Aerodynamic Power Requirements Research Articles

Three-dimensional wing structure attenuates aerodynamic efficiency in flapping fly wings.

The aerial performance of flying insects ultimately depends on how flapping wings interact with the surrounding air. It has previously been suggested that the wing's three-dimensional camber and corrugation help to stiffen the wing against aerodynamic and inertial loading during flapping motion. Their contribution to aerodynamic force production, however, is under debate. Here, we investigated the potential benefit of three-dimensional wing shape in three different-sized species of flies using models of micro-computed tomography-scanned natural wings and models in which we removed either the wing's camber, corrugation, or both properties. Forces and aerodynamic power requirements during root flapping were derived from three-dimensional computational fluid dynamics modelling. Our data show that three-dimensional camber has no benefit for lift production and attenuates Rankine-Froude flight efficiency by up to approximately 12% compared to a flat wing. Moreover, we did not find evidence for lift-enhancing trapped vortices in corrugation valleys at Reynolds numbers between 137 and 1623. We found, however, that in all tested insect species, aerodynamic pressure distribution during flapping is closely aligned to the wing's venation pattern. Altogether, our study strongly supports the assumption that the wing's three-dimensional structure provides mechanical support against external forces rather than improving lift or saving energetic costs associated with active wing flapping.

Birds invest wingbeats to keep a steady head and reap the ultimate benefits of flying together.

Flapping flight is the most energetically demanding form of sustained forwards locomotion that vertebrates perform. Flock dynamics therefore have significant implications for energy expenditure. Despite this, no studies have quantified the biomechanical consequences of flying in a cluster flock or pair relative to flying solo. Here, we compared the flight characteristics of homing pigeons (Columba livia) flying solo and in pairs released from a site 7 km from home, using high-precision 5 Hz global positioning system (GPS) and 200 Hz tri-axial accelerometer bio-loggers. As expected, paired individuals benefitted from improved homing route accuracy, which reduced flight distance by 7% and time by 9%. However, realising these navigational gains involved substantial changes in flight kinematics and energetics. Both individuals in a pair increased their wingbeat frequency by 18% by decreasing the duration of their upstroke. This sharp increase in wingbeat frequency caused just a 3% increase in airspeed but reduced the oscillatory displacement of the body by 22%, which we hypothesise relates to an increased requirement for visual stability and manoeuvrability when flying in a flock or pair. The combination of the increase in airspeed and a higher wingbeat frequency would result in a minimum 2.2% increase in the total aerodynamic power requirements if the wingbeats were fully optimised. Overall, the enhanced navigational performance will offset any additional energetic costs as long as the metabolic power requirements are not increased above 9%. Our results demonstrate that the increases in wingbeat frequency when flying together have previously been underestimated by an order of magnitude and force reinterpretation of their mechanistic origin. We show that, for pigeons flying in pairs, two heads are better than one but keeping a steady head necessitates energetically costly kinematics.

‘No cost of echolocation for flying bats’ revisited

Echolocation is energetically costly for resting bats, but previous experiments suggested echolocation to come at no costs for flying bats. Yet, previous studies did not investigate the relationship between echolocation, flight speed, aerial manoeuvres and metabolism. We re-evaluated the 'no-cost' hypothesis, by quantifying the echolocation pulse rate, the number of aerial manoeuvres (landings and U-turns), and the costs of transport in the 5-g insectivorous bat Rhogeessa io (Vespertilionidae). On average, bats (n = 15) travelled at 1.76 ± 0.36 m s⁻¹ and performed 11.2 ± 6.1 U-turns and 2.8 ± 2.9 ground landings when flying in an octagonal flight cage. Bats made more U-turns with decreasing wing loading (body weight divided by wing area). At flight, bats emitted 19.7 ± 2.7 echolocation pulses s⁻¹ (range 15.3-25.8 pulses s⁻¹), and metabolic rate averaged 2.84 ± 0.95 ml CO₂ min⁻¹, which was more than 16 times higher than at rest. Bats did not echolocate while not engaged in flight. Costs of transport were not related to the rate of echolocation pulse emission or the number of U-turns, but increased with increasing number of landings; probably as a consequence of slower travel speed when staying briefly on ground. Metabolic power of flight was lower than predicted for R. io under the assumption that energetic costs of echolocation call production is additive to the aerodynamic costs of flight. Results of our experiment are consistent with the notion that echolocation does not add large energetic costs to the aerodynamic power requirements of flight in bats.

