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

We present a simple method to generate discrete aerodynamic gust under controlled laboratory condition in the form of a vortex ring which, unlike conventional methods of perturbation, is well studied and highly controllable. We characterized the flow properties of the vortex ring using flow visualization and novel light bead method. Reynolds number of the vortex ring, based on its average propagation velocity and nozzle exit diameter, was 16000. We demonstrate this method by studying the impact of head-on gust on freely flying soldier flies, Reynolds number of which, based on its wingtip velocity and mean wing chord, was 1100. We also present simple theoretical models to characterize the vortex ring based on generating conditions. The device can also be used to generate continuous gust in any direction and can be applied, in general, to study the gust response of natural fliers and swimmers, man-made micro aerial vehicles and aquatic plant lives.

/pdf/design-and-development-of-a-vortex-ring-generator-to-study-3rh2nt8x6s.pdf

Design and development of a vortex ring generator to study the impact of the ring as a gust

Vestibular feedback for flight control in hawkmoths

This Special Issue showcases JEB's central role in historical, current and future comparative biomechanics research. Comparative biomechanics is defined as the scientific study of the mechanics of non-human organisms, including animals, plants and fungi. Mechanics is the branch of physics that addresses the forces and displacements that relate to movement. Comparative biomechanics research is traditionally conducted at the tissue and whole-organism levels, including the mechanical interactions between whole organisms and the environment. JEB's scope is primarily restricted to scientific research on animal systems, yet has included key papers about plants and fungi when the findings have broad relevance to animals. While being an integral part of the newer fields of biophysics (cellular to molecular levels of physics analysis), mechanobiology (transduction of forces at molecular to tissue levels) and bioinspiration/biomimetics (synthetic design based on biological systems), comparative biomechanics enriches ecological and evolutionary biology by integrating mechanics, morphology and the environment through studies across diverse species.The papers in this Special Issue focus on broad biological questions addressed through the lens of comparative biomechanics. Cross-cutting through time, this Special Issue addresses questions from the vantage points of the history of the field, today's research and the future of comparative biomechanics. Leveraging JEB's range of paper categories, these topics are explored through Commentaries, Reviews and Research Articles. The assembled authors represent diverse contributions – from early career researchers (see associated ECR Spotlight interviews) to senior members of the field. The Special Issue builds from the foundational definition of comparative biomechanics (force and displacement; mechanics) to explore influences of comparative biomechanics on other fields, such as environment/ecology, evolution and engineering.Biomechanics, by definition, requires measurements and analyses of force and movement. The historical foundation of kinematic measurements and extraordinary advances in the amount and quality of these measurements are captured in McHenry and Hedrick's (2023) Review of imaging technology used across the past century of biomechanics articles. Their analyses of the published literature reveal the correlates of major shifts in imaging technology that have enabled larger datasets and a greater number of sampled individuals. Demuth et al. (2023) review the remarkable technological advances in 3D reconstruction of morphology and movement, while offering an integrated workflow for researchers wishing to integrate 3D approaches into their studies of organismal movements. Provini et al. (2023) provide a Commentary on the promise and pitfalls of using high-resolution 3D motion data to address questions about complex movement dynamics, and Manafzadeh (2023) offers a Commentary focused on joint mobility with insights arising directly from the major recent strides in 3D imaging and reconstruction.Focusing on the interface of technology and analyses of animal biomechanics, three papers tackle topics within particular systems – bird bills, cheetah locomotion and hummingbird feeding. Krishnan's (2023) Review of the diverse morphologies, materials, mechanics and sensory capabilities of bird bills exemplifies the powerful discovery space arising from the integration of new technologies – from imaging to materials testing – across one widespread yet diverse animal structure. In Shield et al.’s (2023) Review, the extraordinary capabilities of cheetahs are considered from the lens of technology. By reviewing the historical research about cheetah biomechanics and muscle physiology – many of the discoveries driven by technology – the authors offer insights into sensors and methodologies that apply broadly to other biomechanical systems. The Research Article by Rico-Guevara et al. (2023) uses state-of-the-art high-speed videography and backlighting to understand the active role that hummingbird bills play in helping their tongues transport nectar intraorally, from tongue to throat, shedding light on nectarivory in hummingbirds with extremely diverse bill morphologies.Technology and biomechanics have also thrived through their alliance with engineering. Harvey et al. (2023) probe the deeply historical and currently burgeoning interface between biomechanics and engineering, specifically from the perspective of flying systems in natural environments. Their Review not only highlights specific areas of translation – related to bird wings – but also offers a synthesis of the deep history of these synergies even beyond the past century and extending to the inventions of Leonardo da Vinci. The engineering–biomechanics connection continues to be an engine of discovery and the rich, data-driven experimental work over JEB's history offers invaluable insights for quantitatively driven engineering translation.Encapsulating the crucial interconnections of biomechanics and naturally variable environments, Koehl (2023) begins her Review with a quote from Vogel and Wainwright's lab manual ‘Structure without function is a corpse, and function without structure is a ghost’, and follows with her own twist: ‘and an organism without its environment is a mirage’. Koehl's Review examines classic biomechanics topics – from locomotion to biomaterials – and for each example, she highlights the shift in understanding when the role of the environment is included, such as animals carrying cargo or materials adjusting to environmental loads. Clifton et al. (2023) probe a similar theme from a pragmatic position – how can researchers systematically yet broadly study animal walking on naturally variable substrates? Taking these themes to the air, Combes et al. (2023), in a Research Article, focus on measuring insect flight in natural environmental conditions. Their study exemplifies how new technology enables massive datasets from which subtle but crucial adjustments by animals in the natural environments are quantitatively addressed.The integration between biomechanical systems, technological developments and environment–system interactions is exemplified in Nirody (2023) and Jimenez et al.’s (2023) Reviews. Nirody explores exciting new developments emerging from system–environment interactions in a neural framework through studies of panarthropod locomotion. Her Review not only encourages neural–biomechanical integration but also encourages broader taxonomic exploration in biomechanical studies to incorporate deeply historic animals, such as water bears (tardigrades). While Nirody's Review encourages exploration of new systems, Jimenez et al.’s Review encourages revisiting a classic system – fish swimming – via analysis of emergent biomechanical properties of fish bodies in fluids. Like Nirody, Jimenez et al. note the importance of a broad taxonomic incorporation of diverse fishes alongside the use of new technologies to understand system–environmental interactions.Muscle dynamics is a historical foundation of biomechanics and has been a major focus over JEB's history. Mendoza et al. (2023) review the principles of muscle contractions in the context of diverse animal muscle physiology. The authors connect the historical foundations of force–length and force–velocity relationships to newer discoveries in non-model systems and comparative studies. Their Review encourages engagement of veteran muscle physiologists looking toward new and exciting systems and early career researchers interested in tying together core principles of muscle mechanics. James et al.’s (2023) Review integrates these foundational principles of muscle (and tendon) physiology into the realm of anthropogenic impacts, including endocrine disruptors and climate change. They offer examples of evolved abilities ranging from narrow temperature windows of consistent ability to generate muscle-driven motion, to remarkable toleration of highly variable environments and physiological conditions (such as dehydration). Flash and Zullo (2023) examine muscle physiology and dynamic modeling in the context of muscular hydrostats – mechanisms of long-standing interest to biomechanists given the remarkable capabilities and unusual muscle physiology that enables controlled movements in soft systems. Focusing within this topic of muscular hydrostats, Thompson et al.’s (2023) Research Article examines obliquely striated muscle in squid tentacles that informs a broader understanding of the multiple evolutionary origins of these remarkable muscles.We hope that readers will explore all the papers in this Special Issue – many not mentioned in this brief, introductory cover article. We hope that this Centenary Special Issue serves as an influential and enduring reflection on the historical and present-day impact of the field of comparative biomechanics. This collection will hopefully inform wide-ranging communities: early career researchers learning about major historical works and today's relevance, mid-career and senior researchers seeking to enhance their teaching and their own technical skills/perspectives, and funders/scientific administrators who can be provided with these Commentaries, Reviews and Research Articles that exemplify the importance of comparative biomechanics today and into the next century. 

