Thomas L. Daniel

Flexural stiffness in insect wings I. Scaling and the influence of wing venation

SUMMARY During flight, many insect wings undergo dramatic deformations that are controlled largely by the architecture of the wing. The pattern of supporting veins in wings varies widely among insect orders and families, but the functional significance of phylogenetic trends in wing venation remains unknown, and measurements of the mechanical properties of wings are rare. In this study, we address the relationship between venation pattern and wing flexibility by measuring the flexural stiffness of wings (in both the spanwise and chordwise directions) and quantifying wing venation in 16 insect species from six orders. These measurements show that spanwise flexural stiffness scales strongly with the cube of wing span, whereas chordwise flexural stiffness scales with the square of chord length. Wing size accounts for over 95% of the variability in measured flexural stiffness; the residuals of this relationship are small and uncorrelated with standardized independent contrasts of wing venation characters. In all species tested, spanwise flexural stiffness is 1-2 orders of magnitude larger than chordwise flexural stiffness. A finite element model of an insect wing demonstrates that leading edge veins are crucial in generating this spanwise-chordwise anisotropy.

Flexural stiffness in insect wings II. Spatial distribution and dynamic wing bending

SUMMARY The dynamic, three-dimensional shape of flapping insect wings may influence many aspects of flight performance. Insect wing deformations during flight are largely passive, and are controlled primarily by the architecture and material properties of the wing. Although many details of wing structure are well understood, the distribution of flexural stiffness in insect wings and its effects on wing bending are unknown. In this study, we developed a method of estimating spatial variation in flexural stiffness in both the spanwise and chordwise direction of insect wings. We measured displacement along the wing in response to a point force, and modeled flexural stiffness variation as a simple mathematical function capable of approximating this measured displacement. We used this method to estimate flexural stiffness variation in the hawkmoth Manduca sexta, and the dragonfly Aeshna multicolor. In both species, flexural stiffness declines sharply from the wing base to the tip, and from the leading edge to the trailing edge; this variation can be approximated by an exponential decline. The wings of M. sexta also display dorsal/ventral asymmetry in flexural stiffness and significant differences between males and females. Finite element models based on M. sexta forewings demonstrate that the measured spatial variation in flexural stiffness preserves rigidity in proximal regions of the wing, while transferring bending to the edges, where aerodynamic force production is most sensitive to subtle changes in shape.

Into thin air: Contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta.

SUMMARY During flapping flight, insect wings must withstand not only fluid-dynamic forces, but also inertial-elastic forces generated by the rapid acceleration and deceleration of their own mass. Estimates of overall aerodynamic and inertial forces vary widely, and the relative importance of these forces in determining passive wing deformations remains unknown. If aeroelastic interactions between a wing and the fluid-dynamic forces it generates are minor compared to the effects of wing inertia, models of insect flight that account for passive wing flexibility would be far simpler to develop. We used an experimental approach to examine the contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta. We attached fresh Manduca wings to a motor and flapped them at a realistic wing-beat frequency and stroke amplitude. We compared wing bending in normal air versus helium (approx. 15% air density), in which the contribution of fluid-dynamic forces to wing deformations is significantly reduced. This 85% reduction in air density produced only slight changes in the pattern of Manduca wing deformations, suggesting that fluid-dynamic forces have a minimal effect on wing bending. We used a simplified finite element model of a wing to show that the differences observed between wings flapped in air versus helium are most likely due to fluid damping, rather than to aerodynamic forces. This suggests that damped finite element models of insect wings (with no fluid-dynamic forces included) may be able to predict overall patterns of wing deformation prior to calculations of aerodynamic force production, facilitating integrative models of insect flight.

Flexible Wings and Fins: Bending by Inertial or Fluid-Dynamic Forces?