Elastic deformation and energy loss of flapping fly wings

During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m(2) near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m(2)). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.

Flying in a flock comes at a cost in pigeons

Flying birds often form flocks, with social1, navigational2 and anti-predator3 implications. Further, flying in a flock can result in aerodynamic benefits, thus reducing power requirements4, as demonstrated by a reduction in heart rate and wingbeat frequency in pelicans flying in a V-formation5. But how general is an aerodynamic power reduction due to group-flight? V-formation flocks are limited to moderately steady flight in relatively large birds, and may represent a special case. What are the aerodynamic consequences of flying in the more usual ‘cluster’ 6,7 flock? Here, we use data from innovative back-mounted GPS and 6 degree of freedom inertial sensors to show that pigeons 1) maintain powered, banked turns like aircraft, imposing dorsal accelerations of up to 2g, effectively doubling body weight and quadrupling induced power requirements; 2) increase flap frequency with increases in all conventional aerodynamic power requirements; and 3) increase flap frequency when flying near, particularly behind, other birds. Therefore, unlike V-formation pelicans, pigeons do not gain an aerodynamic advantage from flying in a flock; indeed, the increased flap frequency – whether due to direct aerodynamic interactions or requirements for increased stability or control – suggests a considerable energetic cost to flight in a tight cluster flock.

Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl

Dragonflies are dramatic, successful aerial predators, notable for their flight agility and endurance. Further, they are highly capable of low-speed, hovering and even backwards flight. While insects have repeatedly modified or reduced one pair of wings, or mechanically coupled their fore and hind wings, dragonflies and damselflies have maintained their distinctive, independently controllable, four-winged form for over 300 Myr. Despite efforts at understanding the implications of flapping flight with two pairs of wings, previous studies have generally painted a rather disappointing picture: interaction between fore and hind wings reduces the lift compared with two pairs of wings operating in isolation. Here, we demonstrate with a mechanical model dragonfly that, despite presenting no advantage in terms of lift, flying with two pairs of wings can be highly effective at improving aerodynamic efficiency. This is achieved by recovering energy from the wake wasted as swirl in a manner analogous to coaxial contra-rotating helicopter rotors. With the appropriate fore–hind wing phasing, aerodynamic power requirements can be reduced up to 22 per cent compared with a single pair of wings, indicating one advantage of four-winged flying that may apply to both dragonflies and, in the future, biomimetic micro air vehicles.

Contractile properties of the pigeon supracoracoideus during different modes of flight

The supracoracoideus (SUPRA) is the primary upstroke muscle for avian flight and is the antagonist to the downstroke muscle, the pectoralis (PECT). We studied in vivo contractile properties and mechanical power output of both muscles during take-off, level and landing flight. We measured muscle length change and activation using sonomicrometry and electromyography, and muscle force development using strain recordings on the humerus. Our results support a hypothesis that the primary role of the SUPRA is to supinate the humerus. Antagonistic forces exerted by the SUPRA and PECT overlap during portions of the wingbeat cycle, thereby offering a potential mechanism for enhancing control of the wing. Among flight modes, muscle strain was approximately the same in the SUPRA (33-40%) and the PECT (35-42%), whereas peak muscle stress was higher in the SUPRA (85-126 N m(-2)) than in the PECT (50-58 N m(-2)). The SUPRA mainly shortened relative to resting length and the PECT mainly lengthened. We estimated that elastic energy storage in the tendon of the SUPRA contributed between 28 and 60% of the net work of the SUPRA and 6-10% of the total net mechanical work of both muscles. Mechanical power output in the SUPRA was congruent with the estimated inertial power required for upstroke, but power output from the PECT was only 42-46% of the estimated aerodynamic power requirements for flight. There was a significant effect of flight mode upon aspects of the contractile behavior of both muscles including strain, strain rate, peak stress, work and power.

