Inertial Costs Research Articles

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths.

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

Contingent Design & The Court Reform Debate

Once unimaginable, the prospect of Supreme Court reform now seems real. Republican presidents have appointed fifteen of the last twenty Justices despite losing the popular vote in seven of the last eight elections, and these figures can no longer be chalked up to the timing of vacancies alone. After blocking President Obama’s nominee for Justice Scalia’s seat for almost a year to purportedly give “the American people a voice in selecting their next Supreme Court Justice,” Senate Republicans filled Justice Ginsburg’s seat with President Trump’s nominee mere weeks before the 2020 election. With Democrats now in control, the debate has turned to what new policies might replace the old, defunct norms. According to conventional wisdom, this debate revolves around one task: identifying the reform plan that best threads a needle between political reality and legal rigor. This is because Congress will presumably get “one shot” before the benefits of time and inertia shift to the Court itself. The consequences of this framing are profound: reformers water down popular policies to protect against invalidation, court-packing dominates the debate based on its constitutional credentials, and the chance to achieve real change quickly starts to slip away. This Article challenges the premise Congress must take such a passive approach to judicial review, expressing policy preferences in seriatim fashion (and being “sent back to the drawing board” each time a policy fails). This approach merely reflects institutional habits. And by failing to question these habits, reformers forfeit an enormous amount of legislative power. Congress can reclaim this power by strategically structuring judicial review using two methods. First, Congress can constitutionally safeguard its reform agenda by layering its policy preferences from most politically desirable to most legally defensible using “fallback” (or “backup”) law. If the Court holds the first preference unconstitutional, the second will automatically take its place—and so on. Thus, the Court shoulders the inertial cost of its own unpredictability. While it retains the power to evaluate each layer’s lawfulness, it cannot wage a war of attrition against Congress. Second, Congress can politically safeguard its power by designing appellate procedures that consolidate and prioritize all challenges to the law. By giving the same coalition that enacted the law a chance to respond to the Court’s decision, this approach insures against the tail risk of total invalidation and prevents the Court from “running out the clock” against Congress. By identifying how existing court-reform proposals price in the inertia- and time-related risks of a passive approach and by proactively neutralizing those risks, this more strategic frame opens up new reform possibilities. It also offers two warnings. First, because the time available to Congress is a source of institutional power, Congress should begin its work straightaway and enact a reform package as early as possible in the current session. Second, Congress should avoid pursuing a single “best” policy given that this could perversely shrink the space for agreement. Instead, Congress should layer its reform proposals in whatever way produces the strongest coalition and the most durable plan.

Size, History-Dependent, Activation and Three-Dimensional Effects on the Work and Power Produced During Cyclic Muscle Contractions.

Muscles undergo cycles of length change and force development during locomotion, and these contribute to their work and power production to drive body motion. Muscle fibers are typically considered to be linear actuators whose stress depends on their length, velocity, and activation state, and whose properties can be scaled up to explain the function of whole muscles. However, experimental and modeling studies have shown that a muscle's stress additionally depends on inactive and passive tissues within the muscle, the muscle's size, and its previous contraction history. These effects have not been tested under common sets of contraction conditions, especially the cyclic contractions that are typical of locomotion. Here we evaluate the relative effects of size, history-dependent, activation and three-dimensional effects on the work and power produced during cyclic contractions of muscle models. Simulations of muscle contraction were optimized to generate high power outputs: this resulted in the muscle models being largely active during shortening, and inactive during lengthening. As such, the history-dependent effects were dominated by force depression during simulated active shortening rather than force enhancement during active stretch. Internal work must be done to deform the muscle tissue, and to accelerate the internal muscle mass, resulting in reduced power and work that can be done on an external load. The effect of the muscle mass affects the scaling of muscle properties, with the inertial costs of contraction being relatively greater at larger sizes and lower activation levels.

Muscle shortening velocity depends on tissue inertia and level of activation during submaximal contractions.