Abstract Flapping flight and swimming in many organisms is accompanied by significant bending of flexible wings and fins. The instantaneous shape of wings and fins has, in turn, a profound effect on the fluid dynamic forces they can generate, with non-monotonic relationships between the pattern of deformation waves passing along the wing and the thrust developed. Many of these deformations arise, in part, from the passive mechanics of oscillating a flexible air- or hydrofoil. At the same time, however, their instantaneous shape may well emerge from details of the fluid loading. This issue—the extent to which there is feedback between the instantaneous wing shape and the fluid dynamic loading—is core to understanding flight control. We ask to what extent surface shape of wings and fins is controlled by structural mechanics versus fluid dynamic loading. To address this issue, we use a combination of computational and analytic methods to explore how bending stresses arising from inertial-elastic mechanisms compare to those stresses that arise from fluid pressure forces. Our analyses suggest that for certain combinations of wing stiffness, wing motions, and fluid density, fluid pressure stresses play a relatively minor role in determining wing shape. Nearly all of these combinations correspond to wings moving in air. The exciting feature provided by this analysis is that, for high Reynolds number motions where linear potential flow equations provide reasonable estimates of lift and thrust, we can finally examine how wing structure affects flight performance. Armed with this approach, we then show how modest levels of passive elasticity can affect thrust for a given level of energy input in the form of an inertial oscillation of a compliant foil.

A pulsed UWB receiver SoC for insect motion control

For decades, scientists and engineers have been fascinated by cybernetic organisms, or cyborgs, that fuse artificial and natural systems. Cyborgs enable harnessing biological systems that have been honed by evolutionary forces over millennia to achieve astounding feats. Male moths can detect a single pheromone molecule, a sensitivity of roughly 10−21 grams. Thus, cyborgs can perform tasks at scales and efficiencies that would ordinarily seem incomprehensible. Semiconductor technology is central to realizing this vision offering powerful processing and communication capabilities, as well as low weight, small size, and deterministic control. An emerging cyborg application is moth flight control, where electronics and MEMS devices are placed on and within a moth to control flight direction. To receive commands on the moth, a lightweight, low power and low volume RX is required. This paper presents a pulsed ultrawideband (UWB) RX SoC designed for the stringent weight, volume and power constraints of the cyborg moth system.

Compliant Realignment of Binding Sites in Muscle: Transient Behavior and Mechanical Tuning

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.

A 9

Biosensors present exciting opportunities in novel medical and scientific applications. However, sensor tags presented to date cannot interface with practical sensors, lack addressability, and/or require a custom (high-cost) interrogator. Our tag provides these features via ultra-low-power circuitry including a low-noise biosignal amplifier, unique tag ID generator, calibration-free 3 MHz oscillator, and EPC C1 Gen2 protocol compatibility. In addition to design details and measurement data from the fabricated IC, we present in vivo muscle temperature measurement from an untethered in-flight hawkmoth.