Resolution of a paradox: Hummingbird flight at high elevation does not come without a cost

Flight at high elevation is energetically demanding because of parallel reductions in air density and oxygen availability. The hovering flight of hummingbirds is one of the most energetically expensive forms of animal locomotion, but hummingbirds are nonetheless abundant at high elevations throughout the Americas. Two mechanisms enhance aerodynamic performance in high-elevation hummingbirds: increase in wing size and wing stroke amplitude during hovering. How do these changes in morphology, kinematics, and physical properties of air combine to influence the aerodynamic power requirements of flight across elevations? Here, we present data on the flight performance of 43 Andean hummingbird species as well as a 76-taxon multilocus molecular phylogeny that served as the historical framework for comparative analyses. Along a 4,000-m elevational transect, hummingbird body mass increased systematically, placing further aerodynamic demands on high-elevation taxa. However, we found that the minimum power requirements for hovering flight remain constant with respect to elevation because hummingbirds compensate sufficiently through increases in wing size and stroke amplitude. Thus, high-elevation hummingbirds are not limited in their capacity for hovering flight despite the challenges imposed by hypobaric environments. Other flight modes including vertical ascent and fast forward flight are more mechanically and energetically demanding, and we accordingly also tested for the maximum power available to hummingbirds by using a load-lifting assay. In contrast to hovering, excess power availability decreased substantially across elevations, thereby reducing the biomechanical potential for more complex flight such as competitive and escape maneuvers.

How cockatiels (Nymphicus hollandicus) modulate pectoralis power output across flight speeds.

The avian pectoralis muscle must produce a varying mechanical power output to achieve flight across a range of speeds (1-13 m s(-1)). We used the natural variation in the power requirements with flight speed to investigate the mechanisms employed by cockatiels (Nymphicus hollandicus) to modulate muscle power output. We found that pectoralis contractile function in cockatiels was generally conserved across speed and over a wide range of aerodynamic power requirements. Despite the 2-fold range of variation in muscle power output, many aspects of muscle performance varied little: duration of muscle shortening was invariant, and overall wingbeat frequency and muscle strain varied to a lesser degree (1.2-fold and 1.4-fold, respectively) than muscle power or work. Power output was primarily modulated by muscle force (accounting for 65% of the variation) rather than by muscle strain, cycle frequency or changes in the timing of force production relative to muscle strain. Strain rate and electromyogram (EMG) results suggest that the additional force was provided via increasing pectoralis recruitment. Due to their effect on the transformation of muscle work into useful aerodynamic work, changes in wing position and orientation during the downstroke probably also affect the magnitude of muscle force developed for a given level of motor recruitment. Analysis of the variation in muscle force and airflow over the wing suggests that the coefficients of lift and drag of the wing vary 4-fold over the speed range examined in this study.

Flight Energetics of Euglossine Bees in Relation to Morphology and Wing Stroke Frequency

ABSTRACT Mass-specific oxygen consumption of euglossine bees during free hovering flight is inversely related to body mass, varying from 66mlO2g−1h−1 in a 1−0·10 bee to 154mlO2g−1h−1 in a 0·10-g bee. Individuals of Eulaema and Eufreisea spp. have smaller wings and higher wing stroke frequency and energy metabolism at any given mass than bees of Euglossa spp. or Exaerete frontalis. Calculated aerodynamic power requirements represent only a small fraction of the energy metabolism, and apparent flight efficiency [aerodynamic power (= induced + profile power)/power input] decreases as size declines. If efficiency of flight muscle = 0·2, the mechanical power output of hovering bees varies inversely with body mass from about 480 to 1130 W kg−1 of muscle. These values are 1·9 to 4·5 times greater than previous predictions of maximum mechanical power output (Weis-Fogh & Alexander, 1977; see also Ellington, 1984c). Mass-specific energy expenditure per wing stroke is independent of body mass and essentially the same for all euglossines. Differences in energy metabolism among bees having similar body mass is primarily related to differences in wing stroke frequency. Scaling of energy metabolism in relation to mass is generally similar to the relationship for sphingid moths despite the fact that bees have asynchronous flight muscle whereas moths have synchronous muscle.

Power and efficiency of insect flight muscle.

The efficiency and mechanical power output of insect flight muscle have been estimated from a study of hovering flight. The maximum power output, calculated from the muscle properties, is adequate for the aerodynamic power requirements. However, the power output is insufficient to oscillate the wing mass as well unless there is good elastic storage of the inertial energy, and this is consistent with reports of elastic components in the flight system. A comparison of the mechanical power output with the metabolic power input to the flight muscles suggests that the muscle efficiency is quite low: less than 10%.