In order to perform external work, muscles must do additional internal work to deform their tissue, and in particular, to overcome the inertia due to their internal mass. However, the contribution of the internal mass within a muscle to the mechanical output of that muscle has only rarely been studied. Here, we use a dynamic, multi-element Hill-type muscle model to examine the effects of the inertial mass within muscle on its contractile performance. We find that the maximum strain-rate of muscle is slower for lower activations and larger muscle sizes. As muscle size increases, the ability of the muscle to overcome its inertial load will decrease, as muscle tension is proportional to cross-sectional area and inertial load is proportional to mass. Thus, muscles that are larger in size will have a higher inertial cost to contraction. Similarly, when muscle size and inertial load are held constant, decreasing muscle activation will increase inertial cost to contraction by reducing muscle tension. These results show that inertial loads within muscle contribute to a slowing of muscle contractile velocities (strain-rates), particularly at the submaximal activations that are typical during animal locomotion.

Suction power output and the inertial cost of rotating the neurocranium to generate suction in fish.

To expand the buccal cavity, many suction-feeding fishes rely on a considerable contribution from dorsal rotation of the dorsal part of the head including the brains, eyes, and several bones forming the braincase and skull roof (jointly referred to as the neurocranium). As the neurocranium takes up a large part of the total mass of the head, this rotation may incur a considerable inertial cost. If so, this would suggest a significant selective pressure on the kinematics and mass distribution of the neurocranium of suction feeders. Here, an inverse dynamic model is formulated to calculate the instantaneous power required to rotate the neurocranium, approximated by a quarter ellipsoid volume of homogeneous density, as well as to calculate the instantaneous suction power based on intra-oral pressure and head volume quantifications. We applied this model to largemouth bass (Micropterus salmoides) and found that the power required to rotate the neurocranium accounts for only about 4% of the power required to suck water into the mouth. Furthermore, recovery of kinetic energy from the rotating neurocranium converted into suction work may be possible during the phase of neurocranial deceleration. Thus, we suggest that only a negligible proportion of the power output of the feeding muscles is lost as inertial costs in the largemouth bass. Consequently, the feeding performance of piscivorous suction feeders with generalised morphology, comparable to our model species, is not limited by neurocranial motion during head expansion. This suggests that it is thus not likely to be a factor of importance in the evolution of cranial shape and size.

The Analysis of the UKF-Based Navigation Algorithm during GPS Outage

The unscented Kalman filter (UKF) became very attractive for the navigation sensors data fusion, because of algorithm significant accuracy and implementation advantages. The unscented Kalman filter is based on the unscented transform (UT) to perform the estimation of the system states. The main idea of the unscented transformation is following. It’s more effective to approximate probability distribution function than arbitrary transformation or nonlinear function. The developed sensors data fusion algorithm using the UKF is considered in this work. This algorithm was applied for the state estimation of the loosely coupled GPS/INS integrated navigation system. GPS/INS integrated navigation system contains low cost inertial sensors and low cost GPS receiver. To demonstrate the estimation performance, the processing of sensors data was done using linear Kalman filter (KF), extended Kalman filter (EKF) and UKF. As a result, UKF has lower velocity estimation error than EKF during simulated GPS signal outage. DOI: http://dx.doi.org/10.5755/j01.eee.19.10.5886

Upstroke wing flexion and the inertial cost of bat flight

Flying vertebrates change the shapes of their wings during the upstroke, thereby decreasing wing surface area and bringing the wings closer to the body than during downstroke. These, and other wing deformations, might reduce the inertial cost of the upstroke compared with what it would be if the wings remained fully extended. However, wing deformations themselves entail energetic costs that could exceed any inertial energy savings. Using a model that incorporates detailed three-dimensional wing kinematics, we estimated the inertial cost of flapping flight for six bat species spanning a 40-fold range of body masses. We estimate that folding and unfolding comprises roughly 44 per cent of the inertial cost, but that the total inertial cost is only approximately 65 per cent of what it would be if the wing remained extended and rigid throughout the wingbeat cycle. Folding and unfolding occurred mostly during the upstroke; hence, our model suggests inertial cost of the upstroke is not less than that of downstroke. The cost of accelerating the metacarpals and phalanges accounted for around 44 per cent of inertial costs, although those elements constitute only 12 per cent of wing weight. This highlights the energetic benefit afforded to bats by the decreased mineralization of the distal wing bones.