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The scleractinian (reef-building) coral Agaricia tenuifolia (Dana) is one of the most common constituents of the barrier reef of Belize, Central America. This species grows almost exclusively in aggregations of clonemates and conspecifics, in which rows of thin, upright blades line up behind one another facing the dominant direction of flow. We quantified patterns in colony morphology, light levels and mainstream flow over a range of physical habitats (fore reef, patch reef and lagoon locations) near Carrie Bow Cay and in the Pelican Cays. Water flow and light levels both decreased with depth on the fore reef. Light levels in the lagoon environment (1 m depth) were comparable to those at the same depth on the fore reef, but flow speeds were markedly lower. Aggregation size, branch spacing, height and width all varied with location. Mean branch spacing increased with depth on the fore reef by approximately 50%, but total branch height increased by only 20–25%, indicating that the shape of colonies did not remain constant. Colonies in the 1 m lagoon habitat (high light, low flow) were very similar to those at 1 m on the fore reef (high light, high flow). These results thus suggested that colony morphology was insensitive to the flow regime, despite previous studies that have linked flow-dependent mass flux to both coral respiration and symbiont (zooxanthellae) photosynthesis. Because of this discrepancy, we examined the effect of one aggregation parameter, branch spacing, to test the null hypothesis that mass flux to a corals tissues is unaffected by colony morphology. We used two non-dimensional parameters, the Reynolds number (Re) and the Sherwood number (Sh), to examine the interaction between flow, morphology and mass transport. Using physical scaling arguments, we measured water loss rates from scale models in air as proxies for gas flux from corals in water. We created two types of solitary models, horizontal (unifacial) and upright (bifacial) plates and two types of aggregations, widely-spaced (5 cm between rows) and tightly-spaced (2.5 cm spacing), to examine how morphology affects mass flux to a branchs surface under conditions of uniform flow. Measurements at two Re (4 000 and 21 000) and two turbulence levels in uniform flow showed that mass flux is significantly higher in solitary models compared to aggregations. Mass flux from branches within aggregations was highest at branch tips and decreased closer to the bottom. Measurements of boundary layer profiles overlying aggregations indicated higher boundary layer diffusivities to the surface of the tightly-spaced aggregation, per unit of substrate area. However, the increased amount of tissue surface area in these aggregations led to a lower flux per unit of coral tissue. Our results suggest that the coral A. tenuifolia displays different aggregation structures in response to light but not water flow, at least in shallow, high light environments. Nonetheless, our laboratory experiments show that branch spacing within an aggregation has significant effects on the flux of gases to the surface of corals. Because photosynthesis depends upon both mass flux and light, this apparent contradiction between field patterns and laboratory results suggests that A. tenuifolia and its symbionts may adapt physiologically rather than morphologically to variation in the local flow regime. The optimal branch spacing in any given environment is thus unlikely to result from a single selective pressure but rather from a suite of environmental parameters acting in concert, including light, water flow, sedimentation rate, hydromechanical stresses and competition for space.

A, Addressable Gen2 Sensor Tag for Biosignal Acquisition

The evolution of septal complexity in fossil ammonoids has been widely regarded as an adaptive response to mechanical stresses imposed on the shell by hydrostatic pressure. Thus, septal (and hence sutural) complexity has been used as a proxy for depth: for a given amount of septal material greater complexity permitted greater habitat depth. We show that the ultimate septum is the weakest part of the chambered shell. Additionally, finite element stress analyses of a variety of septal geometries exposed to pressure stresses show that any departure from a hemispherical shape actually yields higher, not lower, stresses in the septal surface. Further analyses show, however, that an increase in complexity is consistent with selective pressures of predation and buoyancy control. Regardless of the mechanisms that drove the evolution of septal complexity, our results clearly reject the assertion that complexly sutured ammonoids were able to inhabit deeper water than did ammonoids with simpler septa. We suggest that while more complexly sutured ammonoids were limited to shallower habitats, the accompanying more complex septal topograhies enhanced buoyancy regulation (chamber emptying and refilling), through increased surface tension effects.

Morphological variation in coral aggregations: branch spacing and mass flux to coral tissues

SUMMARY Moving animals orchestrate myriad motor systems in response to multimodal sensory inputs. Coordinating movement is particularly challenging in flight control, where animals deal with potential instability and multiple degrees of freedom of movement. Prior studies have focused on wings as the primary flight control structures, for which changes in angle of attack or shape are used to modulate lift and drag forces. However, other actuators that may impact flight performance are reflexively activated during flight. We investigated the visual–abdominal reflex displayed by the hawkmoth Manduca sexta to determine its role in flight control. We measured the open-loop stimulus–response characteristics (measured as a transfer function) between the visual stimulus and abdominal response in tethered moths. The transfer function reveals a 41 ms delay and a high-pass filter behavior with a pass band starting at ~0.5 Hz. We also developed a simplified mathematical model of hovering flight wherein articulation of the thoracic–abdominal joint redirects an average lift force provided by the wings. We show that control of the joint, subject to a high-pass filter, is sufficient to maintain stable hovering, but with a slim stability margin. Our experiments and models suggest a novel mechanism by which articulation of the body or ‘airframe’ of an animal can be used to redirect lift forces for effective flight control. Furthermore, the small stability margin may increase flight agility by easing the transition from stable flight to a more maneuverable, unstable regime.