new era of robots - drones - that can autonomously fly in natural and man-made environments. These robots, often associated with defence applications, could have a major impact on civilian tasks, including transportation, communication, agriculture, disaster mitigation and environment preservation. Autonomous flight in confined spaces presents great scientific and technical challenges owing to the energetic cost of staying airborne and to the perceptual intelligence required to negotiate complex environments. We identify scientific and technological advances that are expected to translate, within appropriate regulatory frameworks, into pervasive use of autonomous drones for civilian applications.

/pdf/science-technology-and-the-future-of-small-autonomous-drones-1bc8o99b9w.pdf

Science, technology and the future of small autonomous drones

Flies are among the most agile flying creatures on Earth To mimic this aerial prowess in a similarly sized robot requires tiny, high-efficiency mechanical components that pose miniaturization challenges governed by force-scaling laws, suggesting unconventional solutions for propulsion, actuation, and manufacturing To this end, we developed high-power-density piezoelectric flight muscles and a manufacturing methodology capable of rapidly prototyping articulated, flexure-based sub-millimeter mechanisms We built an 80-milligram, insect-scale, flapping-wing robot modeled loosely on the morphology of flies Using a modular approach to flight control that relies on limited information about the robot's dynamics, we demonstrated tethered but unconstrained stable hovering and basic controlled flight maneuvers The result validates a sufficient suite of innovations for achieving artificial, insect-like flight

http://science.sciencemag.org/content/sci/340/6132/603.full.pdf

Controlled Flight of a Biologically Inspired, Insect-Scale Robot

The enhanced aerodynamic performance of insects results from an interaction of three distinct yet interactive mechanisms: delayed stall, rotational circulation, and wake capture. Delayed stall functions during the translational portions of the stroke, when the wings sweep through the air with a large angle of attack. In contrast, rotational circulation and wake capture generate aerodynamic forces during stroke reversals, when the wings rapidly rotate and change direction. In addition to contributing to the lift required to keep an insect aloft, these two rotational mechanisms provide a potent means by which the animal can modulate the direction and magnitude of flight forces during steering maneuvers. A comprehensive theory incorporating both translational and rotational mechanisms may explain the diverse patterns of wing motion displayed by different species of insects.

https://science.sciencemag.org/content/sci/284/5422/1954.full.pdf

Wing rotation and the aerodynamic basis of insect flight.

We used a dynamically scaled model insect to measure the rotational forces produced by a flapping insect wing. A steadily translating wing was rotated at a range of constant angular velocities, and the resulting aerodynamic forces were measured using a sensor attached to the base of the wing. These instantaneous forces were compared with quasi-steady estimates based on translational force coefficients. Because translational and rotational velocities were constant, the wing inertia was negligible, and any difference between measured forces and estimates based on translational force coefficients could be attributed to the aerodynamic effects of wing rotation. By factoring out the geometry and kinematics of the wings from the rotational forces, we determined rotational force coefficients for a range of angular velocities and different axes of rotation. The measured coefficients were compared with a mathematical model developed for two-dimensional motions in inviscid fluids, which we adapted to the three-dimensional case using blade element theory. As predicted by theory, the rotational coefficient varied linearly with the position of the rotational axis for all angular velocities measured. The coefficient also, however, varied with angular velocity, in contrast to theoretical predictions. Using the measured rotational coefficients, we modified a standard quasi-steady model of insect flight to include rotational forces, translational forces and the added mass inertia. The revised model predicts the time course of force generation for several different patterns of flapping kinematics more accurately than a model based solely on translational force coefficients. By subtracting the improved quasi-steady estimates from the measured forces, we isolated the aerodynamic forces due to wake capture.

/pdf/the-aerodynamic-effects-of-wing-rotation-and-a-revised-quasi-5e50hdu4o1.pdf

The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight.

We used a dynamically scaled mechanical model of the fruit fly Drosophila melanogaster to study how changes in wing kinematics influence the production of unsteady aerodynamic forces in insect flight. We examined 191 separate sets of kinematic patterns that differed with respect to stroke amplitude, angle of attack, flip timing, flip duration and the shape and magnitude of stroke deviation. Instantaneous aerodynamic forces were measured using a two-dimensional force sensor mounted at the base of the wing. The influence of unsteady rotational effects was assessed by comparing the time course of measured forces with that of corresponding translational quasi-steady estimates. For each pattern, we also calculated mean stroke-averaged values of the force coefficients and an estimate of profile power. The results of this analysis may be divided into four main points. 

(i) For a short, symmetrical wing flip, mean lift was optimized by a stroke amplitude of 180° and an angle of attack of 50°. At all stroke amplitudes, mean drag increased monotonically with increasing angle of attack. Translational quasi-steady predictions better matched the measured values at high stroke amplitude than at low stroke amplitude. This discrepancy was due to the increasing importance of rotational mechanisms in kinematic patterns with low stroke amplitude. 

(ii) For a 180° stroke amplitude and a 45° angle of attack, lift was maximized by short-duration flips occurring just slightly in advance of stroke reversal. Symmetrical rotations produced similarly high performance. Wing rotation that occurred after stroke reversal, however, produced very low mean lift. 

(iii) The production of aerodynamic forces was sensitive to changes in the magnitude of the wing’s deviation from the mean stroke plane (stroke deviation) as well as to the actual shape of the wing tip trajectory. However, in all examples, stroke deviation lowered aerodynamic performance relative to the no deviation case. This attenuation was due, in part, to a trade-off between lift and a radially directed component of total aerodynamic force. Thus, while we found no evidence that stroke deviation can augment lift, it nevertheless may be used to modulate forces on the two wings. Thus, insects might use such changes in wing kinematics during steering maneuvers to generate appropriate force moments. 

(iv) While quasi-steady estimates failed to capture the time course of measured lift for nearly all kinematic patterns, they did predict with reasonable accuracy stroke-averaged values for the mean lift coefficient. However, quasi-steady estimates grossly underestimated the magnitude of the mean drag coefficient under all conditions. This discrepancy was due to the contribution of rotational effects that steady-state estimates do not capture. This result suggests that many prior estimates of mechanical power based on wing kinematics may have been grossly underestimated.

/pdf/the-control-of-flight-force-by-a-flapping-wing-lift-and-drag-1t46zqx5sq.pdf

The control of flight force by a flapping wing: lift and drag production.

Flying insects have evolved sophisticated sensory capabilities to achieve rapid course control during aerial maneuvers. Among two-winged insects such as houseflies and their relatives, the hind wings are modified into club-shaped, mechanosensory halteres, which detect Coriolis forces and thereby mediate flight stability during maneuvers. Here, we show that mechanosensory input from the antennae serves a similar role during flight in hawk moths, which are four-winged insects. The antennae of flying moths vibrate and experience Coriolis forces during aerial maneuvers. The antennal vibrations are transduced by individual units of Johnston's organs at the base of their antennae in a frequency range characteristic of the Coriolis input. Reduction of the mechanical input to Johnston's organs by removing the antennal flagellum of these moths severely disrupted their flight stability, but reattachment of the flagellum restored their flight control. The antennae thus play a crucial role in maintaining flight stability of moths.

/pdf/antennal-mechanosensors-mediate-flight-control-in-moths-4cidbqtcsi.pdf

Sanjay P. Sane

Papers

Wing rotation and the aerodynamic basis of insect flight.

The aerodynamics of insect flight

The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight.

The control of flight force by a flapping wing: lift and drag production.

Antennal mechanosensors mediate flight control in moths.