The musculoskeletal anatomy of the reindeer (Rangifer tarandus): fore- and hindlimb

Reindeer are numerous and widespread across the northern Holarctic. They are eYcient long distance migrants and are able to cope with variations in substrate, such as ice, snow, uneven forest Xoor, wetland and Xat grassland. However, as with the vast majority of quadrupe- dal vertebrates, no quantitative musculoskeletal anatomical information exists for these animals making it diYcult to analyse the biomechanics of their locomotor behaviour. In this paper, we describe the gross anatomy of the limb mus- culature and quantify muscle and tendon morphology. Reindeer show slight hindlimb dominance in muscle and tendon mass, with muscle mass primarily proximally situ- ated and tendon distally situated. Extensor muscles are heavier than Xexors, but tendon mass is broadly similar in both extensors and Xexors. The only complete quadrupedal data sets available for comparison are for hares and grey- hounds making it diYcult to identify general patterns. There are no obvious body mass eVects and reindeer often comes out as intermediate between hare and greyhound. However, greyhound seem less hindlimb dominated in terms of muscle but both greyhound and hare have much higher masses of tendon compared to reindeer, particularly in their hindlimbs. All these quadrupeds show the com- monly observed trait of much larger tendons and less mas- sive muscles in distal limb segments; this reduces the inertial cost of accelerating the limbs. Generally, there is a dearth of available quantitative anatomical data of complete animals. This lack of information is hindering attempts to gain a better understanding of musculoskeletal function in quadrupeds.

Is mass loss in Brünnich's guillemots Uria lomvia an adaptation for improved flight performance or improved dive performance?

Breeding Brünnich's guillemots Uria lomvia show stepwise mass loss at the time of hatch. This mass loss has usually been explained as an adaptation to reduce the cost of flight during the chick‐rearing period because flight time increases during that period. It is possible, however, that mass loss also increases dive performance during the chick‐rearing period because time spent diving also increases during that period. Reduced mass could reduce basal metabolic rate or costs associated with buoyancy and therefore increase aerobic dive limit. To examine the role of mass loss in dive behavior, we attached time‐depth‐temperature recorders for 24–48 h to chick‐rearing and incubating Brünnich's guillemots at Coats Island, Nunavut (2005: n=45, 2006: n=40), and recorded body mass before and after each deployment. There was no relationship between mass and dive duration during either incubation or chick‐rearing. Seventeen of the birds we sampled during incubation were resampled during chick‐rearing. For this group, dive duration increased with mass loss between incubation and chick‐rearing (r2=0.67–0.75). Mass loss occurred through reductions in metabolically‐active tissues (liver, bladder) and buoyant tissues (lipids) although muscle and gut mass did not change. Despite the large change in lipids, buoyancy only changed by 0.1%, and mass loss therefore did not have much effect on costs associated with buoyancy. Nonetheless, surface pause duration for a given dive depth decreased during chick‐rearing, supporting the idea that reduced mass led to increased aerobic dive limit through reduced metabolic rate and inertial costs; oxygen stores did not increase. We also attached neutrally (n=9) and negatively (n=11) buoyant handicaps to the legs of adults to assess the effect of artificial mass increases on time budgets. Artificially increasing mass decreased total time spent diving but did not change time spent flying. There was no change in shift length between incubation and chick‐rearing, and therefore no support for the idea that mass loss reflected a change in fasting endurance requirements. An energetic model suggested that the observed mass reduction reduced dive costs by 5–8% and flight costs by 3%. We concluded that mass loss may be as important for increasing dive performance as increasing flight performance.

CONSENSUS MODELLING IN GROUP DECISION MAKING: DYNAMICAL APPROACH BASED ON FUZZY PREFERENCES

The. notion of consensus plays an important role in group decision making, particularly when the collective preference structure is generated by a dynamical aggregation process of the single individual preference structures. In this dynamical process of aggregation each single decision maker gradually transforms his/her preference structure by combining it, through iterative weighted averaging, with the preference structures of the remaining decision makers. In this way, the collective decision emerges dynamically as a result of the consensual interaction among the various decision makers in the group. From the point of view of applied mathematics, the models of consensual dynamics stand in the context of multi-agent complex systems, with interactive and nonlinear dynamics. The consensual interaction among the various agents (decision makers) acts on their state variables (the preferences) in order to optimize an appropriate measure of consensus, which can be of type 'hard' (unanimous agreement within the group of decision makers) or 'soft' (partial agreement within the group of decision makers). In this paper, we study the modelling of consensus reaching when the individual testimonies are assumed to be expressed as fuzzy preference relations. Here consensus is meant as the degree to which most of the experts agree on the preferences associated to the most relevant alternatives. First of all we derive a degree of dissensus based on linguistic quantifiers and then we introduce a form of network dynamics in which the quantifiers are represented by scaling functions. Finally, assuming that the decision makers can express their preferences in a more flexible way, i.e. by using triangular fuzzy numbers, we describe the iterative process of opinion transformation towards consensus via the gradient dynamics of a cost function expressed as a linear combination of a dissensus cost function and an inertial cost function.