A century of comparative biomechanics: emerging and historical perspectives on an interdisciplinary field.

Editorial overview: Insect-inspired engineering: mechanisms, processes and algorithms.

The mechanics of Dipteran thorax is dictated by a network of exoskeletal linkages which, when deformed by the flight muscles, generate coordinated wing movements. In Diptera, the forewings power flight, whereas the hindwings have evolved into specialized structures called halteres which provide rapid mechanosensory feedback for flight stabilization. Although actuated by independent muscles, wing and haltere motion is precisely phase-coordinated at high frequencies. Because wingbeat frequency is a product of wing-thorax resonance, any wear-and-tear of wings or thorax should impair flight ability. How robust is the Dipteran flight system against such perturbations? Here, we show that wings and halteres are independently-driven, coupled oscillators. We systematically reduced the wing length in flies and observed how wing-haltere synchronization was affected. The wing-wing system is a strongly-coupled oscillator, whereas the wing-haltere system is weakly-coupled through mechanical linkages which synchronize phase and frequency. Wing-haltere link acts in a unidirectional manner; altering wingbeat frequency affects haltere frequency, but not vice-versa. Exoskeletal linkages are thus key morphological features of the Dipteran thorax which ensure wing-haltere synchrony, despite severe wing damage.

Sanjay P. Sane

Papers

Design and development of a vortex ring generator to study the impact of the ring as a gust

Vestibular feedback for flight control in hawkmoths

A century of comparative biomechanics: emerging and historical perspectives on an interdisciplinary field.

Editorial overview: Insect-inspired engineering: mechanisms, processes and algorithms.

Wings and halteres act as coupled dual oscillators in flies.