The changes in power requirements and muscle efficiency during elevated force production in the fruit fly Drosophila melanogaster.

The limits of flight performance have been estimated in tethered Drosophila melanogaster by modulating power requirements in a 'virtual reality' flight arena. At peak capacity, the flight muscles can sustain a mechanical power output of nearly 80 W kg-1 muscle mass at 24 degrees C, which is sufficient to generate forces of approximately 150% of the animal's weight. The increase in flight force above that required to support body weight is accompanied by a rise in wing velocity, brought about by an increase in stroke amplitude and a decrease in stroke frequency. Inertial costs, although greater than either profile or induced power, would be minimal with even modest amounts of elastic storage, and total mechanical power energy should be equivalent to aerodynamic power alone. Because of the large profile drag expected at low Reynolds numbers, the profile power was approximately twice the induced power at all levels of force generation. Thus, it is the cost of overcoming drag, and not the production of lift, that is the primary requirement for flight in Drosophila melanogaster. By comparing the estimated mechanical power output with respirometrically measured total power input, we determined that muscle efficiency rises with increasing force production to a maximum of 10%. This change in efficiency may reflect either increased crossbridge activation or a favorable strain regime during the production of peak forces.

How a Long Tail and Changes in Mass and Wing Shape Affect the Cost for Flight in Animals

1. Relationships between foraging strategy, flight performance and wing shape in animals can be demonstrated with the use of aerodynamic theory. The optimal morphology is dictated not only by foraging behaviour and habitat selection but also by size of prey and migratory habits, as well as flight display. Here I demonstrate how changes in body size and structure of wings and tail affect the optimal flight speeds and power required to fly. 2. Long-tailed birds flying with their tails hanging downwards-backwards (e. g. widowbirds) are predicted to fly more slowly than short-tailed birds to save energy or to have larger wings (broader and/or longer wings giving lower wing loading) to compensate for increased tail drag during flight. Assuming that the tail length is five times as long in a long-tailed bird than in a short-tailed (normal) one, the minimum power and maximum range power would be about 30% higher in the long-tailed bird and the corresponding speeds about 40% slower. Ignoring wing inertial loads as a cost (inertial power) the corresponding percentages would become 16-18% higher powers and slower speeds. 3. I predict that members of a bird family that display in hovering or vertical take-off flights should not have elongated wings if wing inertia is important. In contrast to most other widowbird species, males of Jackson's widowbird (Euplectes jacksoni) do not have elongated wings (Anderson 1992), although they have particularly costly tails (Thomas 1993). This species has abandoned forward flight display and instead uses a vertical take-off and hovering flight display. Inertial costs appear to explain this result. 4. An increase in weight causes an increase in wing loading, which in turn requires higher flight speed for production of enough lift. A 50% increase in body mass (as fat, an egg or a fetus inside the body), would increase P mr and P mp by about 45-50% and V mr and V mp by about 20-25% (symbols defined in Fig. 1), when inertial power is taken to be zero. 5. A bird or bat carrying prey in the beak/mouth or claws should use about the same speed for minimization of flight costs as when flying without prey. 6. For low flight costs, and assuming a perfect elastic storage (zero inertial power), fast-flying species should benefit from short, narrow, high-aspect-ratio wings, hovering species should have long wings and slow-flying species should have larger wings (lower wing loadings) but with no particular demands on the aspect ratio. Ignoring inertial power the best flight economy is attained by the combination of a low wing loading (enabling slow flight) and high aspect ratio (Norberg & Rayner 1987; Norberg 1990). If we assume that inertial power is an important cost in hovering, a hovering animal should have short wings to minimize mechanical power